Page 154 - Modern physical chemistry

146 Relationships among Reactants

and rewrite (7.9) as
[7.11 ]
In estimating PAY, one may neglect the volumes of condensed phases and get the
volumes of gases from the ideal gas law. At constant temperature, we would have

[7.12]
where An is the change in number of moles of gas in the reaction as written. Then equa-
tion (7.11) becomes
[7.13]

ExampleZ3
Relate the isobaric reaction heat to the isochoric one for the process

CIOHS (s) + 120 2 (g) ~ 10COz (g) + 4H 20 (1).
In this reaction there are 10 moles of gaseous product and 12 moles of gaseous reac-
tant. Consequently,
An = 10 -12 = -2
and
MIp = D.Ev -2RT
whence
qp =qv -2RT.

Z5 Variation in Heat of Reaction with Temperature
Whenever the heat capacity of the products in a reaction differs from the heat capac-
ity of the reactants for the specified conditions, the heat q for the reaction varies with
the temperature.
Let A represent the reactants and B the products of a reaction occurring at temper-
ature T:
A (T)~ B (T). [7.14]
When the volume of the products is the same as the volume of the reactants, the heat
of reaction is
[7.15]

Here EB is the internal energy of the specified amount of products and E A that of the cor-
responding amount of reactants.
Differentiating the second equality in (7.15) at constant volume yields

(8:1 =(8:: 1-(8:; 1 =(CV)B-(cvt =ACv· [7.16]

In the second step, the energy capacities have been introduced with equation (4.35). Inte-
grating over temperature then gives us the formula

[7.17]

relating the energy of reaction at temperature T2 to that at temperature Tb and by (7.15)
the corresponding heats.