A first order gas-phase reaction has an energy of activation of $240 k J m o l^{- 1}$ . If the frequency factor of the reaction is $1. \times 10^{13} s^{- 1}$ , calculate its rate constant at $600 K$ .

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Solution

Applying the arhenius equation-
$K = A [e^{- \frac{E_{a}}{R T}}]$
Taking log both side
$l o g_{10} K = l o g_{10} A - \frac{E_{a}}{2.303 R T}$
$l o g_{10} K = l o g_{10} 10^{13} - \frac{240 \times 10^{3}}{2.303 \times 8.314 \times 600}$
$l o g_{10} K = 13 - \frac{240 \times 10^{3}}{2.303 \times 8.314 \times 600}$

$K = 2.056 \times 10^{- 8} S^{- 1}$

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