QJEEAdv19Ch9645: JEE Advanced 2019 Chemistry - Class 12 JEEAdv19Ch9645 Solution: The decomposition reaction 2 N 2 O 5 ( g ) ⟶ Δ 2 N 2 O 4 ( g )…

Question

Verified Solution • 2025–26 Session moderate

The decomposition reaction

2 N_{2} O_{5} (g) \overset{Δ}{⟶} 2 N_{2} O_{4} (g) + O_{2} (g)

is started in a closed cylinder under isothermal isochoric condition at an initial pressure of 1 atm. After Y

\times

10³ s, the pressure inside the cylinder is found to be 1.45 atm. If the rate constant of the reaction is 5

\times

10^-4s^-1, assuming ideal gas behaviour, the value of Y is ...............

Accepted Answer

At constant V, T

At initial t = 0 and final t = y

\times

10³ sec

\begin{matrix} 2 N_{2} O_{5} (g) \overset{Δ}{⟶} & 2 N_{2} O_{4} (g) + & O_{2} (g) \\ 1 & 0 & 0 \\ 1 - 2 p & 2 p & p \end{matrix}

p_Total = 1

-

2p + 2p + p

1.4 = 1 + p

p = 0.45 atm

According to first order reaction,

k = \frac{2.303}{t} \log \frac{p_{i}}{p_{i} - 2 p}

p_i = 1 atm (given)

2p = 2

\times

0.45 = 0.9 atm

On substituting the values in above equation,

2 k . t = 2.303 \log \frac{1}{1 - 0.9}

2 \times 5 \times 10^{- 4} \times y \times 10^{3} = 2.303 \log \frac{1}{0.1}

y = 2.303 = 2.3

Note : Unit of rate constant (k), i.e. s^{$-$ 1} represents that it is a first order reaction.

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