A gas mixture of 4 litres of ethylene and methane on complete combustion at `25^(@)C` produces `6` litres of `CO_(2)`. Find out the amount of heat evolved on burning one litre of the gas mixture. The heats of combustion of ethylene and methane are`-1464` and `-976 KJ mol^(-1)` at `25^(@)C`

Explanation

gt `X "moles"" " (4-x)"moles" " "6"moles"`
Applying `POAC` for `C` atoms,
`2xxx+1xx(4-x)=1xx6, x=2 "lit"`
Thus, the volume of ` C_(2)H_(4)=2"lit"`, and volume of `CH_(2)=2"lit"`.
`:.` volume of `C_(2)H_(4)` in a `1` litre mixture `=2//4=0.5 "lit"`.
and volume of `CH_(4)` in a `1` litre mixture `=1-0.5=0.5"lit"`
Now, thermochemical reactions for `C_(2)H_(4)` and `CH_(4)` are
`{:(C_(2)H_(4)+3O_(2)rarr2CO_(2)+2H_(2)O, Delta H= -1464KJ,,,,),(CH_(4)+2O_(2)rarrCO_(2)+2H_(2)O, Delta H= -976 KJ,,,,):}`
As `Delta H` values given at `25^(@)C`. let us first calculate the volume occupied by one mole of any gas at `25^(@)C` (supposiong pressures as `1 atm`)
Volume per mole at `25^(@)C=(298)/(273)xx22.4=24.4"lit"`
Thus, heat evolved in the combustion of `0.5` lit of `C_(2)H_(4)=(1464)/(24.4)xx0.5= -30KJ`
and heat evolved in the combustion of `0.5` lit of `CH_(4)=(976)/(24.4)xx0.5=-20KJ`.
`:.` total heat evolved in the combustion of `1` litre of the mixture `= -30+(-20)= -50 KJ`