Systems and surroundings
The part of the universe we study is the system; the rest is the surroundings.
Type of system | Exchanges energy? | Exchanges matter? | Example |
|---|---|---|---|
Open | yes | yes | reactants in an open beaker |
Closed | yes | no | reactants in a sealed metal flask |
Isolated | no | no | an ideal thermos flask |
State functions depend only on the state of the system, not on how it got there: U, H, S, G, P, V, T. Path functions depend on the route: heat q and work w.
Extensive properties depend on the amount of matter (mass, volume, U, H). Intensive properties don't (temperature, pressure, density, molar heat capacity).
The first law in chemistry
ΔU = q + w
In chemistry the sign convention is taken from the system's point of view: q is positive when heat is absorbed by the system, and w is positive when work is done on the system.
For expansion against a constant external pressure, w = −p_ext ΔV.
At constant volume, w = 0, so ΔU = qᵥ. ΔU is measured in a bomb calorimeter.
Enthalpy
Most reactions happen at constant pressure, open to the atmosphere. The heat absorbed at constant pressure is the enthalpy change:
H = U + pV, so ΔH = ΔU + pΔV = qₚ
For reactions involving gases, ΔH = ΔU + Δn_g RT, where Δn_g = moles of gaseous products − moles of gaseous reactants.
Example. For N₂(g) + 3H₂(g) → 2NH₃(g), Δn_g = 2 − 4 = −2, so ΔH is less than ΔU by 2RT.
Exothermic reactions release heat: ΔH < 0 (burning fuels).
Endothermic reactions absorb heat: ΔH > 0 (decomposing CaCO₃).
Standard enthalpies
The standard state of a substance is its pure, most stable form at 1 bar (usually quoted at 298 K). Standard enthalpies are marked ΔH°.
Enthalpy | Definition | Example |
|---|---|---|
Standard enthalpy of formation, ΔfH° | change when 1 mol of a compound forms from its elements in their standard states | ½N₂ + 3⁄2 H₂ → NH₃ |
Standard enthalpy of combustion, ΔcH° | change when 1 mol of a substance burns completely in oxygen | CH₄ + 2O₂ → CO₂ + 2H₂O |
Enthalpy of atomisation | change when 1 mol of bonds is broken completely to give gaseous atoms | H₂(g) → 2H(g) |
Enthalpy of fusion / vaporisation | change on melting / boiling 1 mol at constant temperature | H₂O(s) → H₂O(l) |
By convention, ΔfH° of an element in its standard state is zero.
From formation enthalpies:
ΔrH° = Σ ΔfH°(products) − Σ ΔfH°(reactants)
Hess's law
If a reaction takes place in several steps, its overall enthalpy change is the sum of the enthalpy changes of the steps, whatever the route taken.
This follows because H is a state function. It lets us find enthalpies that are hard to measure directly.
Example. The enthalpy of formation of CO can't be measured directly, because carbon burns partly to CO₂. But:
C(graphite) + O₂ → CO₂; ΔH = −393.5 kJ/mol
CO + ½O₂ → CO₂; ΔH = −283.0 kJ/mol
Subtracting the second from the first: C + ½O₂ → CO; ΔH = −393.5 − (−283.0) = −110.5 kJ/mol.
Bond enthalpies
Breaking bonds absorbs energy and forming bonds releases it. For gas-phase reactions:
ΔrH° ≈ Σ bond enthalpies of reactants − Σ bond enthalpies of products
Spontaneity and entropy
A spontaneous process happens by itself, without outside help, once started: water flows downhill, ice melts at room temperature, gases mix. Spontaneous doesn't mean fast.
Being exothermic is not enough to decide spontaneity: ice melting is endothermic yet spontaneous above 0 °C.
Entropy (S) measures the disorder or randomness of a system. Gases have more entropy than liquids, and liquids more than solids. Dissolving, melting, evaporating and reactions that produce more gas molecules usually increase entropy.
For a reversible process at temperature T: ΔS = q_rev ⁄ T.
Second law: the total entropy of the system and surroundings increases in every spontaneous process.
Third law: the entropy of a perfectly crystalline substance at absolute zero is zero.
Gibbs energy
To judge spontaneity using only the system's properties, we use the Gibbs energy: G = H − TS. At constant temperature and pressure:
ΔG = ΔH − TΔS
ΔG < 0: spontaneous
ΔG > 0: non-spontaneous (the reverse is spontaneous)
ΔG = 0: at equilibrium
ΔH | ΔS | ΔG | Spontaneous? |
|---|---|---|---|
− | + | always − | at all temperatures |
+ | − | always + | never |
− | − | − at low T | at low temperatures |
+ | + | − at high T | at high temperatures |
Example. For a reaction with ΔH = +30 kJ/mol and ΔS = +100 J/K/mol, ΔG = 0 when T = 30,000 ⁄ 100 = 300 K. Above 300 K the reaction is spontaneous.
Gibbs energy and equilibrium: ΔG° = −RT ln K = −2.303 RT log K. A large negative ΔG° means a large equilibrium constant, so the reaction goes nearly to completion.
Summary
ΔU = q + w; at constant volume ΔU = qᵥ; at constant pressure ΔH = qₚ; ΔH = ΔU + Δn_g RT.
Hess's law: enthalpy changes add up along any route.
Entropy measures disorder; total entropy rises in spontaneous processes.
ΔG = ΔH − TΔS < 0 for a spontaneous process; ΔG° = −RT ln K.