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Rate of Reaction

A vessel cont...

Question

A vessel contains dimethy 1 ether at a pressure of 0.4 atm. Dimethyl ether decomposes as $C H_{3} O C H_{3} (g) \to C H_{4} (g) + C O (g) + H_{2} (g) .$ The rate constant of decomposition is $4.78 \times 10^{- 3} m i n .$ The ratio of initial rate of diffusion after 4.5 hours of initiation of decomposition is:

0.26 : 1

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1 : 0.26

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0.34 : 2

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2 : 0.34

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Solution

The correct option is D 0.26 : 1
The pressure after 4.5 hours is $P = P_{o} e^{- k t} = 0.4 e^{- 4.78 \times 10^{- 3} \times 4.5 \times 60} = 0.11 a t m$ .
The unit of the rate constant indicates first order reaction.
The expression for the rate of the reaction is $r = k p$ .
The ratio of initial rate of diffusion after 4.5 hours of initiation of decomposition is $\frac{r_{t}}{r_{o}} = \frac{P_{t}}{P_{o}} = \frac{0.11}{0.4} = \frac{0.26}{1}$ .

Suggest Corrections

Similar questions

C H_{3} O C H_{3} (g) \to C H_{4} (g) + C O (g) + H_{2} (g)

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C H_{3} O C H_{3} (g) ⟶ C H_{4} (g) + H_{2} (g) + C O (g)

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C H_{3} O C H_{3} (g) \to C H_{4} (g) + H_{2} (g) + C O (g)

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(C H_{3})_{2} O (g) \to C H_{4} (g) + H_{2} (g) + C O (g)

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Time (sec)	390	1195	3155	$\infty$
Pressure increase (mm Hg)	96	250	467	619

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