A gas mixture of `3.67L` of ethylene and methane on complete combustion at `25^(@)C` produces `6.11 L` of `CO_(2)`. Find out the heat evolved on buring `1L` of the gas mixture. The heats of combustion of ethylene and methane are `-1423` and `-891kJ mol^(-1)`, respectively, at `25^(@)C`.

Explanation

`or x "moles (3.67-x)moles6.11moles"`
Applying POAC for C atoms,
`2xxx+1xx(3.67-x)=1xx6.11,x=2.44 "lit"`
Thus, the volume of `C_(2)H_(4)=2.44` lit, and volume of `CH_(4)=1.23` lit.
`:.` volume of `C_(2)H_(4)` in a 1-litre mixture `=(2.44)/(3.67)=0.665` lit
and volume of `CH_(4)` in a 1-litre mixture `=1-0.665=0.335` lit.
Now, thermochemical reactions for `C_(2)H_(4)` and `CH_(4)` are
`C_(2)H_(4)+3O_(2) to 2CO_(2)+2H_(2)O,DeltaH=-1423 "kJ"`
`CH_(4)+2O_(2) to CO_(2)+2H_(2)O, DeltaH=-891 "kJ"`
As DeltaH values given are at `25^(@)C` (supposing pressure as 1 atm)
Volume per mole at `25^(@)C=(298)/(273)xx22.4=24.45 "lit"`
Thus, heat evolved in the combustion of 0.665 lit. of `C_(2)H_(4)`
`=-(1423)/(24.45)xx0.665=-38.70"kJ"`
and heat evolved in the combustion of 0.335 "lit". of `CH_(4)`
`=-(891)/(24.45)xx0.335=-12.20"kJ"`
`:.` total heat evolved in the combustion of 1 litre of the mixture
`=-38.70+(-12.20)`
`=-50.90 kJ`