Calorimetry

The foundational principle of calorimetry is the First Law of Thermodynamics, specifically the Law of Conservation of Energy. In an isolated system, the total energy remains constant; therefore, any heat lost by a chemical reaction must be gained by the surrounding medium (usually water and the calorimeter itself).

The mathematical expression for this relationship is $q_{\text{system}} = -q_{\text{surroundings}}$. If a reaction is exothermic, it releases heat ($-q_{\text{rxn}}$), which causes the temperature of the water to rise ($+q_{\text{soln}}$).

The heat absorbed or released by a substance is calculated using the formula $q = m \cdot c \cdot \Delta T$. In this equation, $m$ is the mass, $c$ is the specific heat capacity, and $\Delta T$ is the change in temperature ($T_{\text{final}} - T_{\text{initial}}$).

For processes occurring at constant pressure, the heat flow ($q_p$) is equal to the Enthalpy Change ($\Delta H$). This allows calorimetry to be a direct method for determining the heat of reaction, heat of solution, or heat of fusion for various substances.

Constant-Pressure Calorimetry (often called coffee-cup calorimetry) is used for reactions occurring in solution. Because the cup is open to the atmosphere, the pressure remains constant, and the measured heat change directly represents the enthalpy change ($\Delta H$).

Constant-Volume Calorimetry (Bomb Calorimetry) is used for combustion reactions. The sample is ignited inside a rigid steel container (the 'bomb') submerged in water; since the volume cannot change, the heat measured represents the change in internal energy ($\Delta E$ or $\Delta U$) rather than enthalpy.

To perform a calorimetry experiment, one must first measure the initial temperatures of the reactants. After the reaction occurs, the mixture is stirred to ensure uniform temperature, and the maximum (or minimum) final temperature is recorded to determine $\Delta T$.

When calculating the total heat, it is vital to account for the Calorimeter Constant ($C_{\text{cal}}$). This value represents the heat absorbed by the hardware of the calorimeter itself (the walls, thermometer, and stirrer) and is added to the heat absorbed by the solution: $q_{\text{total}} = q_{\text{soln}} + q_{\text{cal}}$.

Check the Sign: Always remember that $q_{\text{rxn}} = -q_{\text{soln}}$. If the water temperature increases, the reaction is exothermic and $\Delta H$ must be negative; if the temperature decreases, the reaction is endothermic and $\Delta H$ is positive.

Mass Consistency: When calculating $q_{\text{soln}}$, use the total mass of the final solution (solute + solvent), not just the mass of the water. Forgetting to include the mass of the added solid or second liquid is a frequent source of error.

Unit Management: Specific heat is often given in Joules ($J$), but enthalpy changes are typically reported in kilojoules ($kJ$). Always perform a final conversion by dividing by $1,000$ to match standard reporting requirements.

Assumptions: In many introductory problems, you are expected to assume the density of an aqueous solution is $1.00 \text{ g/mL}$ and its specific heat is $4.184 \text{ J/(g} \cdot ^\circ C)$, identical to pure water.

The 'Final Temperature' Trap: Students often confuse the final temperature of the system with the change in temperature. Always subtract $T_{\text{initial}}$ from $T_{\text{final}}$ to get $\Delta T$; a negative result correctly indicates a cooling process.

Ignoring the Calorimeter: In precise experiments, the heat absorbed by the calorimeter container cannot be ignored. If a calorimeter constant is provided, you must calculate $q_{\text{cal}} = C_{\text{cal}} \cdot \Delta T$ and include it in your energy balance.

Molar Enthalpy vs. Total Heat: $q$ represents the heat for the specific amount used in the experiment, while $\Delta H_{\text{molar}}$ is the heat per mole. To find the molar value, you must divide the calculated $q_{\text{rxn}}$ by the number of moles of the limiting reactant.