How to Do Calorimetry
The Calorimetry Equation
The basic calorimetry equation q = mc delta T connects measurable quantities (mass, temperature change) to the heat transferred. The specific heat capacity c is a material property that indicates how much energy is needed to raise one gram (or one kilogram) of a substance by one degree. Water has an unusually high specific heat of 4.184 J/(g K), meaning it takes 4.184 joules to heat one gram of water by one kelvin. Metals have much lower specific heats, typically 0.1 to 0.9 J/(g K).
When two objects at different temperatures are placed in thermal contact inside an insulated calorimeter, heat flows from the hotter object to the cooler one until they reach the same final temperature. The heat lost by the hot object equals the heat gained by the cold object (assuming no heat escapes the calorimeter): m{sub}hot{/sub} c{sub}hot{/sub} (T{sub}hot{/sub} - T{sub}final{/sub}) = m{sub}cold{/sub} c{sub}cold{/sub} (T{sub}final{/sub} - T{sub}cold{/sub}). This equation allows you to determine an unknown specific heat by measuring masses and temperatures.
For chemical reactions in solution, the heat released or absorbed by the reaction is calculated from the temperature change of the solution: q{sub}rxn{/sub} = -(m{sub}soln{/sub} c{sub}soln{/sub} delta T). The negative sign indicates that if the solution temperature rises (exothermic reaction), the reaction released heat, so q{sub}rxn{/sub} is negative. If the temperature drops (endothermic reaction), q{sub}rxn{/sub} is positive.
Coffee-Cup Calorimetry
A coffee-cup calorimeter is a simple, constant-pressure calorimeter made from two nested polystyrene (Styrofoam) cups with a lid and a thermometer. Because the cups are open to the atmosphere, the process occurs at atmospheric pressure, and the measured heat equals the enthalpy change (delta H) of the reaction. This is the standard calorimeter used in introductory chemistry courses and for measuring heats of solution, neutralization, and other reactions in aqueous solution.
The main sources of error in coffee-cup calorimetry are heat loss to the surroundings and the heat capacity of the calorimeter itself. Heat loss can be minimized by working quickly, using a lid, and nesting the cups for better insulation. The calorimeter heat capacity can be determined by calibration: adding a known amount of heat (such as mixing hot and cold water of known masses and temperatures) and measuring the temperature change.
To perform a coffee-cup calorimetry experiment, measure the mass and initial temperature of the solution, add the reactant or mix the two solutions, stir continuously, and record the maximum (or minimum) temperature reached. Calculate q = mc delta T using the total mass of the solution, the specific heat of the solution (approximately 4.18 J/(g K) for dilute aqueous solutions), and the temperature change. Divide by the moles of limiting reactant to obtain the molar enthalpy of reaction.
Bomb Calorimetry
A bomb calorimeter is a constant-volume device used to measure the heat of combustion of fuels, foods, and other materials. The sample is placed in a sealed, heavy-walled steel container (the bomb), which is filled with excess oxygen and submerged in a water bath. An electrical ignition wire ignites the sample, and the temperature rise of the water bath is measured precisely.
Because the bomb is rigid, the volume is constant and no PV work is done. The measured heat equals the change in internal energy (delta U), not the enthalpy change (delta H). To convert to enthalpy: delta H = delta U + delta(nRT), where delta n is the change in moles of gas during the reaction. For many combustion reactions, the PV correction is small (a few percent) but must be included for accurate results.
Bomb calorimeters are much more precise than coffee-cup calorimeters because the sealed, insulated design minimizes heat loss, and the large water bath provides a stable thermal environment. The calorimeter constant (total heat capacity of bomb plus water) is determined by burning a standard substance of known heat of combustion (usually benzoic acid). Modern bomb calorimeters achieve precisions of 0.01 to 0.1 percent.
Calorimetry provides the experimental foundation for all tabulated thermodynamic data. Every enthalpy of formation, heat of combustion, and specific heat value was measured using some form of calorimetry.
Advanced Calorimetry Techniques
Differential scanning calorimetry (DSC) measures the heat flow to or from a sample as a function of temperature. A small sample and an inert reference are heated at the same rate, and the difference in heat flow needed to maintain equal temperatures is recorded. DSC reveals phase transitions, glass transitions, crystallization events, and thermal decomposition, making it indispensable in polymer science, pharmaceutical development, and materials characterization.
Isothermal titration calorimetry (ITC) measures the heat released or absorbed when one solution is titrated into another at constant temperature. Each injection produces a heat pulse whose magnitude depends on the extent of binding or reaction. ITC is the gold standard for measuring binding affinities, stoichiometries, and thermodynamic parameters (delta H, delta S, delta G) of molecular interactions in biochemistry and drug discovery.
Reaction calorimetry monitors heat flow during chemical reactions in real time, allowing researchers to study reaction kinetics, determine the heat of reaction under process conditions, and assess the thermal safety of chemical processes. This information is critical for scaling up reactions from laboratory to industrial scale, where inadequate thermal management can lead to runaway reactions and safety hazards.