K^{‡}

is the dimensionless equilibrium-like constant for forming the activated complex from the reactants under the chosen standard-state convention. It is not the equilibrium constant for forming the stable product.

Δ_{r} G^{\circ, ‡}

Δ_{r} H^{\circ, ‡}

the standard activation enthalpy, and

Δ_{r} S^{\circ, ‡}

the standard activation entropy. Each is the activated-complex quantity minus the corresponding sum for the reactants, with the unstable reaction-coordinate motion treated by the transition-state flux construction.

[]^{\circ} = c^{\circ}

is the standard concentration, conventionally

1 mol d m^{- 3}

for the rate units used here. Its inverse converts the attempt frequency

k_{B} T / h

into the units of a bimolecular rate constant. The stated Eyring equation assumes unit transmission coefficient.

ii

Solution

k_{2} = \frac{k _{B} T}{h c ^{\circ}} exp (\frac{Δ S ^{‡\circ}}{R}) exp (- \frac{Δ H ^{‡\circ}}{RT}) .

Taking logarithms of numerical values in fixed, consistent units gives

ln \frac{k _{2}}{T} = - \frac{Δ H ^{‡\circ}}{R} \frac{1}{T} + ln \frac{k _{B}}{h c ^{\circ}} + \frac{Δ S ^{‡\circ}}{R} .

Thus for slope

s

and intercept

b

Δ H^{‡\circ} = - R s, Δ S^{‡\circ} = R [b - ln \frac{k _{B}}{h c ^{\circ}}] .

The logarithms imply reference units, as made explicit in the supplied numerical plot. Approximate linearity requires the activation parameters and transmission coefficient to vary little over the temperature interval; a significant activation heat-capacity difference produces curvature.

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