Thermochemistry and Energetics

Thermochemistry is the study of heat changes that accompany physical and chemical processes. The PMDC MDCAT 2026 syllabus tests the basic vocabulary (system, surroundings, state functions), the first law of thermodynamics, the difference between ΔU and ΔH, and especially the use of Hess's law to combine standard enthalpies. Expect 2-3 MCQs from this chapter.

PMC Table of Specifications. This chapter covers seven PMDC subtopics — Thermodynamics; System/Surrounding/State-function terms; Internal Energy; First Law; Enthalpy; Exo- vs Endothermic; Hess's Law. Skim the headings below to confirm full coverage.

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 idealisation).
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

Types of standard enthalpy change (per mole)
Type	Symbol	Definition	Sign
Formation	ΔH°_f	Forming 1 mol of compound from elements in standard states	Usually −ve (some +ve, e.g. NO)
Combustion	ΔH°_c	Complete combustion of 1 mol in excess O₂	Always −ve
Neutralisation	ΔH°_neut	1 mol H₂O formed from H⁺ + OH⁻ (dilute)	~ −57 kJ/mol (strong acid + strong base)
Solution	ΔH°_sol	1 mol solute dissolved in excess solvent	Can be + or −
Atomisation	ΔH°_at	1 mol of gaseous atoms formed from element	Always +ve
Bond enthalpy	ΔH°_BE	Energy to break 1 mol of a specific bond in gas phase	Always +ve
Lattice enthalpy	ΔH°_L	1 mol of ionic solid formed from gaseous ions	Always −ve (release of energy)
Hydration	ΔH°_hyd	1 mol of gaseous ions dissolved in water	Always −ve
Fusion / vaporisation	ΔH°_fus / ΔH°_vap	1 mol melted / vaporised	+ve (endothermic phase changes)

Calorimetry (qualitative)

Bomb calorimeter — constant volume; measures ΔU directly. Sealed steel "bomb" surrounded by water bath; ΔT measured.
Coffee-cup (open) calorimeter — constant pressure; measures ΔH directly. q = 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), neutralisation, 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.

Common trap. Heat (q) and work (w) are not state functions. Two reactions that go from the same start to the same end can absorb very different amounts of heat depending on whether they are run at constant pressure (q = ΔH) or constant volume (q = ΔU). Only U, H, S, G are path-independent.

Memory aid. "EXO leaves the system." Negative ΔH = exothermic = energy exits. Positive ΔH = endothermic = energy enters. Pair with: products lower than reactants ↔ exothermic.

Worked MCQs

Five 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.

Q1. Which of the following is NOT a state function?

Internal energy (U)
Enthalpy (H)
Work (w)
Pressure (P)

U, H, S, G, T, P, V are state functions — they depend only on the current state. Heat (q) and work (w) are path functions; the same change in state can involve different q and w depending on how the change is carried out.

Q2. The first law of thermodynamics is mathematically expressed as:

ΔG = ΔH − TΔS
ΔU = q + w
PV = nRT
ΔH = ΔU + PΔV

The first law is the conservation of energy: ΔU = q + w (heat added to the system + work done on the system). The other equations are real, but describe Gibbs free energy, the ideal gas law, and the H−U relation respectively.

Q3. An exothermic reaction is one in which:

ΔH is positive
ΔH is negative
ΔS is always negative
The system absorbs heat from surroundings

In an exothermic reaction the system loses heat to the surroundings, so ΔH < 0. Combustion, neutralisation and respiration are textbook examples.

Q4. Hess's law is a direct consequence of:

Conservation of mass
Heat being a path function
Enthalpy being a state function
The ideal gas law

Because H depends only on the initial and final states, the total ΔH for any path from reactants to products is the same. Hess's law allows you to add or subtract reaction enthalpies as if you were doing algebra.

Q5. For the reaction N₂(g) + 3H₂(g) → 2NH₃(g) at 298 K, Δn_gas equals:

+1
0
+2
−2

Δn_gas = (moles of gaseous products) − (moles of gaseous reactants) = 2 − (1 + 3) = −2. This is what enters ΔH = ΔU + Δn_gasRT.

Quick Recap

System / surroundings / boundary; open / closed / isolated.
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.
ΔH = ΔU + Δn_gasRT.
Exothermic ΔH < 0; endothermic ΔH > 0.
Standard enthalpies: ΔH°_f, ΔH°_c, ΔH°_neut (~−57 kJ mol⁻¹), ΔH°_sol.
Hess's law: ΔH_total independent of path; gives access to lattice energy via Born–Haber cycle.

Test yourself. Take a timed Thermochemistry quiz or browse all Chemistry MCQs to lock these concepts in.