The following reaction descomposes N 2 O 5 → 2NO 2 + 1 2 O 2 . At a 25 degree centigrade the rate constant of the reaction is 5 × 1 0 - 2 sec - 1 ⁡ . The initial pressure of N 2 O 5 is 0 .2 atm . If t

Question

The following reaction descomposes N 2 O 5 → 2NO 2 + 1 2 O 2 . At a 25 degree centigrade the rate constant of the reaction is 5 × 1 0 - 2 sec - 1 ⁡ . The initial pressure of N 2 O 5 is 0 .2 atm . If total pressure of gaseous mixture becomes 0 .35 atm, then calculate the time of decomposition of N 2 O 5 .

TestHub · Accepted Answer

(i) The decomposition reaction is represented by

Total pressure $= p_{0} - x + 2 x + \frac{x}{2} = p_{0} + \frac{3}{2 x} = 0.2 a t m .$
or $\frac{3 x}{2} = 0.35 - 0.2 = 0.15$
$x = 0.1 a t m$
Pressure of $N_{2} O_{5}$ after $t$ seconds,
$P = P_{0} - x = (0.2 - 0.1) = 0.1 a t m$
Now applying first order rate law
$t = \frac{2.303}{k} {log}_{10} \frac{0.2}{0.1}$
$= \frac{2.303}{5 \times 1 0^{- 3}} \log_{10} \frac{0.2}{0.1} = 138.6 s e c o n d s$

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