$$2.4 \text{ g}$$ coal is burnt in a bomb calorimeter in excess of oxygen at $$298 \text{ K}$$ and $$1 \text{ atm}$$ pressure. The temperature of the calorimeter rises from $$298 \text{ K}$$ to $$300 \text{ K}$$. The enthalpy change during the combustion of coal is $$-x \text{ kJ mol}^{-1}$$. The value of $$x$$ is ______ (Given: Heat capacity of bomb calorimeter $$20.0 \text{ kJ K}^{-1}$$. Assume coal to be pure carbon)

We are given that 2.4 g of coal (pure carbon) is burnt in a bomb calorimeter with a heat capacity of 20.0 kJ K$$^{-1}$$, and the temperature rises from 298 K to 300 K.

The heat released in the calorimeter is calculated as

$$q = C_{cal} \times \Delta T = 20.0 \times (300 - 298) = 20.0 \times 2 = 40 \text{ kJ}$$

The moles of carbon burnt are found using the molar mass of carbon (12 g/mol) as

$$n = \frac{2.4}{12} = 0.2 \text{ mol}$$

The enthalpy change per mole is then

$$\Delta H = -\frac{q}{n} = -\frac{40}{0.2} = -200 \text{ kJ mol}^{-1}$$

Since the enthalpy change is given as $$-x$$ kJ mol$$^{-1}$$, we have

$$x = 200$$

Therefore, the correct answer is 200.