Enthalpy of Hydration and Solution

Learning Objectives (OCR Spec 5.2.1)

By the end of this lesson you should be able to:

• Define enthalpy of hydration and enthalpy of solution
• Construct a cycle linking lattice enthalpy, hydration enthalpies and enthalpy of solution
• Explain the trend in hydration enthalpies down a group and across similar ions
• Use the cycle to calculate any missing enthalpy
• Explain why some salts dissolve and others do not in terms of the balance between lattice and hydration energies

The Dissolving Process

When an ionic solid dissolves in water, two things happen:

1. The lattice breaks apart into separate ions - this requires energy equal to the magnitude of the lattice enthalpy (so it is endothermic, opposite sign to LE).
2. Each ion becomes surrounded by polar water molecules in a process called hydration, releasing energy.

Whether the overall process is exothermic or endothermic depends on the balance between these two contributions. The overall enthalpy change is called the enthalpy of solution.

Enthalpy of Hydration

Definition (OCR): The enthalpy of hydration is the enthalpy change when one mole of gaseous ions dissolves in water to form one mole of aqueous ions under standard conditions.

Examples:

Na+(g) + aq -> Na+(aq) ΔH°_hyd = -406 kJ mol^-1

Cl-(g) + aq -> Cl-(aq) ΔH°_hyd = -364 kJ mol^-1

Hydration is always exothermic because the partial charges on water molecules are attracted to the ion. Water behaves as a dipolar molecule: the slightly negative oxygen attracts cations, and the slightly positive hydrogens attract anions.

graph TD
  A[Gaseous ion Na+] -->|water shell forms<br/>exothermic hydration| B[Aqueous ion Na+ aq]

Factors Affecting Hydration Enthalpy

Hydration enthalpy follows the same kind of electrostatic logic as lattice enthalpy: the stronger the interaction between the ion and the surrounding water dipoles, the more exothermic the hydration enthalpy.

1. Ion charge: higher charge attracts water dipoles more strongly. Mg^2+ (-1920) is much more negative than Na+ (-406).
2. Ion radius: smaller ions have a higher charge density and bind water more tightly. Li+ (-519) is more exothermic than Cs+ (-276).

Ion	Charge	Radius / pm	ΔH°_hyd / kJ mol^-1
Li+	+1	76	-519
Na+	+1	102	-406
K+	+1	138	-322
Rb+	+1	152	-301
Cs+	+1	167	-276
Mg^2+	+2	72	-1920
Ca^2+	+2	100	-1650
F-	-1	133	-506
Cl-	-1	181	-364
Br-	-1	196	-335
I-	-1	220	-293

Enthalpy of Solution

Definition (OCR): The enthalpy of solution is the enthalpy change when one mole of an ionic compound dissolves in a given amount of water (usually enough to produce an "infinitely dilute" solution) under standard conditions.

Example: NaCl(s) + aq -> Na+(aq) + Cl-(aq) ΔH°_sol = +3.9 kJ mol^-1

Note the small, positive value: dissolving NaCl is slightly endothermic, which is why a cold pack containing solid NH4NO3 (much more endothermic) gets cold when crushed.

The Thermodynamic Cycle

To relate everything we construct a Hess-law cycle with three routes or arrows:

Route 1: Solid ionic compound -> aqueous ions directly (ΔH°_sol)

Route 2: Solid -> gaseous ions (minus lattice enthalpy) -> aqueous ions (sum of hydration enthalpies)

graph TD
  A[NaCl s] -->|enthalpy of solution<br/>direct route| B[Na+ aq plus Cl- aq]
  A -->|minus lattice enthalpy<br/>break lattice| C[Na+ g plus Cl- g]
  C -->|hydration of Na+<br/>plus hydration of Cl-| B

Hess's law gives:

ΔH°_sol = -ΔH°_LE + ΔH°_hyd(cation) + ΔH°_hyd(anion)

Remember the minus sign in front of ΔH°_LE: the lattice step in the cycle goes in the reverse direction to lattice enthalpy (breaking the lattice instead of forming it).

Worked Example: NaCl