Q49 / 120 · NEET 2012 (Mains) · Chemistry

Activation energy $\left(E_a\right)$ and rate constants $\left(k_1\right.$ and $\left.k_2\right)$ of a chemical reaction at two different temperatures $\left(T_1\right.$ and $\left.T_2\right)$ are related by

  • A
    $\ln \frac{k_2}{k_1}=-\frac{E_a}{R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)$
  • Correct answer
    B
    $\ln \frac{k_2}{k_1}=-\frac{E_a}{R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right)$
  • C
    $\ln \frac{k_2}{k_1}=-\frac{E_a}{R}\left(\frac{1}{T_2}+\frac{1}{T_1}\right)$
  • D
    None of the above

Solution

According to Arrhenius equation, activation energy $\left(E_a\right)$ and rate constants $\left(k_1\right.$ and $\left.k_2\right)$ of a chemical reaction at two different temperatures ( $T_1$ and $\left.T_2\right)$ are related as $$ \begin{aligned} \ln \frac{k_2}{k_1} & =\frac{E_a}{R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right) \\ & =-\frac{E_a}{R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right) \end{aligned} $$

Hence, the correct answer is option: 'B'.

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