Question

Consider two reactions having same Arrhenius factor A, but different energies of activation.
(i) $A\to B;E{a}_1=20kJ$
(ii) $C\to D;E{a}_2=30kJ$
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.