Question

Consider the Arrhenius equation given below and mark the correct option. $k=A{e}^{-E_a/RT}$

• 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)

$<br/>\begin{array}{l}<br/>k=A{e}^{-E_a/RT}\dots ..(i)\\ <br/>\Rightarrow \ln k=\ln \left(A{e}^{-E_2/RT}\right)\\ <br/>\Rightarrow \ln k=\ln (A)+\ln \left(e^{-E_2/RT}\right)\\ <br/>\Rightarrow \ln k=\ln (A)-\frac{E_a}{RT}\ln (e)\\ <br/>\Rightarrow \ln k=\ln (A)-\frac{E_a}{RT}<br/>\end{array}<br/>$
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)