Energy and its forms
Chemical thermodynamics rests on the concept of energy — a conserved quantity per the first law. A thermodynamic system is the portion of matter under study; the rest is the surroundings. Systems are classified as:
- Isolated: neither matter nor energy is exchanged.
- Closed: energy (work, heat) is exchanged but not matter.
- Open: both matter and energy are exchanged.
State functions depend only on the current state, not on the path taken. Internal energy U, enthalpy H, entropy S, and Gibbs energy G are all state functions.
First law: conservation of energy
For a closed system, the change in internal energy ΔU is:
ΔU = Q + W
where Q is the heat received and W is the work received (IUPAC sign convention: positive when received by the system). For an infinitesimal change: dU = δQ + δW.
Mechanical work of compression/expansion: W = −∫ P_ext dV.
At constant volume (rigid container): W = 0, so ΔU = Q_v.
Enthalpy — the right function for constant pressure
Most chemical reactions occur at constant pressure (atmospheric). Enthalpy is defined as:
H = U + PV → ΔH = ΔU + Δ(PV)
For an ideal gas, Δ(PV) = Δn_gas · RT, where Δn_gas is the change in moles of gas.
At constant pressure: ΔH = Q_p (the heat exchanged at constant pressure equals the enthalpy change).
| Condition | Measured quantity |
|---|---|
| V = const (bomb calorimeter) | Q_v = ΔU |
| P = const (most reactions) | Q_p = ΔH |
Quantitative calorimetry
Calorimetry measures Q from the temperature change: Q = C · ΔT, where C is the heat capacity of the system (J·K⁻¹). For a mass m of a substance with specific heat c_p: Q = m · c_p · ΔT.
Standard enthalpies (standard state: pure substances, T = 298.15 K, P° = 100 kPa): - Standard enthalpy of formation Δ_f H°: formation of 1 mol of compound from elements in their reference states. - Δ_f H° = 0 for elements in their reference state. - Hess's law: ΔH°_{reaction} = Σ Δ_f H°(products) − Σ Δ_f H°(reactants).
Example: methane combustion: CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H₂O(l) ΔH°_comb = Δ_f H°(CO₂) + 2 Δ_f H°(H₂O) − Δ_f H°(CH₄) − 0 = (−393.5) + 2(−285.8) − (−74.8) = −890.3 kJ·mol⁻¹
Thermodynamic cycles and Hess's law
Hess's law exploits the fact that H is a state function: ΔH is path-independent. Reaction equations and their ΔH values can therefore be added to calculate an unmeasurable ΔH.
Useful cycles: - Born-Haber cycle: calculate the lattice energy of ionic solids (NaCl, etc.). - General Hess cycle: route through intermediates with known Δ_f H°.
"The energy of the universe is constant." — Rudolph Clausius (paraphrase of the first law)
First-law thermodynamics says nothing about the spontaneity of reactions — that is the role of the second law and G = H − TS.