Question

Consider two reactions having same Arrhenius factor A, but different energies of activation.
(i) $A \rightarrow B;Ea_{1}=20\,kJ$
(ii) $C \rightarrow D;Ea_{2}=30\,kJ$
Both are at temperature $25^\circ C$
If temperature in both reaction is increased slightly in such a way that change in temperature in both case is same then, choose the correct option.

• A. The second reaction is faster
• B. The second reaction is more sensitive towards temperature variation
• C. If temperature increases, rate of first reaction increase more sharply
• D. All the above are correct

Answer 1

Answer: (B)

Arrhenius equation;
$\text{d}\left(lnk\right)=\frac{E_{a}}{\left(RT\right)^{2}}dT\frac{d \left(lnk\right)}{dT}=\frac{E_{a}}{\left(RT\right)^{2}}$
Hence, when $dT=$ same, the change in $d(lnK)$ will be highest $\left(\text{when E}\right)_{a}$ is highest.
So, if temperature increases, then rate of reaction having more $E_{a}$ increases sharply and the reaction becomes more sensitive to temperature changes.