Question

A reactant (A) forms two products :
$A \xrightarrow{k_1} B, $ Activation Energy $Ea_1$
$A \xrightarrow{k_2} C,$ Activation Energy $Ea_2$
If $Ea_2 = 2 Ea_1$, then $k_1$ and $k_2$ are related as :

• A. $k_{2} = k_{1}e^{Ea_{1} /RT}$
• B. $k_{2} = k_{1}e^{Ea_{2} /RT}$
• C. $k_{1} = Ak_{2}e^{Ea_{1} /RT}$
• D. $k_{1} = 2k_{2}e^{Ea_{2} /RT}$

Answer 1

Answer: (C)

$k_{1} = A_{1} e^{-Ea_{1} /RT}$
$k_{2} = A_{2} e^{-Ea_{2} /RT}$
$\frac{k_{1}}{k_{2}} = \frac{A_{1}}{A_{2}}e^{\left(E_{a_2}- E_{a_1} \right) /RT}$
$k_{1} = A_{1} \times e^{Ea_{1} /RT}$