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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)

Text Solution

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`k=(0.693)/(t_(1//2))=(0.693)/(14.5)=0.047793 "min"^(-1)`
Let the pressure of dimethyl ether after 12 minutes by p atom. Applying frist order equation.
`k=(0693)/(t)log_(10).(P0)/(P)`
`log_(10).(0.4)/(p)=(0.047793xx12)/(2.303)=0.2490`
or `(0.4)/(p)=1.7743`
or `p=(4)/(1.7743)`
`=0.2254` atm
Decrease in pressue , x=0.4-0.2254=0.1746 atm
`CH_(3)underset(po-x)(OCH)(g)rarrCH_(4)underset(x)((g))+H_(2)underset(x)((g))+COunderset(x)((g))`
Total pressure `=P0+2x`
`=0.4+2xx0.1746`
`=0.7492` atm
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