S
298:15
isoÀbutane abs ¼ S
298:15
isoÀbutane À S
0
isoÀbutane
¼ 70:4 À 0 ¼ 70:4 cal deg
À1 mol
À1
The entropy change for the isomeric transformation of one mole of
n-butane to iso-butane at one atmosphere and 298.15 K is therefore given by
DS
h
¼ S
298:15
isoÀbutane abs À S
298:15
nÀbutane abs
¼ 70:4 À 74:0 ¼ À3:6 cal deg
À1 mol
À1
:
Another way to look at this is to consider the reversible path from n-butane
to iso-butane via absolute zero. Firstly, cool one mole of n-butane at atmospheric pressure from 298.15 K to absolute zero. The entropy change is
−74.0 cal deg
−1 mol
−1 . Perform the transformation from n-butane to isobutane at absolute zero. If both reactant and product are perfect crystalline
solids then DS
0 = 0. Now warm the iso-butane to 298.15 K, the entropy
change being 70.4 cal deg
−1 mol
−1
. DS
h is the sum of these heat changes, i.e.
DS
h
¼ À74:0 þ 0 þ 70:4 ¼ À3:6 cal deg
À1 mol
À1
:
Given that;
DG
h
¼ DH
h
À TDS
h
substitution allows us to calculate the standard free energy change as,
DG
h
¼ À1630 À ð298:15  ðÀ3:60ÞÞ ¼ À556:66 cal mol
À1
Table B.2 Entropy changes for iso-butane from 0 to 298.15 K
Temperature, K
Entropy calculated from
Entropy change
0–12.53
Debye extrapolation
0.247
12.53–113.74
R
T2
T1
ðCp=TÞdT
16.115
113.74
Fusion 1085.4/113.74
9.543
113.74–261.44
R
T2
T1
ðCp=TÞdT
22.030
261.44
Evaporation 5089.6/261.44
19.468
261.44–298.15
R
T2
T1
ðCp=TÞdT
2.910
522
Appendix B: The Third Law in Action …