A mixture of hydrocarbons containing acetylene and ethane, when burned under controlled consitions produced `16.20g` of water and `139.7 kcal` of heat. Given the molar composition of the mixture. Standard heats of combustion for acetylene and ethane are, respectively, `-310.6` and `-373.8 kcal`.

Explanation

`CHunderset(x)-=CH+(5)/(2)O_(2)rarrunderset(2x)2CO_(2)+H_(2)ODeltaH_(1)=-310.6kcal`
`C_(2)underset(y)(H_(6))+(7)/(2)O_(2)rarrunderset(2y)2CO_(2)+underset(3y)3H_(2)O DeltaH_(2)=-372.kcal`
Total mole of water `=(x +3y) = (16.20)/(18)`
`x = (0.9 -3y)`
`x (-310.6) +y (-373.8) =- 139.7`
`-310.6x - 372.8y =- 139.7`
`-310.6 (0.9-3y) - 372.8y =- 139.7`
`-310.6 xx 0.9 +3 xx310.6y - 373.8y =- 139.7`
`-279.54 +559y =- 139.7`
`559y = 139.84`
`y = 0.25 mol`
`x +3y = 0.9`
`x +3 xx 0.25 = 0.9`
`x = 0.15 mol`
Acetylene `= 0.15 mol`
`C_(2)H_(6) = 0.25 mol`