Q.In a constant volume calorimeter, 3.5 g of a gas with molecular weight 28 was burnt in excess oxygen at 298 K. The temperature of the calorimeter was found to increase from 298 K to 298.45 K due to the combustion process. Given that the calorimeter constant is 2.5 kJ K$^{-1}$. Calculate the enthalpy of combustion of the gas in kJ mol$^{-1}$.

A calorimeter converts an observed temperature change into a heat quantity via $C=q/(m\Delta T)$, under one of two conditions. Bomb calorimeter (constant volume): a sealed, pressurised steel vessel holding the sample, electrically ignited, immersed in stirred water inside an insulated jacket. Since the sealed bomb's volume cannot change, whatever heat is measured IS the constant-volume heat of combustion, $\Delta U_C^0=(k+m_wC_w)\Delta T$, where $k$ (the calorimeter constant) is calibrated by burning a known mass of benzoic acid (known $\Delta H_C=-3227$ kJ mol$^{-1}$); the constant-PRESSURE enthalpy is then recovered via $\Delta H_C^0=\Delta U_C^0+\Delta n_gRT$. Applications: measuring combustion heat, the calorific value of food, and industrial metabolic/explosive-testing work. …