Page 176 - Physical chemistry understanding our chemical world

THE TEMPERATURE DEPENDENCE OF ENTROPY 143

and hence

T 2
S = C p ln (4.17)
T 1
(b) C p is not independent of temperature (over larger temperature
ranges). We employ a similar approach to that above, except that C p is incorporated
into the integral, yielding

S 2 T 2
C p
dS = dT (4.18)
T
S 1 T 1
which, on integration, yields Equation (4.9).

Worked Example 4.7 What is the increase in entropy when warming 1 mol of chlo-
roform (III) from 240 K to 330 K? Take the value of C p for chloroform from the Aside
box on p. 142.

H

Cl
Cl Cl
(III)

We start with Equation (4.9), retaining the position of C p within the The ‘T’ontop and
integral; inserting values:
bottom cancel in the
330 K −2 second term within the
91.47 + 7.5 × 10 T
S = S 330 K − S 240 K = dT integral.
240 K T
Rearranging:
330 K 91.47
S = + 7.5 × 10 −2 dT
240 K T
Performing the integration, we obtain

S = [91.47 ln T ] 330 K + 7.5 × 10 −2 [T ] 330 K
240 K 240 K
Then, we insert the variables:

330 K −2

S = 91.47 ln + 7.5 × 10 (330 K − 240 K)
240 K
to yield
S = (29.13 + 6.75) JK −1 mol −1

so
S = 35.9JK −1 mol −1