Lesson 1 · 25 min

Energy, heat and enthalpy

System and surroundings exchange energy in only two ways: heat and work. Enthalpy turns heat at constant pressure into a state function, so exothermic and endothermic changes fit on one energy-level diagram.

In this lesson

Separate system from surroundings and name the two ways energy crosses between them: heat and work
Keep the energy books with the first law ΔU = q + w, using the sign convention correctly
Explain why enthalpy equals the heat at constant pressure and convert with ΔH = ΔU + Δn(g)RT
Draw enthalpy-level diagrams for exothermic and endothermic reactions and say what a state function is

Tear open a hand warmer and it heats up: the iron powder inside slowly rusts in air, $\ce{4Fe} + \ce{3O2} \mathrel{\ce{->}} \ce{2Fe2O3}$ , releasing about 7.4 kJ for every gram of iron. Squeeze a sports cold pack and it turns icy: ammonium nitrate dissolves in water, drawing 25.7 kJ per mole from its surroundings. Both happen by themselves, yet one sends heat out and the other pulls heat in. To say exactly where the energy goes we first draw a boundary, then keep books on every transfer across it.

Predict first

One mole of zinc dissolves in acid: $\ce{Zn(s) + 2H+(aq)} \longrightarrow \ce{Zn^2+(aq) + H2(g)}$ . Once in a sealed rigid flask (constant volume), once under a freely moving piston (constant 1 bar). Which run gives more heat to the surroundings?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

The sealed flask (constant volume) gives more heat The piston flask (constant pressure) gives more heat Exactly the same: one reaction, one amount of heat

System, surroundings and the first law

The system is the part we care about — the reactants and products in the flask; everything else (the flask, the water bath, the air) is the surroundings. Together they make “the universe”. By what can cross the boundary, a system is:

open: matter and energy both cross (an open cup of hot tea);
closed: energy crosses but matter does not (a stoppered bottle);
isolated: nothing crosses (an ideal vacuum flask).

Energy can cross the boundary in only two ways: heat $q$ , which flows because of a temperature difference, and work $w$ , every other kind of transfer — pushing a piston, driving a current. The energy stored in the system itself is its internal energy $U$ , the sum of all molecular kinetic and potential energies. Conservation of energy then says:

\Delta U = q + w

The first law of thermodynamics. This site uses the IUPAC convention: heat into the system and work done on the system are both positive.

$\Delta U$: change in the system’s internal energy
$q$: heat absorbed by the system (negative when it gives heat out)
$w$: work done on the system (negative when the system expands and does work)

The most common work in chemistry is expansion work: gas produced pushes the outside world back, $w = -p_\mathrm{ext}\Delta V$ . For ideal gases at constant temperature and pressure, $p\Delta V = \Delta n(\mathrm{g})RT$ , where $\Delta n(\mathrm{g})$ is the change in moles of gas. At 298 K, $RT = 2.48$ kJ/mol — small beside reaction heats of hundreds of kJ, but not zero. The volume changes of solids and liquids are small enough to ignore.

Enthalpy: the heat at constant pressure

Almost every bench reaction runs open to the atmosphere, at constant pressure. The heat measured then, $q_p$ , contains the change in internal energy minus the work the system did pushing the atmosphere back. To avoid counting that work separately every time, chemists define a new quantity — enthalpy, $H = U + pV$ . At constant pressure, $\Delta H = \Delta U + p\Delta V = q_p$ : the enthalpy change is the heat at constant pressure.

Like internal energy, enthalpy is a state function: its change depends only on the start and the finish, not on the path — just as the difference in altitude between two towns does not depend on which mountain road you take. Heat and work are not state functions: one change can split its energy between $q$ and $w$ in different ways (the zinc above), but their sum $\Delta U$ is fixed.

\Delta H = \Delta U + \Delta(pV) \approx \Delta U + \Delta n(\mathrm{g})\,RT

ΔH and ΔU differ only when the amount of gas changes; for reactions in solution and between solids they are almost equal.

$\Delta n(\mathrm{g})$: moles of gaseous products minus moles of gaseous reactants
$R$: gas constant, 8.314 J/(K·mol)
$T$: thermodynamic temperature / K

First law ΔU = q + w · data from the formation table

The energy ledger: heat, work and enthalpy

Reaction (1 mol as written)

Extent of reaction ξ · 1.00

$\ce{CH4(g)} + 2\,\ce{O2(g)} \longrightarrow \ce{CO2(g)} + 2\,\ce{H2O(l)}$ Change in moles of gas Δn(g) = −2

Exothermic: heat flows to the surroundings

Heat q (into the system +) −890.6 kJ
Work w (done on the system +) +4.96 kJ
Internal energy change ΔU = q + w −885.6 kJ
Enthalpy change ΔH = ΔU + Δn(g)RT −890.6 kJ

Work is only 0.6% of ΔH

Try other reactions: methane combustion loses gas (Δn = −2), so the atmosphere does work on the system and more heat comes out at constant pressure than ΔU; limestone releases CO₂ and must absorb heat and do work; neutralisation has no gas change, so w = 0 and ΔH = ΔU. Drag the extent of reaction and watch the bath temperature follow.

Exothermic, endothermic and enthalpy diagrams

A reaction with $\Delta H < 0$ is exothermic: the products have less enthalpy than the reactants, and the difference flows into the surroundings as heat, warming them. With $\Delta H > 0$ the reaction is endothermic: the system absorbs heat and the surroundings cool. Draw reactants and products as two levels at different heights with an arrow between them and you have an enthalpy-level diagram.

When writing a thermochemical equation, remember three things:

give every state — $\ce{H2O(l)}$ and $\ce{H2O(g)}$ differ by 44 kJ/mol in enthalpy;
$\Delta H$ refers to one mole of reaction as written; double the equation and $\Delta H$ doubles;
run the reaction backwards and $\Delta H$ keeps its size but changes sign.

ΔrH° of some reactions (298 K, per equation as written; from standard enthalpies of formation)
Reaction	ΔrH° / kJ	Type
$\ce{CH4(g) + 2O2(g)} \longrightarrow \ce{CO2(g) + 2H2O(l)}$	−890.6	exothermic
$\ce{4Fe(s) + 3O2(g)} \longrightarrow \ce{2Fe2O3(s)}$	−1648.4	exothermic (hand warmer)
$\ce{H+(aq) + OH-(aq)} \longrightarrow \ce{H2O(l)}$	−55.8	exothermic (neutralisation)
$\ce{NH4NO3(s)} \longrightarrow \ce{NH4+(aq) + NO3-(aq)}$	+25.7	endothermic (cold pack)
$\ce{CaCO3(s)} \longrightarrow \ce{CaO(s) + CO2(g)}$	+179.2	endothermic (lime kiln)
$\ce{6CO2(g) + 6H2O(l)} \longrightarrow \ce{C6H12O6(s) + 6O2(g)}$	+2802.7	endothermic (photosynthesis)

Source: Computed from the 298.15 K formation data in the atlas table “Standard thermodynamic data” (CODATA 1989; NBS 1982; CRC Handbook, 97th ed.).

Worked example

ΔU for burning methane

For $\ce{CH4(g) + 2O2(g)} \longrightarrow \ce{CO2(g) + 2H2O(l)}$ , $\Delta H^\circ = -890.6$ kJ. Find $\Delta U^\circ$ at 298 K and say which way the work flows when it burns at constant pressure.

Concept check

Limestone decomposes in an open kiln: $\ce{CaCO3(s)} \longrightarrow \ce{CaO(s) + CO2(g)}$ , $\Delta H^\circ = +179.2$ kJ. What are the signs of q and w for the system?

q > 0, w > 0 q > 0, w < 0 q < 0, w < 0 q < 0, w > 0

Try the calculation

Using $\Delta H^\circ = +179.2$ kJ, calculate $\Delta U^\circ$ (kJ) for $\ce{CaCO3(s)} \longrightarrow \ce{CaO(s) + CO2(g)}$ at 298.15 K.

Key takeaways

Energy crosses the system boundary only as heat q and work w; ΔU = q + w (into the system is positive).
Enthalpy H = U + pV is a state function; at constant pressure ΔH = q_p, at constant volume ΔU = q_V.
ΔH ≈ ΔU + Δn(g)RT: they differ only when the amount of gas changes, by about 2.5 kJ per mole of gas at 298 K.
ΔH < 0 is exothermic and warms the surroundings; ΔH > 0 is endothermic and cools them; doubling the equation doubles ΔH, reversing it flips the sign.

Progress is stored only in this browser and never uploaded.

Data and references

P. Atkins, J. de Paula, J. Keeler, Atkins’ Physical Chemistry, 11th ed., Oxford (2018), Topics 2A–2B (internal energy, enthalpy).
J. D. Cox, D. D. Wagman, V. A. Medvedev, CODATA Key Values for Thermodynamics, Hemisphere (1989).
D. D. Wagman et al., “The NBS tables of chemical thermodynamic properties”, J. Phys. Chem. Ref. Data 11, Suppl. 2 (1982).
IUPAC, Quantities, Units and Symbols in Physical Chemistry (Green Book), 3rd ed. (2007), §2.11 (sign convention for work).