Question

The gas phase decompoistion of dimethyl ether follows first order kinetics.
`CH_(3)-O-CH_(3)(g)rarrCH_(4)(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 1

Correct Answer - `0.7492 atm`
`{:(CH_(3)-,O-CH_(3)to,CH_(4)+,H_(2),+CO),("Inital",0.4,0,0,0),("Final",(0.4-x),x,x,x):}`
For first order reaction,
Half life `=(0.693)/(k)`
or `14.5=(0.693)/(k)`
or `k=(0.693)/(14.5)= 4.78xx10^(-2) min^(-1)`
Also,
`k=(2.303)/(t) log.(A_(0))/(A_(t)) = (2.303)/(t) log.(P_(0))/(P)`
or `(0.693)/(14.5) = (2.303)/(12) log.(0.40)/((0.40-x))`
or `x = 0.1746 atm`
Total pressure of container after `12 min` is
`(0.40 -x)+x+x+x = 0.4 + 2x`
`= 0.4 + 2xx 0.1746`
`= 0.7492 atm`

Answer 2

Correct Answer - `0.7492 atm`
`{:(CH_(3)-,O-CH_(3)to,CH_(4)+,H_(2),+CO),("Inital",0.4,0,0,0),("Final",(0.4-x),x,x,x):}`
For first order reaction,
Half life `=(0.693)/(k)`
or `14.5=(0.693)/(k)`
or `k=(0.693)/(14.5)= 4.78xx10^(-2) min^(-1)`
Also,
`k=(2.303)/(t) log.(A_(0))/(A_(t)) = (2.303)/(t) log.(P_(0))/(P)`
or `(0.693)/(14.5) = (2.303)/(12) log.(0.40)/((0.40-x))`
or `x = 0.1746 atm`
Total pressure of container after `12 min` is
`(0.40 -x)+x+x+x = 0.4 + 2x`
`= 0.4 + 2xx 0.1746`
`= 0.7492 atm`