Temkin-Pyzhev, rate equation

Problon 2-6 (Level 2) The Temkin-Pyzhev rate equation for ammonia synthesis (N2 -I- 3H2 2NH3) on certain catalysts is... 

The less-than-satisfactory agreement with experimental data at higher pressures of the Temkin-Pyzhev rate equation has been mentioned. In 1950, Temkin modified the original equation by introducing fugacities instead of partial pressures [34]. Furthermore, the original equation, Eq. (21), was multiplied by a term... 

The fourth chapter is written by Dr. John Bogild Hansen and is entitled, Kinetics of Ammonia Synthesis and Decomposition on Heterogeneous Catalysts"". The scope of the chapter is limited to promoted and non-promoted iron catalysts. The chapter includes discussions of the Temkin-Pyzhev rate equation, it deals with rate equations derived from the Langmuir isotherm and reports on the kinetics based on surface science techniques. In the last section of the chapter a discussion of transfer phenomena - as these are found in experimental reactors and in industrial converters - is included. 

The rate constant ki or in Temkin-Pyzhev kinetics equation, r = klfN2fkANHs - k2fNHjHA-... 

Table 8.1. Comparison of experimental and theoretical rate parameters in the Temkin-Pyzhev rate expression for NH3 synthesis (Equation 2 with m = 1 /2).

The Temkin-Pyzhev equation deseribes the net rate of synthesis over promoted iron eatalyst as ... 

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

Adopting the mechanism involving steps (VII.2)-(VII.7) and introducing special assumptions in order to account for the heterogeneity of the surface, Temkin and Pyzhev (73) have deduced the rate equation... 

Based on the experimental data which covered the pressure range from below 1 atm up to 500 atm, it was proposed that near equilibrium, the reaction rate is described by the following equation, which is often referred to in the literature as the Temkin-Pyzhev equation... 

The rate equations used in these simulations is that proposed by Temkin and Pyzhev [118] ... 

Under the assumption that dissociative nitrogen chemisorption is the ratedetermining step and that the heat of adsorption varies linearly with coverage, Temkin and Pyzhev (18) derived their famous and widely used rate equation for the kinetics of ammonia synthesis ... 

A logarithmic value of the reaction-rate constant taken from Temkin-Pyzhev equation as a function of reciprocal temperature for the catalysts pressed at different pressures is presented in figure 1. This function is nonlinear, the reason for this being an increase of the diffusion effects together with increasing temperature. 

One of the first rate equation for engineering purposes was published by Temkin and Pyzhev (1940) ... 

Temkin-Pyzhev equations mentioned above was in agreement with a number of kinetic measurement made on various catalysts such as Mo, W, Tc, Ru, Os and promoted Fe. One characteristic feature of ammonia synthesis rate is the retardation by the product ammonia, and reasonably explained by the Temkin theory. The assumption of rate determining step is also supported by the chemisorption of nitrogen. 

Based on Temkin-Pyzhev mechanisms (steps 1- 3), the rates for ammonia decomposition can be expressed by Eq. (2.27), and its kinetic parameters calculated from equation V = fc (PnH3) /(Eh2) are given in Table 2.7. The value of parameter n/m in Table 2.7 is about 3/2, demonstrating that the Temkin Pjrahev mechanisms can be used for most metal catalysts, such as Re, Fe, Co, Ni, Ru and Rh, at the common conditions of ammonia decomposition. 

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 ... 

An attempt was made by Ozaki et al to verify the mechanism, on which the Temkin-Pyzhev equation was derived, by comparing the rate of the following two reactions obtained on the same catalyst ... 

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. 

Before the topic of nonuniform surfaces is concluded, it is interesting to compare the rate equation obtained by Temkin and Pyzhev for ammonia synthesis on iron (and discussed in Illustration 8.1) to one associated with a uniform surface using the same reaction model. Comparing only the forward rate in either sequence, one would have... 

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 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. 

Temkin and Pyzhev tested the rate equation by applying Eq. (28) to a series of experiments at atmospheric pressure with a doubly promoted catalyst, first by varying the H2/N2 ratio at 400°C using a space velocity of 30000h As predicted by Eq. (22), the H2/N2 ratio giving the highest yield at low conversion was 1.5. 

Temkin and Pyzhev derived the following integrated form of their rate equation without making any simplifying assumptions, except assuming H2/N2 to be 3. 

Temkin and Pyzhev used Eq. (31) to test their rate equation with the data of Larson and Tour [2] at 10, 31.6 and 200 atm and at 420 and 450 °C. They concluded that the data agreed well with Eq. (21), however, the rate constants... 

In 1943, Emmett and Kummer [23] presented the results of high pressure experiments on a doubly promoted catalyst (3.02% AI2O3,0.94% K2O) at 33.3, 66.6 and 100 atm, H2/N2 ratios 3/1,1/1 and 1/3 and space velocities from 25 000 to 125000 h" at 370, 400 and 450°C were used. The data were analysed with the Temkin-Pyzhev equation using a = P = 0.5. The rate constant k was constant with variations in space velocity, except at 370 °C where it decreased with an increase in space velocity of 5. Apparent activation energy for decomposition was found to be from 45 000 to 53 000 cal/mol. 

Although the Temkin-Pyzhev equation seemed to fit the data reasonably well with respect to variations in space velocity and temperature, all data sets exhibited a clear decrease in the rate constant with increasing pressure. 

Using a P value of approx. 0.3 as found by Love and Emmett [26] an attempt was made to calculate the data by the Temkin-Pyzhev equation with a = 0.67, but this gave a poorer agreement. With respect to changes in gas composition the agreement with a = 0.67 was fair at 370 and 400 °C, but the rate constant varied by a factor 2 at 450 °C between the 3 1 and 1 3 H2/N2 mixtures. 

In a series of experiments with triply promoted catalyst at 1 atm, 400 °C and SV = 30000 at different H2/N2 ratios Nielsen [35] found that maximum conversion was obtained at a H2/N2 ratio of 1.5 as predicted by the Temkin-Pyzhev equation (Eq. (22)) when the backward reaction can be ignored. At 330 atm, 450 °C, and SV = 15 000 the decomposition rate constant (k in Eq. (31)) was however found to increase with approximately a factor of two when the H2/N2 was increased from 1/1 to 6/1. 

For a given inlet gas composition, pressure, and temperature, numerical integration was carried out throughout the reactor. The rate constant k2 in the Temkin-Pyzhev equation was adjusted so that the calculated temperature profiles matched the measured ones. Radial gradients and axial heat conduction were ignored. The catalyst particles were assumed to have the same temperature... 

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