Question 14 Marks
The rate constant for the first order decomposition of $H_{2}O_{2}$ is given by the following equation: $log~k=14.2-\frac{1.0\times10^{4}K}{T}$. Calculate $E_a$ for this reaction and rate constant k if its half-life period be 200 minute.
( given $R =8.314 J K ^{-1} mol^{-1}$)
( given $R =8.314 J K ^{-1} mol^{-1}$)
Answer
View full question & answer→$\log A =14.2-\frac{10^4 K}{ T }$ ...(i)
Arrhenius equation : $K = A e^{- E _\alpha / RT }$
$\log k=\log A-\frac{E_a}{2.303 RT}$...(ii)
Comparing equations (i) and (ii),
$\frac{- E _a}{2.303 RT }=\frac{-10^4}{T}$
$\Rightarrow \quad E _a=10^4 \times 2.303 \times R$
$\Rightarrow \quad E _a=10^4 \times 2.303 \times 8.314$
$\therefore \quad E _a=191.47 kJ / mol$
$k=\frac{0.693}{t_{1 / 2}}$ (for 1 st order reaction)
$\therefore \quad k=5.78 \times 10^{-5} s e c ^{- 1 }$
Arrhenius equation : $K = A e^{- E _\alpha / RT }$
$\log k=\log A-\frac{E_a}{2.303 RT}$...(ii)
Comparing equations (i) and (ii),
$\frac{- E _a}{2.303 RT }=\frac{-10^4}{T}$
$\Rightarrow \quad E _a=10^4 \times 2.303 \times R$
$\Rightarrow \quad E _a=10^4 \times 2.303 \times 8.314$
$\therefore \quad E _a=191.47 kJ / mol$
$k=\frac{0.693}{t_{1 / 2}}$ (for 1 st order reaction)
$\therefore \quad k=5.78 \times 10^{-5} s e c ^{- 1 }$