For the decomposition of $N_2O_5$ according to the equation $2N_2O_5(g) \to 4NO_2(g) + O_2(g)$,the reaction is of first order. After $30 \, \min$ from the start of the reaction in a closed vessel,the total pressure is $305.5 \, mm \, Hg$,and at the end of complete decomposition,the total pressure is $587.5 \, mm \, Hg$. Calculate the rate constant of the reaction.
- A$3.72 \times 10^{-3} \, \min^{-1}$
- B$3.72 \times 10^{-2} \, \min^{-1}$
- C$2.15 \times 10^{-3} \, s^{-1}$
- D$1.15 \times 10^{-4} \, s^{-1}$
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The experimental data for decomposition of $N_2O_5$ in the gas phase at $318 \, K$ are given below:
$t/s$ $0$ $400$ $800$ $1200$ $1600$ $2000$ $2400$ $2800$ $3200$ $10^2 \times [N_2O_5] / mol \, L^{-1}$ $1.63$ $1.36$ $1.14$ $0.93$ $0.78$ $0.64$ $0.53$ $0.43$ $0.35$
$(i)$ Plot $[N_2O_5]$ against $t$.
$(ii)$ Find the half-life period for the reaction.
$(iii)$ Draw a graph between $\log[N_2O_5]$ and $t$.
$(iv)$ What is the rate law?
$(v)$ Calculate the rate constant.
$(vi)$ Calculate the half-life period from $k$ and compare it with $(ii)$.
| $t/s$ | $0$ | $400$ | $800$ | $1200$ | $1600$ | $2000$ | $2400$ | $2800$ | $3200$ |
|---|---|---|---|---|---|---|---|---|---|
| $10^2 \times [N_2O_5] / mol \, L^{-1}$ | $1.63$ | $1.36$ | $1.14$ | $0.93$ | $0.78$ | $0.64$ | $0.53$ | $0.43$ | $0.35$ |
$(i)$ Plot $[N_2O_5]$ against $t$.
$(ii)$ Find the half-life period for the reaction.
$(iii)$ Draw a graph between $\log[N_2O_5]$ and $t$.
$(iv)$ What is the rate law?
$(v)$ Calculate the rate constant.
$(vi)$ Calculate the half-life period from $k$ and compare it with $(ii)$.
Difficult
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