PHYSICAL CHEMISTRY

I. A. Smirnov, N. M. Morozov, M. I. Temkin

KINETICS OF AMMONIA SYNTHESIS DURING POISONING OF THE CATALYST BY WATER VAPOR

(Presented by Academician N. M. Zhavoronkov, 20 VII 1963)

The influence of oxygen-containing poisons on the activity of an iron catalyst for ammonia synthesis has been investigated in a number of works \((^{1-5})\). Almkvist and Black \((^2)\) established that \(\mathrm{O_2}\) and \(\mathrm{H_2O}\), in equivalent amounts, produce the same poisoning effect, because under synthesis conditions \(\mathrm{O_2}\) is converted into \(\mathrm{H_2O}\). They found that, in a flow system at constant space velocity, the partial pressure of ammonia at the outlet, \(P_{\mathrm{NH_3}}\), is related to the partial pressure of water vapor \(P_{\mathrm{H_2O}}\) by the equation

\[ P_{\mathrm{NH_3}}\sqrt{P_{\mathrm{H_2O}}}=\text{const}. \tag{1} \]

Emmett and Brunauer \((^3)\) indicated that equation (1) can be obtained by integrating an equation of the form

\[ \omega=\frac{f(P_{\mathrm{N_2}},P_{\mathrm{H_2}})} {P_{\mathrm{NH_3}}\cdot P_{\mathrm{H_2O}}}, \tag{2} \]

where \(\omega\) is the reaction rate, if the partial pressures of nitrogen and hydrogen \(P_{\mathrm{N_2}}\) and \(P_{\mathrm{H_2}}\) are regarded as constant. S. L. Kiperman \((^{6,7})\) proposed the equation

\[ \omega=\left[ k_1P_{\mathrm{N_2}}\left(\frac{P_{\mathrm{H_2}}^3}{P_{\mathrm{NH_3}}^2}\right)^{\alpha} - k_2\left(\frac{P_{\mathrm{NH_3}}^2}{P_{\mathrm{H_2}}^3}\right)^{1-\alpha} \right]\frac{P_{\mathrm{H_2}}}{P_{\mathrm{H_2O}}}, \tag{3} \]

which, at \(\alpha=0.5\), gives equation (2), if the term containing \(k_2\), i.e., the rate of the reverse reaction, is neglected.

Equation (3), at \(P_{\mathrm{H_2O}}=0\), does not pass into the kinetic equation for synthesis

\[ \omega=k_+P_{\mathrm{N_2}} \left(\frac{P_{\mathrm{H_2}}^3}{P_{\mathrm{NH_3}}^2}\right)^{\alpha} - k_-\left(\frac{P_{\mathrm{NH_3}}^2}{P_{\mathrm{H_2}}^3}\right)^{1-\alpha}, \tag{4} \]

which is valid in the absence of catalytic poisons, but gives \(\omega=\infty\). Equations (1) and (2) have the same shortcoming.

The derivation of equation (4) assumes \((^{8,9})\) that, in the course of synthesis, equilibrium is established between adsorbed nitrogen \(\mathrm{N}_{2\,\mathrm{ads}}\) and the gas phase

\[ \mathrm{N}_{2\,\mathrm{ads}}+3\mathrm{H}_2=2\mathrm{NH}_3. \tag{5} \]

The rate of synthesis is determined by the rate of adsorption of nitrogen on the free surface. In addition, we shall assume that, in the presence of water vapor in the gas mixture, the equilibrium

\[ \mathrm{O}_{\mathrm{ads}}+\mathrm{H}_2=\mathrm{H_2O} \tag{6} \]

is established.

The adsorption of two substances on a heterogeneous surface can be considered similarly to the way in which the adsorption of one substance was considered earlier \((^{10})\). Let \(a\) and \(a'\) denote the adsorption coefficients of the two gases, and let \(s\) denote the ratio of the number of a site on the surface to the total number of sites (the sites may be numbered, for example, in the order of decreasing values of \(a\)). Assuming that the surface is uniformly heterogeneous with respect to the standard free energies of adsorption of both gases, we obtain

\[ a=a_0e^{-fs}; \tag{7} \]

\[ a'=a'_0e^{-f's}, \tag{8} \]

where \(a_0\) and \(a'_0\) are the values of \(a\) and \(a'\) at \(s=0\). For simplicity, let us assume that \(f=f'\), i.e., that the change in the standard free energy of adsorption in passing from one surface site to another is the same for both gases.

We shall assume that, during the adsorption process, an equilibrium distribution of particles over the surface sites is established. This could be the result of surface migration; in the case of interest to us, the equilibrium distribution is ensured by the mobile equilibria (5) and (6). The existence of an equilibrium distribution permits the introduction of quantities common to all

instead of the quantities \(p\) and \(p'\)—the fugacities of the substances in the surface layer, i.e., those partial pressures of these substances in the ideal gas phase that would correspond to equilibrium with the surface layer. The probability that a given site is free is equal to \(\dfrac{1}{1+ap+a'p'}\). Let \(P\) denote the partial pressure of the first gas, and let \(\varkappa\) denote its adsorption rate constant (which is a function of \(s\)); then the rate of adsorption of this substance is

\[ v=\int_0^1 \frac{\varkappa P}{1+ap+a'p'}\,ds. \tag{9} \]

Let us assume that

\[ \varkappa=Ga^\alpha, \tag{10} \]

where \(\alpha\) and \(G\) are constants \((0<\alpha<1)\); then \(\varkappa=\varkappa_0 e^{-\alpha fs}\), where \(\varkappa_0\) is the value of \(\varkappa\) at \(s=0\). Substitution of (7) and (8) into (9), after introducing the variable \(y=(a_0p+a'_0p')e^{-fs}\) and transformation, gives

\[ v=\frac{\varkappa_0P}{f(a_0p+a'_0p')^\alpha} \int_{a_1p+a'_1p'}^{a_0p+a'_0p'} \frac{y^{\alpha-1}\,dy}{1+y}. \tag{11} \]

Here \(a_1\) and \(a'_1\) are the values of \(a\) and \(a'\) at \(s=1\). In the region of intermediate coverages \(a_0p+a'_0p'\gg 1\) and \(a_1p+a'_1p'\ll 1\). Therefore, for the region of intermediate coverages, the limits of the integral may be replaced by 0 and \(\infty\). This gives

\[ v=\frac{\pi}{\sin\alpha\pi}\, \frac{\varkappa_0P}{f(a_0p+a'_0p')^\alpha}. \tag{12} \]

For the case of NH\(_3\) synthesis, \(p\) is the fugacity of adsorbed N\(_2\), and \(p'\) is the fugacity of adsorbed O. These quantities are determined by equilibria (5) and (6); therefore

\[ p=K^{-1}\frac{P_{\mathrm{NH}_3}^2}{P_{\mathrm{H}_2}^3}, \tag{13} \]

where \(K\) is the equilibrium constant of ammonia synthesis, and

\[ p'=K'\frac{P_{\mathrm{H}_2\mathrm{O}}}{P_{\mathrm{H}_2}}. \tag{14} \]

According to equation (12), the rate of the forward reaction is

\[ \omega_+=k_+\frac{P_{\mathrm{N}_2}} {\left(P_{\mathrm{NH}_3}^2/P_{\mathrm{H}_2}^3+RP_{\mathrm{H}_2\mathrm{O}}/P_{\mathrm{H}_2}\right)^\alpha}, \tag{15} \]

where

\[ k_+=\frac{\pi}{\sin\alpha\pi}\frac{\varkappa_0}{f} \left(\frac{K}{a_0}\right)^\alpha \]

and

\[ R=\frac{a'_0}{a_0}KK'. \]

It is easy to verify that \(R\) is the constant of the following equilibrium:

\[ \mathrm{N}_{2\,\mathrm{ads}}+\mathrm{H}_2\mathrm{O}+2\mathrm{H}_2 =\mathrm{O}_{\mathrm{ads}}+2\mathrm{NH}_3; \tag{16} \]

reaction (16) has been observed directly \((^{11})\).

A consideration of the reverse reaction analogous to that given above, or application of Horiuti’s theorem \((^{12})\), gives for the rate of the reverse reaction

\[ \omega_-=k_-\frac{P_{\mathrm{NH}_3}^2} {P_{\mathrm{H}_2}^3\left(P_{\mathrm{NH}_3}^2/P_{\mathrm{H}_2}^3+RP_{\mathrm{H}_2\mathrm{O}}/P_{\mathrm{H}_2}\right)^\alpha}. \tag{17} \]

The observed reaction rate \(\omega=\omega_+-\omega_-\) is determined by the equation

\[ \omega= \frac{k_+P_{\mathrm{N}_2}-k_-\dfrac{P_{\mathrm{NH}_3}^2}{P_{\mathrm{H}_2}^3}} {\left(P_{\mathrm{NH}_3}^2/P_{\mathrm{H}_2}^3+RP_{\mathrm{H}_2\mathrm{O}}/P_{\mathrm{H}_2}\right)^\alpha}. \tag{18} \]

At \(P_{\mathrm{H_2O}}=0\), equation (18) becomes equation (4). When the poisoning is large, i.e. \(RP_{\mathrm{H_2O}}/P_{\mathrm{H_2}}\gg P_{\mathrm{NH_3}}^2/P_{\mathrm{H_2}}^3\), and, in addition, the reverse reaction as well as changes in \(P_{\mathrm{N_2}}\) and \(P_{\mathrm{H_2}}\) can be neglected, equation (18) leads to equation (1) (with \(\alpha = 0.5\)).

Table 1

To check equation (18), measurements were carried out of the rate of NH\(_3\) synthesis from a stoichiometric nitrogen–hydrogen mixture at atmospheric pressure by a flow-circulation method (13). The apparatus was analogous to the previously described system with double circulation (14), but was supplemented with a device for dosing water vapor and determining its concentration. A small part (on the order

Table 2

of 0.01) of the gas stream of the additional cycle, controlled by a rotameter, was saturated with water vapor at room temperature, after which part of the vapor was condensed at a lower temperature maintained to an accuracy of 0.05°. The humidified gas returned to the main cycle. The water-vapor content in the main cycle was determined from the dew point.

The experiments were carried out on an iron catalyst containing 3.8% Al₂O₃ and 2.1% K₂O, and on an iron catalyst containing 3.8% Al₂O₃, 0.97% K₂O, 3.4% CaO, and 1.0% SiO₂ (the weight content of promoters is given for the unreduced catalyst). Reduction was carried out with a gradual rise in temperature from 200 to 550°. The specific surface area (from low-temperature adsorption of nitrogen) was 13.6 m²/g for the catalyst with 2 promoters and 13.7 m²/g for the catalyst with 4 promoters. Catalyst grains of size 0.1–0.25 mm were used.

Control determinations of the reaction rate with a dry nitrogen–hydrogen mixture showed that the activity of the catalysts remained constant throughout the entire set of measurements. Thus, the poisoning was reversible.

To test equation (18), the usually used constant \(k = ({}^{4}/_{3})^{3(1-\alpha)} k_{-}\) was calculated. Taking \(\omega = Vz\), where \(V\) is the space velocity (reduced to 0°) and \(z\) is the mole fraction of NH₃, we obtain

\[ k = \frac{ V z^{1+2\alpha} P^{1-\alpha} \left[1 + R ({}^{3}/_{4})^{2} P_{\mathrm{H_2O}} / z^{2}\right]^{\alpha} }{ z_{\mathrm{eq}}^{2} - z^{2} }. \tag{19} \]

Here \(z_{\mathrm{eq}}\) is the value of \(z\) at equilibrium. The value \(\alpha = 0.5\), usual for iron catalysts, was adopted. The values of \(R\) for the catalyst with 2 promoters were determined by fitting; they are given in Table 3, where the values of \(z_{\mathrm{eq}}\) used in calculating \(k\) are also given.

Table 3

The data of Table 3 are satisfactorily represented by the equation

\[ R = 1.30 \cdot 10^{-6} \exp \frac{8930}{T}. \tag{20} \]

Hence, for reaction (16), \(\Delta H = -17.7\) kcal.

The experimental data and the values of \(k\) for the catalyst with 2 promoters are given in Table 1. The data for the catalyst with 4 promoters are described by equation (19) with the value of \(R\) obtained by multiplying the values of Table 3 by 6 (consequently, this catalyst is more sensitive to the poisoning action of water vapor than the catalyst with 2 promoters). These data are given in Table 2. The constants \(k\) in Tables 1 and 2 are sufficiently constant.

Calculations of \(k\) were made using equation (18), integrated for a flow system, on the basis of literature data for catalysts with 2 promoters, using the values of \(R\) from Table 3. These data cover pressures of 1 atm (³), 31.6 atm (¹), 300 atm (⁵), and 330 atm (⁴). In all cases satisfactory constancy of \(k\) was obtained. This makes it possible to regard equation (18) as applicable also at high pressures.

Physicochemical Institute
named after L. Ya. Karpov

Received
9 VII 1963

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