For a first order parallel reaction,

k₁ and k₂ are e sec^-1 and 1 sec^-1
respectively at 300 K If the activation energy for B and C is respectively 20 kJ and 28.314 kJ then calculate temperature (in Kelvin) at which B and C will be formed in equimolar ratio.

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answer is 429.

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Detailed Solution

$\frac{A_{1} e^{- \frac{20}{R \times 300}}}{A_{2} e^{- \frac{28.314}{R \times 300}}} = \frac{e}{1}; k_{1}^{'} = k_{2}^{'}$

$\begin{array}{l} \Rightarrow \frac{A_{1}}{A_{2}} = e^{- \frac{7}{3}} \\ \Rightarrow \frac{A_{1}}{A_{2}} \times e^{- \frac{20}{R T}} = e^{- \frac{28.314}{R T}} \\ \Rightarrow \frac{20 \times 10^{3}}{R \times T} + \frac{7}{3} = \frac{28.314 \times 10^{3}}{R \times T} \\ \Rightarrow T = \frac{3000}{7} K = 429 K \end{array}$