Constant Volume Calorimetry

At constant volume, the change in volume (ΔV) equals zero, making pressure-volume work equal to zero. This means the heat measured by the bomb calorimeter directly equals the internal energy change of the reaction. According to the first law of thermodynamics, internal energy change equals heat plus work, so eliminating work simplifies the measurement significantly.

A bomb calorimeter operates at constant volume and measures internal energy change, making it ideal for vigorous combustion reactions. A coffee cup calorimeter operates at constant pressure and measures enthalpy change for reactions in solution. The bomb's sealed design prevents volume changes, while the coffee cup allows atmospheric pressure conditions.

Heat absorbed by the calorimeter equals its heat capacity multiplied by the temperature change: qcal = Ccal × ΔT. In the naphthalene example, a heat capacity of 3.20 kJ/°C and temperature rise of 6.42 °C yielded 20.5 kJ absorbed. This relationship allows calculation of reaction heat from measured temperature changes.

Divide the total internal energy change by the number of moles of reactant that underwent combustion. For naphthalene, the reaction released 20.5 kJ, and 0.512 grams equals 3.99 × 10−3 moles, giving −5140 kJ/mol. This molar value allows comparison across different quantities of the same reactant.

Calibration determines the heat capacity of the calorimeter assembly, which is essential for accurate calculations. A known reaction, such as benzoic acid with a measured heat value, is ignited to produce a known temperature change. This temperature change reveals the calorimeter's heat capacity, ensuring reliable results for subsequent unknown reactions.

The insulated container prevents heat loss to the environment, ensuring all heat released by the reaction is absorbed by the calorimeter assembly and water. This isolation guarantees that the measured temperature increase reflects only the reaction's heat output, making the calculation of internal energy change accurate and reliable.

Oxygen is used because bomb calorimeters measure combustion reactions, which require oxygen as a reactant. Filling the bomb with oxygen at high pressure ensures complete combustion of the sample, maximizing the heat released and allowing accurate measurement of the reaction's energy output.