In the first order thermal decomposition of $\mathrm{C}_2 \mathrm{H}_5 \mathrm{I}(\mathrm{g}) \longrightarrow \mathrm{C}_2 \mathrm{H}_4(g)+\mathrm{HI}(g)$, the reactant in the beginning exerts a pressure of 2 bar in a closed vessel at $600 \mathrm{~K}$. If the partial pressure of the reactant is 0.1 bar after 1000 minutes at the same temperature the rate constant in $\min ^{-1}$ is $(\log 2=0.3010)$

Question

In the first order thermal decomposition of $\mathrm{C}_2 \mathrm{H}_5 \mathrm{I}(\mathrm{g}) \longrightarrow \mathrm{C}_2 \mathrm{H}_4(g)+\mathrm{HI}(g)$, the reactant in the beginning exerts a pressure of 2 bar in a closed vessel at $600 \mathrm{~K}$. If the partial pressure of the reactant is 0.1 bar after 1000 minutes at the same temperature the rate constant in $\min ^{-1}$ is $(\log 2=0.3010)$, $6.0 \times 10^4$, $60 \times 10^{-3}$, $3.0 \times 10^3$, $3.0 \times 10^{-1}$

MARKS App · Accepted Answer

$\begin{array}{lccr} & \mathrm{C}_2 \mathrm{H}_5 \mathrm{I} & \mathrm{C}_2 \mathrm{H}_4(g) & +\mathrm{HI}(g) \ \text { At } t=0 & 2 \text { bar } & 0 & 0 \end{array}$ $\begin{array}{cc} \text{After 1000 minutes 0.1} & (2-0.1) & (2-0.1) \ & =1.9 & =1.9 \end{array}$ Since, the reaction is first order, $\begin{aligned} k & =\frac{2.303}{t} \log \frac{p}{p_0-x} \ k & =\frac{2.303}{1000} \log \frac{2}{2-1.9} \ & =\frac{2303}{1000} \log 20 \ k & =3 \times 10^{-3} \mathrm{~min}^{-1} \end{aligned}$

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