Difficulty: Intermediate | Prerequisites: basic understanding of chemical reactions, moles, gas laws.
Thermochemistry sits at the intersection of chemistry and physics. It asks a deceptively simple question: where does the energy go when a chemical reaction happens? This chapter builds the tools to track energy in and out of a system, which matters for everything from industrial processes to understanding why your hand feels cold when you hold an ice pack. You should already be comfortable with balancing equations and working in moles.
Thermochemistry tracks the energy that flows in and out of chemical reactions, mostly as heat. The first law of thermodynamics says energy is conserved: whatever leaves the system enters the surroundings, and vice versa. The main tools are enthalpy (H), Hess's law, standard enthalpies of formation, and calorimetry, all of which let you calculate how much heat a reaction produces or absorbs.
Internal energy (E)
The total energy of a system, equal to the sum of its kinetic and potential energies. In simple terms, it is everything the particles in your system have, from their motion to the forces holding them together. A lower internal energy means a more stable system.
First law of thermodynamics
Energy cannot be created or destroyed; the total energy of the universe is constant. Think of it as a strict accounting rule: every joule that leaves one place must show up somewhere else.
Heat (q)
Energy transferred between a system and its surroundings because of a temperature difference. Positive q means the system absorbs heat; negative q means the system releases heat.
Work (w)
Energy transferred when a force acts over a distance. In chemistry this usually means pressure-volume (PV) work, such as a gas expanding against external pressure. Positive w means work is done on the system; negative w means the system does work on its surroundings.
Enthalpy (H)
Defined as H = E + PV. At constant pressure, the change in enthalpy equals the heat exchanged: ΔH = q_p. Think of it as the "heat content" of a reaction at constant pressure, which is how most lab and real-world reactions run.
Extensive property
A property whose value depends on the amount of substance present. Enthalpy is extensive: double the moles, double the ΔH.
Endothermic process
A process that absorbs heat from the surroundings (ΔH is positive). Bonds are being broken and the system needs energy input. The surroundings cool down.
Exothermic process
A process that releases heat to the surroundings (ΔH is negative). New bonds form and the system gives off energy. The surroundings warm up.
State function
A property that depends only on the current state of the system, not on how it got there. E and H are both state functions. In simple terms, it does not matter which route you took; the starting point and endpoint are all that count.
Hess's law
If a reaction can be expressed as the sum of two or more steps, the overall ΔH is the sum of the ΔH values of those steps. This works because enthalpy is a state function.
Standard state
The reference conditions used when tabulating thermodynamic data: 1 atm for gases, 1 mol/L for solutions, and the most stable form of an element at 1 atm and 298 K.
Standard enthalpy of formation (ΔH°f)
The enthalpy change when one mole of a compound is formed from its elements in their standard states. By definition, ΔH°f for any element in its standard state is zero.
Specific heat capacity (c)
The amount of heat needed to raise the temperature of one gram of a substance by one degree (units: J/(g·K)). In simple terms, it tells you how stubborn a material is about changing temperature. Water has a famously high specific heat.
Calorimetry
The experimental measurement of heat changes in a reaction. A "coffee cup" calorimeter measures heat at constant pressure, so q_p = ΔH for the process.
E (internal energy) = kinetic energy + potential energy of all particles in the system.
A lower energy state is more stable; systems tend toward lower energy.
The total energy of the universe is constant: E_universe = E_system + E_surroundings = 0.
Energy is neither created nor destroyed, only transferred between system and surroundings.
ΔE = q + w, where q is heat and w is work.
q positive: system absorbs heat from surroundings.
q negative: system releases heat to surroundings.
w positive: work done on the system (surroundings push in).
w negative: work done by the system (system expands out).
w = –PΔV (external pressure times the change in volume).
Alternatively, for reactions involving gases: w = Δn·R·T, where Δn is the change in moles of gas and R = 8.314 J/(mol·K).
When external pressure drops, the system can expand and do work on the surroundings (w is negative).
H = E + PV.
At constant pressure, ΔH = q_p (the heat measured at constant pressure).
Enthalpy is an extensive property: scale the amount of substance, and ΔH scales with it.
Endothermic: ΔH > 0. The system absorbs heat. Energy goes in to break bonds. Heat appears as a reactant in a thermochemical equation.
Exothermic: ΔH < 0. The system releases heat. Energy comes out as bonds form. Heat appears as a product in a thermochemical equation.
For reactions involving only liquids and solids, Δ(PV) ≈ 0, so ΔH ≈ ΔE.
If the number of moles of gaseous reactants equals the number of moles of gaseous products, ΔH ≈ ΔE as well.
They diverge when Δn_gas is not zero.
Endothermic: heat is written on the left (as a reactant).
Exothermic: heat is written on the right (as a product).
The stoichiometric coefficients refer to moles, and ΔH is proportional to those coefficients.
A state function depends only on the current state, not the route taken to get there.
E and H are state functions; q and w individually are not.
This is why Hess's law works: the overall ΔH depends only on initial and final states.
If a reaction can be written as a sum of steps, the total ΔH is the sum of the ΔH values of those steps.
Practical approach: flip reactions (change the sign of ΔH), multiply them (multiply ΔH by the same factor), then add.
Standard state: 1 atm for gases, 1 mol/L for solutions, most stable form of an element at 298 K.
ΔH°f for any element in its standard state is zero by definition (e.g. O₂(g), Na(s)).
For a reaction: ΔH°_rxn = Σ[ΔH°f(products)] – Σ[ΔH°f(reactants)].
Each ΔH°f value must be multiplied by its stoichiometric coefficient from the balanced equation.
Specific heat capacity: c = q / (m · ΔT). Units are J/(g·K).
"Coffee cup" calorimetry runs at constant pressure, so the measured heat equals ΔH.
q_p = c · m · ΔT, where ΔT = T_final – T_initial.
Mixing problems: when two bodies at different temperatures are combined, heat lost by the hot body equals heat gained by the cold body (assuming no heat escapes).
\Delta E = q + ww = -P \Delta Vw = \Delta n \cdot R \cdot T \quad (R = 8.314\;\text{J/(mol·K)})H = E + PV\Delta H = q_p \quad (\text{at constant pressure})\Delta H^\circ_{\text{rxn}} = \sum \Delta H^\circ_f(\text{products}) - \sum \Delta H^\circ_f(\text{reactants})c = \frac{q}{m \cdot \Delta T}q_p = c \cdot m \cdot \Delta T \quad (\Delta T = T_{\text{final}} - T_{\text{initial}})Calorimetry is how food scientists measure the energy (calories) in food: burn it, measure the heat, and you know its energy content. Hess's law and standard enthalpies of formation are how chemical engineers design heat exchangers, size reactors, and predict whether a process will need cooling or heating.
Students often confuse the sign of q with the sign of ΔT. A negative q does not mean the temperature dropped; it means the system released heat. The surroundings may warm up.
"Exothermic" does not mean "explosive." Many gentle, everyday reactions (like dissolving NaOH in water) are exothermic.
Students sometimes forget that ΔH°f values must be multiplied by stoichiometric coefficients before summing. The table gives per-mole values.
Hess's law does not require the intermediate steps to be physically real. They are a mathematical convenience; the only requirement is that the overall equation balances.
⚠️ Sign conventions for q and w are tested constantly. Know the system-centric convention cold.
⚠️ Be able to combine reactions using Hess's law: flip, scale, add. Watch signs carefully when you reverse a reaction.
⚠️ Calorimetry calculations (q = mcΔT) appear on virtually every exam. Make sure ΔT = T_final – T_initial, not the other way round.
⚠️ Standard enthalpy of formation for an element in its standard state is always zero. This is a common multiple-choice trap.
⚠️ Know when ΔH ≈ ΔE (reactions with no change in moles of gas, or reactions involving only liquids/solids).
True or false: Enthalpy is a state function.
True.
Fill in the blank: When a gas expands against external pressure, w is ______ (positive/negative).
Negative.
True or false: ΔH°f for O₂(g) is zero.
True.
Fill in the blank: In an endothermic reaction, heat is written as a ______ in the thermochemical equation.
Reactant (left side).
True or false: q and w are both state functions.
False. q and w are path-dependent; only ΔE and ΔH are state functions.
Q: A reaction has ΔH = –285.8 kJ/mol. Is it endothermic or exothermic, and will the surroundings warm up or cool down?
A: Exothermic (negative ΔH). The surroundings warm up because the system releases heat.
Q: Using Hess's law, if Reaction 1 has ΔH = +100 kJ and Reaction 2 has ΔH = –250 kJ, what is ΔH for the overall reaction (Reaction 1 + Reaction 2)?
A: ΔH = +100 + (–250) = –150 kJ.
Q: Calculate the heat absorbed when 200 g of water (c = 4.184 J/(g·K)) is heated from 25.0 °C to 75.0 °C.
A: q = mcΔT = 200 g × 4.184 J/(g·K) × 50.0 K = 41,840 J (about 41.8 kJ).
Q: The standard enthalpy of formation of CO₂(g) is –393.5 kJ/mol and that of H₂O(l) is –285.8 kJ/mol. What is ΔH°f for O₂(g)?
A: Zero. O₂ in the gas phase is an element in its standard state.
Q: A system does 150 J of work on its surroundings and absorbs 200 J of heat. What is ΔE?
A: ΔE = q + w = +200 J + (–150 J) = +50 J.
This connects to quantum theory (Chapter 7) because the energy of photons and the quantisation of energy levels build directly on the idea that energy comes in discrete amounts. Thermochemistry also feeds forward into chemical kinetics and equilibrium: ΔH tells you whether a reaction is energetically favourable, while later chapters address how fast it happens and how far it goes.
Thermochemistry, enthalpy, ΔH, heat of reaction, Hess's law, calorimetry, specific heat capacity, endothermic, exothermic, internal energy, first law of thermodynamics, state function, standard enthalpy of formation, ΔH°f, PV work, coffee cup calorimeter, constant pressure calorimetry, thermochemical equation, energy conservation, general chemistry, UMN, University of Minnesota