Page 186 - Physical Chemistry

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This H° is taken as the sum of contributions from six COH bonds and one COC Section 5.10
298
bond. Use of the CH value 416 kJ mol 1 for the COH bond, gives the COC bond Estimation of Thermodynamic
4
Properties
energy as [2826 6(416)] kJ/mol 330 kJ/mol.
The average-bond-energy method would then estimate the heat of atomization of
propane CH CH CH (g) at 25°C as [8(416) 2(330)] kJ/mol 3988 kJ/mol. We
3
2
3
break the formation of propane into two steps:
3C1graphite2 4H 1g2 S 3C1g2 8H1g2 S C H 1g2
2
8
3
The Appendix H° data give H° for the first step as 3894 kJ/mol. We have esti-
f
298
mated H° for the second step as 3988 kJ/mol. Hence the average-bond-energy es-
298
timate of H° of propane is 94 kJ/mol. The experimental value is 104 kJ/mol,
298
f
so we are off by 10 kJ/mol.
Some values for average bond energies are listed in Table 19.1 in Sec. 19.1. The
COH and COC values listed differ somewhat from the ones calculated above, so as
to give better overall agreement with experiment.
The bond-additivity-contribution method and the average-bond-energy method of
finding H° are equivalent to each other. Each bond contribution to H° of a hy-
f
298
298
f
drocarbon is a combination of bond energies and the enthalpy changes of the processes
C(graphite) → C(g) and H (g) → 2H(g) (see Prob. 5.55).
2
To estimate H° 298 for a gas-phase reaction, one uses (5.44) to write H° 298
H° 298,re H° 298,pr , where H° and H° , the heats of atomization of the reac-
at
at
pr
at
re
at
tants and products, can be found by adding up the bond energies. Corrections for strain
energies in small-ring compounds, resonance energies in conjugated compounds, and
steric energies in bulky compounds are often included.
Thus, the main contribution to H° of a gas-phase reaction comes from the
change in electronic energy that occurs when bonds are broken and new bonds
formed. Changes in translational, rotational, and vibrational energies make much
smaller contributions.
Group Additivity
Bond additivity and bond-energy calculations usually give reasonable estimates of
gas-phase enthalpy changes, but can be significantly in error. An improvement on
bond additivity is the method of group contributions. Here, one estimates thermody-
namic quantities as the sum of contributions from groups in the molecule. Corrections
for ring strain and for certain nonbonded interactions (such as the repulsion between
two methyl groups that are bonded to adjacent carbons and that are in a gauche con-
formation) are included. A group consists of an atom in the molecule together with
the atoms bonded to it. However, an atom bonded to only one atom is not considered
to produce a group. The molecule (CH ) CCH CH Cl contains three C–(H) (C)
3 3
2
3
2
groups, one C–(C) group, one C–(C) (H) group, and one C–(C)(H) (Cl) group,
2
2
4
2
where the central atom of each group is listed first.
The group-contribution method requires tables with many more entries than the
bond-contribution method. Tables of gas-phase group contributions to H°, C° , and
P,m
f
S° for 300 to 1500 K are given in S. W. Benson et al., Chem. Rev., 69, 279 (1969),
m
and S. W. Benson, Thermochemical Kinetics, 2d ed., Wiley-Interscience, 1976. See
also N. Cohen and S. W. Benson, Chem. Rev., 93, 2419 (1993). These tables give C° P,m
and S° ideal-gas values with typical errors of 1 cal/(mol K) and H° ideal-gas values
f
m
with typical errors of 1 or 2 kcal/mol. Some gas-phase group additivity values for
H° /(kJ/mol) are
298
f
C–(C)(H) 3 C–(C) (H) 2 C–(C) H C–(C) 4 O–(C)(H) O–(C) 2 C–(C)(H) O C–(H) (O)
3
3
2
2
41.8 20.9 10.0 0.4 158.6 99.6 33.9 41.8