Given below a first order reaction in the gas phase
\(\mathrm{A}(\mathrm{g}) \rightarrow \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})\)
If the initial pressure of the system is \(\mathrm{P}_{\mathrm{i}}\) and the total pressure at \(\mathrm{t}\) seconds is \(\mathrm{P}_{\mathrm{t}}\), the rate constant \(\mathrm{k}\) for the reaction is:

1. A \(\mathrm{k}=\dfrac{2.303}{\mathrm{t}} \log \dfrac{\mathrm{P}_{\mathrm{i}}}{\left(2 \mathrm{P}_{\mathrm{i}}+\mathrm{x}\right)}\)
2. B \(\mathrm{k}=\dfrac{2.303}{\mathrm{t}} \log \dfrac{\mathrm{P}_{\mathrm{i}}}{\mathrm{P}_{\mathrm{t}}}\)
3. C \(\mathrm{k}=\dfrac{2.303}{\mathrm{t}} \log \dfrac{\mathrm{P}_{\mathrm{i}}}{\left(\mathrm{P}_{\mathrm{i}}+\mathrm{x}\right)}\)
4. D \(\mathrm{k}=\dfrac{2.303}{\mathrm{t}} \log \dfrac{\mathrm{P}_{\mathrm{i}}}{\left(2 \mathrm{P}_{\mathrm{i}}-\mathrm{P}_{\mathrm{t}}\right)}\)