The reaction $2 N_{2} O_{5} (g) ⟶ 4 {NO}_{2} (g) + O_{2} (g)$ follows first order kinetics. The pressure of a vessel containing only $N_{2} O_{6}$ was found to increase from 50 mm Hg to 87.5 mm Hg in 30 min. The pressure exerted by the gases after 60 min. will be (Assume temperature remains constant):

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106.25 mm Hg

116.25 mm Hg

125 mm Hg

150 mm Hg

answer is A.

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Detailed Solution

General the first order reaction ,

$\begin{array}{l} 2 N_{2} O_{5} ⟶ 4 {NO}_{2} + O_{2} \\ \frac{3 x}{2 x - x} = {37.5}^{\frac{x}{2}} \\ x = 25 \\ t_{1 / 2} = 30 \min \\ At t = 60; P = \frac{50}{4} + \frac{5}{2} \times \frac{3}{4} \times 50 = 106.25 \end{array}$

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