(a) Derive the unit of rate constant for a first order reaction. (b) The activation energy of a reaction is 94.14kJ mol-1 and the value of rate constant at 313K is 1.8×10-5 s-1. Calculate frequency factor A.

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Solution

For a first order reaction rate law is given by :

$\ln (\frac{[A_{t}]}{[A_{o}]}) = - k t o r k = - \frac{2.303 \log (\frac{[A_{t}]}{[A_{o}]})}{t} U n i t s o f r a t e c o n s \tan t k : t i s i n s e c o n d s \frac{[A_{t}]}{[A_{o}]} = \frac{m o l d m^{- 3}}{m o l d m^{- 3}} T h e r e f o r e U n i t s o f k i s = \frac{1}{s e c o n d s} = s^{- 1}$

b) k = Ae^-E_a^/RT

or
ln k = ln A - (E_a/RT)

ln (1.8 x 10^-5 ) = ln A - [(94.1 x 10³)/(8.314 x 313)]

-10.925 = ln A -36.1605
ln A = 36.1605-10.925

ln A = 25.2355

A = 9.0169 x 10¹⁰ sec^-1

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