Le Châtelier’s Principle a Language, Methodological and Ontological Obstacle: An Analysis of General Chemistry Textbooks

Abstract

This study discusses how textbook educational approaches concerning Le Châtelier’s principle (LCP) may hinder student comprehension and prediction of chemical equilibrium disturbances. Firstly, after summarising students’ LCP erroneous assertions/explanations, a categorisation of the potential barriers that may originate student misunderstandings is performed. The discussed obstacles are the following: (a) language difficulties; (b) limited range of applicability; (c) official examinations and chemistry syllabi and (d) educational research. Then, it is examined how general chemistry textbooks’ authors deal with the evolution of chemical equilibria when they are disturbed. The different qualitative formulations of LCP provided in textbooks use mainly polysemic teleological vocabulary, which are difficult to understand in this context. Moreover, textbooks’ writers normally do not specify the conditions under which an equilibrium system is disturbed. In this textbook presentation, LCP is introduced as an easy and infallible rule, without limitations. Thus, several problematic perturbations reported in the chemical education research literature are not considered in these materials. Hence, this study concludes that their lacks and misleading use and application of LCP may certainly affect proper student understanding of the concepts related to chemical equilibrium disturbances.

1 Introduction

Science textbooks play a central role in school science education (Kahveci, 2010) as they usually provide fundamental resource for teachers to implement specifically the content and orientation of official syllabi. Therefore, the majority of science teachers find these educational materials as essential aids of information for planning and developing their science lessons (Justi & Gilbert, 2002; Sánchez & Valcárcel, 1999). As a result, teachers’ preparation and instruction of science content lessons are significantly influenced by these traditional educational instruments (Gabel, 1983). Thus, presentations in science textbooks usually also play a marked influence on the learning experiences of students (McDonald, 2016; Tulip & Cook, 1993). This implies that these materials should be carefully examined in order to investigate the organization and accuracy of their contents (Eltinge & Roberts, 1993).

Hence, the evaluation of textbooks has become an important research topic in science education (Khine, 2013; Vojíř & Rusek, 2019). Particularly, a major subject has been the identification of possible inconsistencies and erroneous teaching approaches that may be present in science textbooks. Various educational articles have noted science textbook misleading and even incorrect definitions, explanations and applications of an increasing number of scientific concepts (e.g. Quílez, 2019a; Zang et al., 2019). Additionally, chemical education studies have discussed how those confusing or erroneous textbook presentations could eventually hinder student learning and even induce misconceptions. For instance, the case of particular physical chemistry concepts (e.g. chemical kinetics or equilibrium quantities such as entropy, Gibbs energy and equilibrium constants) has been examined by several authors (Gegios et al., 2017; Quílez, 2012, 2016, 2019b; Sözbilir, 2004; Tsaparlis, 2014). These research studies suggest that one of the sources of students’ understanding difficulties in chemistry lies in how textbooks and teachers deal with chemical ideas. Thus, a poor student comprehension of these concepts may have its origin in the way they are taught (Gabel, 1999). Another important physical chemistry issue that should be investigated this way is Le Châtelier’s principle (LCP).

2 Le Châtelier’s Principle: Students’ Chemical Equilibrium Learning Obstacles

This article revolves around the question of to what extent Le Châtelier’s taught rule may become a student learning obstacle when they try to cope with chemical equilibrium disturbances. The study consists of two related parts. First, it ís carried out a categorisation of the potential barriers that may both hinder student learning and be possible sources of student erroneous explanations concerning their understanding and application of LCP. This initial critical examination focuses on the generality, accuracy and pedagogical value of LCP. An overview of five LCP essential issues have been considered: (i) Le Châtelier’s principle: student erroneous assertions/explanations, difficulties and misconceptions; (ii) language difficulties concerning the vagueness, ambiguity and (mis)understanding of its different formulations; (iii) limited character (i.e. the exceptions and inadequacies of the original qualitative formulation of this principle); (iv) official examinations and chemistry syllabi and (v) educational research. This first analysis needs a broad and elaborate discussion and will serve as the conceptual framework for the empirical textbook examination performed in the second section of this study. That is, once those possible learning obstacles concerning LCP have been examined, the purpose of the second part of this study is particularly specified and the corresponding research questions are formulated. This investigative examination has allowed to perform an intended comprehensive discussion on how general chemistry textbook presentations regarding LCP may inhibit students’ accurate understanding in their analysis and prediction of the evolution of disturbed chemical equilibrium systems.

2.1 Le Châtelier’s Principle: Erroneous Assertions/Explanations, Difficulties and Misconceptions

One of the areas in which chemical equilibrium educational research has identified numerous difficulties and misunderstandings is students’ and teachers’ (mis)application of Le Châtelier’s rules. Several surveys have provided an overview of students’ (and teachers’) misunderstandings (Özmen, 2008; Quílez, 2009; van Driel & Gräber, 2002). A summary of the main erroneous assertions/explanations, difficulties and misconceptions regarding LCP misapplication by students and even by teachers is the following:

• a) Ontological view of LCP:

• Le Châtelier’s principle is viewed as an action/reaction universal principle that easily allows to make correct predictions when a chemical equilibrium system is disturbed.

• b) Incorrect assumptions and problems regarding changes in mass/concentration:

• When one of the reactants is added to an equilibrium mixture, equilibrium always shifts to products’ side. Specifically, cases involving (a) the addition of a reactant at constant pressure and temperature and (b) the addition of a solid in a heterogeneous equilibrium mixture.

• Erroneous predictions/explanations regarding the addition of an inert gas to an equilibrium mixture. For example, (a) if an inert gas is added to an equilibrium mixture, equilibrium is never disturbed as (i) inert gases do not react; (ii) inert gases are not included in the equilibrium constant expression; (iii) it only increases the volume of the system, but does not affect its pressure; (iv) it does not alter the fraction molar of each of the species involved; (b) if it is added at constant volume and temperature, it increases total pressure shifting equilibrium in the direction that produces less number of gaseous substances.

• Changes in mass produced in the evolution of disturbed equilibria are considered that always parallel the corresponding variations of concentration or partial pressure.

• Inability to predict the equilibrium shift after a simultaneous addition of one reactant and one product.

• c) Difficulties when considering changes in the amount of water in aqueous equilibrium solutions:

• Erroneous predictions regarding the addition of solvent (i.e. water) in aqueous homogeneous chemical equilibrium solutions. For instance, students make incorrect predictions concerning changes of the degree of ionisation of solutions of weak acids and bases, caused upon dilution of the solutions. Also, adding water to aqueous equilibria is viewed as (a) similar to the case involving the addition of solids in heterogeneous equilibria. Thus, no shift is predicted; (b) the addition of one reactant/product and then a forward/reverse shift is predicted, but without considering the increased volume of the solution.

• Inability to predict changes in concentration of the species involved; for instance, students find it difficult to correctly argue changes of the pH in acid-base solutions after dilution.

• d) Misconceptions concerning temperature changes in chemical equilibria:

• In cases where the temperature of the system is altered, the equilibrium constant (i) does not change; (ii) always increases its value; (c) increases with increasing temperature in an exothermic reaction.

The examination of those review studies shows that there is an agreement considering that many students as well as some teachers apply LCP rules by rote without understanding the chemical ideas behind them. For instance, several researchers (Cheung, 2009a, 2009b; Quílez, 1998, 2004, 2008; Quílez & Solaz, 1995; Tyson et al., 1999) have studied how both secondary and university students as well as high school teachers solved questions about changes in chemical equilibria. They found that in most of their answers a qualitative-based pattern predominated. That is, they displayed a great resistance to using and interpreting mathematical expressions in this context. Thus, they seldom used the equilibrium constant to predict a change in chemical equilibrium. Instead, they usually tried to interpret the problem in terms of Le Châtelier’s rules, which then very often led to wrong answers. Hence, recalling algorithms, based on assumed logical, easy-to-apply and hopefully infallible rules, was the main procedure employed to solve those equilibrium questions. Moreover, as in other fields of both physics (e.g. Viennot & Rozier, 1994) and chemistry (e.g. Maeyer & Talanquer, 2013), students’ reasoning demonstrated strong over-reliance on variable reduction strategies, in which linear causal reasoning predominated (Quílez, 1997a, 2004). This way of application of Le Châtelier’s rules may have an ontological foundation based on an action/reaction chemical behaviour (Quílez, 2004), i.e. transferring an inappropriate sequential understanding of Newton’s third law to disturbed chemical equilibria. That is, a specific reasoning pattern may be used as follows: firstly (action), a ‘stress’ is applied to a system, and secondly (reaction), the system ‘responds’ trying to ‘oppose’ the stress. This Newtonian foundation can be traced back to Nernst (1904) and Le Châtelier (1888a, 1888b).

Consequently, several authors (Özmen, 2008; Quílez, 1998, 2004; van Driel & Gräber, 2002) have asserted that the mechanical and learned-by-heart qualitative statements labelled as LCP are usually considered easier to learn than other ways of reasoning that are based on the proper handling of the equilibrium law. Therefore, this way of thinking would compete with other forms of better rigorous foundation that would be viewed as more difficult to understand due to their mathematical language. Hence, those qualitative rules would prove themselves to be strongly anchored, which could explain that chemistry students (and teachers) persistently and almost exclusively employ them. Particularly, the conceptual analysis of the meaning of the value of the reaction quotient (Q) compared to the one of the equilibrium constant (K) (Allsop & George, 1984; Katz, 1961) is hardly used (Cheung, 2009a, 2009b). Thus, after having learnt LCP in pre-university chemistry courses, a later advanced exposition to the essentials of thermodynamics, in which the fundamentals of Q-K criteria are normally introduced, has little effect on an accurate use of the equilibrium law by both students and teachers (Quílez, 1998, 2004, 2008; Quílez & Solaz, 1995). This case may be another example of how taught rules may act as blocks to progression in the development of the concept area (Taber, 1995).

It can be concluded that this LCP supposed logical and thus easy-viewed rules are usually the main and almost exclusively conceptual tools used to predict equilibrium shifts when changing mass, volume, pressure or temperature. Students very often misunderstand and misapply those limited qualitative rules, causing them to make incorrect answers in their predictions of chemical equilibrium shifts. Moreover, in some cases, incorrect rules lead students to make correct predictions (e.g. Voska & Heikinnen, 2000).

2.2 Language Difficulties

Chemical equilibrium terminology manifests as a key factor that may hinder the development of students’ understanding of chemical equilibrium (Tyson et al., 1999). Particularly, language used in textbooks may give rise or reinforce student alternative conceptions about this topic (Pedrosa & Dias, 2000).

Several studies (Driscoll, 1960; Gold & Gold, 1984, 1985; Haydon, 1980; Jordaan, 1993; Quílez, 1995; Quílez & Sanjosé, 1996; Treptow, 1980) noticed that the different ways in which LCP had been formulated as an educational tool had several problematic language features. Specifically, each of its singular statements was found vague and ambiguous as they employed both terms that had a great polysemic spectrum and complicated syntax impeding a proper precise understanding. For instance, Palacios (1958) pointed out that its vagueness and ambiguity can result that in some cases it seems to be confirmed or contradicted depending on the specific set of words employed in its formulation.

This language obstacle was also indicated by Piquette (2001) as he found that teachers were discouraged by the particular vocabulary that is traditionally used to formulate LCP, noticing that they had difficulty to explain the precise meaning of the words used in the usual textbook qualitative statements. Additionally, Talanquer (2007) reported that LCP was an exemplary case where teleological explanations are provided by chemistry textbooks. These purposive-based claims may reinforce the student general belief that chemical systems have actual needs or wants (Talanquer, 2013) as this way of thinking is perceived by them as a simple, comprehensible, familiar and productive method to account for chemical behaviour. Therefore, LCP teleological language may certainly act as a learning impediment for students as it would hinder that students base their predictions concerning chemical equilibrium perturbations on a more accurate and deeper foundation.

Closely related to the above findings, the above referred studies have suggested that the words that are used in its qualitative formulations, as well as the ideas that are behind the diverse, imprecise and unclear statements, may lead to wrong predictions.

2.3 Limited Character

In this section, a brief historical account is provided concerning the exceptions and inadequacies of the original qualitative formulations provided for his principle by Henry Louis Le Châtelier.

In 1884, van’t Hoff (1884) formulated his principle of mobile equilibrium stating how an equilibrium shifts when changing the temperature of the system:

Every equilibrium between two different conditions of matter (systems) is displaced by lowering the temperature, at constant volume, towards that system the formation of which evolves heat (van’t Hoff, 1896, p. 217).

Based on this previous statement, the same year, Le Châtelier tried to generalise the evolution of perturbed equilibrium systems caused by variations in temperature, pressure and concentration. Without providing any theoretical proof for his principle, Le Châtelier’s first formulation was a general statement that tried to integrate a large number of observations. This empirical rule was the following:

Any system in stable chemical equilibrium, subjected to the influence of an external cause which tends to change either its temperature or its condensation (pressure, concentration, number of molecules in unit volume), either as a whole or in some of its parts, can undergo such internal modifications as would, if produced alone, bring about a change of temperature or of condensation of the opposite sign to the resulting from the external cause (Le Châtelier, 1884, p. 787).

This first rule was reformulated four years later. Le Châtelier published a longer and more detailed work in which he provided a new shorter and supposedly similar statement. He restated his initial formulation as follows:

Every change in one of the factors of an equilibrium occasions a rearrangement of the system in such a direction that the factor in question experiences a change in a sense opposite to the original (Le Châtelier, 1888a, b, p. 48).

Particularly, concerning changes in mass and concentration he stated that ‘the variation of condensation of only one of the elements determines a transformation in a direction such that a certain quantity of this element disappears, decreasing its condensation’ (Le Châtelier, 1888b, p. 57). Later on, in his book of 1908 he asserted that ‘in a homogeneous system the increase in the mass of one of the substances in equilibrium leads to a reaction that tends to decrease its mass’ (Le Châtelier, 1908, p. 357).

The success achieved in the implementation of different industrial processes and the apparent simplicity in which his second generalised statement was formulated, which did not need any mathematical support, gave it an initial acknowledgement going on nowadays as LCP has been reformulated as an appealing simple rule in nearly all textbooks of general chemistry.

However, a change in a variable may or may not shift equilibrium in a direction that counteracts the change. Since the early years of twentieth century, different reputed authors (e.g. Ehrenfest, 1911) began to point out the limited character of LCP and its equivocal and imprecise formulation. This author discussed that the rule formulated by Le Châtelier must be supplemented with the condition that one of the variables involved must be intensive and the other extensive. This line of argumentation was followed by several outstanding writers of thermodynamics textbooks (e.g. Epstein, 1937; Verschaffelt, 1938). In essence, they discussed that in some cases perturbed equilibrium systems evolve ‘opposing’ to the perturbation, but in other situations they experiment a change ‘relieving’ the disturbance. In this regard, Raveau (1909) also remarked that in some circumstances equilibrium systems counteract the change performed but in others the tendency is just the opposite. The most relevant of these two different response behaviours (i.e. ‘resistant’ and ‘adaptable’, translating literally the terms Ehrenfest employed) when equilibria are disturbed is that they are mutually contradictory (de Heer, 1986). For instance, Posthumus (1933) discussed that if N₂(g) is added, at constant T and P, to an equilibrium system represented by the equation: N₂(g) + 3 H₂(g) ⇌ 2 NH₃(g), and the mole fraction of nitrogen in the original equilibrium mixture is less than 0.5, the result is the formation of some NH₃(g), but if that quantity is greater than 0.5, the perturbation leads to the decomposition of some NH₃(g), under the formation of even more N₂(g). New examples of this type were also discussed by Etienne (1933). More recent theoretical analyses of these two possibilities for reaction behaviour of perturbed equilibrium mixtures can be found in several educational studies (e.g. Canagaratna, 2003; de Heer, 1957; Katz, 1961; Solaz & Quílez, 2001; Uline & Corti, 2006). In this regard, Prigogine and Defay (1954) provided a general thermodynamical foundation for the study of disturbed equilibria, noticing that LCP suffers from a number of important exceptions and that the attempts to restate this principle in a completely general form necessarily produces very complex statements.

Another related controversial issue was that in chemical equilibrium systems the changes in concentration do not always follow the changes in the mass of each of the chemicals involved in the reaction. Le Châtelier himself, almost fifty years after the publication of his first article on this subject, examined theoretically the perturbations caused by changes in the mass of one of the reactants (Le Châtelier, 1933). After citing previous works on this issue (Ariès, 1904; Montagne, 1933), he noticed the following:

I have realized that my different statements of the law of the displacement of the equilibrium were not all equivalent, as I had believed... The mistake made was to consider that the increase in concentration and that of the mass were always parallel... The first statement I gave to this law in 1884 is correct... Conversely, the statement I gave four years later, which I considered as equivalent to the preceding one, is incorrect (Le Châtelier, 1933, p. 1559).

Eventually, his former formulation concerning concentration (Le Châtelier, 1888) was restated as follows:

In a homogeneous mixture in chemical equilibrium, the increase in concentration of one of the reacting substances causes the displacement of the equilibrium in a direction such that the reaction tends to decrease the concentration of this substance (Le Châtelier, 1933, p. 1560).

In this last statement, the term concentration refers to the mole fraction and not to mass per unit of volume as he had stated in 1884. This new qualitative rule was criticised in a new study by Posthumus (1934) and later by Verschaffelt (1945). Specifically, Posthumus (1934) employed the same example he had discussed one year before (Posthumus, 1933) in his analysis of the mass factor. In this second study, he deduced that addition of N₂(g), at constant T and P, to mixtures in equilibrium in which the mole fraction of nitrogen is greater than 0.5, produces a reaction that increases its total amount still further, but decreases its concentration. Conversely, addition of this substance to equilibrium mixtures in which the mole fraction of nitrogen is less than 0.5 causes a reaction producing more NH₃(g), thus decreasing the total amount of N₂(g), but increasing its concentration.

Verschaffelt (1945) also discussed the variation of molarity caused by a change in the volume of the vessel in a gaseous homogeneous equilibrium mixture stating that this variation firstly modifies the molar concentration of all the components participating in the reaction. Once the equilibrium has been disturbed, the direction of the subsequent reaction increases the masses of some constituents and therefore decreases the masses of the others, concluding that the moderation in their molar concentration only takes place for some of them. From a pedagogical point of view, more recently, Allsop and George (1984) warned that changes in the volume of an equilibrium system may lead to changes in mass that do not parallel the variations that take place in concentration (i.e. molarity). The detailed discussion concerning the specific teaching/learning problems that have arisen due to this mass/concentration variation (Banerjee, 1991; Gold & Gold, 1984, 1985; Quílez, 1998, 2004) exceeds the scope of this paper.

Several studies (e.g. Bever & Rocca, 1951; de Heer, 1957; Treptow, 1980) have tried to restate LCP providing an unambiguous and precise qualitative formulation. These attempts usually follow the initial thermodynamic treatment performed by Ehrenfest (1911). However, these alternate statements seem pedagogically inaccurate in the early introduction of LCP to students. For instance, de Heer (1957, p. 378) provided the following qualitative formulations:

The change of an intensive variable caused by changing the corresponding extensive variable is smaller if chemical equilibrium is maintained than if no reaction could take place to the system.

The change of an extensive variable caused by changing the corresponding intensive variable is larger if chemical equilibrium is maintained than if no reaction could take place in the system.

Eventually, several authors have discussed the pedagogical value of LCP. When referring to it they have used different critical terms: dethroned (Haigh, 1957); sacred cow (de Heer, 1958); infidelity (Wright, 1969), false (Levine, 2009) or highly unreliable (Scerri, 2019).

Thus, it seems that general chemistry textbook authors should have noticed and therefore considered the critical research examinations regarding student LCP erroneous assertions and explanations, as well as the associated language difficulties and the limited character of LCP when presenting their educational approaches concerning chemical equilibrium disturbances. Hence, this study has analysed if writers of general chemistry textbooks have contemplated those problematic issues concerning LCP.

2.4 Official Examinations and Chemistry Syllabus

Studies from countries such the UK (Wheeldon et al., 2012), South Africa (Kolobe & Hobden, 2019) and Spain (Quílez, 2006, 2017) are examples where both official examinations and chemistry syllabus favour the application of algorithmic rote-learning procedures based on LCP rules. Thus, it seems that assessment is another important issue to be considered when dealing with how LCP may be deeply rooted as a valued educational tool.

The analysis carried out in the UK (Wheeldon et al., 2012) reported that examinations favour the application of LCP. This study demonstrated that students could use a ‘blind’ application of those memorised rules and obtain the highest grade with little understanding of the basic concepts supporting chemical equilibrium theory. Thus, although this learning context does not promote deeper thinking on students, teachers understandably may focus on this rote-recall strategy as it enables to attain the best examination results possible in the shortest amount of time. Similarly, in South Africa, only LCP is assessed and thus, South African secondary chemistry teachers only teach the application of Le Châtelier’s principle (Kolobe & Hobden, 2019). That is, official curriculum assessment determines that these teachers do not consider alternative methods of dealing with changes on an equilibrium system. Hence, this situation represents another case where the current instructional context is determined by the form of curriculum assessment.

On his part, Quílez (2006, 2017) reported that official exams in Spain did not specify under which conditions the system is perturbed. This lack in the control of the variables involved was mainly manifested in cases dealing with (a) the addition of a gas reactant at constant temperature (i.e. it was not specified if volume or pressure remained constant); (b) changes in the pressure of a gaseous system without specifying how this variation was made (e.g. changing temperature, varying the volume of the reactor, adding an inert gas, adding or eliminating one of the species participating in the reaction equilibrium); (c) variation of temperature without specifying if this change was performed at constant pressure or constant volume. Also, it was discussed that this lack or poor control of the variables involved did not allow precise predictions. Moreover, in several cases, the question requested the variation of the concentration of one of the substances participating in the reaction when the volume of the vessel was changed. In this case, students as well as their teachers always assumed parallel variations in mass and concentration of all the chemicals involved in the reaction. According to this initial analysis, secondary chemistry textbooks were also examined (Quílez, 2006). These books performed similar statements as official exams concerning perturbations of chemical equilibria and employed algorithmic LCP rules to incorrectly predict the evolution of the system. Additionally, as in the case of the UK, Spanish secondary school students tried to apply memorised rules that were restated by themselves in a meaningless way, causing most of the misunderstandings reported in a previous section.

LCP is also widely used by teachers in several countries. Western Australia is another representative region where teachers have expressed preference for using LCP when teaching students how to predict the effect of changes to equilibrium mixtures (Tyson et al., 1999). These teachers think that these rules are straightforward, easy to explain, more logical and less difficult. Another place is Hong Kong, where teachers relied solely on LCP (Cheung, 2009a, 2009b; Cheung et al., 2009) in cases where it is limited, assuming, thus, that LCP is valid to the prediction of how chemical equilibrium reactions evolve whatever the circumstances.

The above valued pedagogical view of LCP can be exemplified in the case of a prestigious textbook author. Linus Pauling stated the following in this acclaimed College Chemistry textbook (Pauling, 1957, p. 349):

The student (or the scientist) would be wise to refrain from using the mathematical equation unless he understands the theory that it represents, and can make a statement about the theory that does not consist just in reading the equation. It is fortunate that there is a general qualitative principle, called Le Châtelier's principle, that relates to all the applications of the principles of chemical equilibrium. When you have obtained a grasp of Le Châtelier's principle, you will be able to think about any problem of chemical equilibrium that arises, and, by use of a simple argument, to make a qualitative statement about it... Some years after you have finished your college work, you may (unless you become a chemist or work in some closely related field) have forgotten all the mathematical equations relating to chemical equilibrium. I hope, however, that you will not have forgotten Le Châtelier's principle.

2.5 Educational Research

The above discussed lack in the control of the variables involved when disturbing chemical equilibria was also found in a recent research paper (Aydeniz & Dogan, 2016), which creates a concern on both the way LCP is considered a teaching tool and thus how it is applied by some chemical education researchers. Those authors based their discussion on the analysis of the argumentations performed by pre-service teachers when solving several disturbed chemical equilibrium systems. The examinations carried out in that study can be paradigmatic examples of what may be widely considered teachers’ rigorous conceptual knowledge for teaching their students how to deal with those perturbed equilibrium systems. Thus, this issue needs a careful and detailed discussion. Particularly, the authors of that research requested teachers to solve two questions (also employed in a previous paper (Quílez, 2004)):

• Question 1

• Consider the following chemical reaction at equilibrium.

  $$ \mathrm{N}{\mathrm{H}}_4\mathrm{Cl}\left(\mathrm{s}\right)\rightleftharpoons \mathrm{N}{\mathrm{H}}_3\left(\mathrm{g}\right)+\mathrm{HCl}\left(\mathrm{g}\right) $$

• If we add some NH₃(g) how will the equilibrium get affected? Consider all factors that might affect the equilibrium in your answer and justify your rationale.

• Question 2

• Consider the following chemical reaction.

  $$ {\mathrm{N}}_2{\mathrm{O}}_4\left(\mathrm{g}\right)\rightleftharpoons 2\mathrm{N}{\mathrm{O}}_2\left(\mathrm{g}\right)\ \Delta \mathrm{H}=+14\ \mathrm{kcal} $$

  colourless darker/brownish

What will happen to the chemical system when we make the following changes to the system? Please justify your rationale.

• I. Increasing the temperature of the system

• II. Decreasing the volume of the system

The authors’ argumentation for these questions considering that they corresponded to the greatest quality (level 4) are the following:

• Level 4 Answer for question 1

When we add NH₃ to the system equilibrium will change in favor of reactants, producing more NH₄Cl. As a result, this will negatively affect the concentration level of HCl. However, because NH₄Cl is a solid, its concentration will not change. There will just be more NH₄Cl produced. The amount of products and reactants will no longer be the same, however, equilibrium constant Ka will remain the same. Because Ka only changes with temperature.

• Level 4 Answer for question 2

Because, ΔH = +14 kcal this reaction is endothermic. In endothermic reactions, an increase in temperature changes the direction of equilibrium in favour of products. An increase in temperature will move the direction of equilibrium towards products. This means, while the concentration of the products will increase, that of the reactants will decrease with time. The color of the mixture will look like brownish with time. Eventually, the system will reach the equilibrium but the equilibrium constant will now be different. If we reduce the volume of the system, the concentration of the ingredients will increase. A similar increase will be observed in the partial pressure of the ingredients in the gaseous phase. The equilibrium will react towards the less pressure side. The reaction will proceed towards the side that has fewer moles of the same ingredients. Therefore, the reaction will proceed towards the side that has fewer moles, (i.e., towards reactants). Therefore, the color of the gas mixture will be lighter.

The answer given for question 1 is only valid if the volume of the vessel is kept constant; addition of NH₃(g), at constant pressure and temperature, may cause the decomposition of the solid substance. This case is an example where LCP principle is limited (Quílez, 2004, 2017; Quílez & Solaz, 1995) . The reader should also notice that the argumentation provided is entirely qualitative. That is, it applies a general rule that assumes that addition of one of species participating in a chemical equilibrium reaction always causes a shift consuming part of the amount added.

For question 2, a qualitative argumentation was also provided. The rule employed is not based on how the variation of the equilibrium constant affects the composition of the new equilibrium. In addition, it should be noted that the question does not specify if the change in temperature is performed at constant pressure or constant volume. If pressure is kept constant, the sign of ΔH° must be considered when discussing the variation of the equilibrium constant, but if volume does not change, then the sign of ΔU° must be accurately contemplated as there are cases (e.g. the equilibrium of this question 2) where these two quantities (i.e. ΔH° and ΔU°) may have different sign (Bridgart & Kemp, 1985; de Berg, 1996; Solaz & Quílez, 1998). When this situation occurs, the variation of the equilibrium constant is different in each of the two situations and thus at constant volume the equilibrium shift may be different from the one corresponding when pressure is kept constant.

Additionally, the question requests for the changes caused in the initial equilibrium mixture when volume is decreased. Once again, the answer provided is entirely qualitative as a typical case of application of Le Châtelier’s rules. Consequently, the discussion concerning the colour of the mixture is erroneous as the reaction mixture does not become lighter. This is a misconception found in several general chemistry textbooks (Jordaan, 1993; Leenson, 2000; Yang, 1993). An argumentation based on the equilibrium constant will predict not only the chemical equilibrium shift but also the resulting changes in concentration. If the volume is diminished, the initial position of equilibrium is broken up, for Q_c > K_c; therefore, the reverse reaction proceeds in a greater extent till a new equilibrium position is attained (Q_c = K_c). We can surely predict that the new concentration of N₂O₄(g) is greater than the one corresponding to the first equilibrium because its mass has increased and the volume has been diminished. Thus, taking into account the mathematical equation of K_c, it is easy to reason that the concentration of NO₂(g) will change in the same way (but notice that both its mass and the volume have diminished). As NO₂(g) is brown, and N₂O₄(g) is colourless, this change favours the colour of the system becoming darker. Conversely, the colour of system becomes lighter when the concentrations of both NO₂(g) and N₂O₄(g) diminish (the volume is increased). Thus, changes in colour parallel change in the concentration of NO₂(g), which in this case are opposite to changes in its amount.

2.6 Educational Suggestions

Several research studies have suggested to avoid LCP when discussing chemical equilibrium disturbances (Allsop & George, 1984; Canagaratna, 2003; Cheung, 2009a; Katz, 1961; Quílez, 1997b, 2004, 2008; Quílez & Solaz, 1996; Stavridou & Solomonidou, 2000; Tyson et al., 1999; van Driel & Gräber, 2002). In essence, research literature recommends to focus on the two central factors responsible for disturbing equilibrium mixtures: (a) change in temperature; (b) variation of concentration of one or more of the species involved in the equilibrium mixture. Consequently, the alternative approaches should consider (a) the variation of the equilibrium constant in cases corresponding to changes in temperature and (b) the meaning of the Q-K inequalities in isothermal analyses (i.e. (a) changes in mass in both homogeneous and heterogeneous equilibria; (b) changes in pressure in gaseous equilibrium mixtures; (c) changes in volume in aqueous equilibrium solutions. In these examinations, it is necessary to perform a proper control of the variables involved. This accurate way of reasoning is exemplified throughout this study in the discussion of several LCP problematic applications.

3 Aim

Bearing in mind the previous general analysis concerning LCP as a learning obstacle for students’ (and teachers’) comprehension and prediction of chemical equilibrium disturbances, in this study I examine to what extent those referred research studies have influenced the way chemistry textbooks’ authors deal with the evolution of chemical equilibria when they are disturbed. I will study if either textbooks’ writers rely on LCP as the major predictive instrument or if they have adopted other more accurate criteria. Specifically, two main alternative theoretical tools are examined: (a) the use of the quotient of reaction (Q) in order to compare its value to the one of the equilibrium constant (K) in isothermal perturbations and (b) the variation of K with temperature. This aim has allowed the formulation of two main questions:

• a) How does the great number of educational research studies dealing with Le Châtelier’s problematic situations affect current high school chemistry textbook presentations of this topic? In other words: Do current high school chemistry textbooks incorporate the findings of the research literature dealing with the limitations, inaccurate interpretation and incorrect application of LCP?

• b) Which are the main differences between pre-university chemistry textbooks and some of the most common first-year university chemistry textbooks when they present, discuss an apply LCP?

Particularly, to assist in obtaining data that allow making discussed answers to those main questions, the following detailed research questions have been considered:

• a) How do textbooks formulate LCP? Are those formulations equivalent? Are there particular instances that may hinder students to understand those statements? That is, it is examined if there are terms employed in the different qualitative formulations chemistry textbooks provide for this principle that may cause possible student understanding problems. Also, it is studied both possible textbook situations inducing to employ a blind application of rote-learning rules and misleading textbook expressions and even erroneous discussions that may induce student misunderstandings.

• b) Which are the perturbations that are studied? Specifically, how do textbooks study the following cases? (i) changes in mass/concentration of one of the species participating in the chemical equilibrium reaction; (ii) changes in volume/pressure; (iii) changes in volume in aqueous equilibrium solutions; (iv) changes in temperature. In each of those four situations an analysis will be carried out concerning the proper control of the variables involved.

• c) Do they discuss the meaning of the reaction quotient (Q)? Which are the disturbances in which the meanings of Q-K inequalities are analysed?

• d) Do textbooks study situations that are particularly difficult for students or even that may be a source of erroneous interpretations/applications? Regarding this question, the following situations are studied: (i) addition/removal of solids/liquids in heterogeneous equilibria; (ii) addition of an inert gas; (iii) simultaneous addition of a reactant and a product.

• e) Do they mention any limitation of LCP?

4 Sample and Method

The sample of textbooks examined consists of two groups (Appendix 1):

• a) Pre-university chemistry textbooks

• i) Spanish grade-12 chemistry textbooks (n = 11)

• ii) International Baccalaureate (IB) chemistry textbooks (n = 4) and A level (UK syllabus) chemistry textbooks (n = 3)

• b) First-year university chemistry textbooks (n = 8).

The first sample consists of pre-university chemistry textbooks and is composed of two subgroups. The first one corresponds to Spanish grade-12 chemistry textbooks. They pertain to the most important publishers of chemistry textbooks of this level in Spain. These books were all published in 2016 complying with the new established compulsory curriculum, in which LCP is included. A second sample of pre-university chemistry textbooks is assigned to books that add an international perspective to this study: (a) four books that develop the chemistry curriculum for the IB Diploma; (b) three A level chemistry textbooks published in the UK. All these books have been included as they study chemical equilibrium disturbances. Moreover, a growing number of Spanish students study in an international school or in a public high school where the international baccalaureate or the UK chemistry syllabus is applied. Thus, the examination of these textbooks may provide a wide-ranging perspective beyond a specific national high school chemistry outlook to accomplish the aim of this study. Finally, the second sample of textbooks corresponds to first-year university chemistry textbooks. They have been selected considering that they are well known by a great audience as all of them have been in the market for several years and have been subjected to several editions, which represents a signal of their approval by many chemistry teachers. Moreover, university chemistry students can find these textbooks in English or translated into Spanish in most of the Spanish university libraries. Ultimately, they have been chosen for similar examinations in previous educational research papers.

Eventually, the analysis of those two samples will allow to ascertain in which way pre-university chemistry textbooks and first-year university textbooks differ in their presentation and application of LCP.

The first two specific research questions will be answered providing a qualitative discussion on the way textbooks deal with LCP. Particular exemplary textbook statements will be given in order to help in the illustration of how textbook writers both formulate LCP and apply it in isothermal equilibrium changes as well as in perturbations involving variation of temperature. The evaluation corresponding to the last three specific research questions entails the production of data for each of the two textbook samples analysed. According to the formulation of those questions, it has thus involved to perform a dichotomic analysis for each textbook that eventually has allowed to make a simple classificatory textbook arrangement in several tables. Particularly, this quantitative examination was performed the following way. The author of this study and an experienced researcher in chemical education separately evaluated two textbooks, which were selected randomly, one corresponding to the pre-university textbook sample and the other was one of the eight first-year textbooks chosen in this study. It was found that both evaluators coincided on the evaluation of all criteria on the two textbooks. This absence of disagreement was expected as the assessment performed did not involve major interpretative issues. Hence, this concurrence seemed to guarantee the author of this study that his evaluation of textbooks was reliable and thus confidently proceeded to evaluate the rest of textbooks.

5 Results and Discussion

5.1 Formulations of Le Châtelier’s Principle

Appendix 2 contains all the formulations that have been found in the textbooks that make up the sample analysed. Also, a miscellaneous set of statements is provided. This additional group of statements corresponds mainly to classical textbooks although some other examples have been included in order to exemplify the great diversity of textbooks’ qualitative formulations that can be found in both general chemistry and advanced textbooks throughout more than one hundred years. A first remarkable feature of these instructional statements is their different length in terms of the number of words used. The shortest formulations contain 13–14 words, while the longest employ more than 40, with some other middle ones that use around 25 words.

An integration of those statements into a general expression can be formulated as follows:

• 1) If in an equilibrium system is modified [changed] any of the factors that have an influence on any of the values that effect it [If in an equilibrium system an external perturbation/constraint is introduced that alters/upsets the equilibrium] [If an equilibrium system experiments a transformation/variation] [If a system at equilibrium is subjected to a disturbance/stress] [If a system is forced out of equilibrium]

• 2) the system will evolve [reorganise] [respond] [adjust] [readjust] [react] [shift] [undergo] [undo] [becomes displaced] [determine a reorganization of the system] in the direction [in a way] [in order to] [that tends]

• 3) to counteract [counteract partially the modification] [oppose] [minimise] [cancel] [partially cancel] [reduce] [annul] [partially annul] [eliminate] [restore] [restore the original conditions] [offset] [partially offset] [negate] [decrease] [mitigate] [accommodate] [compensate] [absorb] [weaken] [re-establish] [relieve] [undo] [return] [neutralize]

  • a) the variation/change performed [the perturbation, modification produced, introduced] [the transformation experienced]

  • b) the effect of the modification/change produced.

That is, the different textbook formulations may be analysed considering three main parts. Notice that each section of this integrative Le Châtelier’s statement contains several different key terms (mainly verbs and nominalised words) that indeed may represent understanding problems to students. This obstacle is highlighted in the following terminological summary of the main different terms employed in each of the three parts in which textbook writers usually state LCP:

• 1) modification, change, perturbation, transformation, disturbance, alteration, stress, variation, impact, constraint, upset, force out, suffer, introduce.

• 2) evolve, reorganise, respond, adjust, readjust, react, shift, undergo, displace, undo, determine.

• 3) counteract, oppose, minimise, cancel, reduce, annul, eliminate, restore, offset, negate, decrease, mitigate, accommodate, compensate, absorb, weaken, relieve, re-establish, undo, return, neutralize.

The many different qualitative formulations found in the sample analysed demonstrate the difficulty to state this principle unambiguously (Quílez & Sanjosé, 1996). Notice that the different main terms employed in each of the three usual parts in which this principle is normally formulated are not equivalent. Additionally, those key words are polysemic and have an imprecise meaning in this context. That is, the usage of normal English in these cases is composed of many words that have specific chemical meanings students must both understand and apply. However, these conceptual processes do not appear to be easy and straightforward tasks for them (Song & Carheden, 2014; Quílez, 2019a).

In this thinking comprehension and implementation of key terms, when one attempts to apply each of the different textbook formulations, it is usually only possible to accurately understand the concepts behind several of those main words if the correct answer to the particular perturbation performed is previously known (Driscoll, 1960). Hence, trying to make accurate responses to new unknown problems can really trouble students causing that they misunderstand one or more sections of the three-part referred statements. As a result, all of these terminological problems and thus the associated inferring difficulties may stand behind an improper understanding of LCP textbook statements.

Closely related with the previous paragraph, one can easily notice another feature of the different qualitative rules normally given in general chemistry textbooks, which has already been introduced when presenting the difficulties students usually find in their understanding and application of LCP taught rule. Specifically, many of the terms employed can be categorised as teleological vocabulary (Talanquer, 2007, 2013). These purposive explanations may generate student illusion that they accurately understand chemical equilibrium concepts. Eventually, this thinking may become a roadblock in their development of more exact and precise equilibrium ideas.

Lastly, it should also be remarked that there are two different endings for most of the LCP statements found in textbooks, as can be seen in the third part of its integrative formulation performed. Driscoll (1960) and Haydon (1980) discussed this issue demonstrating that the literal application of these distinct final words produces in each case an opposite shift prediction. Thus, this particular aspect represents an important barrier for student learning as textbooks misleadingly produce the correct answer regardless of the ending of Le Châtelier’s rule used.

5.2 Perturbations Discussed

The way textbooks of the sample apply LCP is discussed in the following sections. Although some references have been made concerning how classical textbooks state LCP in the previous section (i.e. Appendix 2), this study has not examined how these books may differ from modern textbooks in their application of LCP. Nonetheless, this author must report that there is a great diversity in the way it is treated in those classical textbooks. For instance, Glasstone (1946) used LCP as a support for his mathematical discussion of disturbances involving equilibrium changes of temperature and pressure, which was based on the equilibrium law, but Partington (1949) only formulated this principle without providing any example of its application, and Nernst (1904) formulated LCP as a final integration of previous discussion concerning chemical equilibrium variations of temperature and pressure.

5.2.1 Changes in Mass/Concentration

Changes in concentration are normally associated to changes in mass. That is, textbook authors usually label mass perturbation as change in concentration and then they discuss this case for the addition or removal of one of the species involved in the equilibrium system. This conceptual restriction may hinder student understanding as isothermal perturbations are, in fact, all related to concentration changes (Allsop & George, 1984).

In none of the textbooks analysed, it is explicitly performed a control of the variables involved when discussing changes in mass. That is, although mass changes are treated in all the textbooks of the sample, none of them explicitly states what are the variables that remain unchanged. Thus, it is usually implicitly assumed that the variation in mass is performed keeping constant the volume of the equilibrium vessel. This way, a change in mass is considered equivalent to a change in concentration as can be exemplified in two statements provided in the same textbook:

If a substance is added to a system at equilibrium, the system reacts to consume some of the substance. If a substance is removed from a system, the system reacts to produce more of (the) substance (Brown et al., 2012, p. 631)

If a chemical system is already at equilibrium and the concentration of any substance in the mixture is increased (either reactant or product), the system reacts to consume some of that substance. Conversely, if the concentration of a substance is decreased, the system reacts to produce some of that substance (Brown et al., 2012, p. 632).

Normally, nothing is said about keeping constant pressure instead of volume in gaseous mixtures. Therefore, textbooks do not deal with cases in which the change in the amount of one of the species involved is performed at constant temperature and pressure. Thus, one of the most discussed problematic situations in which LCP has been proved to be limited and source of student and teacher misunderstandings (e.g. Cheung, 2009a, 2009b; Quílez et al. 1993; Quílez & Sanjosé, 1995; Quílez & Solaz, 1995) is not mentioned in general chemistry textbooks.

5.2.2 Changes in Pressure/Volume

As in the case of variations of mass/concentration, in almost all pre-university chemistry textbooks and in many first-year textbooks, the disturbance corresponding to changes in pressure is usually restricted to the discussion of only one situation, without mentioning other possibilities in which pressure can be changed. Only in one pre-university textbook (Grence et al., 2016) and in three first-year textbooks (Moore et al., 2011; Petrucci et al., 2017; Zumdahl & DeCoste, 2017) there are discussed different ways for changing isothermally the pressure of the system (i.e. changing the amount of one of the species involved in the equilibrium mixture, adding an inert gas and changing the volume of the equilibrium vessel).

Particularly, modifications in pressure in gaseous equilibrium mixtures are usually associated exclusively to alterations in the volume of the equilibrium vessel (usually stating explicitly Boyle’s law). Then, applying LCP, the equilibrium shift is conceptualised assuming that the change in pressure experienced causes the corresponding inverse variation in the number of gaseous molecules. For example:

If we reduce the volume of the reaction mixture, we cause the pressure to increase. The system can counteract the pressure increase if it is able to produce fewer molecules of gas, because fewer molecules exert a lower pressure (Jespersen et al., 2012, p. 711)

In some cases, the statement seems accurate as the prediction is correct, but the explanation provided is not fully clear as it appears quite difficult to understand its actual meaning. Two examples of this type of argumentation are provided:

If p increases, the system will shift towards where there are fewer gaseous moles (according to the stoichiometry of the reaction) in order to counteract the effect of the decrease in the volume, and vice versa. (Pozas et al., 2016, p. 107).

When the volume of the container holding a gaseous system is reduced, the system responds by reducing its own volume. This is done by decreasing the total number of gaseous molecules in the system (Zumdahl & DeCoste, 2017, p. 191).

The application of rules similar to the ones quoted above and the assumption that mass changes parallel concentration variations caused the presence of the previous discussed misconception regarding the following equilibrium system: N₂O₄(g)   ⇌  2 NO₂(g) in three textbooks (Fontanet, 2016; Owen, 2014; Ritchie & Gent, 2015). In those exemplars, it is discussed that the effect of increasing pressure (i.e. reducing the volume of the vessel) means that the position of equilibrium shifts towards the side with fewer gas molecules, which implies that more colourless N₂O₄(g) is formed and thus the brown colour fades.

5.2.3 Changes in Volume in Aqueous Equilibrium Solutions

The addition of water to an aqueous equilibrium solution (e.g. A(aq) ⇌ B(aq) + C(aq)) is another change that may disturb the equilibrium system as the concentrations of all reactants and products decrease. This change in volume cannot be understood in the way textbooks usually apply LCP for pressure variations in gaseous equilibria. Moreover, the application of LCP rules corresponding to a change in the concentration of a single reactant or product does not apply to this perturbation. However, the effect of simultaneously deceasing the concentrations of all reactants and products can be analysed interpreting the meaning of the equation Q < K (obviously, if instead of diluting the above solution it is concentrated, then Q > K). Thus, as this issue has been reported difficult for students to cope with when attempting to apply LCP, the examination of how general chemistry textbooks deal with this disturbance is another case that has been taken into account in this study.

The perturbation corresponding to a variation in the volume of the vessel in aqueous equilibria is normally not analysed in the chapter devoted to chemical equilibrium, as only one first-year textbook (Moore et al., 2011) was found treating this disturbance. In one pre-university textbook, the following is stated: ‘a change in the volume only disturbs the equilibrium when gases are involved’ (Pozas et al., p. 107), which really may confuse students when they try to transfer their learnt principles of chemical equilibrium for gaseous systems to acid-base equilibria or solubility equilibria. Conversely, this thinking transference is intended by some authors when they examine this change in their discussion of the behaviour of weak acids. Only one pre-university textbook (Talbot et al., 2015) deals with this variation, although it is studied implicitly considering the variation of the percentage of ionisation with the concentration of the weak acid. This is also the approach performed in the case of several first-year textbooks. In some exemplars, a particular extended LCP application is provided (e.g. Brown et al., 2012; Chang & Goldsby, 2016). For instance:

The extent to which a weak acid ionizes depends on the initial concentration of the acid. The more dilute the solution, the greater the percent ionization. In qualitative terms, when an acid is diluted, the concentration of the “particles” in the solution is reduced. According to Le Châtelier’s principle, this reduction in particle concentration (the stress) is counteracted by shifting the reaction to the side with more particles; that is, the equilibrium shifts from the nonionized acid side (one particle) to the side containing the H⁺ ion and the conjugate base (two particles): HA ⇌ H⁺ + A^-. Consequently, the percent ionization of the acid increases (Chang & Goldsby, p. 686).

Instead, other authors prefer to base the variation in the degree of ionisation of a weak acid on the equilibrium law. Specifically, Petrucci et al. (2017) analyse the changes in the quantities involved in the equilibrium constant expression and Moore et al. (2011) compare the value of reaction quotient (Q) with that of the equilibrium constant (K). Nonetheless, in any case, textbook writers do not go beyond discussing that despite the increase on the ionisation degree, the concentration of all species diminishes. This fact cannot be easily predicted and is difficult for students to understand. Thus, textbooks’ absence of the analysis of this case is quite noticeable as several relevant LCP misunderstandings have been found concerning the increase in volume in aqueous solutions (Demerouti et al., 2004; Mavhunga, 2020; Quílez, 2008; Quílez & Sanjosé, 1995; Quílez & Solaz, 1995; Özmen, 2008; Tyson et al., 1999). For instance, Demerouti et al. (2004) reported grade-12 students’ difficulties and failure to predict changes of the pH of solutions of weak acids and bases, caused upon addition of water. Other studies (e.g. Mavhunga, 2020; Quílez, 2008; Quílez & Solaz, 1995) found that many students as well several teachers viewed this change similar to (a) the case involving the addition of solids in heterogeneous equilibria; (b) the addition of one reactant. As a general pattern, the explanations concerning equilibrium shift did not realise that the evolved changes in the amount of substance produced in the species involved did not follow a parallel variation in their concentration for some of them (e.g. ionic products in common molecular acid-base equilibria and solubility equilibria).

5.2.4 Changes in Temperature

All textbooks deal with the evolution of the equilibrium mixture when changing temperature. This change is normally discussed considering the sign of ΔH, which allows textbook authors to apply LCP in their own way. For instance, in one textbook, when discussing the following system: C(s) + H₂O(g) ⇌ CO(g) + H₂(g); ΔH = + 131.2 kJ, it is reasoned this way:

According to Le Châtelier’s principle, increasing temperature in an equilibrium system results in the reaction in the sense that is endothermic, which entails an absorption of heat that counteracts partially the rise in temperature that disturbed the initial equilibrium (del Barrio et al., 2016, p. 175).

In another textbook, their authors assert this explanation:

Let’s suppose the following reaction that releases heat towards right (exothermic). Obviously, the reverse reaction will be endothermic: A + B ⇌ C + D + heat (ΔH° < 0). If once the equilibrium is reached temperature is increased, keeping volume and pressure constant (simply by warming up), the system will tend to eliminate heat shifting towards left. Conversely, if temperature is decreased (by cooling), the system will tend to replace heat, and for this purpose will shift towards right (Carriedo et al., 2016, p. 147).

Notice the different wording of these two examples on the behaviour of the system after increasing temperature. In the first example, the system ‘absorbs’ heat whereas in the second one it ‘eliminates’ heat. It does seem quite complicated to establish a connection between these two dissimilar verbs concluding that they have the same meaning in this context. In both cases, the final result predicted is the same (i.e. the direction that is endothermic), but the explanation given appears to be contradictory. Therefore, this is an exemplary case where the terminology employed by textbook writers is not equivalent and thus may originate student understanding problems. That is, although students are not normally confronted with two dissimilar textbook statements, it seems that the purpose is that they must blindly apply Le Châtelier’s taught rules by rote, regardless of the formulation given.

Additionally, the reader can also observe the way the textbook writers state how temperature is changed in the second example provided. This improper control of the variables involved may induce student understanding problems regarding their prerequisite knowledge.

Another feature found in textbooks is that in most of them heat is treated as a material entity, including it as such in the equation representing equilibrium. This misrepresentation causes a great concern as it can reinforce previous student wrong ideas regarding the nature of heat (Brookes & Etkina, 2015). Additionally, it would seem completely meaningless to add heat to one of the sides of the reaction as this process of transfer of energy can be done considering the whole system at equilibrium. Eventually, this presentation allows textbook writers to apply LCP as in the case of addition/removal of a reactant/product to the equilibrium mixture. For instance:

If the temperature of a system at equilibrium is increased, the system reacts as if we added a reactant to an endothermic reaction or a product to an exothermic reaction. The equilibrium shifts in the direction that consumes the “excess reactant,” namely heat (Brown et al., 2012, p. 631).

We can deduce the rules for the relationship between K and temperature from Le Châtelier’s principle. We do this by treating heat as a chemical reagent. In an endothermic (heat-absorbing) reaction, we consider heat a reactant, and in an exothermic (heat-releasing) reaction, we consider heat a product:

Endothermic: Reactants + heat  ⇌  products

Exothermic: Reactants ⇌ products + heat

When the temperature of a system at equilibrium is increased, the system reacts as if we added a reactant to an endothermic reaction or a product to an exothermic reaction. The equilibrium shifts in the direction that consumes the excess reactant (or product), namely heat (Brown et al., 2012, p. 635).

Summarising, all textbooks provide qualitative Le Châtelier’s explanations concerning a modification in temperature. This way, the argumentation grounded on how the equilibrium constant (K) is changed with temperature is not the main theoretical consideration. Particularly, authors of first-year textbooks usually state that this variation alters the equilibrium constant either providing some exemplary cases or discussing specifically how the value of K can be modified with temperature depending on the sign of ΔH. That is, Le Châtelier’s shift predictions in equilibrium systems when changing temperature are normally confirmed taking into account how the equilibrium constant has been modified. Thus, this discussion does not normally start with the analysis of how the equilibrium constant can be changed with temperature, which would allow to perform an examination on the meaning of this equilibrium constant variation, without needing to refer this way to LCP. That is, the comparison of the two values of the equilibrium constant can be used to infer the variation experienced on the composition of the initial equilibrium after changing temperature. Additionally, in the case of pre-university textbooks, there is less consensus on the discussion of the inclusion of the variation of the equilibrium constant with temperature. In all the A level textbooks, the variation of the equilibrium constant with temperature is not mentioned. Conversely, in all IB textbooks, it is exemplified this equilibrium constant variation for both exothermic and endothermic reactions. In the case of Spanish grade-12 sample in three textbooks, the approach is based exclusively on LCP, without mentioning, therefore, how a change in temperature produces a variation in the value of the equilibrium constant. The other pre-university textbooks perform a treatment similar to first-year textbooks.

Finally, it should be noted that textbook authors use exclusively the value of ΔH° in order to make their predictions, which means that it is implicitly assumed that the variation in temperature is carried out at constant pressure. Thus, these writers do not deal with changes in temperature at constant volume. In this case, the value of ΔU° must be considered in order to make accurate predictions as the sign of ΔH° and ΔU° may be different (Bridgart & Kemp, 1985; de Berg, 1996; Solaz & Quílez, 1998) and thus, the same variation in temperature can produce different equilibrium shifts in these two distinct situations.

5.3 Q-K Inequalities

The results obtained concerning the treatment given in textbooks to the introduction and the application of the meaning of Q-K inequalities are summarised in Table 1. It should be noticed that this methodological approach differs in some extent between the two samples of textbooks (i.e. pre-university and first-year textbooks). In the case of pre-university textbooks, these conceptual criteria are usually restricted to the analysis of non-equilibrium initial conditions (36% of Spanish textbooks and 43% of the pre-university international textbook sample), but this argumentation is normally not extended to the study of the evolution of perturbed equilibria. That is, few pre-university textbooks (18% of Spanish textbooks) use Q-K inequalities to discuss the evolution of equilibrium isothermal perturbations due to changes in both mass and volume/pressure. Thus, they normally only rely on the application of Le Châtelier’s rules. This is mainly the case of the seven pre-university textbooks that compose the international sample; particularly, the three A level textbooks do not introduce the reaction quotient (Q). Conversely, this Q-K analysis is carried out in most of all first-year textbooks (75%) when examining equilibrium isothermal disturbances. This discussion is usually carried out in parallel with the application of LCP.

Table 1 Cases specifying the percentages of textbooks of each sample that use Q-K inequalities.

5.4 Problematic Equilibrium Changes for Students

This section examines how textbooks’ authors deal with some of the main equilibrium disturbances that the research literature reports that are particularly difficult for students or even that may be a source of erroneous predictions/explanations as presented previously. Table 2 summarises the results obtained for the four situations analysed.

Table 2 Percentages of textbooks of each sample that discuss problematic equilibrium disturbances

5.4.1 Change in the Amount of Solids/Liquids in Heterogeneous Equilibria

As it has been discussed in a previous section, in textbooks, the addition/removal of one of the species involved in an equilibrium mixture is equated to changes in their concentration. Therefore, most textbooks analyse this change in mass under the view of variations in their concentration. However, a great proportion of students of different levels and several teachers do not make a proper distinction between these two different quantities: mass and concentration, particularly in the case of heterogeneous equilibria (Furió & Ortiz, 1983; Quílez, 1998; Tyson et al., 1999). Thus, many students and even some teachers assume as a general rule, without exceptions, that introducing a greater amount of a substance to an equilibrium system means to increase its concentration. This assumption may explain why students usually think that changing the mass of solids in heterogeneous equilibria disturbs them. Thus, when dealing with solid substances in heterogeneous equilibria, a great percentage of students and some teachers improperly apply LCP (Furió & Ortiz, 1983; Karpudewan et al., 2015; Özmen, 2008; Quílez, 1998; Quílez & Sanjosé, 1995; Tyson et al., 1999).

This general pattern of reasoning could be avoided if textbook dealt explicitly with this issue. Particularly, the meaning of the following equation Q = K unequivocally allows to conclude that in this singular case the equilibrium is not disturbed. However, only three out of eleven Spanish grade-12 textbooks (27%) and three out of eight first-year textbooks (38%) discuss this issue; none of the international pre-university textbooks deals with this change. Moreover, Le Châtelier’s rules provided in several textbooks may reinforce the misconceptions associated to this particular situation, in a similar way as in the previous discussed case concerning the addition of a reactant at constant temperature and pressure. Two exemplary general textbook statements are given below concerning the evolution of an equilibrium system when adding/removing a reactant or a product:

The position of equilibrium shifts in a way to remove reactants or products that have been added, or to replace reactants or products that have been removed (Jespersen et al., 2012, p. 711)

When an amount of one of the substances present in an equilibrium system is added to it, the system will shift in the sense causing the added substance to disappear. And vice versa, if we remove one of the substances, the equilibrium will shift in the way in which it is formed (Illana et al., 2016, p. 172).

I would like to stress that the rules provided in these textbooks are presented as a general behaviour of equilibria, without discussing any exception to it. Thus, these statements clearly show how textbook presentation of concepts may be a source of student misunderstandings.

5.4.2 Addition of an Inert Gas: V, T Constant and P, T Constant

As can be seen in Table 2, when textbooks deal with the addition of an inert gas to an equilibrium gaseous mixture, this case is normally restricted to the situation that involves keeping temperature and volume constant (55% in the case of Spanish textbooks and 75% in the sample of first-year university textbooks). Normally, it is discussed that the concentrations (or the partial pressures) of all chemical species involved in the equilibrium system do not change. Thus, it is concluded that this addition does not disturb equilibrium. However, in one textbook (Vidal & Peña, 2016) this case is presented within the general discussion of an increase in pressure stating that a rise in pressure shifts the equilibrium towards the production of a lesser amount of gases. This statement matches several student and teacher misconceptions found in a previous study (Quílez, 2006) in the way discussed by Driscoll (1960) on the misinterpretation of LCP for this particular case.

Few textbooks deal with the addition of an inert gas at constant temperature and pressure (18% of Spanish textbooks and 13% of first-year textbooks). Two textbooks (Illana et al., 2016; Petrucci et al., 2017) discuss this effect developing K_c expression and presenting it as composed of two terms, being volume one of them. Then, it is examined how a variation in volume of the vessel affects equilibrium composition. In one textbook (Grence et al., 2016), it is stated that this disturbance corresponds to the case of an increase in the volume of the vessel. Thus, although this kind of perturbation has been reported (Cheung, 2009a; Quílez & Sanjosé, 1995; Quílez & Solaz, 1995) as source of students’ and teachers’ misunderstandings, most textbook authors do not discuss it.

5.4.3 Simultaneous Addition/Removal of a Reactant and a Product

None of the textbooks analysed studies the effect of simultaneous addition of a reactant and a product to an equilibrium mixture. This is another case where LCP is limited to make an accurate prediction. Table 3 presents an example on how the study of the meanings of Q-K inequalities overcomes this LCP limitation.

Table 3 Different shifts corresponding to the equilibrium PCl₅(g) ⇌ PCl₃(g) + Cl₂(g) in three cases of simultaneous addition of the same amount (1 mol) of PCl₅ and PCl₃, when keeping temperature and volume constant (V = 1 L)

The lack in the treatment of this perturbation by textbook authors creates an additional concern that should be remediated as (a) previous research papers (Kousathana & Tsaparlis, 2002) have reported that many students assume that the position of equilibrium does not change if equal numbers of moles of a reactant and a product are added to a system which is at equilibrium; (b) questions related to this perturbation have been included in official exams (Quílez, 2017). As in previous problematic cases, the analysis of the meaning of Q-K inequalities appears to be a powerful accurate alternative to LCP.

5.5 Limitations of Le Châtelier’s Principle

Previous studies on this topic (Cheung, 2009b; Quílez et al. 1993; Quílez, 1997a) revealed that a minimal number of chemistry textbooks of both pre-university and first-year university levels published in countries such as the USA, the UK, Australia, China and Spain provided cases where LCP is limited. Rather, it was presented as infallible rule. This study confirms this trend as in the sample examined neither pre-university textbooks nor first-year textbooks mention a single case where LCP principle cannot provide an accurate prediction. Thus, the textbooks analysed in this paper do not cite previous research in science education on LCP and no other indications were found that textbooks writers were reading or considering the major chemistry education literature on this topic. By this token, these textbooks do not discuss any historical reference to the controversial issue concerning the validity of this pseudo principle.

6 Summary Discussion, Concluding Remarks and Suggestions

Educational research literature discussing chemical equilibrium topic has reported that students usually believe they understand the meaning of LCP textbook formulations as the purposive/intentional vocabulary employed induces them to perceive those rules as simple, comprehensible, logical, confident and easy to apply. That is, chemistry students usually view LCP as a general and clear rule that can effortlessly be remembered. Additionally, in their blind application of those LCP taught rules, they normally experience that the usual associated mechanical linear reasoning allows them to successfully produce quick, undemanding and hopefully correct answers in their prediction of the evolution of disturbed chemical equilibrium systems. Thus, this simplified and superficial way of understanding these processes allows students to exclusively employ those memorised rules, discarding therefore their reflection on other more accurate ways of reasoning. This fixed, reduced and linear sequencing thinking pattern (Talanquer, 2006) may be a general methodological obstacle preventing student proper learning in this context (Quílez, 1997a, 2004). In this regard, many research studies have documented a broad set of students’ and teachers’ incorrect predictions concerning the evolution of disturbed equilibrium systems. These widespread erroneous notions are mainly based on their attempt to apply LCP. Thus, attending specifically to how this qualitative rule has been criticised, this study has examined what may be several of the particular teaching sources of those erroneous statements and misunderstandings. This initial extensive analysis has allowed to focus on how LCP is formulated and used by writers of general chemistry textbooks.

The above summary concerning student ontological view of LCP may have been originated in their chemistry classroom. Specifically, it must be stressed that from the analysis performed in this study it can be concluded that LCP is introduced in textbooks as an uncomplicated and exact rule, without limitations as it is normally presented as a statement that can be easily memorised and applied straightforwardly and successfully to the prediction of shifts of all perturbations. This view may certainly hinder student understanding and even could impede a further deeper alternative and accurate foundation as previous works show that students (and many teachers) may prefer the explanation which they perceive as the one that requires the least expenditure of cognitive effort to make expected correct equilibrium shift predictions. Therefore, LCP may act as a learning obstacle limiting the use of the conceptual reasoning based on Q-K inequalities meaning. Thus, this precise and proper scientific reasoning may be eclipsed by those qualitative simple rules as students may manifest a great resistance towards the use of this alternate way of thinking (Quílez, 2004).

In addition, this study has also examined previous works concluding that both current pre-university evaluation methods and chemistry syllabi favour the exclusive and blind application of Le Châtelier’s rules. Hence, chemistry students certainly perceive from their early years of chemical equilibrium study that their teachers value the application of LCP rules as a precise methodological approach.

Besides, it seems that this qualitative LCP teaching procedure is also promoted by some educational researchers. A recent study can exemplify this case (Aydeniz & Dogan, 2016) as their authors’ methodological framework only relied on their own application of LCP qualitative rules, which led them to state predictions that were not fully correct. This key circumstance is relevant for chemistry teachers as well as for researchers as the LCP qualitative argumentations quoted in this study could be misleadingly considered accurate references for teaching chemical equilibrium disturbances as well as to establish the theoretical framework for future related chemical equilibrium works.

At this point, one can sum up that the particular problematic issues concerning LCP mentioned above (i.e. chemistry student views and perceptions, common-sense student reasoning pattern, general chemistry textbook presentations, evaluation methods, chemistry syllabi, chemistry teacher teaching methods and educational research) seem to be closely intertwined, which certainly may fortify inappropriate thinking when dealing with chemical equilibrium disturbances. That is, those hindering factors are conceptually related and support each other, which may indeed explain most of the understanding difficulties students eventually experience regarding this topic. Specifically, the overview of the theoretical frameworks in which research on students’ learning difficulties are embedded provided by Garnett et al. (1995) appears as a useful device when analysing how chemistry textbooks deal with chemical equilibrium (Pedrosa & Dias, 2000). In the context of this study, the following areas manifest as possible sources of student learning obstacles and misconceptions: (a) the use of everyday language in the textbook qualitative formulation of LCP; (b) the textbook promotion of teleological explanations when predicting the evolution of disturbed equilibrium systems; (c) the over-simplification in the study of chemical equilibrium disturbances, in which textbook writers usually state unqualified, general LCP formulations. That is, textbook authors usually provide statements without discussing the range of applicability of those stated rules; (d) textbook writers’ use of multiple different statements that may produce opposite shift predictions for the same disturbance when applied literally. This language problem is particularly evident in the strict application of the two distinct endings in which LCP is usually formulated; (e) the textbook promotion of rote application of authors’ own rules that students do not normally understand.

All chemistry textbooks examined study three general equilibrium perturbations: (a) change in mass (which is usually labelled as change in concentration); (b) change in pressure and (c) change in temperature. A general pattern found in the sample analysed is the lack of control of the variables involved. That is, textbooks’ authors normally do not specify the conditions under which an equilibrium system is disturbed.

Specifically, in the statements given by textbooks and the examples analysed on them, it is usually assumed that if a substance is added to a system in equilibrium, the system always reacts to consume some of it. Thus, cases involving the addition of a gaseous substance, at constant pressure and temperature, are not treated. Also, the change in the amount of solids in heterogeneous equilibria is normally not discussed. Hence, textbook writers have not considered what has been reported in the educational research literature (Cheung, 2009a, 2009b; Cheung et al., 2009; Karpudewan et al., 2015; Quílez, 1998, 2004, 2006; Quílez et al., 1993; Quílez & Sanjosé, 1995; Quílez & Solaz, 1995; Tyson et al., 1999; Wheeler & Kass, 1978) concerning student and teacher misunderstandings of these variations in mass in chemical equilibria.

The change in pressure is usually associated exclusively to a variation in the volume of vessel. In these cases, parallel shift predictions in mass and concentration have been found in several textbooks, which adds a great concern as this issue has also been reported as a source of student and teacher misunderstandings (e.g. Akkus et al., 2003; Quílez, 1998, 2004; Quílez et al., 1993). Moreover, the wordings of some LCP textbook explanations are quite difficult to understand. In these cases, their authors clearly predict the correct answer, but the way they interpret equilibrium behaviour can be labelled in several cases as misleading.

The perturbation corresponding to a variation in the volume of the vessel in aqueous equilibria is not analysed by most pre-university textbook writers. Several first-year textbook authors discuss the variation of the degree of ionisation of weak acids when comparing two different concentrated solutions. However, these writers do not go beyond discussing that despite the increase on the ionisation degree when adding water to the initial weak acid solution, the concentration of all species diminish, which may not help students to overcome the reported misunderstandings concerning this particular perturbation (Demerouti et al., 2004; Özmen, 2008; Quílez, 1998, 2006, 2008; Quílez & Solaz, 1995; Tyson et al., 1999).

As in the previous analysed situations, textbooks’ writers normally study the equilibrium shift caused by a variation in temperature, grounding their examination on their own application of LCP. Once more, the explanations provided to account for equilibrium shifts use terms that may confuse students. In most of these explanations, heat is treated as a material substance, in a similar way as the case of adding/removing a reactant/product, which may reinforce the incorrect ontological view students usually hold on this important concept (Quílez, 2019a). Additionally, the predicted displacements are usually confirmed discussing the variation of the equilibrium constant with temperature in the sample corresponding to first-year textbooks, but there is not a general consensus on this issue in the case of pre-university textbooks, which may not help students to overcome their erroneous assumptions (Özmen, 2008). Finally, it should be remarked that in none of the textbooks analysed the change in temperature is discussed keeping constant volume, as a direct consequence of the general lack of control of variables, which prevents to analyse in a comprehensively way how the equilibrium constant is changed with temperature.

Although the reaction quotient (Q) is introduced in several high school chemistry textbooks, it is scarcely used in order to make precise predictions regarding chemical equilibrium disturbances. However, most of first-year textbooks have incorporated Q-K criteria as a theoretical tool in their discussions for all the isothermal perturbations analysed. This is one of the main instructional differences found in this study between those two textbook samples.

Several additional problematic perturbations reported in the chemical education research literature are not considered in textbooks. Particularly, the addition of an inert gas to a gaseous equilibrium mixture (Cheung, 2009a; Quílez et al., 1993; Quílez & Sanjosé, 1995; Quílez & Solaz, 1995) and the simultaneous addition/removal of a reactant and a product to a chemical equilibrium system (Kousathana & Tsaparlis, 2002; Quílez, 2017) are normally not treated in these general chemistry textbooks. Clearly, this absence may cause some of the student and teacher erroneous assumptions and predictions concerning to these topics as was summarised in the initial section of this study.

The above discussed textbook inadequacies show particular cases that must be remediated as they may affect student understanding. Thus, this study concludes that general chemistry textbooks share a definite accountability the way students incorrectly predict chemical equilibrium shifts when coping with equilibrium disturbances. That is, the lacks found in textbooks, the different ways LCP is formulated, the misleading circumstances in which it is usually applied as well as the discussed peculiar explanations provided may represent significant learning barriers for chemistry students.

Consequently, an alternative educational proposal is suggested. Specifically, given (a) the troubles to formulate qualitatively LCP in an appropriate instructional way; (b) the difficulties arisen when students try to understand the meaning of the terminology employed in current LCP diverse textbook formulations, which definitely generate many misunderstandings when trying to apply them; (c) LCP limited character; (d) student widespread view of LCP as a straight, trusting and quite undemanding rule that can easily be learned by heart, which produces a scarce chemical meaningful understanding and (e) the promotion, as a valued educational tool, of algorithmic rote-learning procedures based on LCP rules performed by official examinations, chemistry syllabi, teachers and textbooks writers, this author supports previous recommendations (Allsop & George, 1984; Cheung, 2009a, 2009b; Cheung et al., 2009; Gold & Gold, 1984, 1985; Katz, 1961; Quílez, 2004; Quílez & Solaz, 1995; Scerri, 2019) calling for a teaching approach grounded solely on the equilibrium law, which means to avoid LCP in the teaching of chemical equilibrium topic. Hence, it is suggested that those teachers considering that, despite its flaws, LCP could play a role in the initial stages of the study of chemical equilibrium should critically reflect on its inaccurate educational features that question it as a valuable teaching tool. Particularly, this critical reflection should focus on LCP as a serious potential methodological learning barrier for students to develop a deep understanding of the properties of the equilibrium constant. That is, the aforementioned usual fixed and restricted LCP thinking pattern may certainly hinder more accurate ways of dealing with chemical equilibrium perturbations and even could also impede a later process of conceptual change when that rule is initially introduced in pre-university courses. Eventually, it would mean to overcome teacher widespread current view of LCP as an appealing useful simple rule. In any case, meaningful and well-controlled situations should be presented to students in the study of the evolution of perturbed equilibria when this topic is firstly introduced. Thus, chemistry syllabus developers, examination authorities, textbook writers and teachers should take care that students are not forced to subsequently unlearn what they have been taught in introductory equilibrium courses, which would imply considering what has been discussed and referred to in this study. In this regard, previous basic methodological approaches (Katz, 1961; Quílez, 2002) can be fundamental sources to change and thus to improve current problematic issues related to the inadequacies and misuse of LCP rules usually found in general chemistry textbooks. Additionally, several research laboratory tasks dealing with Q-K inequalities should be taken as exemplary teaching activities (Ghirardi et al., 2015). Moreover, a few textbook writers (Blackman et al., 2016; Quílez et al., 2009; Stranks et al., 1965) have complied with the above suggestion and therefore have avoided LCP in their discussion of chemical equilibrium disturbances. Thus, those presentations may be taken as essential reference teaching models for the study of chemical equilibrium perturbations as they are based on accurate ways of dealing with the equilibrium law.

Yet, a clarification regarding the previous recommendation should be made. Cartwright (1983) noted that celebrated laws of physics are not approximately true. However, there is no justification in discarding them. Still, the case for LCP should be cautiously considered. What we teachers call LCP is not a single exact statement shared by all members of the chemical education community. LCP has many different textbook and teacher formulations that can even make contradictory predictions. Thus, this ontological and language problem makes a central point when advocating an accurate teaching alternative for LCP. Moreover, the suggested substitute approach is essentially derived from a precise foundation and also is grounded in order to overcome specific learning problems that LCP manifests. Hence, the proposal made in this work is not based exclusively on the limited character of LCP as this suggestion has a deep educational basis. That is, it tries to provide students with accurate conceptual tools for helping them to meaningfully deal with chemical equilibrium disturbances. It may certainly be a powerful teaching alternative that successfully could prevent many of the LCP learning obstacles students usually experience. Nonetheless, avoiding LCP in the specific study of chemical equilibrium perturbations does not mean to completely delete it from syllabus. Rather, LCP could be a fruitful topic in the study of the history of chemical equilibrium as it can find a relevant place in the epistemological analysis involving the construction of the key ideas supporting this concept (Quílez, 2009, 2019c). That is, LCP can serve as an example on how scientific knowledge is constructed, showing how initial attempts to understand and predict chemical equilibrium behaviour had limitations and were overcome by new thermodynamic formulations (Quílez, 1995; Quílez & Sanjosé, 1996; Solaz & Quílez, 1995). Thus, the philosophical aspects that can be developed in this historical context may provide a nice and powerful example for student understanding of the nature of science (Quílez, 2009).

A final comment concerns chemistry teachers’ training, which should consider the following issues: (a) teachers usually rely on textbooks when planning and developing content syllabus; (b) in the particular case examined in this study, official syllabi normally only specify LCP for the discussion of chemical equilibrium disturbances; (c) chemistry students and many of their teachers hold several misunderstandings when trying to apply LCP; (d) the results reported in educational studies on chemical equilibrium seem to have little effect on actual classroom practices. Therefore, in order to effectively transfer the recommendations and reflections coming from chemical education literature to in-class teaching activities (Banerjee & Power, 1991; Özmen & Naseriazar, 2017), chemistry teachers not only must properly know the meaning of concepts of chemical equilibrium and how to apply them (which means that they must not hold misconceptions) but also should understand the origin of student erroneous ideas related to this complex topic and how to both avoid and overcome them (Quílez, 1997b, 2009). All of these learning and teaching issues call for a necessary teacher PCK implementation (Mavhunga, 2020), which involves they engage in critical reflection of the didactic value of LCP as a teaching model (Sjöström et al., 2020). This perusal should consider both the inadequacies of LCP and the difficulties students experience when trying to apply its different formulations, which may allow them to both criticise current textbook presentations and realise how alternative methods may solve the learning problems found.

Appendices

Appendix 1. Textbook sample

1.1 Grade-12 Spanish Chemistry textbooks

Carriedo, G. A., Fernández, J. M. and García, M. J. (2016), Química. Madrid: Paraninfo.

del Barrio, J. I., Sánchez, A., Bárcena, A. I. and Caamaño, A. (2016), Química, Madrid: SM.

Dou, J., Masjuan, M. D. and Costafreda, E. M. (2016), Química, Barcelona: Casals.

Fontanet, A. (2016), Química, Barcelona: VicensVives.

Grence, T. Guardia, C. and Menéndez, A. I. (2016), Química, Tres Cantos: Santillana.

Illana, J., Araque, J. A., Liébana, A. and Teijón, J. M (2016), Química, Madrid: Anaya.

Manuel, M. M. and Fajardo, J. C. (2016), Química, Zaragoza: Edelvives.

Pozas, A., Martín, R., Rodríguez, A. Ruiz, A. and Vasco, A. J. (2016), Química, Madrid: McGrawHill.

Sauret, M. (2016), Química, Madrid: Bruño.

Simón, B., García-Serra, J. and Romero, J. J. (2016), Química, Barcelona: Edebé.

Vidal, M. C. and Peña, J. (2016). Química. San Fernando de Henares: Oxford.

1.2 IB and A level Chemistry textbooks

Brown, C. and Ford, M. (2014), Higher Level Chemistry, Harlow: Pearson.

Bylikin, S., Horner, G., Murphy, B. and Tarcy, D. (2014), Chemistry for the IB Diploma, Oxford: Oxford University Press.

Owen, S. (2014), Chemistry for the IB Diploma, Cambridge: Cambridge University Press.

Ritchie, R. and Gent, D. (2015), A level Chemistry for OCR, Oxford: Oxford University Press.

Ryan, L. (2015), Advanced Chemistry for You, Oxford: Oxford University Press.

Ryan, L. and Norris, R. (2014), A Level Chemistry, Cambridge: Cambridge University Press.

Talbot, C., Harwood, R. and Coates, C. (2015), Chemistry for the IB Diploma, London: Horder Education.

1.3 First-year Chemistry textbooks

Brown, T. L., LeMay, H. E., Bursten, B. E., Murphy, C. J. and Woodward, P. M. (2012), Chemistry. The central science, Boston: Prentice Hall.

Chang, R. and Goldsby, H.A. (2016), Chemistry, New York: McGrawHill.

Gilbert, T., Kirss, R. V., Foster, N., Bretz, S. L. and Davies, G. (2018), Chemistry. The Science in Context, New York: Norton.

Jespersen, N. D., Brady, J. E. and Hyslop, A. (2012), Chemistry. The Molecular Nature of Matter, Hoboken: Wiley.

Kotz, J. C., Treichel, P. M., Townsend, J. R. and Treichel, D. A. (2015), Chemistry & Chemical Reactivity, Stamford: Cengage Learning.

Moore, J. W., Stanitski, C. L. and Jurs, P. C. (2011), Chemistry. The molecular science, Belmont: Brooks/Cole.

Petrucci, R. H., Herring, F. G., Madura, J. D. and Bissonnette, C. (2017), General Chemistry: Principles and Modern Applications, Pearson: Toronto.

Zumdahl, S. S. and DeCoste, D. J. (2017), Chemical Principles, Boston: Cengage Learning.

Appendix 2. Le Châtelier’s principle: textbook statements (italics added by the author of this study; also, translations from Spanish textbooks were made by this author. It was checked using back translation and eventually an official translator that had served in the Spanish administration for more than 30 years verified the initial translation made)

1.1 Spanish Grade-12 chemistry textbooks

If a chemical system in equilibrium is subjected to a change, the reaction of the equilibrium responds shifting in the sense that cancels or minimise that change till reaching a new equilibrium state (Carriedo et al., 2016).

If in a system in equilibrium it is modified any of the factors that influence it, the system evolves in the sense that tends to counteract that change (del Barrio et al., 2016).

When in a system in equilibrium a change of any of the variables determining it (concentration, pressure or temperature) occurs, the equilibrium shifts in the direction that tends to oppose to that change (Dou et al., 2016)

When a system in a state of equilibrium is subjected to a disturbance in the conditions in which it is, the system will shift towards a new state of equilibrium so that the readjustment partially counteracts the effect of the disturbance. (Fontanet, 2016)

When a system in equilibrium is subjected to a change in the concentration of the participant species, pressure or temperature, the system responds reaching a new equilibrium that partially counteracts the effect of the change produced (Grence et al., 2016).

If in a system in equilibrium is introduced an external disturbance that alters the equilibrium, this system will evolve in the sense that tends to counteract the disturbance produced. (Illana et al., 2016)

Any change in one of the factors of an equilibrium (concentration of substances, pressure and temperature) determines a rearrangement of the system so as to reduce the disturbance introduced (Manuel and Fajardo, 2016)

If in a system in equilibrium it is modified the value of any of the values affecting it (temperature, volume, pressure or concentration), the system evolves in a way that shifts in the sense that tends to counteract such a variation (Pozas et al., 2016).

When a variation of any factor affects a system in equilibrium, this equilibrium shifts in the sense that counteracts that variation (Sauret, 2016)

When a system in equilibrium experiments a transformation, this system evolves to reach a new equilibrium in the sense which opposes to the transformation suffered (Vidal and Peña)

If in a system in equilibrium an external factor (temperature, pressure or concentration) is altered, the system evolves to counteract that change and to establish a new equilibrium state (Simón et al., 2016).

1.2 IB Chemistry textbooks

A system at equilibrium when subjected to a change will respond in such a way as to minimize the effect of the change (Brown and Ford, 2014).

If a change is made to a system that is in equilibrium, the balance between the forward and the reverse reactions will shift to offset this change and return the system to equilibrium (Bylikin et al., 2014)

If a system at equilibrium is subjected to a change, the position of equilibrium will shift in order to minimise the effect of the change (Owen, 2014).

The system responds to negate the change by responding in the opposite way (Talbot et al., 2015).

1.3 British A level chemistry textbooks

When a system in equilibrium is subjected to an external change the system readjust itself to minimise the effect of the change (Ritchie and Gent, 2015).

The position of equilibrium shifts to try to cancel out any changes you introduce (Ryan, 2015)

If one or more factors that affect an equilibrium is changed, the position of equilibrium shifts in the direction that reduces (opposes) the change (Ryan and Norris, 2014)

1.4 First-year university chemistry textbooks

If a system at equilibrium is disturbed by a change in temperature, pressure, or a component concentration, the system will shift its equilibrium position so as to counteract the effect of the disturbance (Brown et al., 2012).

If an external stress is applied to a system at equilibrium, the system adjusts in such a way that the stress is partially offset as it tries to re-establish equilibrium (Chang and Goldsby, 2016).

If a system at equilibrium is perturbed (or subjected to an external stress), the position of the equilibrium shifts in either the forward or reverse direction as a response to reduce that stress (Gilbert et al., 2018).

If an outside influence upsets an equilibrium, the system undergoes a change in a direction that counteracts the disturbing influence and, if possible, returns the system to equilibrium (Jerpersen et al., 2012)

A change in any of the factors that determine the equilibrium conditions of a system will cause the system to change in such a manner as to reduce or counteract the effect of the change (Kotz et al., 2015).

If a system is at equilibrium and the conditions are changed so that it is no longer at equilibrium, the system will react to reach a new equilibrium in a way that partially counteracts the change (Moore et al., 2011).

When an equilibrium system is subjected to a change in temperature, pressure, or concentration of a reacting species, the system responds by attaining a new equilibrium that partially offsets the impact of the change (Petrucci et al., 2017).

If a change in conditions (a ”stress”) is imposed on a system at equilibrium, the equilibrium position will shift in a direction that tends to reduce that change in conditions (Zumdahl and DeCoste, 2017).

1.5 Classical Textbooks

If a constraint is applied to a system in equilibrium, the change which occurs is such that it tends to annul the constraint (Butler, 1939)

If a change occurs in one of the factors, such as temperature or pressure, under which a system is in equilibrium, the system will tend to adjust itself so as to annul, as far as possible, the effect of that change (Glasstone, 1946)

Any change in one of the variables that determine the state of a system in equilibrium causes a shift in the position of equilibrium in a direction that tends to counteract the change in the variable under consideration (Moore, 1963)

Every change of one of the factors of an equilibrium occasions a rearrangement of the system in such a direction that the factor in question experiences a change in a sense opposite to the original change (Nernst, 1904)

If a system in equilibrium is subjected to a constraint, whereby the equilibrium is modified, a change takes place, if possible, which partially annuls the constraint (Partington, 1949)

When one or more of the factors determining an equilibrium are altered, the equilibrium becomes displaced in such a way as to neutralize, as far as possible, the effect of the change (Senter, 1919)

If the conditions of a system, initially at equilibrium, are changed, the equilibrium will shift in such a direction as to tend to restore the original conditions (Pauling, 1957).

1.6 Other chemistry textbooks

A change in a variable that determines the state of an equilibrium system will cause a shift in the position of the equilibrium in a direction tending to counteract the effect of the change in the variable (Adamson, 1973)

If a system in equilibrium is subjected to an external effect, the balance will be upset in that direction of the process which will tend to weaken this effect (Akhmetov, 1983).

When a system at equilibrium is subjected to a disturbance, the composition of the system adjusts so as to tend to minimize the effect of the disturbance (Atkins & de Paula, 2009)

When a system is in chemical equilibrium, a change in one of the parameters of the equilibrium produces a shift in such a direction that, were no other factors involved in this shift, it would lead to a change of opposite sign in the parameter considered (Chang & Thoman, 2014)

Any system in chemical equilibrium undergoes, as a result of a variation in one of the factors governing equilibrium, a compensating change in a direction such that, had this change occurred alone it would have produced a variation of the factor considered in the opposite direction (Considine, 2005).

Every equilibrium system reacts to external actions, modifying itself in the sense of absorbing the effects produced in order to restore primitive conditions (Corrales, 1974).

A system forced out of equilibrium readjusts in a manner that tends to undo the change it has just suffered (Le Châtelier’s principle might be called an observation of the natural perversity of a disturbed system) (Harrison & Weaver, 1989)

When a stress is brought to bear on a system at equilibrium, the system tends to change so as to relieve the stress (Keenan & Wood, 1966).

If an external stress is applied to a system in equilibrium, the equilibrium will shift continuously in the direction indicated by the stress until the growing reaction in the system become equal to the external stress (Nekrasov, 1969).