A calorimeter is an apparatus designed to measure the heat exchanged during a chemical reaction or physical process. Two common types of calorimeters in undergraduate laboratory work are:
1. Coffee-Cup Calorimeter (Constant Pressure): Suitable for reactions in aqueous solution at atmospheric pressure.
2. Bomb Calorimeter (Constant Volume): Suitable for combustion reactions of solids and liquids, where the reaction occurs in a sealed vessel.

Description and Operation:
● A coffee-cup calorimeter typically consists of two nested Styrofoam (polystyrene foam) cups to minimize heat loss, with a lid, a thermometer (or temperature probe), and a stirrer.
● One pours a reactant (e.g., a known volume of acid) into the inner cup and adds the other reactant (e.g., a known mass of base dissolved in water) to initiate the reaction.
● The reaction proceeds at constant atmospheric pressure (since the calorimeter is open to air or covered with a loose lid that does not seal pressure), so the measured heat flow equals the reaction’s enthalpy change.

Key Equations and Concepts:
1. Let m_solution be the total mass of the aqueous solution (in grams), c_solution the specific heat capacity of that solution (in J/(g·°C)), and ΔT the observed temperature change (final minus initial, in °C).
The heat absorbed or released by the solution is:
q_solution = m_solution × c_solution × ΔT
2. If ΔT is positive (temperature rises), the reaction is exothermic (heat released by reaction is absorbed by solution).
3. If ΔT is negative (temperature falls), the reaction is endothermic (heat absorbed by reaction comes from solution).

The heat change for the reaction, q_reaction, is the negative of q_solution (because heat lost by the reaction is gained by the solution, and vice versa):
q_reaction = – q_solution
● If we carried out the reaction with n moles of a limiting reagent, then the molar enthalpy change ΔH_rxn (at constant pressure) is:
ΔH_rxn = q_reaction / n (in J/mol or kJ/mol as appropriate)

Limitations and Corrections:
Heat Capacity of the Calorimeter (C_cal): In more precise experiments, one must account for the fact that part of the heat goes into heating the calorimeter itself (the container, the thermometer, stirrer, etc.). To do so, one pre-determines the calorimeter’s heat capacity (in J/°C) by performing a calibration reaction of known ΔH (such as mixing known amounts of hot and cold water). Then:
q_reaction + q_calorimeter + q_solution = 0
● where
q_calorimeter = C_cal × ΔT
● Assumptions:
○ Mixes are homogeneous quickly (stirring ensures uniform temperature).
○ Specific heat and density of solution are approximated as that of water (valid if solution is dilute).
○ Heat losses to the environment are minimized by insulation but often still nonzero; one may correct via calibration or extrapolation techniques.

Description and Operation:
● A bomb calorimeter is a robust vessel (the 'bomb') that can withstand high pressures. A sample of the substance (often a hydrocarbon or sugar) is placed inside the bomb, oxygen is added to ensure complete combustion, and the bomb is sealed. The bomb is immersed in a water bath (the calorimeter jacket).
● The reaction occurs at essentially constant volume (because the bomb is sealed), so no PV work on the surroundings occurs; thus ΔE for the reaction (change in internal energy) equals –q (heat flow) at constant volume.
By measuring the temperature rise of the surrounding water bath (and knowing the overall heat capacity of the water plus the bomb assembly), we calculate the heat released by combustion and hence ΔE_combustion. One can convert this to ΔH_combustion by adding the small PV term, since for gas-producing reactions at constant volume:
ΔH = ΔE + Δ(n_gas) × R × T

Key Equations and Concepts:
● Let C_calorimeter be the total heat capacity of the calorimeter + water bath + any steel or metal parts in contact with the water (units J/°C).
If the temperature of the water bath rises by ΔT, then the heat released by the reaction at constant volume (q_v) is:
q_v = – (C_calorimeter × ΔT)
● The negative sign indicates the system (reaction) releases heat, which is gained by the calorimeter.
To find ΔE for the combustion reaction:
ΔE_combustion = q_v (at constant volume)
● To find ΔH_combustion (enthalpy change at constant pressure), use:
ΔH_combustion = ΔE_combustion + Δ(n_gas) × R × T