Heat Capacity and Calorimetry — AP Chemistry
1. Heat Capacity: Extensive and Intensive Forms ★★☆☆☆ ⏱ 4 min
Heat capacity describes the amount of heat energy required to change the temperature of a given amount of substance by 1°C (or 1 K). Calorimetry is the experimental technique used to measure heat transferred during a chemical or physical change by measuring temperature change of a system with known heat capacity.
- **Specific heat capacity ($c$)**: Intensive property normalized by mass: $c = \frac{q}{m\Delta T}$, units $\text{J}/(\text{g} \cdot ^\circ\text{C})$. Core calculation formula: $q = mc\Delta T$.
- **Molar heat capacity ($C_m$)**: Intensive property normalized by moles: $C_m = \frac{q}{n\Delta T}$, units $\text{J}/(\text{mol} \cdot ^\circ\text{C})$.
Exam tip: Always check that units cancel correctly: if your final answer has leftover mass or mole units, you used the wrong form of heat capacity.
2. Constant-Pressure (Coffee-Cup) Calorimetry ★★★☆☆ ⏱ 4 min
Constant-pressure calorimetry is the most common simple technique for measuring enthalpy change ($\Delta H$) for reactions run in open containers at atmospheric pressure, like dissolution, neutralization, or precipitation. By definition, at constant pressure, the heat transferred by the reaction equals the enthalpy change: $\Delta H = q_p$.
The core assumption of simple coffee-cup calorimetry is that no heat is exchanged with the environment outside the calorimeter, and the heat capacity of the foam cup itself is negligible. This gives the key relationship:
q_{rxn} = -q_{solution} = -(mc\Delta T)_{solution}
Most AP problems assume dilute aqueous solutions have the same density (1.00 g/mL) and specific heat as pure water, so you can use $c = 4.184 \text{ J}/(\text{g} \cdot ^\circ\text{C})$ to calculate heat change.
Exam tip: If the reaction causes a temperature drop, it is endothermic, so $\Delta H$ will be positive — this is a quick sanity check for your final sign.
3. Constant-Volume (Bomb) Calorimetry ★★★☆☆ ⏱ 3 min
Constant-volume (bomb) calorimetry is used for combustion reactions, which require a sealed, high-pressure container. The bomb is filled with oxygen, the sample is ignited, and heat released by combustion raises the temperature of a surrounding water bath. Because volume is constant ($\Delta V = 0$), pressure-volume work $w = -P\Delta V = 0$, so by the first law of thermodynamics, $\Delta U = q_v$, meaning the heat measured directly equals the change in internal energy.
For bomb calorimetry, we use the pre-calibrated total heat capacity of the entire calorimeter assembly ($C_{cal}$, units $\text{kJ}/^\circ\text{C}$), which already accounts for the mass of the bomb, water, and container. The core relationship is:
q_{rxn} = -C_{cal} \Delta T
For most AP problems, you can approximate $\Delta H \approx q_v$, so the calculated value is the approximate molar enthalpy of combustion.
Exam tip: If the problem asks for $\Delta U$ instead of $\Delta H$, the answer is just the calculated $q_v$, no further adjustment is needed for AP-level problems.
4. AP Style Concept Check ★★★★☆ ⏱ 3 min
Common Pitfalls
Why: Students memorize the formula as $q = m_{water}c\Delta T$ and forget the solute adds to the total mass of the solution that absorbs or releases heat.
Why: Students think 'temperature changed by 8 degrees' so they drop the sign, forgetting the sign encodes direction of heat flow.
Why: Specific heat is usually given in J/(g·°C), so $q$ comes out in joules, but AP exam questions almost always request $\Delta H$ in kJ/mol.
Why: Students confuse total heat capacity of the calorimeter with specific heat, which requires a mass term.
Why: Students mix up which system absorbs vs releases heat: if the reaction releases heat, the calorimeter absorbs it, so $q_{cal}$ is positive, $q_{rxn}$ must be negative.