Solid-Liquid solubility: A balancing act of ions

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 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.

This post focuses on the dissolution of ionic salts in water.

The obvious three questions are [1] why there is a limit to the solubility of any material, [2] why the solubility varies at different temperatures, and [3] why some salts don’t dissolve in water at all.

A 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.

At equilibrium, between solute and solvent,

The Gibbs free energy ?G= ?H-T?S= 0.

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.

Thermodynamic solubility vs Kinetic solubility

Example

The solubility of all drug substances is normally determined during the pre-formulation stage, and it is crucial to know whether the determined values represent genuine equilibrium solubilities (i.e., thermodynamic values, ?G=0) or whether they represent the values associated with a metastable condition (i.e., kinetic values). As explained above, the equilibrium solubility of a compound is defined as the maximum quantity of that substance which can be completely dissolved at a given temperature and pressure in a given amount of solvent and is thermodynamically valid as long as a solid phase exists which is in equilibrium with the solution phase. The solubility properties of a drug substance are routinely determined as part of a pre-formulation program since its dissolving tendencies will tend to govern the composition of its dosage form and its ultimate bioavailability. Unfortunately, it is all too often that circumstances associated with either the substance or the dissolution medium lead to the formation of a supersaturated solution, where somehow an amount of solute exceeding the equilibrium solubility has become dissolved. Supersaturated solutions are thermodynamically metastable at best, and any such concentration value represents a kinetic solubility rather than an equilibrium solubility value intrinsic to the drug substance.

Which ions are soluble?

Let us take two cases [1] NaCl – highly soluble in water and [2] Barium sulfate, insoluble and analyze what makes the difference?

What happens when an ionic salt is added to water?

Solvent-Solute Interactions

Since the Coulomb forces that bind ions and highly polar molecules into solids are quite strong, we might expect these solids to be insoluble in most solvents. The attractive interactions between ionic molecules are called lattice energy, and they must be overcome for a solution to form. Ionic solids are insoluble in the majority of non-aqueous solvents, but they tend to have high solubility specifically in water.

NaCl – highly soluble in water 

NaCl lattice

This is the lattice structure of NaCl on the LHS. A lattice is the symmetrical three-dimensional structural arrangement of atoms, ions, or molecules (constituent particles) inside a crystalline solid as points.

The image on LHS shows how coulomb forces are holding together each Na and Cl atom [ q1 and q2] Coulomb force expressed as [c], is proportional to the charge on Na+ and Cl- and inversely proportional the bond distance between Na and Cl charges.

If the product q1q2 is positive, the force between the two charges is repulsive; if the product is negative, the force between them is attractive, when two objects interact, each one exerts a force on the other, the forces can transfer energy between them. Therefore, you can see each Na-Cl molecule owing to its atomic interactions has some energy, and the lattice which is a cluster of several Na-Cl molecules has the contribution of energy made by each Na-Cl. This sum of all energy contributed by several NaCl molecules is the lattice energy of NaCl. Therefore, when you dissolve NaCl in water by separating Na+ and Cl - ions, you need energy and this is the lattice energy.

Lattice energy

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 required to break apart an ionic solid and convert its component atoms into gaseous ions. This definition causes the value for the lattice energy to always be positive since this will always be an endothermic reaction.

The other definition says that lattice energy is the reverse process, meaning it is the energy released when gaseous ions bind to form an ionic solid. As implied in the definition, this process will always be exothermic, and thus the value for lattice energy will be negative. Its values are usually expressed with the units kJ/mol.

The relationship between the molar lattice energy and the molar lattice enthalpy is given by the following equation:

Molar lattice energy, ?U = ?H- p ?Vm where, ?U =  molar lattice energy, ?H = molar lattice enthalpy, ?Vm = change of the volume per mole and p =outer pressure

Therefore, the lattice enthalpy further takes into account that work has to be performed against an outer pressure p when a solute dissolves in a solvent.

 Hydration energy

Upon dissolving a salt in water, the cations and anions interact with the positive and negative dipoles of the water. The trade-off of these interactions’ vs those within the crystalline solid comprises the hydration energy. Hydration energy is correlated with an ionic radius of cations and anions. If the hydration energy is greater than the lattice energy, then the enthalpy of solution is negative (heat is released), otherwise, it is positive (heat is absorbed). If the hydration energy is equal to or greater than the lattice energy, then the salt is water-soluble.

Why NaCl dissolves in water

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

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.

Barium sulfate: Barium sulfate is insoluble in water

Why BaSO4 does not dissolve in water?

If we just compare BaSO4 and NaCl, while in NaCl both Na and Cl have a single charge, in BaSO4 both Ba and SO4 have two charges each. 

Thus, compared to NaCl, both q1 and q2 are much bigger in BaSO4 than NaCl. That makes the Coulomb force acting between Fe+2 and SO4 - - ions much larger than Na and Cl as we have discussed.

Therefore, the lattice energy of BaSO4 is very high and exceeds the hydration energy of water and therefore BaSO4 is insoluble in water.

Effect of temperature and pressure on the solubility: The solubility of most substances depends strongly on the temperature and, in the case of gases, on the pressure. The solubility of most solid or liquid solutes increases with increasing temperature. The components of a mixture can often be separated using fractional crystallization, which separates compounds according to their solubilities. The solubility of a gas decreases with increasing temperature. Henry’s law describes the relationship between the pressure and the solubility of a gas. Credit: Google