   # Chapter 1  Energetics of Solution Formation

The heat of solution, qsolution, can be measured by dissolving a known amount of a solid into a liquid to make a solution.

Below is the dissolution reaction of NaCl (s) in water.

NaCl (s) → Na+ (aq) + Cl (aq)

Performed at constant pressure (atmospheric), the heat of solution is equal to the enthalpy of solution, qsolution = Δ Hsolution.

Enthalpy is a state function meaning a change in enthalpy only depends on the difference between final and initial states and not on the path taken between those states.

 Δ H = Hfinal − Hinitial

The state function nature of enthalpy allows us to contrive any path between initial and final states and still arrive at the correct Δ H, so we will break up the dissolution reaction into a series of reactions that can be easily quantified and described. 1. Δ Hsolute (endothermic) is the energy required to separate the solute particles from each other; for ionic compounds this is the reverse reaction that defines the lattice energy, Δ Hsolute = −Δ Hlattice.
2. Δ Hsolvent (endothermic) is the energy required to separate the solvent particles from each other to make "holes" in the solvent to make room for the solute particles.
3. Δ Hmixing (exothermic) is the energy released as the intermolecular interactions between the solute and solvent particles are formed.

Adding all 3 components together gives the enthalpy of solution.

 Δ Hsolution = Δ Hsolute + Δ Hsolvent + Δ Hmixing

The dissolution of ionic compounds in water has a further specification of the names of the various steps.

The enthalpy of hydration is the sum of the enthalpies of solvent and mixing.

 Δ Hhydration = Δ Hsolvent + Δ Hmixing

Δ Hsolvent is fairly constant since the solvent is always water with only small variations accounting for the size of differently sized ionic solute particles.

The main variation of Δ Hhydration between different ionic compounds is attributable to Δ Hmixing as the strength of interactions (i.e. ion-dipole forces) between water molecules and ionic solute particles is highly dependent on the size and charge of the ionic solute particle; the smaller in size and larger in charge the ionic solute particle, the stronger the ion-dipole force between it and the water, and the more exothermic Δ Hmixing is.

Substituting the negative of the lattice energy in for Δ Hsolute, the enthalpy of solution for an ionic compound in water becomes:

 Δ Hsolution = −Δ Hlattice + Δ Hhydration
##### Example

Silver(I) sulfide, Ag2S, is insoluble in water with a solubility of only 0.14 mg/L H2O.

 2 Ag+ (g) + S2− (g) → Ag2S (s) Δ Hlattice = −2673.6 kJ/mol Ag2S (s) → 2 Ag+ (g) + S2− (g) Δ Hsolute = -Δ Hlattice = +2673.6 kJ/mol 2 Ag+ (g) + S2− (g) → 2 Ag+ (aq) + S2− (aq) Δ Hhydration = −2387.4 kJ/mol Ag2S (s) → 2 Ag+ (aq) + S2− (aq) Δ Hsolution = Δ Hsolute + Δ Hhydration Δ Hsolution = 2673.6 − 2387.4 = +286.2 kJ/mol

The dissolution of Ag2S is is very endothermic because despite the strength of the ion-dipole forces binding the solute and solvent together, it is incredibly endothermically expensive to break the solute apart because the S2− high charge is highly attracted to the Ag+ ions in the solid compound.

To dissolve Ag2S in water would require the net input of 286.2 kJ/mol of energy which is a remarkable amount of energy considering the heat capacity of water is 4.184 kJ/L·K, meaning to take 286.2 kJ from 1 L of water would cool it down by 68.4 K = 68.4C, undoubtedly freezing it to solid water in the process.

So, the result is Ag2S just doesn’t dissolve in water; it’s too energetically expensive.

##### Example

Sodium chloride, NaCl, is soluble in water with a solubility of 36 g/100 g H2O.

 Na+ (g) + Cl− (g) → NaCl (s) Δ Hlattice = −787.3 kJ/mol NaCl (s) → Na+ (g) + Cl− (g) Δ Hsolute = -Δ Hlattice = +787.3 kJ/mol Na+ (g) + Cl− (g) → Na+ (aq) + Cl− (aq) Δ Hhydration = −783.5 kJ/mol NaCl (s) → Na+ (aq) + Cl− (aq) Δ Hsolution = Δ Hsolute + Δ Hhydration Δ Hsolution = 787.3 − 783.5 = +3.8 kJ/mol

The dissolution of NaCl is endothermic, just like Ag2S, but unlike Ag2 the dissolution of 1 mol NaCl in 1 L water is likely only to decrease the temperature of the water by less than 1 K = 1C.

There are many ionic compounds whose Δ Hsolution are ultimately exothermic, meaning they would increase the temperature of the water they were being dissolved in because the energy released by the bonds formed between ions and water molecules (Δ Hmixing) would be greater in magnitude than the energy required to break the solute (Δ Hsolute) and solvent (Δ Hsolvent) molecules apart.   