question_answer

For reaction \[A\to B\]the rate constant \[{{k}_{1}}={{A}_{1}}{{e}^{-{{E}_{{{a}_{1}}}}/RT}}\] and for the reaction \[X\to Y\] the rate constant \[{{k}_{1}}={{A}_{2}}\,{{e}^{-{{E}_{{{a}_{2}}}}/RT}}\], if \[{{A}_{1}}={{10}^{10}}\],\[{{A}_{2}}={{10}^{12}}\] and \[{{E}_{{{a}_{1}}}}=800\,\text{cal/mol}\],\[{{E}_{{{a}_{2}}}}=1600\,\text{cal/mol}\], then temperature at which \[{{k}_{1}}={{k}_{2}}\] is (given R = 2 cal/K-mol)

A)  \[\left( \frac{200}{0.693} \right)K\]                        

B)  \[200\times 0.693K\]

C)  \[\left( \frac{400}{0.693} \right)K\]                        

D)  \[400\times 0.693K\]