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The gas phase decomposition of dimethyl ...

The gas phase decomposition of dimethyl ether follows first order kinetics.
`CH_(3)-O-CH_(3)(g)rarrCH_(4)(g)+H_(2)(g)+CO(g)`
The reaction is carried out in a constant volume container at `500^(@)C` and has a half life of `14.5 min`. Initially, only dimethyl ether is present at a pressure `0.40 atm`. What is the total pressure of the system after `12min`? (Assume ideal gas behaviour)

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(0.75 atm)
`CH_(3) -O-CH_(3) (g) rarr CH_(4) (g) +H_(2) (g) +CO(g)`
At 12 min : `0.40 -p " "p" "p" "p`
Total pressure `=0.4+2P`
Also `kxx12 =" In "(0.40)/(0.40-p) =("In 2")/(14.5) xx12 =1.77 rArr p=0.175`
`rArr` Total pressure `=0.4+2p=0.4+2xx0.175=0.75` atm
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