Page 82 - Mechanism and Theory in Organic Chemistry

Thermochemistry 71

The Hammett and Taft equations are not the only linear free-energy
relationships known. We shall encounter others-for example, the Brcansted
relations, and the Grunwald-Winstein and Swain-Scott equations later in this
book.

2.3 THERMOCHEMISTRY 23
Of importance to the problem of relating structure and reactivity is the therm-
ochemistry of the reaction-that is, the net enthalpy and entropy changes that
occur upon the making of new bonds and the breaking of old ones. If we consider
the reaction in Equation 2.22, for example, a large positive standard free-energy
A + B-+C + D (2.22)

change for the reaction, AGO, means that it will not take place. On the other hand,
if AGO is large and negative, the likelihood is that it will occur.24 AGO in turn is a
function of AH0 and AS0 the standard enthalpy and entropy of reaction, respec-
tively (Equation 2.23).
AGO = AH0 - TAS" (2.2 3)
AH0 is a function of the heats of formation of the molecules being formed or
destroyed, and AS0 is a function of the entropies of the molecules being formed
or destroyed.25 Thus for the reaction in Equation 2.22,
AHo = AH; (C) + AH; (D) - AH," (A) - AH; (B) (2.24)

where AH; (X) is the standard heat of formation of X. Similarly,
AS' = So (C) + So (D) - So (A) - So (B) (2.25)
where SO(X) is the standard entropy of X.26
Experimental heats of formation are not available for all compounds, but,
by Benson's additivity rules, AH; for any molecule in the gas phase can be cal-
culated. When an accurate experimental value is known, the calculated value is
almost always to within a few tenths of a kilocalorie of it, and usually the agree-
ment is even better.
Bensvn's approach is to determine the AH; of a molecule by adding together
the AHYs of the various groups in the molecule. A group is defined as an atom
and its ligands. For example, CH3CH, is made up of two identical groups. The
central atom in the group is carbon, and the ligands are carbon and three

23 (a) S. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. O'Neal, A. S. Rodgers,
R. Shaw, and R. Walsh, Chem. Rev., 69, 279 (1969); (b) S. W. Benson, J. Chem. Educ., 42, 502 (1965).
24 Even if AG is a large negative quantity the reaction is, of course, not necessarily fast. The rate
depends on the activation barrier that the reactants must overcome to reach the transition state. If
the barrier is too high, then no matter how exothermic the reaction is, it cannot take place. However,
in the absence of special effects there is usually a qualitative correlation between a reaction's net
energy change and its energy of activation. This point is discussed further in Section 2.6.
2"he enthalpy change involved in the formation of one mole of a substance from the elements is
called the heat of formation of the substance. The standard heat of formation is the heat of formation
when all substances in the reaction are in their standard states.
26 The standard entropy of a substance is its entropy in the state specified based on So = 0 at 0°K.