A gas mixture of 3.67 lit of ethylene and methane on complete combustion at `25^@C` and at 1 atm pressure produce 6.11 lit of carbon dioxide. Find out the amount of heat evolved in kJ, during this combustion. (`DeltaH_C(CH_4)=-890 "kJ mol"^(-1))` and `(DeltaH_C(C_2H_4)=-1423 "kJ mol"^(-1))` .

Explanation

Given :
`DeltaH_C(CH_4)=-890 "kJ mol"^(-1)`
`DeltaH_C(C_2H_4)=-1423 "kJ mol"^(-1)`
Let the mixture contain x lit of `CH_4` and (3.67-x) lit of ethylene .
`underset" x lit"(CH_4)+2O_2 to underset"x lit"(CO_2) + 2H_2O`
`underset"(3.67-x)lit"(C_2H_4 + 3O_2) to underset"2(3.67-x)lit"(2CO_2 + 2H_2O)`
Volume of carbon dioxide formed =x +2 (3.67 -x) =6.11 lit
x+7.34 -2x =6.11
x=1.23 lit
Given mixture contains 1.23 lit of methane and 2.44 lit of ethylene , hence
`DeltaH_C=[(DeltaH_C(CH_4))/"22.4 lit"xx(x)"lit"]+[(DeltaH_C(C_2H_4))/"22.4 lit"xx(3.67-x)"lit"]`
`DeltaH_C=[(-890"kJ mol"^(-1))/"22.4 lit"xx"1.23 lit"]+[(-1423)/"22.4 lit"xx(3.67-1.23)"lit"]`
`DeltaH_C=[-48.87 "kJ mol"^(-1) ]+[-155 kJ "mol"^(1)]`
`DeltaH_C=-203.87 "kJ mol"^(-1)`