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(C) For a first-order reaction: $k = \frac{2.303}{t} \log \frac{P_i}{P_{SO_2Cl_2}}$Given reaction: $SO_2Cl_{2(g)} 	o SO_{2(g)} + Cl_{2(g)}$At $t = 0$

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$2.23 	imes 10^{-3} 	ext{ s}^{-1}$

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(C) For a first-order reaction: $k = \frac{2.303}{t} \log \frac{P_i}{P_{SO_2Cl_2}}$Given reaction: $SO_2Cl_{2(g)} 	o SO_{2(g)} + Cl_{2(g)}$At $t = 0$,$P_i = 0.5 	ext{ atm}$.At $t = 100 	ext{ s}$,$P_{total} = 0.6 	ext{ atm}$.Let $x$ be the decrease in pressure of $SO_2Cl_2$.$P_{total} = (P_i - x) + x + x = P_i + x$.$0.6 = 0.5 + x \Rightarrow x = 0.1 	ext{ atm}$.$P_{SO_2Cl_2} = P_i - x = 0.5 - 0.1 = 0.4 	ext{ atm}$.$k = \frac{2.303}{100} \log \frac{0.5}{0.4} = \frac{2.303}{100} \log 1.25$.$k = \frac{2.303 	imes 0.0969}{100} = 2.23 	imes 10^{-3} 	ext{ s}^{-1}$.

$S. No.$	$Time$ $(s)$	$Total$ $pressure$ $(atm)$
$1$	$0$	$0.5$
$2$	$100$	$0.6$

Following data was obtained for the first order decomposition of $SO_2Cl_{2(g)}$ at constant volume:
$SO_2Cl_{2(g)} \to SO_{2(g)} + Cl_{2(g)}$
$S. No.$ $Time$ $(s)$ $Total$ $pressure$ $(atm)$
$1$ $0$ $0.5$
$2$ $100$ $0.6$

Calculate the rate constant.

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Following data was obtained for the first order decomposition of $SO_2Cl_{2(g)}$ at constant volume:$SO_2Cl_{2(g)} \to SO_{2(g)} + Cl_{2(g)}$$S. No.$$Time$ $(s)$$Total$ $pressure$ $(atm)$$1$$0$$0.5$$2$$100$$0.6$Calculate the rate constant.