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

Let volume of `C_(2)H_(4)` and `CH_(4)` be `a ` and `b` litre respectively at `25^(@)C`.
`:. a+b=3.67litre ….(1)`
Also `C_(2)H_(4)+3O_(2) rarr 2CO_(2)+2H_(2)O`
`CH_(4)+2O_(2) rarr CO_(2)+2H_(2)O`
`:. `Volume of `CO_(2)` produced by a litre `C_(2)H_(4)=2a`
and Volume of `CO_(2)` produced by a litre `CH_(4)=b`
`:. 2a+b=6.11 ......(2)`
By `eqs. (1)` and `(2)`
`a=2.44 litre, b=1.23 litre`
`:. ` Volume of `C_(2)H_(4)` in 1 litre mixture at `25^(@)C`
`=(2.44)/(3.67)xx1=0.6648litre`
and Volume of `CH_(4)` in 1 litre mixture at `25^(@)C`
`=(1.23)/(3.67)xx1=0.3352 litre`
Now, Volume of `1 mol e C_(2)H_(4) at 0^(@)C=22.4 litre`
`:. ` Volume of `1 mol e C_(2)H_(4) at 25^(@)C`
`=(22.4xx298)/(273)=24.45 litre`
Similarly,
Volume of `1 mol e C_(2)H_(4)` produces `=+1423kJ ` at `25^(@)C` ltbr. `:. 0.6648litre C_(2)H_(4) ` produces
`=(+1423xx0.6648)/(24.45)=+12.22kJ`
Similarly,
`24.45 litre CH_(4)` produces `=+891kJ at 25^(@)C`
`:. 0.3352 litre CH_(4)` produces
`=(+891xx0.3352)/(24.45)=+12.22kJ`
Total heat produced `=38.69+12.22=50.91kJ`