Chemistry - Chemical Kinetics Question with Solution | TestHub

$E_a=\frac{K_1{E}_{a_1}+K_2{E}_{a_2}}{K_1+K_2}=10.5$

$12K_1+9K_2=10.5\left(K_1+K_2\right)$

$1.5K_1=1.5K_2$

$K_1=K_2$

$A_1{e}^{-E_{a1}/RT}=A_2{e}^{-E_{a_2}/RT}$

$e^{-E_{a_1}/RT}=\frac{A_2}{A_1}{e}^{-E_{a_2}/RT}$

$-\frac{E_{a_1}}{RT}=\ln \left(\frac{A_2}{A_1}\right)-\frac{E_{a_2}}{RT}$

$\frac{E_{a_2}-E_{a_1}}{RT}=\ln \left(\frac{A_2}{A_1}\right)=\ln \left(\frac{2\times 10^{14}\times e^{-2}}{2\times 10^{14}}\right)=\ln e^{-2}$

$\frac{E_{a_2}-E_{a_1}}{RT}=-2$

$T=\frac{E_{a_1}-E_{a_2}}{2R}=\frac{3\times 10^3}{2\times 2}=750\mathrm{K}$