For the thermal rearrangement of vinyl allyl ether (g) to allyl acetaldehyde (g) at 175°C, \(A = 5 × 10^{11} exp^{(–128000/RT)}\), where K is in s^–1 and activation energy in J mol^–1. The enthalpy of activation in kJ mol^–1 is:

124.3

The correct answer is option 4. 124.3.

Given,

\(A = 5 × 10^{11} exp^{(–128000/RT)}\)

\(A = 5 × 10^{11} exp^{(–E_a/RT)}\)

\(E_a = 128000 \text{ J mol}^{-1}\)

For Gaseous reaction,

Her, \(\Delta \eta\) is change in the number of molecules, when
the activated complex is formed.
Here \(\Delta \eta = 0\) (unimolecular reaction).

So, \(\Delta H = 128000 − 8.314 × 448 \text{ J mol}^{-1}\)

                    \( = (128000 − 3725) \text{ J mol}^{−1}\)

                     \( = 124275 \text{ J mol}^{−1}\)

                     \( = 124.3 \text{ kJ mol}^{−1}\)