Coeflicients, activity

Ise, N. The Mean Activity Coeflicient of Polyelectrolytes in Aqueous Solutions and Its Related Properties. Vol. 7, pp. 536-593. 

XXXVIII which gives the results for K derived from equation (99) using the theoretical value of Ay i.e., 0.51. The first figures are seen to be virtually constant, as is to be expected, the mean value of K being 1.752 X 10" . At inWte dilution the activity coeflicient factor is unity and so the extrapolation of the dissociation functions k to infinite dilution should give the true dissociation constant K the necessary extrapolation is carried out in Fig. 56, from which it is seen that the limiting value of log fc is — 4.7564, so that K is 1.752 X 10" , as given above. 

Reaction (13) has an activation energy of 7 kcal.mole and a rate coefficient of 3 l.mole. sec at 300 °K. Reaction (14) has an activation energy of 10 kcal. mole and a rate coeflicient of 0.3 l.mole . sec at 300 °K. The reaction rates of XeF4, and XeF2 with NO2 were so slow that attempts to measure them were thwarted. Reactions (13) and (14) are presumably followed by low activation energy steps such as... 

In general, the activity coeflicient of an electrolyte will be larger in a solvent of lower dielectric constant than in water. Transfer activity coefficients are likely to be large if the dielectric constant is small or if the ions are of high charge or small radius. 

Not all the chemical potentials (and therefore, the activity coeflicients) in a mixture are independent of each other. They are all related to one another through the Gibbs-Duhem equation. To derive this equation, we start with tlie fundamental equation of thermodynamics for the Gibbs free energy, which can be written as... 

The Wilson equation is very effective for dilute composition where entropy effects dominate over enthalpy effects. The Orye-Prausnitz form of the Wilson equation for the activity coeflicient, as given in Table 5.3, follows from combining (5-2) with (5-41). Values of A ij < 1 correspond to positive deviations from Raoult s law, while values of A >1 correspond to negative deviations. Ideal solutions result from A, = 1. Studies indicate that Af, and ka are temperature dependent. Values of viJvjL depend on temperature also, but the variation may be small compared to temperature effects on the exponential term. 

This equation neglects activity coeflicients— not a very good approximation under normal experimental conditions—but this is usually compensated for by simply applying a greater voltage than calculated. Equation 4.2 can be used to decide what potential the cathode must attain to eventually reduce the concentration of copper remaining in solution to an acceptable value. For instance, if the initial solution was 10 M in Cu " and it was desired to plate 99.9% of the copper, the following calculation would pertain At the start of the electrolysis the cathode potential would be... 

An important aspect of coking is its influence on the selectivity. As the product distribution or the selectivity depends on the ratios of the various rate coeflicients it is evident that the selectivity may also be affected by changes in catalyst activity, when the different reactions are not influenced in the same way by the catalyst activity decline. Froment and Bischoff [37] worked out the theory for such a situation. Figure 11.5.f-9 shows the results for a complex reaction with parallel coking scheme. The variation of the selectivity for the isomerization of n-pentane... 

Use of Eq. (1.5-17) leqoiies an expiessioa for a Heniy s Law activity coeflicient 7. Sach expressions are usually developed from die conventional expressions for 7, based on Raoult s Law standaid states. For a single-solute-single-solvent mixture die connection betw die two is easily estaUished. By Eqs. (1.2-52), (1.2-38), and (1.4-5), we have... 

Equation (1.6-7) says that, at a given temperature, the ideal stdubility of component 2 depends only on the properties of pore component 2. that is, the solubility is the same in all solvents. Furthermore, Eq. (1.6-7) says that the ideal solubility always rises with increasing temperature. These statements, especially the first, are not in agreement with experiment. To correct the ideal sohdnliqr, it is necessaiy to include the liquid-phase activity coeflicient whidi depends on temperature and composition and on the nature of components I and 2. 

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