Page 156 - Modern physical chemistry

148 Relationships among Reactants

With the empirical function

equation (7.20) becomes

2
/'JI = /'JIo + J (l1a + I1bT + I1CT ) dT = /'JIo + l1aT + ~b T2 + ~C T3.
Coefficients l1a, I1b/2, and I1cl3 calculated from the pertinent numbers in table 7.1 are

l1a = -2.215 J K· 1 , I1b = -1.422 x 10-3 J K- 2 , I1c = 8.533 x 10- 7 J K-3.
2 3
Then term /'JIo is

I1b
2 I1c
3
/'JIo =/'JIT -l1a1i --1i --1i
1 2 3
= -92,312+2.215(298.15)+ 1.422 x 1O-3(298.15r -8.533 x 1O-7(298.15t J = -91,548 J.
Inserting these parameters into the general form gives us
/'JI~ = -91,548 - 2.215T -1.422 x 1O-3T2 + 8.533 x 10- 7 T3 J.

7.6 Calorimetric Entropy
In determining the Gibbs free energy change I1G for a reaction, a person needs not
only /'JI but also 68 for converting the reactants to products. The increment in entropy
is obtained from the entropies of the pure participants. These may be found from energy
capacity measurements made down to very low temperatures coupled with the third law
of thermodynamics.
The entropy change occasioned by raising the temperature of a given phase at con-
stant pressure from Tl to T2 is
68 = rT2 C p dT [7.21]
JTl T '
following formula (5.22). The entropy change occasioned by a first-order transition at
temperature T2 is

[7.22]

following formula (5.23).
Below about 15 K, energy capacity measurements become very difficult. But there a
theoretical result of Paul Debye may be employed. By considering the possible elastic
waves set up in a condensed phase, he determined that

Cp ~aT3 [7.23]
at the low temperatures. So we find that

T C T '7"'3 (C p )
68= r 1 ~ dT= r laT2 dT=a_-l1_= __ T_l. [7.24]
Jo T Jo 3 3