The arrhenius (pre exponential) factors and activation energy values for steps $(i)$ to $(i v)$ are $A_{1}, A_{2}, A_{3}, A_{4} a n d E_{1}, E_{2}, E_{3} a n d E_{4}$ respectively.
Calculate the overall activation energy $E_{t h e r m a l}$ for the thermal decomposition of acetaldehyde.
Write the expression for overall activation energy, $E_{p h o t o c h e m i c a l}$ of photochemical decomposition of acetaldehyde.

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Solution

$R a t e = k_{2} \sqrt \frac{k_{1}}{{2 k}_{4}} {[{C H}_{3} C H O]}_{3}^{3 / 2} D i f f e r e n t i a l f o r m o f A r r h e n i u s e q u a t i o n : d l n \frac{k_{o b s}}{d t} = \frac{E_{o b s}}{{R T}^{2}} \frac{d l n k_{2}}{d t} + \frac{1}{2} \frac{d l n k_{1}}{d t} - \frac{1}{2} \frac{d l n k_{4}}{d t} = \frac{E_{o b s}}{{R T}^{2}} E_{o b s} = E_{2} + \frac{1}{2} E_{1} - \frac{1}{2} E_{4}$

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Rate=k2√k12k4[CH3CHO]3/2Differential form of Arrhenius equation:d lnkobsdt=EobsRT2d lnk2dt+12dlnk1dt−12dlnk4dt=EobsRT2Eobs=E2+12E1−12E4