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A gas phase decomposition of dimethyl ei...

A gas phase decomposition of dimethyl either follows the 1st order kinetics `CH_{3}OCH_{3}CH_{3}OCH_{3}harrCH_{4}(g)+H_{2}_(g)+CO_{(g)}`. The reaction is carried out in a costant volume container at `(500^oC)` and has a half life period of 14.5 (min). Initially only dimethyl ether is present at a pressure of 0.4 atmosphere. What is the total pressure of the system after 12 (min) ? Assume Ideal behaviour

A

0.9833 atm

B

1.201 atm

C

0.7488 atm

D

2.031 atm

Text Solution

Verified by Experts

The correct Answer is:
C
We have
`{:(t = 0,p_(0),0,0,0),(t,p_(0)-p,p,p,p):}`
Total pressure of the system at time `t = p_(0) + 2p`, The rate expression for first order kinetics is `log""([A])/([A]_(0)) = -((k)/(2.303))t`
In the present case, we get
`log""(p_(0) - p)/(p_(0)) = -((0.693//t_(0.5)))/(2.303)t = -((0.693//14.5 "min"))/(2.303) (12 "min") = -0.249` or `(p_(0) - p)/(p_(0)) = 0.564`
`p = p_(0) - 0.564 p_(0) = p_(0)(1-0.564) = (0.40 atm)(0.436 atm) = 0.1744 atm`
Hence, Total pressure of the system is `p_(0) + 2p = (0.40 + 2 xx 0.1744)atm = 0.7488 atm`.
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