Question

Write Arrhenius equation. Derive an expression for temperature variations.

Answer 1

Arrhenius equation

$K=A{e}^{-Ea/RT}$

K=Rate constant, A=Preexponential factor

Ea=Activities energy, T=Temp. (Kelvin)

R=Gas constant.

At temp. $T_1$

$K_1=A{e}^{-Ea/R{T}_1}$ ..... (1)

At temp. $T_2$

$K_2=A{e}^{\frac{-Ea}{R{T}_2}}$......(2)

Take log

3) log $K_1=\log A-\frac{Ea}{2.303R{T}_1}$

4) log $K_2=\log A-\frac{Ea}{2.303R{T}_2}$

$e{q}^n\left(4\right)-E{q}^n\left(3\right)$

$\log K_2-\log K_1=\frac{-Ea}{2.303R{T}_2}+\frac{Ea}{2.303R{T}_1}$

$\log \left(\frac{K_2}{K_1}\right)=\frac{-Ea}{2.303R}[\frac{1}{T_2}-\frac{1}{T_1}]$

$\log \left(\frac{K_2}{K_1}\right)=\frac{Ea}{2.303R}[\frac{1}{T_1}-\frac{1}{T_2}]$