1.250 g of a sample of octane `(C_(8)H_(18))` is burnt in excess of oxygen in a bomb calorimeter. The temperature of the calorimeter rises from 298 K to 304.73 K. If heat capacity of calorimeter is 8.93 kJ/K. Calculate the heat transferred. Also calculate `Delta U` and `Delta H` of the reaction at 298 K. The reaction involved is
`C_(8)H_(18(l)) + (25)/(2)O_(2(g)) rarr 8CO_(2(g)) + 9H_(2)O_((l))`.

Explanation

Let q be the quantity of heat transferred to the calorimeter.
Here, `Delta T = 304.73 - 298.08 = 6.73 K`
Heat absorbed by the calorimeter `= C_(v) xx Delta T`
`= 8.93(kJ K^(-1)) xx 6.73 (K) = 60.1 kJ`
Molar mass of octane `(C_(8)H_(18))`
Heat produced by 1.250 g of `C_(8)H_(18) = 60.1 kJ`
Heat produced by 1 mol `= 114g` of `C_(8)H_(18)`
`= (60.1 xx 114)/(1.250) = 5481.1 kJ`
Thus, `Delta U = -5481.1 kJ mol^(-1)`
`Delta n_((g))` of the reaction `= 8 - (25)/(2) = -4.5`
`Delta H = Delta U + Delta nRT`
`= -5481 + (-4.5) xx 8.314 xx 10^(-3) xx 298`
`= -5492.2 kJ mol^(-1)`