In the first order thermal decomposition of \(\mathrm{C}_2 \mathrm{H}_5 \mathrm{I}(\mathrm{g})…
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 \((\log 2=0.3010)\)
\(6.0 \times 10^4\)
\(60 \times 10^{-3}\)
\(3.0 \times 10^3\)
\(3.0 \times 10^{-1}\)
Solution
\(\begin{array}{lccr}
& \mathrm{C}_2 \mathrm{H}_5 \mathrm{I} & \mathrm{C}_2 \mathrm{H}_4(g) & +\mathrm{HI}(g) \\
\text { At } t=0 & 2 \text { bar } & 0 & 0
\end{array}\)
\(\begin{array}{cc}
\text{After 1000 minutes 0.1} & (2-0.1) & (2-0.1) \\
& =1.9 & =1.9
\end{array}\)
Since, the reaction is first order,
\(\begin{aligned}
k & =\frac{2.303}{t} \log \frac{p}{p_0-x} \\
k & =\frac{2.303}{1000} \log \frac{2}{2-1.9} \\
& =\frac{2303}{1000} \log 20 \\
k & =3 \times 10^{-3} \mathrm{~min}^{-1}
\end{aligned}\)