Under constant-volume conditions, the heat of combustion of benzoic acid (C₆H₅O₆) is 15.57 kJ/g. A 3.500-g sample of sucrose is burned in a bomb calorimeter. The temperature of the calorimeter increases from 20.94 to 24.72 °C. (a) What is the total heat capacity of the calorimeter?

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1. Identify the known values: the heat of combustion of benzoic acid is 15.57 kJ/g, the mass of the sucrose sample is 3.500 g, and the temperature change (\(\Delta T\)) is from 20.94 °C to 24.72 °C.
2. Calculate the total heat released by the combustion of the sucrose sample using the formula \( q = m \times \Delta H \), where \( m \) is the mass of the sucrose and \( \Delta H \) is the heat of combustion per gram.
3. Determine the temperature change \( \Delta T \) of the calorimeter by subtracting the initial temperature from the final temperature.
4. Use the formula for heat capacity \( C = \frac{q}{\Delta T} \) to find the total heat capacity of the calorimeter, where \( q \) is the heat released and \( \Delta T \) is the temperature change.
5. Substitute the values obtained from the previous steps into the formula to calculate the total heat capacity of the calorimeter.

Key Concepts

Heat Capacity

Heat capacity is the amount of heat energy required to raise the temperature of a substance by one degree Celsius. In calorimetry, it is crucial for determining how much heat is absorbed or released by the calorimeter during a reaction. The total heat capacity of a calorimeter can be calculated using the formula C = q/ΔT, where q is the heat exchanged and ΔT is the change in temperature.

Calorimetry

Calorimetry is the science of measuring the heat of chemical reactions or physical changes. In a bomb calorimeter, the heat released from a combustion reaction is absorbed by the calorimeter and the surrounding water, leading to a measurable temperature change. This technique allows for the determination of the energy content of fuels and other substances.

Combustion Reaction

A combustion reaction is a chemical process in which a substance reacts rapidly with oxygen, producing heat and light. In the context of calorimetry, the heat released during the combustion of a sample, such as sucrose, is measured to determine its energy content. The heat of combustion is typically expressed in kJ/g, indicating the energy released per gram of the substance burned.