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InterviewSolution
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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) |
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Answer» 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` 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` |
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