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Solubility

Solubility describes how much of a solute can dissolve in a given volume of a specific solvent. Solubility is usually reported in terms of solute mass per solvent volume or solute mass per solvent mass. For example, the solubility of sodium chloride in water at room temperature is reported as 36 g per 100 mL of water. If solubility is reported in solute mass per solvent mass, the solvent mass will need to be converted to volume for further calculations.

Solubility changes with temperature. For instance, the solubility of sodium carbonate in water is reported as 7 g per 100 mL at about 0 °C, 22 g per 100 mL at room temperature, and 44 g per 100 mL at 100 °C. Solubility tends to increase with temperature, although there are exceptions.

A solution with the maximum amount of solute dissolved in it is called a saturated solution. At this point, further addition of solute will remain undissolved and remain a precipitate in the solution. For example, a solution of 36 g of sodium chloride dissolved in 100 mL of water at room temperature is a saturated sodium chloride solution.

The solubility of a solute varies from solvent to solvent. For example, sodium chloride has a solubility of 36 g per 100 mL in room-temperature water, but its solubility in methanol is only 1.1 g per 100 mL, and its solubility in dimethylformamide is even lower at 0.034 g per 100 mL.

One way to predict how soluble a solute will be in a solvent is to follow the “like dissolves like” rule. Polar solutes, or solutes with ionic bonds or large intramolecular differences in electronegativity, tend to be more soluble in polar solvents and less soluble in nonpolar solvents. Nonpolar solutes tend to be more soluble in nonpolar solvents and less soluble in polar solvents.

#### Solubility Equilibrium

When a solute dissolves, the solvent molecules form weak interactions with the solute molecules through intermolecular forces while simultaneously interacting with each other via intramolecular forces. The process of dissolving and keeping the solute in solution is known as solvation. Dissolution proceeds in different ways depending on the molecule being dissolved. Ionic salts, strong acids, and strong bases will dissociate into their component ions. Transition metal complexes typically exchange some of their ligands for solvent molecules. Other molecules may simply be solvated as-is.

Every reversible dissolution process can be written as a chemical equation and has an equilibrium constant. For example, the dissolution of sodium chloride in water would be written:

NaCl(s) ⇌ Na+(aq) + Cl-(aq)

When a solution is not yet saturated, dissolution is typically favored. Once a solution is saturated, it is at dynamic equilibrium. For every additional molecule of sodium chloride that dissolves, a molecule of sodium chloride will precipitate from solution, so there is no overall change in the system.

For the generic reaction aA + bB cC + dD, the simplified equilibrium constant is written as:

When calculating the equilibrium constant for a dissolution process, the concentrations of any solids can be set to 1. Thus, there is a simpler version of the equation that is designed for compounds that dissociate when they dissolve, such as ionic salts:

AxBy(s) xA+(aq) + yB-(aq)

Ksp = [A]x[B]y

Ksp is called the solubility product and can be used whenever an equilibrium constant is called for.

#### Thermodynamics

One basic principle of thermodynamics is that systems move towards lower-energy, more disordered states whenever possible. This is one of the driving forces of chemical reactions. However, it can be difficult to predict what strikes the best balance of energy and disorder from a chemical equation alone.

For example, there are both increases and decreases in disorder when a solute is dissolved. The change from an ordered solid to solvated molecules moving in solution increases the disorder of the solute, particularly if the molecules dissociate into their component ions as well. However, the solvent molecules must gather into an ordered ‘cage’ around each molecule or dissociated ion to solvate it.

The equilibrium constant of a reaction is related to the amount of energy in the system available to do reversible work, which is called the Gibbs free energy or Gibbs energy and is abbreviated as G. The change in Gibbs energy before and after a reaction or process is written as ΔG, and it can be calculated from the equilibrium constant for that reaction with this equation:

ΔG = –RT ln(K)

where R is the ideal gas constant, T is the temperature in Kelvin, and K is the equilibrium constant.

If ΔG is positive, the system has a higher Gibbs energy at the end of the reaction than the beginning of the reaction. This usually means that the system needs to absorb energy to perform the reaction. If ΔG is negative, the system has a lower Gibbs energy at the end of the reaction. This implies that the system already had enough energy to perform the reaction. Reactions with a negative ΔG are called spontaneous reactions.

Gibbs energy is related to two other useful thermodynamic parameters, entropy (S) and enthalpy (H), by this equation:

ΔG = ΔH – TΔS

Entropy represents the disorder or randomness of a system. We assume that our reactions take place in an isolated system, so there cannot be a net decrease in entropy during the reaction. The final amount of entropy must be equal to or greater than the starting amount – that is, the overall change in entropy (ΔS) must be zero or positive. Once a system is at equilibrium, there is no net change in entropy.

Enthalpy represents the internal energy of a system plus any work caused by pressure or volume changes in the system. Since any pressure or volume change during the dissolution process will be negligible, we can treat the change in enthalpy as the amount of energy transferred to or from the system during the reaction, typically as heat.

If the change in enthalpy (ΔH) is positive, the system has more internal energy at the end of the reaction than at the beginning and therefore absorbed energy during the reaction. This is usually observed as the system getting colder during the reaction, so we call these reactions endothermic. If the change in enthalpy is negative, the system has less internal energy at the end of the reaction. Thus, the system must have released energy during the reaction, usually in the form of heat. These reactions are called exothermic.

#### References

1. Harris, D.C. (2015). Quantitative Chemical Analysis. New York, NY: W.H. Freeman and Company.

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