Solubility: Role of Thermodynamics

There could be many questions about the solubility of a substance in water. A few common questions could be why common salt is so soluble in water. Why calcium carbonate has very little solubility in water? Why barium sulphate has practically no solubility in water.

Thermodynamics can answer all the questions.

A solute would dissolve in water until the solution is saturated with the solute. When the saturation reaches a thermodynamic equilibrium is established between the solute dissolved in the solution and the undissolved solutes in the solution. Both phases reach the maximum entropy and minimum free energy dG = dH – TdS = 0. This means both phases reach a stage when they do not have any useful energy to interact with each other.  

Solubility

The solubility is the ability of a substance called solute to form a solution in a solvent

The solubility of a substance fundamentally depends on the physical and chemical properties of the solute and solvent as well as on temperature, pressure, and the presence of other chemicals (including changes to the pH) of the solution. The extent of the solubility of a substance in a specific solvent is measured as the saturation concentration, where adding more solute does not increase the concentration of the solution and begins to precipitate the excess amount of solute.

The molecular view of solubility

The solubility of one substance in another is determined by the balance of intermolecular forces between the solvent and solute, and the entropy change that accompanies the solvation. Factors such as temperature and pressure will alter this balance, thus changing the solubility. Solubility may also strongly depend on the presence of other species dissolved in the solvent, for example, complex-forming anions in liquids. Solubility will also depend on the excess or deficiency of a common ion in the solution, a phenomenon known as the common ion effect, pH, etc.

Solubility occurs under dynamic equilibrium, which means that solubility results from the simultaneous and opposing processes of dissolution and phase joining (e.g., precipitation of solids). The solubility equilibrium occurs when the two processes proceed at a constant rate.

Saturated solution and the onset of equilibrium

This explains the obvious roles of temperature, pressure, and entropy in a process of solution. Under certain conditions, the equilibrium solubility can be exceeded to give a so-called supersaturated solution, which is metastable.

Role of lattice energy and hydration energy in a solution

Two types of energy, lattice and hydration energy play fundamental roles.

Lattice energy

Image credit: Google

It is a measure of the cohesive forces that bind ions. Lattice Energy is a type of potential energy that may be defined in two ways. In one definition, lattice energy is the energy held by the Coulomb forces holding the ions.

Image credit: Google

Any stable atom always contains the electrostatic force of attraction. An electrostatic force is also known as the Coulombic force. It is the force of attraction between two opposing charges, i.e., protons and electrons.

Coulomb force is directly proportional to the product of charge on the ions, q1 and q2 and inversely proportional to the square of the separated distance, r.   

The lattice energy is always positive since this will always be an endothermic process to separate two ions.

Hydration energy

If the attractive forces between the solvent and solute particles are greater than the attractive forces holding the solute particles together in the lattice, the solvent particles pull the solute particles apart and surround them. The surrounded solute particles then move away from the solid solute and out into the solution. Ions are surrounded by a solvent.

Next step

This process is called solvation. Solvation is the process of reorganizing solvent and solute molecules into solvation complexes and involves bond formation, hydrogen bonding, and van der Walls forces. The solvation of a solute by water is called hydration.

When the hydration energy is equal or greater than the lattice the substance dissolves in water.

Thermodynamics

Why NaCl is highly soluble in water?

Gibbs equation: ∆G = ∆H - T∆S [ G is Gibbs free energy, H enthalpy, T is temperature and S is entropy]

For NaCl

Lattice energy = + 777 kj/mol

Hydration energy = -774 kj / mol

T = 298 k, ∆S = 40 j/k-mol

∆H = Lattice energy + Hydration energy = 777 + [- 774] = 3 kj/ mol

∆G = [3 – 298 x 0.04]

 = - 8.92 kj / mol

Negative Gibbs free energy change makes the dissolution of NaCl in water spontaneous.

Why barium sulphate BaSO4 is insoluble in water?

Lattice energy BaSO4= +2474 kj/mol

Hydration energy BaSO4 = -2368 kj / mol

T = 298 k, ∆S = 102 j/k-mol

∆H = Lattice energy + Hydration energy = 2474 + [- 2368] = +106 kj/ mol

∆G = [106 – 298 x 0.102] = +75.6 kj / mol (positive therefore BaSO4 is insoluble!)

The point to note here is interesting.

In barium sulphate, BaSO4, there are two positive charges on each cation Ba ++ and anion SO4 --, while in the case of common salt, NaCl there is a single charge on each sodium and chlorine Na+ and Cl-, this makes BaSO4 much more tightly held lattice than NaCl which water cannot break.

 The point to note here is interesting.

In barium sulfate, BaSO4, there are two positive charges on each cation Ba ++ and anion SO4 --, while in the case of common salt, NaCl there is a single charge on each sodium and chlorine Na+ and Cl-, this makes BaSO4 much more tightly held lattice than NaCl which water cannot break.