Question

The first order gaseous decomposition of $ N_2O_4 $ into $ NO_2 $ has a $ k $ value of $ 45 \times 10^3\,s^{-1} $ at $ 1^{\circ}C $ and an energy of activation of $ 58\, kJ\, mol^{-1} $ . At what temperature would be $ 1.00 \times 10^4\,s^{-1} $ ?

• A. $ 274 \,K $
• B. $ 283 \,K $
• C. $ 273 \,K $
• D. $ 293 \,K $

Answer 1

Answer: (C)

According to Arrhenius equation
$log \frac{K_2}{K_1} = \frac{E_a}{2.303R} \,\,\,(\frac{T_2-T_1}{T_1T_2})$
$log \frac{1\times 10^4}{4.5 \times 10^3} $
$ = \frac{58\times 1000\,J \,mol^{-1}}{2.3030\times 8.314\,JK^{-1}\,mol^{-1}} \times (\frac{T_2- 274}{274T_2})$
$\Rightarrow T_2 = 2827 \approx 283\,K$