Question

It is generalized that a ${10}^{\circ }C$ increase in temperature causes the rate of reactions to double. Applied to a reaction at 295 K, what is the value of $E_a$?

• A. 120 kcal $mo{l}^{-1}$
• B. 1200 kcal $mo{l}^{-1}$
• C. 1.2 kcal $mo{l}^{-1}$
• D. 12 kcal $mo{l}^{-1}$

Answer 1

Answer: (D)

12 kcal $mo{l}^{-1}$

Only reactions whose $E_a$ falls in the range of 50-55 kJ $mo{l}^{-1}$ or 12-13 kcal $mo{l}^{-1}$ are found to double their rate for ${10}^{\circ }C$ rise in temperature i.e., from 298 to 308 K. Alternatively Use Arrhenius equation $T_1$ = 295 K, $T_2$ = 305 K. $log\frac{k_2}{k_1}=\frac{E_a}{2.3\times 2\times {10}^{-3}}\left(\frac{10}{295\times 305}\right)$

$E_a=\frac{log\left(2\right)\times 2.3\times 2{10}^{-3}\times 295\times 305}{10}$

$E_a=\frac{0.3\times 4.6\times 295\times 305}{{10}^4}$

$=12.4kcalmo{l}^{-1}$

$=12kcalmo{l}^{-1}$