Question

The Arrhenius equation for cis-trans isomerization of but-2-ene $(C{H}_3-CH=CH-C{H}_3)$ and but-2-en-1-nitrite $(C{H}_3-CH=CH-CN)$ are:
$k\left(s^{-1}\right)={10}^{13.8}\times e^{\left(-263.5kJ{mol}^{-1}/RT\right)}$
$k^{\prime }\left(s^{-1}\right)={10}^{11}\times e^{(-214.5kJ{mol}^{-1}/RT)}$
Calculate the temperature at which $4k=k^{\prime }$.

Answer 1

To find temperature at which $4K=K^{\prime }$

$4K=K^{\prime }$

$\Rightarrow 4\times {10}^{13.8}\times e^{\frac{-263.5\times {10}^3}{RT}}={10}^{11}{e}^{-\left(\frac{214.5\times {10}^3}{RT}\right)}\Rightarrow 4\times {10}^{2.8}=e^{\frac{(263.5-214.5)\times {10}^3}{RT}}\Rightarrow \frac{49000}{RT}=l{n}^{(4\times {10}^{2.8})}\Rightarrow t=\mathrm{7.52.41}K$