Calorimetry

Calorimetry is the study of heat exchange between a system and its surroundings. A calorimeter is a device used to measure the heat exchanged between a system and its surroundings. Calorimeters are often used to measure the net heat released or absorbed by a chemical reaction at a constant pressure, called the heat of reaction ($\bold\Delta H_{\rm{rxn}}$). This is also called enthalpy of reaction. If the substances absorb heat from the surroundings, the reaction is endothermic and $\Delta H_{\rm {rxn}}$ is positive. If the substances release heat to their surroundings, the reaction is exothermic and $\Delta H_{\rm {rxn}}$ is negative.

A bomb calorimeter is a constant-volume calorimeter used to measure the heat of a reaction for combustion reactions. The calorimeter contains a bomb chamber into which the reactants are placed, and it is wired to an electric heater that ignites the reactants and causes the combustion to occur. The rest of the calorimeter is filled with water and pressurized oxygen. A stirrer keeps the water mixed so that the heat is evenly distributed, and a thermometer records the temperature of the water.

Combustion is exothermic, so the heat released by the combustion is absorbed by the water inside the calorimeter and causes the temperature of the water to rise. In calorimetry experiments, the heat capacity of the calorimeter, C_cal—not the specific heat—is used. Each calorimeter has a unique C_cal value that must be determined experimentally. The heat capacity of the calorimeter is the heat required to raise the calorimeter by one degree Celsius.

An important caveat is that the entire bomb calorimeter should not lose any heat to its surroundings. Calorimeters are well insulated against heat transfer. A system that does not exchange heat or matter with the surroundings is an isolated system. Thus, a bomb calorimeter is built as an isolated system to ensure that no heat is released to the environment around the device and all of the energy released by the combustion is used to change the temperature inside the calorimeter. Because a bomb calorimeter is an isolated system the sum of the energies of the reactants and the calorimeter must be zero, where q_rxn is the energy released or used by the reaction and q_cal is the heat absorbed or released by the calorimeter. The value of q_cal can be determined by multiplying the heat capacity of the calorimeter by the change in temperature. Thus, $\Delta H_{\rm {rxn}}$ can be calculated from the $\mathit\Delta T$ of the calorimeter. This is because energy is conserved. The energy released by the combustion reaction (q_rxn) is equal in magnitude to the energy absorbed by the calorimeter. However, because the calorimeter absorbs heat, its $\mathit\Delta T$ and energy change are both positive. The energy change for the exothermic combustion is negative. A bomb calorimeter can be used to find the energy available in food. A calorie (cal) is the amount of energy required to change the temperature of one gram of water by 1°C. It is equal to 4.184 J. The chemical energy of food is usually reported in calories. In the United States, calories in food are described by the unit kilocalorie (kcal), but the kilo part is often not used. Some brands report calories in food as "Cal," with a capital c to distinguish it from the scientific definition of calories.

Bomb calorimeters are useful in industrial laboratories, but the more common device in a general chemistry lab is the simple calorimeter, sometimes called a "coffee cup calorimeter," which is a constant-pressure calorimeter. A simple calorimeter works on the same principle as a bomb calorimeter but is usually made of two nested foam cups. A simple calorimeter is typically used to measure the heats of reaction for other types of processes besides combustion reactions. To measure $\Delta H_{\rm {rxn}}$, the reactants are placed inside the inner cup, usually in an aqueous solution, and a stirrer and thermometer are inserted through a cover. The stirrer ensures the heat is distributed throughout the reaction system, and the thermometer measures the temperature of the solution.

Because foam is a good insulator, there is essentially no heat exchange with the surroundings of the calorimeter. Thus, any temperature change of the solution is a result of energy either being absorbed or released by the chemical reaction.

In a coffee cup calorimeter,
where q_rxn is the energy released or used by the reaction (the system), and q_soln is the energy transferred to or from the solution (the surroundings). Therefore, The coffee cup calorimeter measures changes in the solution (the surroundings), not the reaction itself. Because $\Delta H_{\rm{rxn}}$ is equal to –q_soln, a negative q_soln means $\Delta H_{\rm{rxn}}$ is positive. A positive $\Delta H_{\rm{rxn}}$ means the reaction has absorbed energy from the solution, so the reaction is endothermic. For an exothermic reaction, $\Delta H_{\rm{rxn}}$ is negative, so q_soln will be positive and the temperature of the solution will rise. Simple calorimeters can also measure the heat change of processes other than chemical reactions. For example, in order for salt to dissolve, the lattice structure forming the salt must break down. This dissociation has an energy change associated with it, called the heat of solution, or $\Delta H_{\rm{soln}}$. For example, the $\Delta H_{\rm{soln}}$ of NaCl is +3.88 kJ/mol.