When a 0.235 g sample of benzoic acid, \( \mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{2} \), is combusted in a bomb calorimeter, a \( 3.62{ }^{\circ} \mathrm{C} \) rise in temperature occurs. When a 0.305 g sample of citric acid, \( \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7} \), is burned, a \( 1.83^{\circ} \mathrm{C} \) temperature rise is observed. If the heat of combustion of benzoic acid is \( 26.38 \mathrm{~kJ} \mathrm{~g}^{-1} \), what is the heat of combustion of citric acid?

To find the heat of combustion of citric acid, we start by calculating the total heat absorbed by the calorimeter during the combustion of benzoic acid. The heat \( q \) can be calculated using the formula: \[ q = m \times \Delta T \] For benzoic acid: - Mass (\( m \)) = 0.235 g - Heat of combustion = 26.38 kJ/g So, \[ q = 0.235 \, \text{g} \times 26.38 \, \text{kJ/g} = 6.20 \, \text{kJ} \] This heat results in a temperature rise of \( 3.62 \, ^\circ C \). The heat capacity (\( C \)) of the calorimeter can be calculated as follows: \[ C = \frac{q}{\Delta T} = \frac{6.20 \, \text{kJ}}{3.62 \, ^\circ C} = 1.71 \, \text{kJ/}^\circ C \] For citric acid: - Mass (\( m \)) = 0.305 g - Temperature rise (\( \Delta T \)) = \( 1.83 \, ^\circ C \) Now, we can calculate the heat absorbed by the calorimeter during the combustion of citric acid: \[ q = C \times \Delta T = 1.71 \, \text{kJ/}^\circ C \times 1.83 \, ^\circ C = 3.13 \, \text{kJ} \] To find the heat of combustion per gram for citric acid, we divide the total heat released by the mass of the citric acid sample: \[ \text{Heat of combustion of citric acid} = \frac{3.13 \, \text{kJ}}{0.305 \, \text{g}} = 10.26 \, \text{kJ/g} \] So, the heat of combustion of citric acid is approximately \( 10.26 \, \text{kJ/g} \).