Page 172 - Modern physical chemistry

164 Relationships among Reactants

This is related to the standard Gibbs energy change by the fonnula

lnK=- AGo [7.99]
RT
At low pressures, where the solution is approximately ideal, the ith activity is mea-
sured by the corresponding partial pressure,

[7.100]
Then the expression
[7.101]

equals the equilibrium constant K.
At higher pressures, deviations from the ideal gas equation (7.38) occur. However,
fonnula (7.36) still applies. Furthennore, one can construct expression (7.42) for each
constituent and so obtain (7.98) for the equilibrium condition.
But the activity of the ith constituent then differs from its partial pressure. We express
this fact by the equation
[7.102]
in which riis called the ith activity coefficient. Employing fonn (7.102) for each activ-
ity in (7.98) gives us
[7.103]

where
[7.104]

Substituting fonn (7.102) into expression (7.42) leads to
[7.105]

The deviation of l1i from its ideal value is measured by the tenn RT in rio If one could
determine this deviation, one could then construct ri' This is a complicated develop-
ment. Nevertheless, in the next chapter, we will thus estimate the effect of electric inter-
action in electrolytic solutions.

Z 18 Helmholtz Energy of Reaction
At a given temperature and volume, the tendency for a reaction to go is measured by
the pertinent Helmholtz free energy change.
Let us consider a homogeneous system in which the reaction

aA+bB~lL+mM [7.106]
moves forward by dA. unit at a given temperature and volume. Equations (7.44) then
apply and fonnula (5.96) yields

[7. 1 07J