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Rate Constant

The rate cons...

Question

The rate constants of a first order reaction are $0.58 s^{- 1}$ at 313 K and $0.045 s^{- 1}$ at 293 K. What is the energy of activation for the reaction?

A

88.29 K J m o l^{- 1}

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B

103.25 K J m o l^{- 1}

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C

97.5 k J m o l^{- 1}

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D

None of these

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Solution

The correct option is C $97.5 k J m o l^{- 1}$
$∵ {log}_{10} \frac{k_{2}}{k_{1}} = \frac{E_{a}}{2.303 R} [\frac{T_{2} - T_{1}}{T_{2} T_{1}}]$
$⟹ {log}_{10} \frac{0.045}{0.58} = \frac{E_{a}}{2.303 \times 8.314} [\frac{293 - 313}{293 \times 313}]$
$⟹ {log}_{10} 0.0776 = \frac{E_{a}}{19.147} [\frac{- 20}{293 \times 313}]$
$⟹ - 1.110 = \frac{E_{a}}{19.147} [\frac{- 20}{293 \times 313}]$
$⟹ E_{a} = 97.5 k J m o l^{- 1}$

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