Consider a first order gas phase decomposition reaction given below :
\[
\mathrm{A}(\mathrm{g}) \longrightarrow \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})
\]
The initial pressure of the system before decomposition of A was \( p_{i} \). After lapse of time ' \( t \) ', total pressure of the system increased by \( x \) units and became ' \( p_{t} \) ' The rate constant \( k \) for the reaction is given as
(i) \( \quad k=\frac{2.303}{t} \log \frac{p_{i}}{p_{i}-x} \)
(ii) \( k=\frac{2.303}{t} \log \frac{p_{i}}{2 p_{i}-p_{t}} \)
(iii) \( \quad k=\frac{2.303}{t} \log \frac{p_{i}}{2 p_{i}+p_{t}} \)
(iv) \( \quad k=\frac{2.303}{t} \log \frac{p_{i}}{p_{i}+x} \)
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