Enthalpy of solution: what it is and how to calculate it

The enthalpy of solution (ΔsolH) is the enthalpy change for dissolving one mole of an ionic compound in water to make a very dilute solution. You calculate it with an energy cycle: break the lattice into gaseous ions (lattice dissociation enthalpy, positive), then hydrate the ions (hydration enthalpies, negative). The enthalpy of solution is the sum, and can be slightly positive or negative.

Where it fits in A-level Chemistry

In AQA A-level Chemistry, enthalpies of solution come in 3.1.8.1 Born-Haber cycles, which is A-level only (second year). The specification says cycles are used to calculate enthalpies of solution for ionic compounds from lattice enthalpies and enthalpies of hydration, and you should be able to define enthalpy of hydration and do calculations with these cycles.

The three enthalpy changes

AQA notes that lattice enthalpy can be defined as dissociation or as formation. Lattice formation enthalpy is the same size with the opposite sign, so check which one a question gives you.

The enthalpy of solution cycle

If you are given the lattice formation enthalpy instead, change its sign: ΔsolH = −ΔLH(formation) + ΣΔhydH. Here is the cycle for potassium chloride, drawn to scale with the data in the worked example below:

Worked examples

Example 1: enthalpy of solution of potassium chloride

Data from LibreTexts' hydration page: lattice formation (crystallisation) enthalpy of KCl = −715 kJ mol⁻¹; ΔhydH(K⁺) = −322 kJ mol⁻¹; ΔhydH(Cl⁻) = −363 kJ mol⁻¹.

Dissolving potassium chloride is slightly endothermic with these data, so the solution cools. The answer is a small difference between two large numbers, so data from a different table can shift it noticeably: always use the values you are given.

Example 2: caesium chloride

Our Born-Haber cycle guide works out the lattice dissociation enthalpy of CsCl as +668 kJ mol⁻¹. With LibreTexts' hydration enthalpies of −276 kJ mol⁻¹ for Cs⁺ and −363 kJ mol⁻¹ for Cl⁻:

Calculated enthalpies of solution like these are best used to compare compounds rather than as exact values.

Example 3: finding a hydration enthalpy

Data: ΔsolH(MgCl₂) = −155 kJ mol⁻¹; lattice dissociation enthalpy of MgCl₂ = +2492 kJ mol⁻¹; ΔhydH(Cl⁻) = −363 kJ mol⁻¹. Find ΔhydH(Mg²⁺). Remember there are two chloride ions:

Measuring the enthalpy of solution

You can measure ΔsolH directly by calorimetry: dissolve a known mass of solid in a known mass of water in an insulated cup and record the temperature change.

1. Dissolve 5.00 g of KCl (M = 74.6 g mol⁻¹) in 50.0 g of water. The temperature falls by 5.4 °C.
2. Heat taken in: q = mcΔT = 50.0 × 4.18 × 5.4 ≈ 1129 J.
3. Moles of KCl = 5.00 ÷ 74.6 = 0.0670 mol.
4. ΔsolH = +1129 ÷ 0.0670 ≈ +16.8 kJ mol⁻¹. It is positive because the temperature fell.

Heat loss to the surroundings and assuming the solution has the same specific heat capacity as water are the main sources of error.

Why can dissolving be endothermic?

If the hydration enthalpies don't quite make up for the lattice enthalpy, ΔsolH is positive, yet the salt still dissolves. That is because dissolving increases entropy: ordered ions in a lattice become freely moving ions in solution. In AQA 3.1.8.2 you use ΔG = ΔH − TΔS to show such a change can still be feasible.

What affects the size of the values

• Smaller ions and higher charges give more exothermic hydration enthalpies, because the ions attract water molecules more strongly. In LibreTexts' table, Li⁺ is −520 kJ mol⁻¹ against −276 kJ mol⁻¹ for the larger Cs⁺, and the doubly charged Mg²⁺ is −1921 kJ mol⁻¹.
• The same factors make lattice enthalpies larger, so the two effects partly cancel, which is why ΔsolH is a small difference between two large numbers.

For more on hydration, see our enthalpy of hydration guide.

Common mistakes

• Using lattice formation enthalpy without changing its sign. The cycle needs dissociation, which is positive.
• Forgetting to multiply by the number of ions. MgCl₂ has two Cl⁻ ions to hydrate.
• Getting the sign of a calorimetry result wrong. A temperature fall means an endothermic, positive ΔH.
• Dividing by mass instead of moles when working out ΔH from q.

Practise with a short timed paper

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.

Read next

Chemistry · EnergeticsEnthalpy of hydration: definition, trends and cyclesWhat enthalpy of hydration means, why it is always exothermic, how ion charge and size affect it, and how it gives the enthalpy of solution.