Ideal solutions calculating state-dependent activity

In infinitely dilute solutions (in the standard state) ions do not interact, their electric field corresponds to that of point charges located at very large distances and the solution behaves ideally. As the solution becomes more concentrated, the ions approach one another, whence their fields become deformed. This process is connected with electrical work depending on the interactions of the ions. Differentiation of this quantity with respect to rc, permits calculation of the activity coefficient this differentiation is identical with the differentiation 3GE/5/iI and thus with the term RT In y,. 

The ideal-gas and ideal-solution approaches also differ because they are based on different kinds of experimental data. The residual properties and fugadty coeffidents depend on volumetric data measurements of P, v, T, and x. But the excess properties and activity coeffidents depend on density measurements for calorimetric measurements for h, and phase-equilibrium data for and y,-. Modem modeling tends to rely on volumetric data (equations of state), and a prindpal feature of this chapter has been to establish how excess properties can be computed from residual properties and how activity coefficients can be computed from fugadty coeffidents. But note that such calculations can be performed in either direction that is, at least in principle. 

Note that the sensitivity of the net flux between the soil and water to the worms activities depends on the relation between the rate R and the solute concentration. For the calculations in Figures 2.13 and 2.14, R varies linearly with concentration as specified in Equation (2.40), and the flux is sensitive to worm activity. But where the rate is independent of concentration, as for NH4+ formation in Equation (2.39), the net flux, which in this case is roughly Ro/a + LRi, is necessarily independent of worm activity, though the distribution of the flux between burrows and the sediment surface and the concentration profile are not. In practice the rate will always depend to some extent on concentration. But the predictions here for the idealized steady state indicate the expected sensitivities. 

Gas studies are well covered with extensive explanation and interpretation of experimental data, such as steady state calculations, all illustrated by frequent use of worked examples. Solution kinetics are similarly explained, and plenty of practice is given in dealing with the effects of the solvent and non-ideality. Students are given plenty of practice, via worked problems, in handling various types of mechanism found in solution, and in interpreting ionic strength dependences and enthalpies, entropies and volumes of activation. 

Because K, depends on concentrations and the product KyKx is concentration independent, Kx must also depend on concentration. This shows that the simple equilibrium calculations usually carried out in first courses in chemistry are approximations. Actually such calculations are often rather poor approximations when applied to solutions of ionic species, where deviations from ideality are quite large. We shall see that calculations using Eq. (47) can present some computational difficulties. Concentrations are needed in order to obtain activity coefficients, but activity coefficients are needed before an equilibrium constant for calculating concentrations can be obtained. Such problems are usually handled by the method of successive approximations, whereby concentrations are initially calculated assuming ideal behavior and these concentrations are used for a first estimate of activity coefficients, which are then used for a better estimate of concentrations, and so forth. A G is calculated with the standard state used to define the activity. If molality-based activity coefficients are used, the relevant equation is... 

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