Reduction Kinetics of Ag₂MoO₄ by Hydrogen

Abstract

Ag₂O and MoO₃ powders were mechanically (ball) milled with the objective of obtaining a Ag₂MoO₄ phase for subsequent reduction with hydrogen gas. A thermogravimetric unit was used to follow the course of the reduction process aiming at the chemical reaction as the rate controlling step. Isothermal reduction experiments were performed on the individual oxides to establish a ground for the reduction parameters of silver molybdate. Consequently, a nonisothermal treatment was used on Ag₂MoO₄. It was found that Ag₂MoO₄ is reduced in three steps, e.g., Ag₂MoO₄ to MoO₃ and Ag followed by MoO₃ to MoO₂ and finally MoO₂ to Mo. By assuming a shrinking core model, the calculated activation energies for the first and second reduction steps were 69 and 29 kJ/mol, respectively. While the former value is in good agreement with the activation energy obtained from the isothermal reduction of Ag₂O to Ag, 64 kJ/mol, the latter was found to be lower than the corresponding value for MoO₃ to MoO₂ under isothermal conditions, 124 kJ/mol. It was found that the presence of metallic silver obtained from the initial reduction step of Ag₂MoO₄ not only lowers the energy barrier but the reducing temperature of the subsequent reaction steps (i.e., MoO₃ → MoO₂ → Mo).

Introduction

Hydrogen reduction of mixed oxides enables the formation of an alloy containing a low melting metal (e.g., Au) with a high melting metal (e.g., Co). For example, in the reduction of cobalt aluminate (CoAl₂O₄) by hydrogen,[1] to form cobalt with Al₂O₃ particles, indications were obtained that at temperatures higher than 1273 K, part of the alumina was reduced and the produced aluminum formed a binary Al-Co alloy. Similarly, in the reduction of ZnWO4 with hydrogen, a new W-Zn phase was obtained.[2]

The reduction of MoO₃ with hydrogen has been subject of numerous investigations[3–7] with contrasting opinions on the kinetics of the reduction of MoO₃ to Mo. For example, Hawkins et al.[3] studied the reduction of molybdenum oxide by hydrogen in the temperature range 573 to 723 K and found intermediate suboxides between MoO₂ and MoO. Orehotsky et al.[4,5] separately investigated the kinetics of hydrogen reduction of static powder beds of MoO₃ to MoO₂ and MoO₂ to Mo at temperature ranges of 732 to 877 K and 686 to 1083 K, respectively. The activation energies reported for both processes were approximated to 70 kJ/mol. Arnoldy et al.[6] investigated the reduction of MoO₃ and MoO₂ by varying parameters such as heating rate, sample size, H₂O content of the reducing mixture (H₂/Ar), and precalcination temperature. In this study, the reported activation energy values ranged from 80 to 405 kJ/mol. Du Sichen and Seetharaman[7] carefully analyzed the hydrogen reduction of MoO₃ and MoO₂ by using thin pellets of the oxides placed in crucibles with relatively high walls. The activation energies reported by these authors were 211 kJ/mol for the reduction of MoO₃ to MoO₂ and 85 kJ/mol for MoO₂ to Mo. On the other hand, there does not appear to be much information in the literature on the kinetics of the reduction of Ag₂O by hydrogen. This may be due to the fact the Ag₂O starts decomposing at about 473 K. Indeed, the kinetics of the thermal decomposition of Ag₂O has received large attention.[8]

Silver alloys and silver composites find application as electrical contacts due to their high thermal and electrical conductivity. To ensure high electrical conductivity and strong wear resistance, the properties of silver are combined with those of other materials. Powder metallurgy provides a suitable route for the production of refractory alloys especially when the components of refractory alloys have greatly differing melting temperatures, limited mutual solubility, and different densities. Moreover, the powder metallurgy processing route is highly economically competitive. On the synthesis of Ag-Mo base materials, only one reference has been found, Stolk et al.[9] These authors synthesized Ag-Mo composites by heat treating silver molybdate (Ag₂MoO₄) powders in H₂ atmosphere to address the thermal properties of the product material. Silver and its alloys have excellent electrical, thermal, optical, or catalytic properties. An investigation of the reduction kinetics of silver molybdate would be of considerable value. Thus, the objective of this work is to study the reduction kinetics of Ag₂MoO₄ by hydrogen aiming at the rate of the chemical reaction as the rate controlling step. To obtain the silver molybdate phase, Ag₂O and MoO₃ powders, in stochiometric ratios, were ball milled to ensure a uniform distribution of Ag and Mo ions.

Experimental

Silver molybdate (Ag₂MoO₄) was prepared at the stoichiometric composition by mixing Ag₂O (99.0 pct Alfa Aesar, Ward Hill, MA) and MoO₃ (99.5 pct Alfa Aesar) powders in required proportions followed by mechanical ball milling using a shaker ball mill (SPEX 8000, Metuchen, NJ). Stainless steel balls were used in the mill, while the ball-to-powder weight ratio was kept to 10:1. The milling process was limited to 5 hours to minimize iron contamination.

Isothermal experiments were carried out on Ag₂O and MoO₃ powders, while nonisothermal experiments were employed on Ag₂MoO₄. Both types of reduction experiments were carried out using a horizontal thermogravimetric apparatus (Metller Toledo 581e, Mexico, D.F., Mexico), which has an accuracy of 1 μg. The balance was controlled by a personal computer through an interface. The weight change during the reduction experiments was recorded by the computer at 1-second intervals. An alumina crucible with 8-mm inner diameter and 1-mm height was used to hold the sample. Typically, about 35 mg of powder were used in each experiment to just form a thin layer. The crucible containing the sample was placed on one end of an alumina rod from the balance. The reactor was made of dense alumina with 16-mm inner diameter. The temperature of the furnace was controlled by a Pt-13 pct Rh/Pt (R-type) thermocouple placed just below the crucible. The fluid flows of the inert gas and reactant gas were individually regulated using mass-flow controllers. Argon and hydrogen gases (99.99 pct) were used in the reduction experiments, which were not further cleaned; however, the influence of the impurities in the hydrogen gas over the reduction kinetics should be well within the limits of experimental error.

In the isothermal experiments, the reaction chamber was flushed with argon gas for 30 minutes after introducing the sample. Then, the sample was heated to the reduction temperature at a heating rate of 25 K/min under a constant flow of argon of 0.1 L/min. Once the reduction temperature was stabilized, the argon gas was stopped and hydrogen gas was introduced into the reaction chamber to start the reduction process. After no more weight loss of the sample was recorded by the computer, the experiment was terminated by cooling the furnace to room temperature at the highest cooling rate (∼50 K/min). In the case of a nonisothermal experiment, the reaction chamber was initially flushed with hydrogen for 30 minutes after introducing the sample into the furnace. A constant flow of hydrogen gas (0.3 L/min) was maintained throughout the heating cycle. The sample was then heated at a constant heating rate. The experiment was then terminated in a similar fashion as in the case of the isothermal reduction. To eliminate the effect of mass-transfer effect through the powder bed, i.e., gas transport resistance from the bulk stream to the bottom of the crucible, an optimum amount of powder was determined by examining the reduction rate as a function of the mass sample, which is proportional to the thickness of the powder bed. Moreover, to help focus on the rate of chemical reaction as the controlling step, a hydrogen flow rate of 0.3 L/min was established, as it should be well above the starvation rate for the reduction reactions studied given the small amount of particles used.

The phases of the products obtained after ball milling and hydrogen reduction were identified by X-ray diffraction (XRD) analysis using a Siemens D5000 diffractometer (Mexico, D.F., Mexico) at 30 mA, 50 kV, and 0.02 deg/s step size using Cu K _α radiation. The particle size distribution of the oxides was determined using a Horiba centrifugal particle analyzer, model CAPA 500 (Irvine, CA).

Results

The average particle size for the starting powders, Ag₂O and MoO₃, and the milled powders were 0.15, 0.69, and 1.2 μm, respectively. The XRD spectrum of milled powders along with the identified phases are shown in Figure 1. As it can be seen, powders mainly consist of Ag₂MoO₄ with small Bragg peaks of MoO₃ and Ag₂O. The presence of small amounts of MoO₃ and Ag₂O could indicate that the milling time was not sufficient to completely form the Ag₂MoO₄ phase. However, the former two phases should be distributed uniformly within the mixture, which would be favorable for the subsequent reduction process.

Fig. 1

XRD patterns for Ag₂O-MoO₃ mixture (1:1 molar ratio) after ball milling

To better elucidate the reducing mechanism of Ag₂MoO₄, isothermal reduction experiments were individually performed on Ag₂O and MoO₃ powders. Figure 2 shows the isothermal reduction curves of Ag₂O by hydrogen at different temperatures. The dimensionless mass change X represents the ratio of the instant mass loss Δm _t to the theoretical final mass loss Δm _∞ , the latter corresponding to the loss of all the oxygen atoms from the oxide. As it can be seen, the reaction rate increases with increasing temperature with a suitable temperature range between 348 and 398 K. Figure 3 shows the reduction rate of MoO₃ by hydrogen as a function of temperature between 893 and 953 K. To avoid uncertainties in the experimental data, the maximum reducing temperature of MoO₃ was limited to 953 K due to the dramatic sublimation of MoO₃ solid occurring at temperatures above 973 K and below the melting point of MoO₃ (1055 ± 5 K). In each reduction curve, a distinct change in the slope is observed in the range X = 0.2 to 0.3. The change in the slope is expected at about X = 0.3, as the complete reduction of MoO₃ to MoO₂ should theoretically correspond to X = 0.33. To verify the effect of gaseous diffusion between particles on the reaction rate at 923 K, the powder bed height was increased by increasing the weight of the sample from 35 to 50 mg, as shown in Figure 4. As it can be seen, both reduction curves are invariant of the bed height (i.e., sample weight) from the beginning of the process toward the complete reduction of MoO₃ to MoO₂ (X = 0.33). After the complete reduction of MoO₃ to MoO₂, the reduction curves tend to separate from each other, indicating the dependence of the reaction rate (dX/dt) on the bed height.

Fig. 2

Isothermal reduction curves of Ag₂O

Fig. 3

Isothermal reduction curves of MoO₃

Fig. 4

Effect of powder bed height on the isothermal reduction rate of MoO₃ at 923 K

Because the temperature range for the reduction of MoO₃ is higher that that for Ag₂O by about 500 K, it was deemed necessary to study the reduction kinetics of Ag₂MoO₄ under nonisothermal conditions, because an isothermal process would require a very wide temperature range that is not suitable for the evaluations of activation energies. Thus, Figure 5 shows the nonisothermal reduction of Ag₂MoO₄ at different scanning rates. As it can be seen, the reduction curves show a similar pattern independent of the heating rate. Distinctive changes in the slopes indicate that the reduction process goes through intermediate steps. The reduction steps toward the completion of the reaction depend on the heating rate, because there is no overlapping of the reduction curves. Toward the end of the process, the reduction rate becomes slower the lower the scanning rate.

Fig. 5

Nonisothermal reduction curves of Ag₂MoO₄

Discussion

Isothermal Reduction

In the present work, the reduction curves of Ag₂O by H₂ show no discontinuities in their slopes, suggesting a one-step process according to the following reaction:

$$ {\text{Ag}}_{\text{2}} {\text{O}}\, + \,{\text{H}}_{\text{2}} \, = \,{\text{2Ag}}\, + \,{\text{H}}_{\text{2}} {\text{O}} $$

(1)

Because the reduction curves shown in Figure 2 clearly indicate that the process is sensitive to temperature, it is logical to assume that the chemical reaction is the rate controlling step under the given experimental conditions.

Figure 3 shows the reduction curves of MoO₃ at different temperatures. It is evident that these curves present a change in slope at about X = 0.3 being clearer at lower temperatures. This is an interesting observation as the complete reduction of MoO₃ to MoO₂ should theoretically correspond to X = 0.33. Beyond this point, the reduction rate shows a sigmoidal trend for the MoO₂ conversion. While the acceleratory period in the sigmoidal curve indicates the onset of the MoO₂ to Mo conversion, the decaying period would most probably be the result of the diminished reaction surface. Therefore, under the prevailing experimental conditions, the reduction of MoO₃ involves two main reduction steps:

$$ {\text{MoO}}_{\text{3}} \, + \,{\text{H}}_{\text{2}} \, = \,{\text{MoO}}_{\text{2}} \, + \,{\text{H}}_{\text{2}} {\text{O}} $$

(2)

$$ {\text{0}}{\text{.5MoO}}_{\text{2}} \, + \,{\text{H}}_{\text{2}} \, = \,{\text{0}}{\text{.5Mo}}\, + \,{\text{H}}_{\text{2}} {\text{O}} $$

(3)

Reaction [2] would be controlled by the rate of chemical reaction, as Figure 4 shows that the slopes of the reduction curves corresponding to X < 0.3 are nearly the same. In this case, the gas composition at the internal surface of the particles is quite the same as that in the bulk gas phase. Therefore, gas diffusion between particles does not offer any considerable resistance, and only the chemical reaction offers the major resistance to the reduction process. On the other hand, Reaction [3] is likely to be affected by the rate of mass transport due to the fact that the slopes of the reduction curves for X > 0.33 (Figure 4) are relatively different, indicating that gas diffusion between particles proceeds at a slower rate than the rate of chemical reaction. Thus, the resistance caused by the gas diffusion becomes significant.

The existence of suboxide phases during the reduction of MoO₃ with hydrogen has been controversial. For example, Du Sichen and Seetharaman[7] carried out SEM studies on MoO₃ thin compacts partially reduced by hydrogen at 873 and 973 K. Their studies showed that MoO₂ was the unique intermediate phase during the reduction process, although there exist two intermediate phases such as Mo₉O₂₆ and Mo₄O₁₁ between MoO₃ and MoO₂ phases, as illustrated in the phase diagram Mo-MoO₃ constructed by Bygdén et al.[10] Other authors[11] reported the intermediate phase Mo₄O₁₁ before reaching the MoO₂ phase by hydrogen reduction at 823 K. Ressler et al.[12] studied the reduction of MoO₃ with hydrogen in the temperature range from 623 to 823 K and hydrogen concentration from 5 to 100 vol pct. They found that Mo₄O₁₁ forms only under certain reaction conditions (H₂ concentration <20 vol pct and at temperatures above 698 K), where the reduction of MoO₃ is considerably slow that it permits the formation of Mo₄O₁₁. They also reported that the formation Mo₄O₁₁ is not an intermediate product during the reduction of MoO₃ but is rather formed in a parallel reaction from MoO₃ and MoO₂. In the present work, the reduction of MoO₃ proceeds considerably fast due to the higher reducing temperatures employed. Thus, neither Mo₉O₂₆ nor Mo₄O₁₁ phases were identified by XRD on samples partially reduced.

Similar to Reaction [1], Reaction [2] is likely to be controlled by the rate of the chemical reaction in view of the following facts.

• (1) Sample powders used in this investigation were essentially of a few microns in size; therefore, the thickness of the product layer is small and thus it is not likely to offer any appreciable resistance to the reactant and product gas species.

• (2) The change of the height of the bed, by increasing the sample weight from 35 to 50 mg, had a noticeable effect on the reaction rate only beyond X = 2 (Figure 4), implying thereby that the rate of gas diffusion through the powder bed was not mechanism controlling the reduction reaction in the beginning of Reaction [2].

• (3) Under the previous circumstances, using a flow rate of 0.3 L/min, the rate of mass transfer from the bulk of the gas stream to the external surface of the powder bed is not likely to hinder the course of the reaction.

• (4) Given that the amount of the oxide powder used is very small, the impact of the endothermic heat of the reaction on the temperature of the particles could be assumed to be negligible; therefore, the heat-transfer aspect can be ruled out.

Nonisothermal Reduction

From the preceding isothermal results, the nonisothermal reduction of Ag₂MoO₄ is first reduced to Ag and MoO₃ according to the following reaction:

$$ {\text{Ag}}_{\text{2}} {\text{MoO}}_{\text{4}} \, + \,{\text{H}}_{\text{2}} \, = \,{\text{2Ag}}\, + \,{\text{MoO}}_{\text{3}} \, + \,{\text{H}}_{\text{2}} {\text{O}} $$

(4)

Then, continue through Reactions [2] and [3]. This was confirmed by XRD analysis, which revealed Mo and Ag as the unique phases present in the reduced product, as shown in Figure 6. In the reduction of Ag₂MoO₄, changes in the slopes were more evident. To acquire a deeper understanding of the reduction mechanisms associated with these behaviors, the derivative of X with respect to time, dX/dt, from the nonisothermal reduction curve with a scanning rate of 11 K/min was plotted as a function of temperature along with the corresponding reduction curve, as shown in Figure 7. The dashed lines indicate the theoretical fraction of transition from Reaction [4] to Reaction [2] and Reaction [2] to Reaction [3], X = 0.25 and X = 0.5, respectively. Figure 7 shows that dX/dt increases and decreases irregularly with increasing temperature. This behavior may be explained as follows. In the region comprising Reaction [4] (0 < X < 0.25), the reduction of Ag₂O starts at about 350 K and the reduction rate shows a sharp increase as a consequence of the increase in temperature up to 495 K. This temperature is above the temperature range used in the isothermal reduction of Ag₂O (348 to 398 K). From 495 K, the reduction rate decreases up to 545 K. This decreasing trend could indicate that the reduction mechanism changes from chemical control to mix control, because the rate of chemical reaction increases to the extent where it is no longer the slowest rate step, as established by Szekely et al.[13] and Levenspiel.[14] Before the theoretical completion of Reaction [4] (X ≤ 0.25), dX/dt increases again, indicating that the reduction of MoO₃ to MoO₂ might have been initiated before Ag₂O is completely reduced. In the region comprising Reaction [2] (0.25 < X < 0.5), the reduction rate of MoO₃ to MoO₂ increases up to 600 K. Beyond this temperature, dX/dt decreases progressively until the theoretical completion value is reached, X = 0.5. It should be noticed that the reduction of MoO₃ to MoO₂ occurs in the temperature range 570 to 650 K, which is significantly lower with respect to the temperature range found in the isothermal reduction of the single oxide (MoO₃), 893 to 953 K. This disparity cannot be explained on the very basis of particle diameter difference between the single and complex oxide but rather on the possible catalytic effect of the free silver content obtained from the preceding reaction. Namely, silver provides a surface with active catalytic sites on which reactants (H₂ and Mo oxides) temporarily become adsorbed and bonds in the reactants become weakened sufficiently for products to be created. The catalyst releases the products without affecting them. This process increases the reaction rate and lower activation energy. While the catalytic effect of silver explains the initial increase in the reaction rate, the subsequent decrease would most probably be due to the diminished reaction surface besides high concentration of H₂O (g) at the reaction interface caused by the fast consumption of H₂, hindering thus the driving force for the chemical reaction.

Fig. 6

XRD pattern of the product obtained after the nonisothermal reduction of Ag₂MoO₄

Fig. 7

Differential reduction rate dX/dt against temperature for a nonisothermal experiment at 11 K/min

In the last step of reduction (MoO₂ to Mo, X > 0.5), the reaction rate depicts a sigmoidal trend. This behavior may be caused by the action of opposed driving forces. That is to say, on the one hand, the catalytic effect of silver and the increase in temperature tend to increase the reaction rate, and, on the other hand, the reversible character of Reaction [3] makes the course of the reduction highly sensitive to slight variations of H₂O (g) partial pressure buildup at the reaction interface. To account for the catalytic effect, Reactions [2] and [3] involved in the reduction of Ag₂MoO₄ will be henceforth referred to as

$$ {\text{MoO}}_{\text{3}} + {\text{H}}_{\text{2}} \frac{{{\text{Ag}}}} {\Delta }{\text{MoO}}_{\text{2}} + {\text{H}}_{\text{2}} {\text{O}} $$

(2b)

$$ 0.5{\text{MoO}}_{\text{2}} + {\text{H}}_{\text{2}} \frac{{{\text{Ag}}}} {\Delta }{\text{0}}{\text{.5Mo}} + {\text{H}}_{\text{2}} {\text{O}} $$

(3b)

Isothermal Kinetics Analysis

To acquire a kinetic characterization of the individual oxides, the shrinking core model was applied to the gas-solid reaction occurring in each individual particle for Reactions [1] and [2] under isothermal conditions. Attempts to apply this model to Reaction [3] were not made, because it was found that mass diffusion affects the reaction mechanism for X > 0.3, which corresponds to the reduction of MoO₂ to Mo (Figure 4). Mass diffusion affects the reduction stage from MoO₂ to Mo, because this reaction has a very small equilibrium constant, which makes the reduction reaction extremely sensitive to mass-transfer rate steps. Thus, if Reactions [1] and [2] are of first order with respect to hydrogen and are irreversible, the relationship between the reaction time, t, and the fraction of reduction, X, for the chemical reaction control can be expressed as[15]

$$ t = \frac{{\rho _{{\text{oxide}}} \cdot r_0 }} {{M_{{\text{oxide}}} \cdot k \cdot P_{{\text{H}}_2 } }}\left[ {1 - \left( {1 - X} \right)^{1/3} } \right] $$

(5)

where r ₀ is the initial radius of the particle; ρ _oxide and M _oxide stand for the density and molecular weight of oxide, respectively; k is the reaction rate constant; and P _H2 corresponds to the hydrogen partial pressure. Assuming that at given temperature the aforementioned terms remain constant, $\left[ {1 - \left( {1 - X} \right)^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} } \right]$ should be a linear function of t if the reduction is controlled by the chemical reaction at the interface between product layer and the unreacted core in each particle. The plots of $\left[ {1 - \left( {1 - X} \right)^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} } \right]$ against time at different experimental temperatures for Reactions [1] and [2] are presented in Figures 8 and 9, respectively. All curves showed a correlation coefficient better than 0.99. An activation energy for Reactions [1] and [2] was calculated by combining Eq. [5] with Arrhenius rate law as expressed by the following equation:

$$ k = k_o \exp \left( { - \frac{Q} {{{\text{R}}T}}} \right) $$

(6)

where k _o is a constant, Q is the activation energy of the reaction, T is the temperature in K, and R is the gas constant. The combination of Eqs. [5] and [6] leads to the following expression:

$$ \frac{{1 - \left( {1 - X} \right)^{1/3} }} {t} = \frac{{M_{{\text{oxide}}} \cdot P_{{\text{H}}_2 } \cdot k_o }} {{\rho _{{\text{oxide}}} \cdot r_{\text{0}} }}\exp \left( { - \frac{Q} {{{\text{R}}T}}} \right) $$

(7)

Fig. 8

Experimental values and theoretical linear fit corresponding to the chemical reaction rate for the isothermal reduction of Ag₂O

Fig. 9

Experimental values and theoretical linear fit corresponding to the chemical reaction rate for the isothermal reduction of MoO₃

Taking the logarithm on both sides of the Eq. [7] leads to the following relationship:

$$ \ln \left( {\frac{{1 - \left( {1 - X} \right)^{1/3} }} {t}} \right) = \ln \left( {\frac{{M_{{\text{oxide}}} \cdot P_{{\text{H}}_2 } \cdot k_o }} {{\rho _{{\text{oxide}}} \cdot r_{\text{0}} }}} \right) - \frac{Q} {{{\text{R}}T}} $$

(8)

The plot of the term on the left-hand side against 1/T is presented in Figures 10 and 11 for Reactions [1] and [2], respectively. As can be seen in Figure 11, the experimental point corresponding to 923 K lies above the Arrhenius plot; this might suggest that above this temperature the reduction control is shifting due to the increase in temperature, e.g., the faster the rate of chemical reaction is, the less likely to be the rate controlling mechanism. From the slopes of the Arrhenius plots, the activation energies for Reactions [1] and [2] are found to be 64 for Ag₂O and 124 kJ/mol for MoO₃. According to Seetharaman et al.,[16] the stronger the metal-oxygen bond, the higher the activation energy. In addition, the Mo-O bond is expected to be stronger, because its free energy of formation has a larger negative value, which in turn counts for bond forces.

Fig. 10

Arrhenius plot for the isothermal reduction of Ag₂O

Fig. 11

Arrhenius plot for the isothermal reduction of MoO₃

Nonisothermal Kinetic Analysis

For nonisothermal decomposition of carbonates, Arvanitidis et al.[17,18] reported, on a shrinking core model, the activation energy for a chemical-reaction-controlled process. This approach would also be valid at the early stages of Reactions [4] and [2b] involved in the reduction of Ag₂MoO₄. The mathematical expression for the reaction rate is

$$ \frac{{dX}} {{dt}} = \frac{{A_{\text{0}} }} {{\text{R}}} \cdot \frac{{(1 - X)^{2/3} }} {T} \cdot k $$

(9)

The new term, A ₀, is the initial reaction surface area. Inserting Eq. [6] into Eq. [9] leads to the following relationship:

$$ \frac{{dX}} {{dt}} = \frac{{A_{\text{0}} }} {{\text{R}}} \cdot \frac{{(1 - X)^{2/3} }} {T} \cdot k_o \exp \left( { - \frac{Q} {{{\text{R}}T}}} \right) $$

(10)

By taking the logarithm on both sides of Eq. [10] and rearranging the expression, one can obtain

$$ \ln {\text{ }}\left( {\frac{{dX}} {{dt}}} \right) + \ln {\text{ }}(T) - \ln {\text{ }}(1 - X)^{2/3} = \ln {\text{ }}B - \frac{Q} {{{\text{R}}T}} $$

(11)

where B groups A ₀ k _o /R, which are independent of temperature. The three terms of the left-hand side of Eq. [11] can be obtained using the experimental data of Figure 7 taking the early stages of reduction for the regions corresponding to Reactions [4] and [2b]. Thus, plots using Eq. [11] for Reactions [4] and [2b] are presented in Figures 12 and 13, respectively. The value of the activation energy calculated from the slope in Figure 12 is 69 kJ/mol, which is in good agreement with the value obtained by isothermal experiments, 64 kJ/mol. It should be pointed out that, in Figure 12, the experimental point corresponding to the highest experimental temperature was left out of the calculations as it tends to deviate from the regression line. This deviation suggests that the thermal decomposition of Ag₂O (decomposition temperature of Ag₂O ≈ 473 K) starts to play a mayor role in the reduction mechanism. The similarity of the activation energies obtained from both isothermal and nonisothermal temperature programs enables the possibility of predicting the kinetics of reactions from a single nonisothermal experiment. On the other hand, the activation energy of Reaction [2b] evaluated from the slope in Figure 13 is 29 kJ/mol. Because this value is significantly lower than that obtained from the isothermal experiments, e.g., 124 kJ/mol, the assumption of silver lowering the activation energy of the proceeding reaction by catalysis appears to be valid. That is to say, in the reduction of Ag₂O·MoO₃, the strength of the Mo-O bond is likely to be weakened by the attraction of Ag to oxygen, which increases the reduction rate of MoO₃ to Mo. The present results suggest that the reduction process of Ag₂MoO₄ could be best achieved under nonisothermal conditions due to the low decomposition temperature of Ag₂O. In fact, the nonisothermal technique overcomes many limitations of the isotherm technique. For example, the nonisothermal technique represents a more realistic situation, because in most industrial reactors, the reacting materials are heated gradually. By the same token, no reactions take place isothermally, because all reactions are accompanied by a heat change, which is more significant when a large mass of materials react. On the other hand, the isothermal technique is inadequate to study complex reactions involving several series, parallel or overlapping reactions.

Fig. 12

Arrhenius plot for the nonisothermal reduction of Ag₂MoO₄ to Ag and MoO₃

Fig. 13

Arrhenius plot for the nonisothermal reduction of MoO₃ to MoO₂ in the Ag₂O-MoO₃ system

Summary and Conclusions

The reduction of Ag₂MoO₄ by hydrogen was studied by means of thermogravimetric technique under nonisothermal conditions. Previously, isothermal reduction experiments were performed on the individual oxides, viz. Ag₂O and MoO₃. Nonisothermal results indicate that the reduction of Ag₂MoO₄ proceeds in three steps: one involving the reduction of Ag₂MoO₄ to silver and MoO₃, a second step in which MoO₃ is reduced to MoO₂, and the last step wherein MoO₂ is reduced to metallic molybdenum. From the rate of the reactions obtained, the activation energies for the two first steps were calculated to be 69 and 29 kJ/mol, respectively. The activation energy of the isothermal reduction of Ag₂O to Ag is in agreement with the first step of the nonisothermal experiment. On the other hand, the activation energy of the isothermal reduction of MoO₃ to MoO₂, 124 kJ/mol, implies that the presence of silver in the second step of the nonisothermal reduction affects the reaction rate of MoO₃ to MoO₂.