$\begin{aligned} A (g) ⟶ B (g) + C (g) - \frac{d [A]}{d t} = k [A] \end{aligned}$ At the start, pressure is 100 mm and after 10 min, pressure is 120 mm. Hence, rate constant $(\min^{- 1})$ is:

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$\frac{2.303}{10} \log \frac{100}{120}$

$\frac{2.303}{10} \log \frac{120}{100}$

$\frac{2.303}{10} \log \frac{100}{80}$

$\frac{2.303}{10} \log \frac{100}{20}$

answer is C.

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Detailed Solution

In the reaction,

$\underset{100 - x}{A} ⟶ \underset{x}{B} + \underset{x}{C}$

Therefore,

$\begin{array}{l} 10 - x + x + x = 120 \\ \Rightarrow = 20 \\ K \times 10 = \ln (\frac{100}{80}) \end{array}$

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