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Calculate the heat capacity of the calorimeter

The enthalpy of combustion of benzoic acid is -3226.7 kJ/mol. This means that when one mole of benzoic acid is burned, 3226.7 kJ of heat is released.

In this problem, 3.2 g of benzoic acid is burned. This is equivalent to 3.2 g / 122.12 g/mol = 0.0263 mol of benzoic acid.

The heat released by the combustion of 0.0263 mol of benzoic acid is 0.0263 mol * -3226.7 kJ/mol = -84.9 kJ.

This heat is absorbed by the water in the calorimeter and the calorimeter itself.

The temperature of the water increased by 3.8°C. The specific heat capacity of water is 4.187 J/g°C.

The mass of the water in the calorimeter is 2.0 kg = 2000 g.

The heat absorbed by the water is 2000 g * 4.187 J/g°C * 3.8°C = 32095 J = 32.095 kJ.

The heat capacity of the calorimeter can be calculated using the following equation:
Heat capacity of calorimeter = (Heat released by benzoic acid - Heat absorbed by water) / Change in temperature of calorimeter
In this problem, the change in temperature of the calorimeter is not given. However, we can assume that the change in temperature of the calorimeter is negligible compared to the change in temperature of the water.

Therefore, we can approximate the heat capacity of the calorimeter as follows:
Heat capacity of calorimeter ≈ Heat released by benzoic acid / Change in temperature of water

= -84.9 kJ / 3.8°C

≈ -22.3 kJ/°C
Therefore, the heat capacity of the calorimeter is approximately -22.3 kJ/°C.