Write Arrhenius equation. Derive an expression for temperature variations.

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Solution

Arrhenius equation
$K = A e^{- E a / R T}$
K=Rate constant, A=Preexponential factor
Ea=Activities energy, T=Temp. (Kelvin)
R=Gas constant.
At temp. $T_{1}$
$K_{1} = A e^{- E a / R T_{1}}$ ..... (1)
At temp. $T_{2}$
$K_{2} = A e^{\frac{- E a}{R T_{2}}}$ ......(2)
Take log
3) log $K_{1} = log A - \frac{E a}{2.303 R T_{1}}$

4) log $K_{2} = log A - \frac{E a}{2.303 R T_{2}}$

$e q^{n} (4) - E q^{n} (3)$
$log K_{2} - log K_{1} = \frac{- E a}{2.303 R T_{2}} + \frac{E a}{2.303 R T_{1}}$

$log (\frac{K_{2}}{K_{1}}) = \frac{- E a}{2.303 R} [\frac{1}{T_{2}} - \frac{1}{T_{1}}]$

$log (\frac{K_{2}}{K_{1}}) = \frac{E a}{2.303 R} [\frac{1}{T_{1}} - \frac{1}{T_{2}}]$

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