Question

Consider the Arrhenius equation given below and mark the correct option. $k=Ae^{-E_{a} / RT}$

• A. Rate constant increases exponentially with increasing activation energy and decreasing temperature.
• B. Rate constant decreases exponentially with increasing activation energy and decreasing temperature.
• C. Rate constant increases exponentially with decreasing activation energy and decreasing temperature.
• D. Rate constant increases exponentially with decreasing activation energy and increasing temperature.

Answer 1

Answer: (D)

$
\begin{array}{l}
k = Ae ^{- E _{a} / RT } \ldots . .( i ) \\
\Rightarrow \ln k =\ln \left( Ae ^{- E _{2} / RT }\right) \\
\Rightarrow \ln k =\ln ( A )+\ln \left( e ^{- E _{2} / RT }\right) \\
\Rightarrow \ln k =\ln ( A )-\frac{ E _{ a }}{ RT } \ln ( e ) \\
\Rightarrow \ln k =\ln ( A )-\frac{ E _{ a }}{ RT }
\end{array}
$
So from this equation,
$k \propto \frac{1}{ E _{ a }}$ and $k \propto T$
$k$ increases if $E _{ a }$ decreases and increases if $T$ increases.
Moreover, the relation in exponential can be seen in (i)