At 518°C, the rate of decomposition of gaseous acetaldehyde (initially at 363 Torr) was 1.00 text Torr s ^ -1 when 5% had reacted and 0.5 text Torr s ^ -1 when 33% had reacted. Determine the order of this reaction.

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JEE MAIN Chemistry QUESTION #5528

Question 1

At $518°C$, the rate of decomposition of gaseous acetaldehyde (initially at 363 Torr) was $1.00\ \text{Torr s}^{-1}$ when 5% had reacted and $0.5\ \text{Torr s}^{-1}$ when 33% had reacted. Determine the order of this reaction.

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Correct Answer Explanation

Using pressure method: initial pressure $P_0 = 363$ Torr. At 5% reacted: $P = 363 \times 0.95 = 344.85$ Torr, rate = 1.00. At 33% reacted: $P = 363 \times 0.67 = 243.2$ Torr, rate = 0.5. For order $n$: $\frac{r_1}{r_2} = \left(\frac{P_1}{P_2}\right)^n \Rightarrow \frac{1.00}{0.5} = \left(\frac{344.85}{243.2}\right)^n \Rightarrow 2 = (1.418)^n$. Solving: $n = \frac{\ln 2}{\ln 1.418} \approx 2$. The reaction is second order.

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