Chemistry · General chemistry II · Concept
Enthalpy of solution and lattice energy
Build an energy cycle for dissolving: separate the solute, separate the solvent and mix, or for an ionic solid, break the lattice and hydrate the ions. Then use the cycle to find ΔH(soln) and predict whether a solution warms or cools.
Dissolving as three steps
Enthalpy is a state function, so any path from the pure solute and solvent to the solution gives the same ΔH. The convenient path has three steps. Separating solute particles costs energy. Pushing solvent molecules apart to make room also costs energy. Letting solute and solvent attract each other releases energy.
| Step | What happens | Sign |
|---|---|---|
| ΔH(solute) | Solute particles pulled apart | + (always) |
| ΔH(solvent) | Solvent molecules pulled apart | + (always) |
| ΔH(mix) | Solute–solvent attractions form | − (usually) |
| ΔH(soln) | The sum | either sign |
Ionic solids in water: lattice energy and hydration
For an ionic solid, separating the solute means turning the crystal into gaseous ions. That costs the lattice energy with its sign reversed, because lattice energy is defined for forming the solid from gaseous ions and is negative. Making room in water and surrounding each ion with water molecules are combined into the hydration enthalpy, which is large and negative because ion–dipole attractions are strong.
Three outcomes
Compare the size of the two terms. If hydration releases more than the lattice costs, ΔH(soln) is negative and the solution warms: lithium bromide and calcium chloride behave this way. If the lattice costs more, ΔH(soln) is positive and the solution cools, which is how an ammonium nitrate cold pack works. When the two are nearly equal, as for sodium chloride (+3.88 kJ/mol), there is almost no temperature change.
| If | Then ΔH(soln) | The solution |
|---|---|---|
| |ΔH(solute)| < |ΔH(hydration)| | negative | warms |
| |ΔH(solute)| > |ΔH(hydration)| | positive | cools |
| |ΔH(solute)| ≈ |ΔH(hydration)| | near zero | barely changes temperature |
Big numbers, small difference
Lattice and hydration enthalpies are hundreds or thousands of kJ/mol, and ΔH(soln) is their small difference. Tables from different sources can disagree by several kJ/mol, which is enough to change the sign of a near-zero ΔH(soln), so take all the values from one table. And enthalpy is not the whole story: sodium chloride dissolves readily even though dissolving it is slightly endothermic, because entropy increases.
Why ions with more charge hydrate more strongly
Hydration enthalpy grows with charge and shrinks with size, because a small, highly charged ion attracts the water dipoles more strongly. Lattice energy follows the same trend, which is why the two terms so often nearly cancel.
Common mistakes
- Using the lattice energy itself as ΔH(solute) instead of its negative.
- Mixing lattice and hydration values from different tables.
- Forgetting to multiply a hydration enthalpy by the number of those ions per formula unit, as in CaCl₂.
- Assuming a positive ΔH(soln) means the solid won’t dissolve.
- Treating hydration as a cost: it releases energy.
Key terms
- Enthalpy of solution
- The heat absorbed or released when a solute dissolves in a solvent. For an ionic solid in water, ΔHsoln = −ΔHlattice + ΔHhydration: the energy to pull the ions apart plus the energy released as water surrounds them.
- Lattice energy
- The energy change between an ionic solid and its separate gaseous ions. Forming the solid releases this energy and separating it absorbs the same amount, so its sign depends on which direction a book uses.
- Enthalpy of hydration
- The heat released when one mole of gaseous ions dissolves in water and becomes surrounded by water molecules. It is always negative.
- Hess’s law
- If a reaction is the sum of other reactions, its ΔH is the sum of their ΔH values, because enthalpy is a state function. Reversing a reaction flips the sign of ΔH; multiplying it scales ΔH by the same factor.
- Enthalpy
- H = U + PV, a state function. At constant pressure its change, ΔH, equals the heat the system absorbs (positive) or releases (negative).
- Exothermic reaction
- A reaction that releases heat to its surroundings (ΔH < 0).
- Endothermic reaction
- A reaction that absorbs heat from its surroundings (ΔH > 0).
Work through an example
Using a data table with lattice energy −771 kJ/mol for NaCl and hydration enthalpies −406 kJ/mol for Na⁺ and −364 kJ/mol for Cl⁻, build the energy cycle and find ΔH(soln).
Enthalpy of solution of NaCl from a cycle →Sources and scope
Authored study material. Tool results depend on the stated inputs and model assumptions.
- Tro, Chemistry: A Molecular Approach, 4th ed., §13.3 Energetics of Solution Formation, pp. 577–581 (heats of hydration and ΔHsolute = −ΔHlattice, p. 580; NaCl +3.88 kJ/mol, p. 581)
- Tro, Chemistry: A Molecular Approach, 4th ed., §9.4 Ionic Bonding: Lewis Symbols and Lattice Energies, pp. 388–392 (lattice energy of NaCl, −788 kJ/mol, p. 391)
- OpenStax Chemistry 2e — The dissolution process
Try in the workspace
Open the example inputs, change a value and keep a useful result on your board.
Build the cycle in Energy diagrams Try the three-step model Open worked example on a board Chemistry formulas: energy and thermodynamicsYour existing work stays on this device. Examples open as editable copies.