The rate constants of a reaction at $500 K$ and $700 K$ are $0.02 s^{- 1}$ and $0.07 s^{- 1}$ respectively.
Calculate the values of $E a$ and $A$ :

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Solution

At $500 K$ , $K = 0.02 s^{- 1}$

At $700 K, k = 0.07 s^{- 1}$

Calculation of $E_{a}$ and A can be done using Arrhenius equation
$k = A e^{{- E}_{a} / R T} ln k = ln A + (\frac{- E_{a}}{R T})$

$A t 500 K, ln 0.02 = ln A + \frac{- E_{a}}{500 R} ln A = ln (0.02) + \frac{E_{a}}{500 R} ⟶ (1) A t 700 K ln A = ln (0.07) + \frac{E_{a}}{700 R} ⟶ (2)$
Equating (1) and (2)
$ln (0.02) + \frac{E_{a}}{500 R} = ln (0.07) + \frac{E_{a}}{700 R} \frac{1}{100 R} [\frac{E_{a}}{5} - \frac{E_{a}}{7}] = ln [\frac{0.07}{0.02}] E_{a} = \frac{35 \times 100 \times 8.314 \times 1.2528}{2} E_{a} = 18227.6 J E_{a} = 18.2 K J$
Substituting value of $E_{a}$ in (1),
$ln A = ln (0.02) + \frac{18227.6}{500 \times 8.314} = (- 3.9120) + 4.3848 ln A = 0.4728 log A = 1.0889 A = a n t i l o g (1.0889) A = 12.27$

Thus $E_{a}$ is 18.2 KJ and A is 12.27

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The rate constants of a reaction at 500K and 700K are 0.02s−1 and 0.07s−1 respectively. Calculate the values of Ea and A:

The rate constants of a reaction at $500 K$ and $700 K$ are $0.02 s^{- 1}$ and $0.07 s^{- 1}$ respectively.
Calculate the values of $E a$ and $A$ :