Equation of Temkin

Develop the rate equation of Temkin Pyzhev for the rate of the reaction, N2 (A) + 3H2(B) > 2NH3(C), on these assumptions ... 

The first application of Temkin theory in history was on cataljdic reaction for ammonia synthesis on iron catalyst. The famous reation rate equation of Temkin-Pyzhev was obtained, corresponding to the overall reaction ... 

Hence the equation of Temkin-pyzhev predicts that ... 

On iron catalyst, the classical ammonia synthesis reaction kinetics equation of Temkin-Pyzhev is expressed as (with fugacity express when a = 0.5) ... 

There have been some very successful applications of rate equation 8.34 derived for a nonuniform surface. One of the best examples is the rate equation of Temkin and Pyzhev which describes the ammonia synthesis reaction [15], and it is discussed in Illustration 8.1. 

The rate of ammonia formation (kmol ton ) derived from the classical rate equation of Temkin-Pyzhev, slightly modified by introducing activities instead of partial pressures, becomes... 

The low-coverage parts of the adsorption isotherms evaluated at different temperatures have shown a remarkable feature of linear dependence between the adsorption and the logarithm of gas pressure. This sort of behavior corresponds to the well-known Temkin equation of adsorption... 

Since most equations of state are pressure-explicit, Eqs. (6) and (99) are often more convenient than Eqs. (5) and (98). With these equations, basing his calculations on van der Waals equation of state, Temkin (Tl) showed that gas-gas immiscibility may occur if the van der Waals constants a and b... 

As to when to use Frumkin s approach or that of Temkin, as long as one is willing to accept the approximation leading to Eq. (7.156), it does not matter as far as the resulting kinetic equations (see below) are concerned. However, the thought process behind Frumkin s equation is to take account of the interaction between the adsorbed entities and that behind Temkin s is to allow for the difference in adsorption energies in different sites on the surface equation. 

This empirical equation of the adsorption isotherm, giving the relationship between 6 and the pressure, excellently represents many characteristics of chemisorption. Equation (72) is introduced by Frumkin and Slygin (366), who derived it from their electrochemical investigations on hydrogen electrodes. The equation has played an extensive role in the successful theory of ammonia catalysis of Temkin (367) and it has in literature been termed the Temkin equation (368), although Temkin himself and other Russian investigators call it the logarithmic adsorption isotherm. 

The only difference between Eqs. (87) and (77) is that in Eq. (87) we have to take the initial heats of chemisorption as they are when no surface potential effect is noticeable as yet. It may be remarked that the same result would have been obtained if we had started from the conception of Temkin (Sec. IX,8). Equation (87) can be used only when the dipoles of both species have the same electrical direction. 

Introducing the Temkin Isotherm into the Equations of Electrode Kinetics... 

Ivanovskii et al. (1964) found that this expression adequately describes experimental rate data for the shift reaction from 10 to 30 atm and 350°C. The activation energy for the reaction was found to be 36 kcal/mol indicating no diffusional limitations. Sen et al. (1964) used the rate equation of Kul kova and Temkin (eq. 3.125) to correlate kinetic data. Their activation energies of 25.1 to 46.0 kJ/mol (6 to 11 kcal/mol) appear to indicate diffusion control in the shift reaction. 

We have already pointed out (see Section I) the similarity of the multiplet theory and the theory of catalysis by Polanyi. The equations of the multiplet theory [(1I.9)-(1I.11)] were given by the author as early as in 1929 Polanyi suggested similar equations in 1934 (35), how ever, for one reaction only—the para-ortho-conversion of hydrogen. In 1957 Temkin (366) developed the Polanyi theory and also obtained Eqs. (II.9) and (II.10), the same as in the multiplet theory. 

The basic equation most widely accepted to express the kinetics of ammonia synthesis is that of Temkin and Pyzhev (1940). It expresses the reaction rate as a function of the partial pressures of the reactants and products ... 

Symbols Z and Z denote two types of sites. For the sake of simplicity, an irreversible reaction is considered. One can see that for scheme (7.222) there are 5 intermediates in the spirit of Temkin considerations (Z, Z, ZH, Z H+ and ZRH ), three steps, one route and thus according to the Horiuti-Temkin rule (eq. 4.3, 4.4) there should be three balance equations. As there are two types of sites in (7.222) then these balance equations take the form... 

This is because the value of the product 0a0b is decreased by increasing Pa and the reaction is inverse first order in A (see Figure 5.5). Equations of this type can be written to describe a variety of situations. The first systematic analysis was undertaken by M. I. Temkin in 1935 he arrived at the general expression... 

Consider the scheme given above [equations (64)-(66)] for formic acid oxidation. The rate-determining step (65) may be regarded as an adsorption step, since it results in an increase in the number of sites occupied on the surface. The corresponding rate equation, under Temkin conditions will be... 

The third assumption of Temkin. Prom the preceding relations, we can now relate the four rate constants in the rate equation (2.120) to the standard affinity of adsorption. So, the third assumption proposed by Temkin is that Bornsted transfer coefficient is the same for the two chemically similar steps (e.g., adsorption and desorption) ... 

It can be seen from the above-mentioned discussion that the Temkin s theory of catalytic reaction kinetics on heterogeneous surfaces is confirmed not only by overall reaction kinetic data of ammonia synthesis, isotherms and adsorptive rates of nitrogen on iron catalysts, more importantly, perhaps, but also some very useful generalization results derived from this theory. For instance, Temkin s equation is obtained based on two steps or simplified two steps mechanism. So, it can apply to any kind of catalytic reactions. The problem is Are some simplifications required by reasonable formation of two step mechanism, and can the assumption of rate determining step be made for non-uniform surface The answer of Temkin s theory is positive, and especially Temkin s theory of catalytic reaction kinetics on non-uniform plays an important role in solving the selection and improvement of catalysts. 

Smirnov et conducted experiments at ambient pressure and suggested a modification of the conventional Temkin rate equation of ammonia synthesis (see Chapter 7). This equation was later generalized by Smimov to cover higher pressures. The expression was... 

In the case of Temkin expression, the equation is written as follows ... 

The rate equation of ammonia decomposition was expressed in Eq. (7) according to the Temkin-Pyzhev mechanism (Eq. 1-3). The observed parameters in Table 3.9 show that n/m values are mostly 3/2, which indicates that the Temkin-Pyzhev mechanism is applicable on most catalysts (Re, Fe, Co, Ni, Ru and Rh) under normal ammonia decomposition conditions. 

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