Question

The rate constant for the first order decomposition of $H_2{O}_2$ is given by the following equation:
$logk=14.341.25\times {10}^{4}K/T$
Calculate $E_a$ for this reaction and at what temperature will its half-period be $256$ minutes?

Answer 1

The expression for the rate constant is as follows:

$logk=14.34-1.25\times {10}^{4}K/T$...(i)

Comparing it with Arrhenius equation, we get-

$logk=logA-\frac{E_a}{2.303RT}$

Therefore,$\frac{E_a}{2.303R}=1.25\times {10}^4$

$E_a=1.25\times {10}^4\times 2.303\times 8.314$

The activation energy $=E_a=239339J/mol=239.339kJ/mol$

Half life period, $t_{1/2}=256min=256\times 60$ sec

$k=\frac{0.693}{t_{1/2}}$

$k=\frac{0.693}{256\times 60sec}$

$k=4.51\times {10}^{-5}/s$

Substitute in equation (i), we get-

$log4.51\times {10}^{-5}=14.341.25\times {10}^{4}K/T$

$-4.35=14.341.25\times {10}^{4}K/T$

$T=669$ K

Hence, the temperature at which the half-life period is $256$ minutes is $669$ K.