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For a first order decomposition of $N_{2} O_{5} (g)$ to give ${NO}_{2} (g)$ and $O_{2} (g)$ what will be the rate constant if at initial instant, after 10 minutes and after a very long time, total pressure is 200 mm of Hg, 325 mm of Hg and 450 mm of Hg?

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$0.693 \min^{- 1}$

$6.93 \min^{- 1}$

$6.93 \times 10^{- 2} \min^{- 1}$

$\frac{6.93}{2} \times 10^{- 2} \min^{- 1}$

answer is C.

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Detailed Solution

$N_{2} O_{5} ⟶ 2 {NO}_{2} + \frac{1}{2} O_{2}$

$\begin{array}{l} k t = \ln [\frac{P_{\infty} - P_{0}}{P_{\infty} - P_{t}}] \\ k \times 10 = \ln (\frac{250}{125}) \\ k = 6.93 \times 10^{- 2} \min^{- 1} \end{array}$

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