Unit 6: Thermochemistry
Thermochemistry studies heat flow associated with chemical reactions and physical changes (melting, vaporization, dissolving). It is the chemical face of the first law of thermodynamics and sets up enthalpy reasoning used again in equilibrium, acid–base, and thermodynamics / electrochemistry. Balanced equations and stoichiometry from Unit 4 carry mole ratios directly into thermochemical calculations.
System, surroundings, and boundaries
In modeling, the universe is split into the system (what you study) and the surroundings (everything else that can exchange energy with the system). A closed system exchanges energy but not matter across its boundary. An open system can exchange both (an open beaker). An isolated system exchanges neither, and this can be approximated by good calorimeter insulation.
Energy, heat, and work
Heat and Calorimetry
Energy is the capacity to do work or transfer heat. The total energy of an isolated universe is conserved (First Law of Thermodynamics); it is not useful to set “\(E_{\text{universe}} = 0\)” unless you have chosen a specific reference for potential energy.
Heat \(q\) is energy transferred because of a temperature difference. On the AP exam the usual sign convention is from the system’s perspective: \(q_{\text{sys}} > 0\) when heat flows into the system, \(q_{\text{sys}} < 0\) when heat flows out. Spontaneous heat transfer between two objects in thermal contact goes from hotter to colder until thermal equilibrium (related 0th Law of Thermodynamics).
For a pure substance with nearly constant specific heat capacity \(c\),
\[q = mc\Delta T,\]where \(m\) is mass and \(\Delta T\) is temperature change. For water near room temperature, \(c \approx 4.18 \text{ J/(g}\cdot^\circ\text{C)}\) (often \(4.184\) in tables). A coffee-cup calorimeter at constant pressure approximates \(q_{\text{reaction}} \approx -\left(m_{\text{solution}}c_{\text{solution}}\Delta T + C_{\text{cal}}\Delta T\right)\) for the reaction inside, where \(C_{\text{cal}}\) is the calorimeter constant (energy per kelvin for the apparatus), which is like a calibration/error term because calorimeters aren’t perfect insulators. Matching system and surroundings gives
\[q_{\text{sys}} = -q_{\text{surr}}\]when no other work or losses matter (Conservation of energy/matter).
Work and Potential Energy
Work in gas problems often means pressure–volume work (e.g. expansion of a piston). For expansion against constant external pressure,
\[W = -P_{\text{ext}}\Delta V\]for work done on the system (AP-style). Internal energy change obeys the First Law of Thermodynamics:
\[\Delta U = q + W.\]At constant volume (isochoric processes), \(\Delta V = 0\) so \(W = 0\) and \(\Delta U = q\).
Phase changes and heating curves
During melting or boiling at fixed pressure, temperature stays constant while latent heat is absorbed or released:
\[q = n\Delta H_{\text{fus}}, \qquad q = n\Delta H_{\text{vap}},\]with molar enthalpies of fusion and vaporization. A heating curve (temperature vs heat added) shows slopes \(1/(mc)\) and plateaus at phase changes.
Enthalpy
Enthalpy \(H\) is defined as \(H = U + PV\). It is a state function. For a process at constant pressure the change in enthalpy becomes:
\[\Delta H = \Delta U + P\Delta V.\]However, you will usually see enthalpy in the context of heat for AP Chemistry problems, so
\[\Delta H_{\text{rxn}} = \frac{q_{\text{sys}}}{n}.\]where \(n\) is the number of moles, and enthalpy is from the perspective of the system. At constant pressure, \(\Delta H = q_p\) for the system, so it has the same sign as \(q_{\text{sys}}\). It has the opposite sign of the heat change measured for the surroundings in a coffee-cup calorimeter:
\[q_{\text{rxn}} = q_{\text{sys}} = -q_{\text{surr}}.\]Exothermic versus endothermic
In an exothermic reaction, the system evolves so that heat flows out to the surroundings: \(\Delta H < 0\), \(q_{\text{sys}} < 0\), and \(q_{\text{surr}} > 0\).
In an endothermic reaction, the system draws heat in: \(\Delta H > 0\), \(q_{\text{sys}} > 0\), and \(q_{\text{surr}} < 0\).
Always label whether \(q\) refers to system or surroundings when you compare signs across textbooks.
State functions and path
Enthalpy is a state function. State functions depend only on initial and final states, not the path: \(P\), \(V\), \(T\), \(U\), \(H\), and (later) entropy \(S\) and Gibbs free energy \(G\). Heat \(q\) and work \(W\) are path-dependent; their sum \(\Delta U = q + W\) is not.
Standard enthalpies and formation
Standard state means specified reference conditions (For AP: \(1\) atm for gases, \(1\text{ M}\) for solutes in solution chemistry, pure substances in their stable form at \(25^\circ\text{C}\) unless noted). The standard enthalpy of formation \(\Delta H_f^\circ\) is \(\Delta H\) for forming one mole of a compound from its elements in their standard states. Elements in their reference/naturally occuring forms have \(\Delta H_f^\circ = 0\) by definition.
For any reaction,
\[\Delta H_{\text{rxn}}^\circ = \sum \nu\,\Delta H_f^\circ(\text{products}) - \sum \nu\,\Delta H_f^\circ(\text{reactants}),\]where \(\nu\) are stoichiometric coefficients. Thermochemical equations can be scaled; \(\Delta H\) scales with the mole amounts written in the equation.
Hess’s law
Hess’s law states that \(\Delta H\) for an overall process is the sum of \(\Delta H\) values for steps that add up to the same net reaction—because \(H\) is a state function. Reverse a step → flip the sign of \(\Delta H\). Multiply a step by a factor → multiply \(\Delta H\) by the same factor.
Bond enthalpies (estimates)
Bond enthalpy (or bond energy) is the energy required to break one mole of a bond in the gas phase (averaged over similar molecules for tabulated values). For gas-phase estimates,
\[\Delta H_{\text{rxn}} \approx \sum D(\text{bonds broken}) - \sum D(\text{bonds formed}),\]using positive bond energies for each bond listed. This ignores liquids, solvents, and exact environments, so it is less accurate than calorimetry or formation cycles.
Solution formation (preview)
\(\Delta H_{\text{solution}}\) combines lattice (endothermic breakup of solid) and hydration (exothermic ion–solvent interaction) terms. A slightly endothermic \(\Delta H_{\text{solution}}\) can still occur if entropy favors mixing (full explanation in later units). A very endothermic process may give negligible solubility unless entropy dominates strongly.
Vapor pressure and the Clausius–Clapeyron relation
The Clausius–Clapeyron equation relates vapor pressure to temperature for a liquid (using molar enthalpy of vaporization \(\Delta H_{\text{vap}}\) as approximately constant over a modest range):
\[\ln\left(\frac{P_2}{P_1}\right) = -\frac{\Delta H_{\text{vap}}}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right).\]Higher \(T\) increases vapor pressure; stronger IMFs tend to lower vapor pressure at a given \(T\) (see Unit 3). This formula will likely not appear on the AP test, but is good to know