Enthalpy of hydration

The enthalpy of hydration is the enthalpy change for turning a mole of gaseous ions into aqueous ions in water, for example Na⁺(g) → Na⁺(aq). It is always negative (exothermic), because water molecules are attracted to the ion and bonds form between them. It is more negative for ions that are small and highly charged. At A-level you combine it with lattice enthalpy to work out the enthalpy of solution of an ionic compound.

Enthalpy of hydration definition

There is one value for each ion, written with state symbols: Na⁺(g) + aq → Na⁺(aq) and Cl⁻(g) + aq → Cl⁻(aq). AQA A-level Chemistry asks you to define the term and to use it in cycles that calculate enthalpies of solution from lattice enthalpies and enthalpies of hydration (section 3.1.8.1, A-level only).

Why hydration is exothermic

Water molecules are polar: the oxygen is δ− and the hydrogens are δ+. When an ion enters water, the water molecules cluster round it and are attracted to it:

• Positive ions attract the δ− oxygen atoms of water molecules.
• Negative ions attract the δ+ hydrogen atoms.

Forming these attractions releases energy, so every enthalpy of hydration is negative.

What affects the enthalpy of hydration?

The stronger the attraction between the ion and the water molecules, the more energy is released and the more negative the enthalpy of hydration:

So Mg²⁺ has a much more negative enthalpy of hydration than Na⁺ (it has twice the charge and is smaller), and Li⁺ is more negative than K⁺ (same charge, smaller ion). Going down a group, ions get larger and their enthalpies of hydration get less negative.

Enthalpy of solution and the hydration cycle

The enthalpy of solution (ΔsolH) is the enthalpy change for dissolving a mole of an ionic solid in water. You can think of dissolving in two steps: first break up the lattice into gaseous ions, then hydrate the ions. By Hess's law:

Lattice dissociation enthalpy is positive (energy is needed to separate the ions), and hydration enthalpies are negative. The enthalpy of solution is the small difference between two large numbers, so it can be slightly positive or slightly negative.

Example 1: dissolving sodium chloride

Use these data: lattice dissociation enthalpy of NaCl = +787 kJ mol⁻¹; ΔhydH of Na⁺ = −406 kJ mol⁻¹; ΔhydH of Cl⁻ = −364 kJ mol⁻¹. (Values differ a little between data books.)

The answer is small and positive: dissolving salt in water is slightly endothermic. It still dissolves, because the ions spreading out through the water increases entropy, which you meet later in the course.

Example 2: finding a hydration enthalpy

For magnesium chloride, MgCl₂, use: lattice dissociation enthalpy = +2526 kJ mol⁻¹; ΔsolH = −155 kJ mol⁻¹; ΔhydH of Cl⁻ = −364 kJ mol⁻¹. Find the enthalpy of hydration of Mg²⁺.

Remember there are two chloride ions per formula unit, so the chloride hydration enthalpy is doubled. The answer is about five times more negative than for Na⁺, as you would expect for a small 2+ ion.

Check your understanding.

Lattice enthalpy: formation or dissociation?

AQA allows lattice enthalpy to be defined either way, so read the question carefully. Lattice formation enthalpy is negative (gaseous ions coming together to form a lattice); lattice dissociation enthalpy is positive (the reverse). If a question gives the formation value, change its sign before using the equation above. Lattice enthalpies themselves are found with a Born-Haber cycle: see the Born-Haber cycle guide.

The size of the charges and ions also controls how strongly the ions attract each other in a lattice, which is covered in the Chemical Bonding course.

Common mistakes

• Giving hydration enthalpies a positive sign. They are always negative.
• Forgetting to multiply by the number of each ion, such as two Cl⁻ in MgCl₂.
• Using lattice formation enthalpy without changing its sign in the solution cycle.
• Mixing up the trends. Smaller and more highly charged ions have more negative hydration enthalpies.
• Missing state symbols in the definition equation: the ions start as (g) and end as (aq).

Practise with a short timed paper

Born-Haber cycles and enthalpies of solution are in the second year of A-level Chemistry. The daily A-level Chemistry: Year 2 paper is a short timed paper of 8 questions, with a new one every day. For energy changes from data, try the Enthalpy Calculator.

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Chemistry · EnergeticsEnthalpy of solution: definition, cycles and calculationsEnthalpy of solution explained: definition, the cycle with lattice and hydration enthalpies, calculations, calorimetry, and why dissolving can absorb heat.