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)

Answer

75 atm

Explanation

`CH_3OCH_3(g)toCH_4(g)+H_2(g)+CO(g)`
Pressure at t=0 0.40
Pressure at t=12 min (0.40-P) P P P
For ideal gas behaviour moles `prop` pressure
`:.aprop0.40, " " (a-X)prop(0.40-P)`
`because K=2.303/t "log" a/(a-X) or " " 0.693/14.5=2.303/12 "log" 0.40/(0.40-P)`
`:. P=0.175` atm
Thus, total pressure after 12 minutes=0.40-P+P+P+P
=0.40+2P=0.40+2x0.175=0.75 atm