`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. `

Options

A. 0.15
B. 0.1
C. 0.18
D. 0.21

Answer

B

Explanation

Applying PV = nRT for gaseous mixture
`((740)/(760)) xx 1 = n xx 0.082 xx 298 implies 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`.