The folllowing data were obtained during the first order decomposition of \(2 A(g) \rightarrow B(g)+C(s)\) at a constant volume and at a particular temperature



The rate constant in \(\mathrm{min}^{-1}\) is

\[
\begin{array}{lc}
2 A(g) \longrightarrow B(g)+C(s) \\
2-2 x & x
\end{array}
\]
At the end of reaction, only 1 mole of gas is present whose pressure is 200 Pascal.
\(\therefore\) At the beginning of the reaction 2 moles of gas should have a pressure of 400 Pascal.
After time \(10 \mathrm{~min}\)
No. of moles present,
\[
2-2 x+x=2-x
\]
The pressure of 2 moles \(=400\)
\(\therefore \quad 400-x=300\)
\(\therefore \quad x=100\)
\(\therefore\) Pressure due to \(2-2 x\) moles of \(A\)
\[
=400-200=200
\]
\(\begin{aligned} \therefore \quad k &=\frac{2.303}{t} \log \left(\frac{a}{a-x}\right)=\frac{2.303}{10} \log \left(\frac{400}{200}\right) \\ &=\frac{2.303}{10} \log 2=\frac{0.693}{10} \\ &=0.0693 \mathrm{~min}^{-1} \end{aligned}\)