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For ${SO}_{2} {Cl}_{2 (g)} \to {SO}_{2 (g)} + {Cl}_{2 (g)}$ Pressures of ${SO}_{2} {Cl}_{2} at t = 0 and t = 20$ minutes respectively are 700 mm & 350 mm. When log $(P_{0} / p)$ is plotted against time (t), slope equals to

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$1.505 \times 10^{- 2} s^{- 1}$

$1.202 \times 10^{- 3} \min^{- 1}$

$1 .505 \times 10^{- 2} \min^{- 1}$

$0 .3465 \min^{- 1}$

answer is C.

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Detailed Solution

${SO}_{2} {Cl}_{2 (g)} \to {SO}_{2 (g)} + {Cl}_{2 (g)}$ is a first order reaction

$K = \frac{2.303}{t} \log \frac{P_{0}}{P}$

$\log \frac{P_{0}}{P} = \frac{K}{2.303} \times t$

y = mx

slope = $\frac{K}{2.303} = \frac{1}{t} \log \frac{P_{0}}{P} = \frac{1}{20} \log \frac{700}{350} = \frac{0.3010}{20} = 0.01505$ min^-1

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