Constant Volume Calorimetry

The change in the internal energy of a reaction, ΔE, is the sum of both heat, q, and work, w.

While it is simple to measure heat through temperature changes, measuring the pressure-volume type work through changes in volume is inconvenient.

For gaseous chemical reactions, if the volume is not allowed to change, then ΔV equals zero, and consequently, w will be zero. Thus, the internal energy change of the reaction will exactly equal the heat transferred.

Under constant volume conditions, the heat transferred in a reaction is measured using a bomb calorimeter.

This is different from a coffee cup calorimeter, which measures the heat of a reaction under constant pressure conditions.

In a bomb calorimeter, 0.512 grams of naphthalene is placed in a stainless steel bomb. Through an inlet, the ignition coil is placed in contact with the sample.

The bomb is then filled with oxygen and immersed in an insulated container filled with a known mass of water. Electrically igniting the reactant initiates the combustion reaction inside the bomb.

The heat released is absorbed by the water and the various components of the calorimeter assembly, which all together make up the surroundings. This causes the temperature to rise by 6.42 °C.

The heat absorbed by the entire calorimeter assembly, q_cal, equals its heat capacity, C_cal, multiplied by the temperature change, ΔT.

If the experimentally determined value for C_cal is 3.20 kJ/°C, then substituting this, along with the value for ΔT gives the heat of the calorimeter as 20.5 kJ.

The heat gained by the calorimeter exactly equals the heat released by the reaction. The bomb being sealed, the reaction occurs at constant volume, and work done is zero. Thus, the heat of the reaction equals its internal energy change, −20.5 kJ.

Dividing this value by the number of moles in 0.512 grams of naphthalene (3.99 × 10⁻³ moles) gives the change in internal energy per mole of naphthalene, which is −5140 kJ/mol.