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232 Physical Organic Chemistry

TABLE VI Relative Rate Constants for Reaction by fragmenting the molecule into C 6 H 5 CH 2 and ArSO
−
of Cl with CH 3 I radicals. There is a substantial positive entropy because
Solvent ε k/k CH 3 OH the transition state is disorganized, owing to the creation
of two particles from one. There is also a higher enthalpy
CH 3 OH 32.6 1
than in entry 1 because a carbon–sulfur bond must be
broken. For entry 3 racemization proceeds via transition
HC( O)NH 2 109.5 12.5
state 99 and reversible conversion to an achiral interme-
HC( O)NHCH 3 165.5 45.3
diate 100. There is a substantial negative entropy because
HC( O)N(CH 3 ) 2 37 1.2 × 10 6
the transition state is highly ordered, with the position of
CH 3 C( O)N(CH 3 ) 2 37.8 7.4 × 10 6
the CH 2 CHCH 2 group restricted. There is also a lower
enthalpy than in entry 2 because formation of a carbon–
chloride is present as a “naked” nucleophile, of enhanced
oxygen bond compensates for breaking the carbon–sulfur
reactivity.
bond.
C. Temperature Dependence of Reactivity
Table II showed how rates can depend strongly on temper-
ature. Since G = H − T S the free energy of activa-
tion in Eq. (23) can be separated into entropy and enthalpy
D. Isotope Effects
components, leading to the logarithmic form
‡ ‡ According to the Heisenberg uncertainty principle, it is
k k B S H 1
ln = ln + − . (40) impossible to determine exactly both the position and mo-
T h R R T
mentum of a particle. Therefore a hydrogen atom cannot
Therefore a plot of ln(k /T ) versus 1/T has a slope be motionless at the distance r 0 , where the energy of
‡ CH
equal to − H /R and an intercept equal to ln(k B /h) + aC H bond (Fig. 16) is minimum, since then its po-
‡
‡
‡
‡
S /R, or S /R + 23.76. Thus both H and S can sition would be known, and also its kinetic energy and
be evaluated experimentally. hence its momentum would be known to be zero. Instead
These quantities are often called activation parame- it must have nonzero kinetic and potential energy, the sum
ters. The enthalpy contribution generally comes from the of which is its zero-point energy. According to quantum
energy required to break or reorganize the bonds. The mechanics, that energy is given as follows, where k F is the
entropy contribution generally comes from the need to ratio F/(r CH − r CH ) of restoring force to distortion and µ
0
organize the atoms into the precise arrangement of the
is the reduced mass, which is approximately equal to m H
transition state. Thus these parameters provide informa- or m D :
tion about the nature of the transition state. 1/2
Table VII lists activation parameters for the racem- 1 k F
E 0 = . (41)
ization of some sulfoxides, RS( O)Ar (97, Ar = C 6 H 4 4π µ
CH 3 -p). The sulfur is a tetrahedral stereocenter, owing
to its four substituent groups (R, O, Ar, and lone pair).
Racemization usually occurs by distorting the sulfur to
an achiral transition state 98, with R, O, and Ar coplanar.
For entry 1 there is a substantial enthalpy of activation
[Eq. (11)] because the sulfur must be distorted from tetra-
hedral bond angles to trigonal. There is no entropy con-
tribution because reactant and transition state are equally
well organized. For entry 2 racemization proceeds instead

TABLE VII Activation Parameters for Racemization of
Sulfoxides, RS( O)C 6 H 4 CH 3 -p
‡
‡
Entry R ∆H (kcal/mole) ∆S (cal/mole K)
1 C 6 H 5 39 0
2 C 6 H 5 CH 2 43 24
FIGURE 16 Energy to dissociate a C HorC D bond, each with
3 CH 2 CHCH 2 22 −9
its zero-point energy.