`1.0`litre sample of a mixture of `CH_(4)` and `O_(2)` measured at `25^(@)C` and `740 ` torr, was allowed to react at constant pressure in a calorimeter, together with its contents had a heat capacity of `1260 cal K^(-1)`. The complete combustion of `CH_(4)` to `CO_(2)` and water caused a temperature rise in calorimeter of `0.667K`. Calculate mole `%` of `CH_(4)` in the original mixture. Heat of combustion of `CH_(4)` is `-210.8 kcal. `

Explanation

Applying PV = nRT for gaseous mixture.
`(740/760) xx 1 xx 0.082 xx 298`
`n=0.0398`
Heat generated = Heat capacity `xx` Temperature rise
`=1260 xx 0.667 = 840 cal`
Mole of `CH_(4)` in the mixture `=840/(210.8 xx 10^(3)) = 3.98 xx 10^(-3)`
Mole per cent of `CH_(4)= (3.98 xx 10^(-3))/0.398 xx 100 =10`