Definition of enthalpy of activation, Ho (SI unit kJ mol^-1)

The standard enthalpy difference between the transition state and the ground state of the reactants at the same temperature and pressure. It is related to the temperature coefficient of the rate constant according to the equation:

H = RT2( ln k/T)p - RT = Ea - RT

= -R(ln(k/T)/(1/T))p

where Ea is the energy of activation, providing that the rate constants for reactions other than first-order reactions are expressed in temperature-independent concentration units (e.g., mol dm-3, measured at a fixed temperature and pressure). if lnk is expressed as

ln k = (a/T) + b + c ln T + dT,

then

H = -aR + (c - 1)RT + dRT2.

If enthalpy of activation and entropy of activation are assumed to be temperature independent, then

H = -aR

If the concentration units are mol dm-3, the true and apparent enthalpies of activation differ by (n - 1)/(RT2), where n is the order of reaction and the thermal expansivity. See also entropy of activation, Gibbs energy of activation.