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Question:

The decomposition reaction 2N_2O_5(g) → 2N_2O_4(g) + O_2(g) is started in a closed under isothermal isochoric condition at an initial pressure of 1atm. After Y × 10^3s, the pressure inside the cylinder is found to be 1.45atm. If the rate constant of the reaction is 5 × 10^-4s^-1, assuming ideal gas behavior, the value of Y is_____[Give your answer upto 2 dacimal points]

2.30

Solution:

Correct option is A. 2.30
From unit of k reaction is first first order
2N_2O_5 → N_2O_4 + O_2
t=0 1atm 0 0
t=t (1-P) P P/2
t=∞ 0 1atm 0.5atm
P_0=1atm P_t=1.45atm P_∞=1.5atmt=1/k ln(P_∞-P_0/P_∞-P_t)
t=2.303/2 × 5 × 10^-4 log(1.5-1/1.5-1.45)
t=2.303 × 10^3=y × 10^3
so y=2.303
Answer after rounding off & truncation=2.30