# Enthalpy of Solution

A solution is a homogeneous mixture of two or more substances. A solution can either be in the gas phase, the liquid phase, the solid phase, or in a combination of these phases. The enthalpy change of solution refers to the overall amount of heat which is released or absorbed during the dissolving process (at constant pressure). The enthalpy of solution can either be positive (endothermic reaction) or negative (exothermic reaction). The enthalpy of solution is commonly referred to as ΔHsolution.

When understanding the enthalpy of solution, it is easiest to think of three processes happening between two substances. One substance is the solute, let’s call that A. The other substance is the solvent, let’s call that B. The first process that happens deals only with the solute, A; A has to break apart from the intramolecular forces holding it together. This means the solute molecules separate from each other. The enthalpy of this process is called ΔH1. This is an endothermic process because energy is required for this reaction, so ΔH1 > 0.

The second process is very similar to the first step. Much like how the solute, A, needed to break apart from itself, the solvent, B, also needs to overcome the intermolecular forces holding it together. This causes the solvent molecules separate from each other. The enthalpy of this process is called ΔH2. Like the first step, this reaction is an endothermic one and ΔH2 > 0 because energy is required to break the forces between the B molecules.

At this point, let us visualize what has happened so far. The solute, A, has broken from the intermolecular forces holding it together and the solvent, B, has broken from the intermolecular forces holding it together as well. It is at this time that the third process happens. We also have two values ΔH1 and ΔH2. Both of these values are greater than zero (again, because both processes are endothermic).

The third process is when substance A and substance B mix. The separated solute molecules and the separated solvent molecules join together to form a solution. This solution will contain one mole of the solute A in an infinite amount of the solvent B.The enthalpy of combining these two substances to form the solution is called ΔH3. This is an exothermic reaction, because energy is given off as the two substances bond together; therefore, ΔH3 < 0.

Figure 1: Energy Diagram for Endothermic Dissolving Process (where ΔHsolution > 0)

The final value for the enthalpy of solution can either be endothermic or exothermic (so ΔHsolution can either be greater than zero or less than zero), depending on how much energy is required or given off in each step. The enthalpy of solution can be written as a formula; ΔHsolution = ΔH1 + ΔH2 + ΔH3. If ΔHsolution = 0, then these solutions are called ideal solutions. If ΔHsolution > 0 or ΔHsolution < 0, then these solutions are called non-ideal solutions. The diagrams below can be used as visuals to help facilitate the understanding of this concept. Figure 1 is for an endothermic reaction, where ΔHsolution > 0. Figure 2 is for an exothermic reaction, where ΔHsolution < 0. Figure 3 is for an ideal solution, where ΔHsolution = 0.

Figure 2: Energy Diagram for Exothermic Dissolving Process (where ΔHsolution < 0)

The enthalpy of solution depends on the intermolecular forces of the solute and solvent. If the solution is ideal, and ΔHsolution = 0, then that means ΔH1 added to ΔH2 is equal to ΔH3. This means the forces of attraction between like (the solute-solute and the solvent-solvent) and unlike (solute-solvent) molecules are the same (Figure 3). If the solution is non-ideal, then either ΔH1 added to ΔH2 is greater than ΔH3 or ΔH3 is greater than the sum of ΔH1 and ΔH2. The first case means the forces of attraction of unlike molecules is greater than the forces of attraction between like molecules. The second case means the forces of attraction between like molecules is greater than the forces of attraction between unlike molecules (Figure 2). If ΔH3 is much greater than the sum of ΔH1 and ΔH2, then a heterogeneous mixture occurs. Dissolution occurs to a very small extent (Figure 1).

Enthalpy change is part of the driving force in the formation of solutions. The effect of enthalpy change should be combined with the entropy change to get the Gibbs free energy change, ΔG. Gibbs free energy change is the ultimate driving force in the formation of solutions (at constant temperature and pressure).

An example of this concept is the dissolution of salts. NaCl (table salt) dissolves readily in water. In solid NaCl, the positive sodium ions are attracted to the negative chloride ions. The same is true of the solvent, water; the partially positive hydrogen atoms are attracted to the partially negative oxygen atoms. While NaCl dissolves in water, the positive sodium cations and chloride anions are being stabilized by the water molecule electric dipoles. Thus, the intermolecular bonds between NaCl are broken and the salt is dissolved. The overall chemical equation for this reaction is as follows:

$\ce{NaCl (s) -> Na^+ (aq) + Cl^- (aq)}$

Figure 3: Energy Diagram for an Ideal Solution (ΔHsolution = 0)

### Examples

1. If ΔHsolution = 230 J/mol, ΔH2 = 108 J/mol, and ΔH3 = - 47 J/mol, what is the value of ?H1?

ΔHsolution = ΔH1 + ΔH2 + ΔH3

230 J/mol = ΔH1 + 108 J/mol + - 47 J/mol

ΔH1 = 230 J/mol - 108 J/mol +47 J/mol

ΔH1 = 169 J/mol

2. If ΔHsolution = -219 J/mol, is the solution ideal or nonideal?

Solution is only ideal when ΔHsolution = 0

-219 J/mol does not equal 0

Therefore, the solution is non-ideal.

### References

1. Petrucci, Harwood, Herring, Madura. General Chemistry: Principles & Modern Applications, Ninth Ed. Upper Saddle River, NJ: Pearson Education, Inc., 2007.
2. McMurray, Fay. Chemistry, Third Ed. Upper Sadle River, NJ: Prentice-Hall, Inc., 2001.

### Contributors

• Zafir Javeed, Mark Tye (DVC)