For the first order thermal decomposition reaction, following data was obtained : \[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(\mathrm{~g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})+\mathrm{HCl}(\mathrm{~g}) \]

S. No.	Time(s)	Total Pressure (atm)
$\displaystyle 1$	$\displaystyle 0$	$\displaystyle 0.30$
$\displaystyle 2$	$\displaystyle 30$	$\displaystyle 0.50$

Calculate rate constant. [Given : $\displaystyle \log 3=0.48$ ]

\[\mathrm{C_2H_5Cl} \rightarrow \mathrm{C_2H_4} + \mathrm{HCl} \]$\displaystyle t = 0$    $\displaystyle \mathrm{Pi}$      $\displaystyle 0$      $\displaystyle 0$$\displaystyle t = t$    $\displaystyle \mathrm{Pi}-x$      $\displaystyle x$      $\displaystyle x$\[\mathrm{P_t} = \mathrm{Pi} - \cancel{x} + \cancel{x} + x \]\[x = \mathrm{P_t} - \mathrm{Pi} \]\[\mathrm{K} = \frac{2.303}{t} \log \frac{\mathrm{Pi}}{2\mathrm{Pi} - \mathrm{P_t}} \]\[\mathrm{K} = \frac{2.303}{30} \log \frac{0.30}{2 \times 0.30 - 0.50} \]\[\mathrm{K} = \frac{2.303}{30} \log \frac{0.30}{0.10} \]\[\mathrm{K} = \frac{2.303}{30} \times 0.48 \]\[\mathrm{K} = 0.037\ \mathrm{atm}^{-1} \]