Q. The rate constant, the activation energy and the Arrhenius parameter of a chemical reaction at $25°C$ are $3.0\times 10^{- 4}s^{-}$ , $104.4kJmol^{- 1}$ and $6\times 10^{14}s^{- 1}$ respectively. The value of the rate constant at temperature $T=\in fty$ is
NTA AbhyasNTA Abhyas 2022
Solution:
$k=Ae^{- E a / R T}$ (Arehenius equation)
when $T \rightarrow \in fty$
$=A\times \frac{1}{e^{\frac{E_{a}}{RT}}}T \rightarrow \infty =\frac{1}{T}=0 \rightarrow \frac{Ea}{RT}=0e^{0}=1Puttheabovevalueingivenequation=A\times \frac{1}{e^{\frac{E_{a}}{RT}}}K=ASo,A=6.0\times 10^{14}s-1$
It means at high temperature low activation energy favour larger rate constant.
when $T \rightarrow \in fty$
$=A\times \frac{1}{e^{\frac{E_{a}}{RT}}}T \rightarrow \infty =\frac{1}{T}=0 \rightarrow \frac{Ea}{RT}=0e^{0}=1Puttheabovevalueingivenequation=A\times \frac{1}{e^{\frac{E_{a}}{RT}}}K=ASo,A=6.0\times 10^{14}s-1$
It means at high temperature low activation energy favour larger rate constant.