Chemical energetics

📚The chemistry

AS energetics (topic 5) measured enthalpy changes and used Hess’s law. This topic applies Hess’s law to ionic compounds, which cannot be formed in one step from gaseous ions, and then asks a deeper question: why do some reactions happen and others not? The answer needs entropy as well as enthalpy.

23.1 Lattice energy and Born–Haber cycles

The new terms

• Standard enthalpy change of atomisation, ΔH_at^⦵ — the enthalpy change when one mole of gaseous atoms is formed from the element in its standard state. Na(s) → Na(g); ½Cl₂(g) → Cl(g). Always endothermic. For a diatomic gas it is half the bond energy: ΔH_at(Cl) = ½ × 242 = +121 kJ mol⁻¹.
• First electron affinity, EA — the enthalpy change when one electron is added to each atom in one mole of gaseous atoms, forming one mole of gaseous 1− ions: Cl(g) + e⁻ → Cl⁻(g). Usually exothermic.
• Lattice energy, ΔH_latt^⦵ — the enthalpy change when one mole of an ionic compound is formed from its gaseous ions: Na⁺(g) + Cl⁻(g) → NaCl(s). This syllabus defines it in the direction gas ions → solid, so lattice energies are always negative (exothermic).

Electron affinity: factors and trends

An electron is attracted by the nucleus, so adding one releases energy. The same factors as ionisation energy decide how much: nuclear charge, atomic radius (distance of the incoming electron from the nucleus) and shielding.

• Group 17: the first EA becomes less exothermic down the group from chlorine to iodine, because the incoming electron enters a shell further from the nucleus and more shielded. Fluorine is the exception: its EA is less exothermic than chlorine’s, because its atom is so small that the incoming electron is repelled strongly by the electrons already crowded in the second shell.
• Group 16: the same pattern — sulfur’s first EA is more exothermic than oxygen’s, for the same reason as Cl and F.
• Second electron affinities are endothermic. O⁻(g) + e⁻ → O²⁻(g) means forcing an electron onto an ion that is already negative, against repulsion. Energy must be put in.

Born–Haber cycles

Lattice energy cannot be measured directly. A Born–Haber cycle finds it by Hess’s law: forming the solid from its elements directly (ΔH_f) must equal forming it through gaseous atoms and then gaseous ions.

Build it in this order, drawn as an energy-level diagram with endothermic steps going up and exothermic steps going down:

1. elements in standard states (zero);
2. atomise the metal (up);
3. ionise the metal — first IE, and for a 2+ ion the second IE too (up);
4. atomise the non-metal — as many moles of atoms as the formula needs (up);
5. add electrons to the non-metal — first EA (down), and for a 2− ion the second EA (up);
6. the gaseous ions come together: lattice energy (a long way down) to the solid;
7. ΔH_f connects the elements directly to the solid.

For MgCl₂ remember the 2×: two chlorine atoms to atomise, two electron affinities. For MgO, the first and second EA of oxygen.

What controls the size of a lattice energy

Lattice energy comes from the electrostatic attraction between the ions, so it is more exothermic when:

• the ionic charges are larger — MgO (2+, 2−) has a lattice energy about four times that of NaCl (1+, 1−);
• the ions are smaller — they can get closer together. NaF is more exothermic than NaCl, and LiCl than KCl.

The two ideas are often combined as charge density: high charge on a small ion.

23.2 Enthalpies of solution and hydration

• Enthalpy change of hydration, ΔH_hyd^⦵ — the enthalpy change when one mole of gaseous ions dissolves in water to form an infinitely dilute solution: Na⁺(g) → Na⁺(aq). Always exothermic: water molecules are attracted to the ion (the δ− O to cations, the δ+ H to anions).
• Enthalpy change of solution, ΔH_sol^⦵ — the enthalpy change when one mole of an ionic solid dissolves in water to form an infinitely dilute solution: NaCl(s) → Na⁺(aq) + Cl⁻(aq). May be exothermic or endothermic.

The cycle: dissolving a solid is the same as breaking the lattice into gaseous ions (the reverse of lattice energy) and then hydrating the ions:

Hydration enthalpy follows the same rule as lattice energy: it is more exothermic for smaller, more highly charged ions, which attract water molecules more strongly. Mg²⁺ is hydrated far more exothermically than Na⁺, and Li⁺ more than K⁺.

23.3 Entropy

Entropy, S, is a measure of the number of possible arrangements of the particles and their energy in a system. The more ways the particles and their energy can be arranged, the higher the entropy. Standard entropies, S^⦵, are measured in J K⁻¹ mol⁻¹ (note: joules, not kilojoules) and are always positive.

Predicting the sign of ΔS:

• Change of state: solid → liquid → gas increases entropy (melting, boiling, sublimation: ΔS positive); the reverse decreases it. Dissolving a solid usually increases entropy, as the ions or molecules spread through the solvent.
• Temperature: heating a substance increases its entropy, because the particles have more energy and more ways of distributing it.
• Number of gas molecules: a reaction that increases the number of gas molecules has a positive ΔS. Gases dominate, because gas particles have far more possible arrangements than solids or liquids. CaCO₃(s) → CaO(s) + CO₂(g): ΔS positive. N₂(g) + 3H₂(g) → 2NH₃(g): four gas molecules become two, ΔS negative.

Unlike ΔH_f, the standard entropy of an element is not zero. Every substance in the equation counts, multiplied by its coefficient.

23.4 Gibbs free energy

A reaction is feasible (can happen spontaneously) when ΔG is negative or zero. Feasible does not mean fast: a feasible reaction may still have a high activation energy and not happen at a measurable rate.

Units need care: ΔH is in kJ mol⁻¹ and ΔS in J K⁻¹ mol⁻¹, so divide ΔS by 1000 before substituting. T is in kelvin.

How temperature affects feasibility depends on the signs:

The changeover temperature is where ΔG = 0: