Page 185 - Physical Chemistry

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Chapter 5 S° m,298 that arises from the symmetry of the molecule must be included to obtain valid
Standard Thermodynamic results (see the discussion of the symmetry number in Chapter 21).
Functions of Reaction
For example, some bond additivity contributions to H° /(kcal/mol) are
298
f
COC COH COO OOH
2.73 3.83 12.0 27.0

H° /(kcal/mol) of C H (g) and C H (g) are then predicted to be 2.73 6( 3.83)
f
298
4
2
10
6
20.2 and 3(2.73) 10( 3.83) 30.1, as compared with the experimental values
20.0 for ethane, 30.4 for butane, and 32.1 for isobutane. Since the H° 298
f
values are for formation from graphite and H , the bond-contribution values have
2
built-in allowances for the enthalpy changes of the processes C(graphite) → C(g) and
H (g) → 2H(g).
2
Bond Energies
Closely related to the concept of bond contributions to H° is the concept of average
f
bond energy. Suppose we want to estimate H° 298 of a gas-phase reaction using
molecular properties. We have H° U° (PV)° . As noted in Sec. 5.4, the
298
298
298
(PV)° term is generally substantially smaller than the U° term, and H° generally
varies slowly with T. Therefore, H° will usually be pretty close to U°, the reac-
0
298
tion’s change in ideal-gas internal energy in the limit of absolute zero. Intermolecular
forces don’t contribute to ideal-gas internal energies, and at absolute zero, molecular
translational and rotational energies are zero. Therefore U° is due to changes in
0
molecular electronic energy and in molecular zero-point vibrational energy (Sec. 2.11).
We shall see in Chapter 20 that electronic energies are much larger than vibrational
energies, so it is a good approximation to neglect the change in zero-point vibrational
energy. Therefore U° and H° are largely due to changes in molecular electronic
298
0
energy. To estimate this change, we imagine the reaction occurring by the following
path:
1a2 1b2
Gaseous reactants S gaseous atoms S gaseous products (5.44)
In step (a), we break all bonds in the molecule and form separated atoms. It seems
plausible that the change in electronic energy for step (a) can be estimated as the sum
of the energies associated with each bond in the reacting molecules. In step (b), we
form products from the atoms and we estimate the energy change as minus the sum of
the bond energies in the products.
To show how bond energies are found from experimental data, consider the gas-
phase atomization process
CH 1g2 S C1g2 4H1g2 (5.45)
4
(Atomization is the dissociation of a substance into gas-phase atoms.) We define the
average COH bond energy in methane as one-fourth of H° for the reaction (5.45).
298
From the Appendix, H° 298 of CH is 74.8 kJ/mol. H° 298 for sublimation of
4
f
graphite to C(g) is 716.7 kJ/mol. Hence H° of C(g) is 716.7 kJ/mol, as listed in
f
298
the Appendix. (Recall that H° is zero for the stable form of an element. At 25°C,
f
the stable form of carbon is graphite and not gaseous carbon atoms.) H° of H(g)
f
298
1
is listed as 218.0 kJ/mol. [This is H° for H (g) → H(g).] For (5.45) we thus have
2
298
2
¢H° 3716.7 41218.02 1 74.824 kJ>mol 1663.5 kJ>mol
298
Hence the average COH bond energy in CH is 416 kJ/mol.
4
To arrive at a carbon–carbon single-bond energy, consider the process C H (g) →
6
2
2C(g) 6H(g). Appendix H° values give H° 2826 kJ/mol for this reaction.
f
298
298