Chapter 14 Notes Dr. Floyd Beckford

The extent to which a substance dissolves to produce a stable solution is called its stability. We determine the solubility of a substance by dissolving as much of it as possible in a given amount of solvent at a given temperature.

A solution may be classified as saturated, unsaturated or supersaturated, depending on the concentration of its solute.

Saturated: A saturated solution is one in which the maximum amount of solute has been dissolved in a solvent. At the point saturation occurs, the solution is said to be in equilibrium.

Unsaturated: An unsaturated solution is one in which more solute can dissolve.

Supersaturated: Supersaturated solutions contain more solute than the saturation amount. They can be prepared by saturating a solution at a high temperature and then slowly cooling the solution.

THE DISSOLUTION PROCESS
A substance may dissolve with or without reaction with the solvent.

2Na(s) + 2H₂O(l) 2[Na⁺(aq) + OH^-(aq)] + H₂(g)

NaCl(s) Na⁺(aq) + OH^-(aq)

The dissolution process is favored by:
1. A decrease in the energy of the system which corresponds to an exothermic process.
2. An increase in the disorder or randomness of the system.

When a solvent gets hotter as a substance dissolves heat energy is being released. This energy, called heat of solution, H_solution, depends on the intermolecular forces of attraction between solute and solvent particles. If the intermolecular forces broken are stronger than those formed then H_solution is positive whereas as if the forces formed are stronger than those broken then H_solution is negative. Dissolution is favored by more negative values of H_solution.

Put another way, strong solvent-solute, weak solvent-solvent and weak solute-solute interactions favor solubility.

The dissolution of many solids is an endothermic process. These occur because the endothermic factor is outweighed by the large increase in disorder of the solute during the dissolution process. The solute particles which are ordered in the solid state, becomes free and move randomly through the liquid in solutions.

When substances have similar intermolecular forces, they tend to form solutions with each other. So polar solutes dissolve well in polar solvents and nonpolar solutes dissolve well in nonpolar solvents. In other words “like dissolves like”.

DISSOLUTION OF SOLIDS IN LIQUIDS
The extent to which mixed substances form solutions is controlled primarily by the relative strengths of their intermolecular forces. Energy is required to separate particles from each other but it can be recovered when different particles are brought together in solution.

The ability of a solid to go into solution depends on its crystal lattice energy which is defined as the energy change accompanying the formation of one mole of formula units in the crystalline state from constituent particles in the gaseous state.

This process is always exothermic. That is, crystal lattice energy is always negative.

M⁺(g) + X^-(g) MX(s) + energy

For an ionic compound to dissolve, its ions must first separate and then be solvated as they enter solution. The process involves the transfer of energy
1. to overcome the lattice energy of the compounds
2. to solvate the ions.

The solvation energy (called hydration energy when the solvent is water) is defined as the energy involved in the solvation of one mole of gaseous ions.

Mⁿ⁺(g) + x(Sol) M(Sol)_xⁿ⁺ + energy (for cation)
X^m-(g) + y(Sol) X(Sol)_y^m- + energy (for anions)

The magnitude of the lattice energy depends on the charge on the ions. As the charge-to-size ratio (charge density) increases for ions in the solid state, the magnitude of the crystal lattice energy usually increase more than the hydration. This makes the dissolution of solids such as AlF₃ and MgO very endothermic. As a result the compounds are not very soluble in water.

Solutions of Liquids in Liquids
Miscibility is the ability of one liquid to dissolve in another. The solute-solvent and solvent-solvent interactions are key to miscibility. The solute-solute interactions are lower for liquid solutes than for solids and so this factor is not as important in miscibility. The result is that two liquids mixing is always an exothermic process.

Dissolution of Gases in Liquids
Generally polar gases are most soluble in polar solvents. Although CO₂ is nonpolar it dissolves in water as follows:

CO₂(g) + H₂O(l) H₂CO₃(aq)

HCl(g) + H₂O(l) H₃O⁺(aq) + Cl^-(aq)

Hydrogen fluoride, HF, is only slightly ionized. Very strong hydrogen bonds exist between H₂O and HF molecules.

It is clear that only those gases that ionize (HCl, HBr, HI), form hydrogen bonds (HF, NH₃) or reacts (CO₂) dissolve appreciably in water.

Effect of temperature on solubility
Le Chatelier’s Principle states that when a stress is applied to a system at equilibrium, the system responds in a way that best relieves the stress.

Substances that dissolve by endothermic processes usually increase in solubility with an increase in temperature.

KCl + energy K⁺(aq) + Cl^-(aq)

Substances that dissolve by exothermic processes usually decrease in solubility with an increase in temperature.

Na₂SO₄ products + heat

Effect of pressure on solubility
The effect of pressure is only significant for solutions of gases in liquids. Gases become more soluble in all solvents as the pressure of the gas is increased.

This can be expressed as Henry’s Law which states that the solubility of a gas in a liquid is directly proportional to the pressure of the gas. That is, the higher the pressure, the more soluble the gas.

Molality
The molality, m, of a solute in a solution is the number of moles of solute per kilogram of solvent.

COLLIGATIVE PROPERTIES
Physical properties of solutions that depend on the number, but not the type, of solute particles in a given amount of solvent, are called colligative properties. In dissolution, what happens in essence, is that the solute interferes with the normal actions of the solvent molecules. The degree of interference is simply a function of the concentration of the solute. There are 4 important colligative properties:

1. VAPOR PRESSURE - Raoult’s Law
Vapor pressure depends on the ease with which the molecules are able to escape from the surface of a liquid. It can be said that the vapor pressure of the solution is proportional to the fraction of solvent molecules found at the surface.

Addition of a nonvolatile solute to a pure liquid solvent decreases the solvent’s vapor pressure. When a solute is added, some of its molecules occupy space on the surface of the liquid, displacing volatile solvent molecules. Because there are fewer solvent molecules now at the surface, fewer can escape and the vapor pressure of the solution decreases.

The lowering of vapor pressure of a solvent by a nonvolatile solute, is given by Raoult’s law.

P_solvent = X_solvent P°_solvent
P_solvent = vapor pressure of solvent in the solution
X_solvent = mole fraction of solvent
P°_solvent = vapor pressure of the pure solvent

Solutions that obey Raoult’s law are called ideal solutions.
Let the change in vapor pressure = Psolvent
So Psolvent = P°_solvent - P_solvent
But P_solvent = X_solvent P°_solvent
Therefore P_solvent = P°_solvent – (Xsolvent_solvent P°_solvent) = (1-X_solvent) P°_solvent
Now X_solvent + X_solute = 1; So 1-X_solvent = X_solute
P_solvent = X_soluteP°_solvent

When an ideal solution consists of two volatile components, the vapor pressure of each component is proportional to its mole fraction in the solution.
P_A = X_AP°_A , P_B = X_BP°_B , …..
The total vapor pressure is given by Dalton’s Law.
So P_total = P_A + P_B = X_AP°_A + X_BP°_B +…

This means that when a vapor in equilibrium with a solution containing two or more volatile components is richer (contains more) than the liquid in the more volatile component.

Not all solutions behave ideally. When the vapor pressure is greater than that predicted by Raoult’s law, we get positive deviation. This is due to differences in polarity of the two components.

When the vapor pressure is lower than that predicted by Raoult’s law, we get negative deviation. Such an effect is due to unusually strong attractions between unlike molecules. The unlike species hold one another especially tightly in the liquid phase, so fewer molecules escape into the vapor phase. Thus the observed vapor pressure is less than ideal.

2. BOILING POINT ELEVATION
The presence of solute particles reduces the effective surface area where boiling occurs. The boiling point of a liquid is raised on dissolution of a nonvolatile solute. The change is a consequence of the lowered vapor pressure.

The magnitude of the change in boiling point depends on the concentration of solute particles.

T_b = K_bm

3. FREEZING POINT DEPRESSION
Like boiling, the pressure of solute particles reduces the effective surface area where freezing occurs.

A solute lowers the freezing point of its solvent. When a solution freezes, the solvent molecules solidify first. The solute particles inhibit solvent particles from leaving the liquid phase by keeping them more separated than in the pure liquid.

T_f = K_fm Tf = change in boiling point, K_f = molal freezing point depression constant (different for different solvents and does not depend on solute), m = molality of solute

The most common application of this principle is the use of antifreeze (ethylene glycol, HOCH₂CH2OH) in the automobile radiators.

4. OSMOSIS
Osmosis is the movement of solvent molecules through a semi-permeable membrane from a solution of lower solute concentration into a solution of higher solute concentration.

Osmosis will continue until an equilibrium of concentrations on both sides of the membrane is reached. The pressure at this point is called the osmotic pressure, p. Osmotic pressure depends on the number of solute molecules and therefore is a colligative property.

For a solution of gas in a liquid: p = nRT/V (n = no. of moles of solute)

In terms of molarity: p = MRT

Osmotic pressure increases with temperature and molarity.