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)

Explanation

`{:(,CH_(3).OCH_(3(g)),rarr,CH_(4(g)),+,H_(2(g)),+,CO_((g))),("Initial P","0.40 atm",,,,,,),("Final P (at 12 min)",(0.40-P),,P,,P,,P):}`
For ideal gas behaviour, mole `prop` Pressure, (at consatnt V and T)
`:. a prop 0.40, (a-x) prop (0.40-P)`
`:. K=K=2.303/t"log"_(10)a/(a-x)`
`0.693/14.5=2.303/12"log"_(10)0.40/((0.40-P))`
`:. P=0.175 atm`
`:.` Pressure of ether decomposed= `0.175`
Now, total pressure `=0.40-P+P+P+P`
`=0.40+2P=0.40+2xx0.175`
`=0.75 atm`