To find the numerical value for the enthalpy of combustion of the gas in kJ mol$$^{-1}$$, we first need to determine the total heat released by the combustion of the gas within the calorimeter. We then convert this amount of heat into per mole of the gas. Step 1: Calculate the total heat released, $$ q $$.

The heat released, $$ q $$, due to combustion in the calorimeter can be calculated using the formula:

$$ q = C \cdot \Delta T $$

where:

• $$ C $$ is the heat capacity of the calorimeter, and


• $$ \Delta T $$ is the change in temperature.

In this problem:

• $$ C = 2.5 \text{ kJ K}^{-1} $$


• $$ \Delta T = 298.45 \text{ K} - 298.0 \text{ K} = 0.45 \text{ K} $$

Substituting these values into the equation gives:

$$ q = 2.5 \text{ kJ K}^{-1} \times 0.45 \text{ K} = 1.125 \text{ kJ} $$

The total heat released by the process is therefore 1.125 kJ, where this amount of heat is a measure of energy released and absorbed by the calorimeter, therefore it is positive.

To convert the heat released into per mole of the gas, we first need to calculate the number of moles of the gas that was burnt. The number of moles, $$ n $$, can be calculated from the mass of the gas and its molecular weight:

$$ n = \frac{\text{mass}}{\text{molecular weight}} $$

In this problem:

• The mass of the gas = 3.5 g


• Molecular weight of the gas = 28 g mol$$^{-1}$$

Substituting these values gives:

$$ n = \frac{3.5 \text{ g}}{28 \text{ g mol}^{-1}} = 0.125 \text{ mol} $$

The enthalpy of combustion per mole, $$ \Delta H $$, is given by:

$$ \Delta H = \frac{q}{n} $$

Substituting the values we obtained:

$$ \Delta H = \frac{1.125 \text{ kJ}}{0.125 \text{ mol}} = 9 \text{ kJ mol}^{-1} $$

Therefore, the enthalpy of combustion of the gas is $$ -9 \text{ kJ mol}^{-1} $$.

Note: The negative sign indicates that the process is exothermic (releases heat).