Chemistry · General chemistry II · Worked example
Enthalpy of solution of sodium chloride from an energy cycle
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).
Break the lattice
Going from the solid to gaseous ions reverses the lattice-energy process, so it costs +771 kJ/mol.
Hydrate each ion
Each gaseous ion releases its hydration enthalpy as water surrounds it. NaCl gives one of each.
Close the cycle
Add the two paths. The lattice cost and the hydration payback almost cancel.
Judge the result
+1 kJ/mol is the difference of two numbers near 770, so its size and even its sign depend on the table. The measured value is +3.88 kJ/mol: slightly endothermic, with almost no temperature change. The salt still dissolves because entropy increases.
Result
ΔH(soln) ≈ +1 kJ/mol from this table (measured +3.88 kJ/mol): nearly thermoneutral, slightly endothermic.
Your turn
For CaCl₂, use a lattice energy of −2258 kJ/mol and hydration enthalpies of −1616 kJ/mol for Ca²⁺ and −364 kJ/mol for Cl⁻. Find ΔH(soln), and say whether the solution warms or cools.
Show the answer and explanation
About −86 kJ/mol; it warms.
ΔH(solute) = +2258 kJ/mol. Hydration counts two chloride ions: −1616 + 2(−364) = −2344 kJ/mol. The sum is −86 kJ/mol, so dissolving releases heat. The measured value is close, about −83 kJ/mol, which is why CaCl₂ is used in hot packs and to melt ice.
Keep exploring
Open the cycle in Energy diagrams, then switch to CaCl₂ with two chloride ions and watch ΔH(soln) turn negative.
Return to the concept →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