Page 173 - Modern physical chemistry

Questions 165

whence
[ VA) =lPL +mpM -apA -bpB' [7.108]

vA. T,v
Derivative (aNaA. )T, v is the increase in Helmholtz energy per unit of reaction when only
an infinitesimal amount of reaction occurs. If the reacting system were of infinite extent,
it would be the Helmholtz energy change when a moles A reacted with b moles B to
produce l moles L and m moles M. So it is called the Helmholtz energy of reaction M:
[7.109]

When each reactant and product is in its standard state, formula (7.109) becomes

[7.110]
When the standard state for each substance is the substance at unit concentration
and the corresponding activity coefficient is 1, we have

Pi = p? + RTlnCi' [7.111]
Substituting this into formula (7.109) and reducing yields

M=Mo+RTlnQc [7.112]
where
_ CLCM
Q c- lm . [7.113]
C%C~
At equilibrium, this reaction quotient equals the equilibrium constant,
[7.114]
and the change in A vanishes,
M=O. [7.115]
Then equation (7.112) reduces to
[7.116]

When the activity coefficients differ from 1, equation (7.113) is replaced with

_ aLaM
Q )C- I m , [7.117]
a%a~
and equation (7.116) with
[7.118]

Questions

7.1 How are standard states defined?
7.2 How are reaction heats measured?
7.3 Explain how the heat of a reaction varies with temperature.
7.4 How is the calorimetric entropy determined?
7.5 How is the calorimetric entropy corrected to the ideal gas state?