Dependence of K on pressure

The standard chemical potential for substances other than gases depends on pressure, and so equilibrium constants for reactions in solution depend on pressure. Often a considerable dependence is found. This is highly relevant to the study of electrolyte solutions. 

From this it follows that, at constant temperature  

This corresponds to a plot of loge K vs. p at constant T, and there are several situations which can occur. 

The following table brings together data for propanoic acid and butanoic acid and the results, for 25°C, obtained in Worked Problems 8.5 to 8.7. Comment on and interpret these results. 

Contributions to AH would be expected to be large and positive for bond breaking. Formation of ions from molecular species would be expected to give a large negative A// due to solvation. The observed values are close to zero suggesting that the contributions from bond breaking and solvation approximately cancel out. 

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Karty et al. [21] pointed out that the value of the reaction order r and the dependence of k on pressure and temperature in the JMAK (Johnson-Mehl-Avrami-Kolmogorov) equation (Sect. 1.4.1.2), and perhaps on other variables such as particle size, are what define the rate-limiting process. Table 2.3 shows the summary of the dependence of p on growth dimensionality, rate-limiting process, and nucleation behavior as reported by Karty et al. [21]. 

Standard thermodynamic operations (Prigogine and Defay, 1954) on the Gibbs function, AG, yield expressions for related thermodynamic activation parameters. Thus the dependence of k on T can be used to calculate the enthalpy of activation, A, for processes at constant pressure or the thermodynamic energy of activation, A, for processes at constant volume, which in turn lead to the related entropies of activation, ASp and AS respectively. The dependence of k on pressure can be used to calculate the volume of activation, AV which is related to AHp by eqn (5) where a is the thermal... 

Using the values of kh k, and k2 found as above the dependence of klst on pressure can be found. 

The roller coaster patterns mentioned on p. 210 are normally observed in plots of activation parameters against x2, calculated from the dependence of rate constant on either temperature or pressure, rather than in the dependence of k on x2. Thus a careful examination is usually made of the dependence of k on T at fixed p and x2, and on p at fixed T and x2. The analysis of these separate dependences has been discussed by Kohnstam (1967) who points out the various pitfalls which await the unsuspecting. Indeed, a growing... 

The problems of interest are finding the conditions for onset of vaporization, the bubble-point for the onset of condensation, the dewpoint and the compositions and the relative amounts of vapor and liquid phases at equilibrium under specified conditions of temperature and pressure or enthalpy and pressure. The first cases examined will take the A, to be independent of composition. These problems usually must be solved by iteration, for which the Newton-Raphson method is suitable. The dependence of K on temperature may be represented adequately by... 

The behaviour of N distributions at different pressures is very similar in the two mechanisms (see Fig. 10). The dramatic dependence of k on v-v and v-t rates has been pointed in previous work4-6 The accuracy of k j values depends on e-v and DEM rate coefficients rather than on v-v and v-t ones. This point can be understood by noting that the portion of the Nj, distribution involved in JVE (i.e., the first levels and the plateau) does not depend too much on v-v and v-t cross sections. For example an increase by a factor of 2 of all v-v rates and a decrease by the same factor of corresponding v-t rates produce no appreciable variations in kjj values (ne = 10ucm 3,... 

The dependence of K on temperature and pressure can give a lot of information about details of the reaction involved. The kinetic analogues likewise give much information about the mechanism of the reaction involved. 

The dependence of k on pin the mean field theory (p ) is different from that in the scaling theory by a factor of Such difference is related to a correlation effect given by the number of contacts between monomers. The reduced osmotic pressure (K/Kjdeai) plotted as a function of the reduced concentration pip ), in a double logarithm scale, displays a curve that shows the change in slope to 5/4 for pip > 1 (Fig. 25.9). 

There is a little information available from repeller studies. In their paper on methanol, Thynne et al. (40) present, without analysis, data on the variation of the phenomenological cross-sections of Reactions J and K with the ion-exit energy obtained from conventional low pressure measurements. These data can be used to examine the dependence of k(Ee) upon Ee via the relation ... 

Consequently, additional runs were carried out using different H2 NH3 ratios isothermally at 773 K. The results shown in Fig. 7 clearly demonstrate the dependency of rate on NH3 partial pressure as evidenced from the decrease in peak magnitude (and time of appearance) with increased H2iNH3 ratio. In fact, application of the power law expression ... 

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