For a first order reaction :
$A (g) ⟶ B (g) + C (g) + D (g)$
Occurring at 1 bar pressure and 300 K if initial volume of the container containing only A is $V_{0}$ and after 10 minutes it is $V_{10}$ then average life of A will be (in minutes) :

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$0.1 \ln \frac{2 V_{0}}{3 V_{0} - V_{10}}$

$\frac{10}{\ln \frac{2 V_{0}}{3 V_{0} - V_{10}}}$

$0.1 \ln \frac{V_{0}}{V_{0} - V_{10}}$

$\frac{10}{\ln \frac{V_{0}}{V_{0} - V_{10}}}$

answer is B.

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Detailed Solution

In the reaction we have,

$\underset{t = 0 \underset{}{a}}{A} ⟶ \underline{B} + \underline{C} + \underline{D} t = \infty - a a a$

$\begin{array}{l} V_{\infty} = 3 V_{0} \\ k \times t = \ln [\frac{V_{\infty} - V_{0}}{V_{\infty} - V_{t}}] \\ k \times 10 = \ln [\frac{2 V_{0}}{3 V_{0} - V_{10}}] \\ t_{avg} = \frac{1}{k} = \frac{10}{\ln [\frac{2 V_{0}}{3 V_{0} i - V_{10}}]} \end{array}$