Thermochemistry and Energetics

Thermochemistry is the study of heat changes that accompany physical and chemical processes. For the MCAT you should know the vocabulary (system, surroundings, state functions), the first and second laws of thermodynamics, the difference between ΔU and ΔH, calorimetry (q = mcΔT), Hess's law and bond enthalpies, and—most heavily tested of all—entropy (S) and Gibbs free energy (ΔG = ΔH − TΔS) as the predictor of spontaneity.

Thermodynamics

Thermodynamics is the branch of science that deals with energy changes accompanying physical and chemical processes, especially the inter-conversion of heat and work. Chemical thermodynamics applies these ideas to chemical reactions; the predictions are independent of the path or the rate.

System / Surrounding / State Function Terms

System

The portion of the universe under study (e.g. the chemicals in a beaker).

Surroundings

Everything outside the system that can interact with it.

Boundary

The real or imaginary surface separating system from surroundings.

Open system

Exchanges both matter and energy with surroundings (e.g. boiling water in an open pan).

Closed system

Exchanges only energy, not matter (e.g. a stoppered flask).

Isolated system

Exchanges neither matter nor energy (e.g. a perfect thermos flask — an idealization).

State function

Property whose value depends only on the present state of the system, not on how it got there. Examples: U, H, S, G, T, P, V.

Path function

Property whose value depends on the path taken between states. Examples: q (heat) and w (work).

Standard state

Pure substance at 1 atm (101.3 kPa) and a specified temperature, conventionally 298 K. Quantities measured under these conditions are denoted by a degree sign, e.g. ΔH°.

Internal Energies

The internal energy U of a system is the total energy stored in it — the sum of the kinetic energies of all particles plus the potential energies of all interactions (intermolecular forces, bonds). U is a state function. Its absolute value cannot be measured, but changes ΔU can.

For a chemical reaction at constant volume in a closed system, the heat absorbed equals ΔU:

ΔU = q_v (no expansion work)

This is what a bomb calorimeter measures.

First Law of Thermodynamics

The first law is the principle of conservation of energy applied to thermodynamic systems: energy can be transformed from one form to another but cannot be created or destroyed. Mathematically:

ΔU = q + w

Sign convention (IUPAC):

• q > 0 — heat absorbed by the system.
• q < 0 — heat released by the system.
• w > 0 — work done on the system (volume decreases).
• w < 0 — work done by the system on surroundings (expansion).

For pressure-volume (expansion) work at constant external pressure: w = −P_ext ΔV.

Enthalpy

Enthalpy H is defined as H = U + PV. Like U, H is a state function. The change in enthalpy at constant pressure equals the heat absorbed:

ΔH = q_p

This is why most laboratory reactions in open vessels are described by ΔH, not ΔU.

Relation between ΔH and ΔU

For reactions involving gases: ΔH = ΔU + Δn_gasRT, where Δn_gas = (moles of gaseous products) − (moles of gaseous reactants). For reactions with no change in moles of gas, ΔH ≈ ΔU.

Standard enthalpy changes

Calorimetry

Calorimetry measures heat flow from the temperature change of a known mass of water (or other substance). The core MCAT equation is:

q = m c ΔT

where q is heat (J), m is mass (g), c is the specific heat capacity (J g⁻¹ °C⁻¹; for water c = 4.18 J g⁻¹ °C⁻¹), and ΔT = T_final − T_initial. If molar heat capacity C is used, q = n C ΔT.

• Bomb calorimeter — constant volume; the heat released equals ΔU (q_v). A sealed steel "bomb" is surrounded by a water bath and ΔT is measured; q = (m c ΔT)_water + C_calΔT.
• Coffee-cup (open) calorimeter — constant pressure; the heat released equals ΔH (q_p). q_reaction = −q_water = −m c ΔT.

Exothermic and Endothermic Reactions

• Exothermic: system releases heat; ΔH < 0; products lie at lower energy than reactants. Examples: combustion (CH₄ + 2O₂ → CO₂ + 2H₂O, ΔH = −890 kJ mol⁻¹), neutralization, respiration, condensation.
• Endothermic: system absorbs heat; ΔH > 0; products at higher energy. Examples: photosynthesis, melting, evaporation, decomposition of CaCO₃, dissolving NH₄NO₃ (cold packs).

Hess's Law

Hess's law of constant heat summation (Germain Hess, 1840): the total enthalpy change for a reaction is independent of the route taken from reactants to products, provided the initial and final states are the same.

This is a direct consequence of enthalpy being a state function. It allows enthalpy changes that cannot be measured directly to be calculated from those that can.

General form

ΔH_reaction = ΣΔH°_f(products) − ΣΔH°_f(reactants)

Example — formation of CO

The direct combustion C(s) + ½O₂(g) → CO(g) cannot be measured cleanly because some CO₂ always forms. Hess's law lets us combine:

• (i) C(s) + O₂(g) → CO₂(g); ΔH₁ = −393.5 kJ
• (ii) CO(g) + ½O₂(g) → CO₂(g); ΔH₂ = −283.0 kJ

(i) − (ii): C(s) + ½O₂(g) → CO(g); ΔH_f(CO) = ΔH₁ − ΔH₂ = −110.5 kJ.

Applications of Hess's law

• Calculating ΔH_f of compounds that cannot be made directly from their elements.
• Calculating lattice energies via the Born–Haber cycle.
• Calculating bond enthalpies and resonance energies.

Bond Enthalpies

A bond enthalpy is the energy required to break one mole of a given bond in the gas phase; breaking bonds is always endothermic (+) and forming bonds is always exothermic (−). For a gas-phase reaction the MCAT lets you estimate ΔH from average bond enthalpies:

ΔH_rxn = Σ(bonds broken) − Σ(bonds formed)

Note the sign carefully: this is "bonds broken minus bonds formed" (reactant bonds minus product bonds), the opposite ordering of the ΔH°_f formula. Values are averages, so bond-enthalpy estimates are approximate.

Second Law and Entropy

The second law of thermodynamics states that the total entropy of the universe (system + surroundings) increases in any spontaneous process: ΔS_universe = ΔS_system + ΔS_surroundings > 0 for a spontaneous change, and = 0 at equilibrium.

Entropy S is a state function that measures the dispersal of energy and matter—often described as "disorder" or the number of accessible microstates. Units: J K⁻¹ mol⁻¹. The third law sets S = 0 for a perfect crystal at 0 K, so unlike H, absolute entropies (S°) can be tabulated.

• Entropy generally increases: solid → liquid → gas; dissolving a solid; heating; increasing the number of gas-phase molecules.
• ΔS°_rxn = ΣS°(products) − ΣS°(reactants).
• Quick sign check: if a reaction produces more moles of gas, ΔS_system > 0.

Gibbs Free Energy and Spontaneity

Combining the first and second laws gives the single most tested equation in MCAT thermodynamics—the Gibbs free energy, which folds both enthalpy and entropy into one spontaneity criterion at constant T and P:

How the signs of ΔH and ΔS set spontaneity

The crossover temperature at which a reaction switches between spontaneous and non-spontaneous is found by setting ΔG = 0, giving T = ΔH / ΔS.

Worked MCQs

Seven MCQs that capture the high-yield testing patterns for this chapter. Read the explanation even when you get the answer right — it's where the deeper concept lives.

Quick Recap

• State functions (U, H, S, G, T, P, V) are path-independent. q and w are not.
• First law: ΔU = q + w. At constant V: ΔU = q_v; at constant P: ΔH = q_p.
• Calorimetry: q = mcΔT; water c = 4.18 J g⁻¹ °C⁻¹. Bomb calorimeter → ΔU; coffee-cup → ΔH.
• ΔH_rxn = ΣΔH°_f(products) − ΣΔH°_f(reactants); from bonds, ΔH = Σ(broken) − Σ(formed).
• Exothermic ΔH < 0; endothermic ΔH > 0. Hess's law: ΔH_total is path-independent.
• Second law: ΔS_universe > 0 for a spontaneous process; entropy rises solid → liquid → gas.
• ΔG = ΔH − TΔS: ΔG < 0 spontaneous, ΔG = 0 equilibrium, ΔG > 0 non-spontaneous. ΔG° = −RT ln K.
• Crossover temperature (spontaneity flips) at T = ΔH / ΔS.