A sample of n-octane (1.14 g) was completely burnt in excess of oxygen in a bomb calorimeter, whose heat capacity is 5 kJ $$K^{-1}$$. As a result of combustion reaction, the temperature of the calorimeter is increased by 5 K. The magnitude of the heat of combustion of octane at constant volume is ________ kJ mol$$^{-1}$$ (nearest integer).

The heat released by the burning fuel is absorbed by the bomb calorimeter.

For a calorimeter, the heat absorbed is given by
$$q_{cal} = C_{cal}\,\Delta T$$

The heat capacity of the calorimeter is $$C_{cal} = 5\; \text{kJ K}^{-1}$$ and the observed temperature rise is $$\Delta T = 5\; \text{K}$$.

Substituting,
$$q_{cal} = 5 \times 5 = 25\;\text{kJ}$$

The combustion of the fuel releases heat, so for the system (octane) the heat of combustion at constant volume is
$$q_{comb} = -q_{cal} = -25\;\text{kJ}$$

Next, find the number of moles of $$n$$-octane burnt.
Molar mass of $$\mathrm{C_8H_{18}}$$ is
$$8(12) + 18(1) = 96 + 18 = 114\;\text{g mol}^{-1}$$

Given mass of octane is $$1.14\;\text{g}$$, hence
$$n = \frac{1.14}{114} = 0.01\;\text{mol}$$

The molar heat of combustion (constant volume) is
$$\Delta U_{comb} = \frac{q_{comb}}{n} = \frac{-25\;\text{kJ}}{0.01\;\text{mol}} = -2500\;\text{kJ mol}^{-1}$$

The magnitude is therefore $$\mathbf{2500\;kJ\;mol^{-1}}$$.