Why does salt dissolve in water?

Two energies, pulling opposite ways

Dissolving costs energy and pays energy back.

• It costs the energy needed to pull the lattice apart into separate gaseous ions. For sodium chloride this lattice dissociation enthalpy is about +787 kJ mol⁻¹. It is large because the ions are small and close together.
• It pays back the energy given out when each gaseous ion is surrounded by water. These are hydration enthalpies, and they are always negative. Common data-book values are −406 kJ mol⁻¹ for Na⁺ and −364 kJ mol⁻¹ for Cl⁻, which add up to −770 kJ mol⁻¹.

By Hess’s law the enthalpy change of solution is the sum of the two:

With those numbers the cycle gives +787 − 770 = +17 kJ mol⁻¹. The two big terms nearly cancel, and what is left is small and positive: dissolving salt is slightly endothermic.

The measured value is smaller still, about +3.9 kJ mol⁻¹. The gap is not a mistake in your sum. No one can measure the hydration of one kind of ion on its own, so every table of hydration enthalpies rests on an assumption about how to split the total between the positive and negative ion, and different books disagree by ten or twenty kJ mol⁻¹. Take two large numbers that each carry that uncertainty, subtract them, and a small answer moves a lot. Use the cycle to explain why the answer is small, and trust the measurement for its size. In an exam, use the data you are given.

What makes hydration strong

Hydration enthalpy is more negative when the ion has a higher charge and a smaller radius, because water’s δ− oxygen (or δ+ hydrogens) can get closer to more concentrated charge. That is why Mg²⁺ (about −1920 kJ mol⁻¹) is hydrated far more strongly than Na⁺ (about −406 kJ mol⁻¹). The same two things also make lattice enthalpies bigger, which is why the overall answer is so often a close contest.

So why does it dissolve at all?

If dissolving salt takes in a little heat, something else has to drive it. That something is entropy. A crystal is highly ordered. Ions spread through the water have far more ways to be arranged. The entropy change of solution for sodium chloride is about +43 J K⁻¹ mol⁻¹.

ΔG is negative at 298 K, so dissolving is feasible. Notice the units: ΔS is in J K⁻¹ mol⁻¹, so it has to be divided by 1000 to match ΔH in kJ. Forgetting this is one of the most common ways to lose a mark here.

The same reasoning explains instant cold packs, where an ionic solid such as ammonium nitrate dissolves strongly endothermically and still goes ahead, and why compounds like silver chloride barely dissolve: their lattice is held more tightly than hydration can repay, and the entropy gain isn’t enough to make up the difference.