A solution is a homogeneous mixture of a solute and a solvent. Solutions can be formed in any state of matter; that is they may be solid, liquid, or gas. A solution is prepared by dissolving a solute into the solvent. Solute is either the smaller component of a mixture or, when liquid solutions are considered, the gaseous or solid substance added to the solution. Solutions could be composed of either complete molecules - molecular solution, or ions - ionic solution. The latter usually is referred to aqueous solutions of salts. Fluids that mix or dissolve in each other in all proportions are call miscible fluids, lacking that property fluids are called immiscible. So gases are always miscible.

The number of grams of solute that can just be dissolved in 100 ml of solvent at 20C is defined as the solubility (36g for NaCl). At the maximum solubility the solution is saturated and in dynamic equilibrium with the unsoluble part of solute. Such a solution is called saturated. Solution with less concentration is call unsaturated.

NaCl(s) <==> Na+(aq) + Cl-(aq)

If there is more solute dissolved than saturation allows, the solution is said to be supersaturated. Supersaturated solutions are not in equilibrium with the solid substance. If a small crystal of sodium thiosulfate is added to a supersaturated solution of sodium thiosulfate, the excess immediately crystallizes out.

Factors affecting solubility include intermolecular forces, viscosity, and entropy. Solubility varies dramatically. General 'rule' - "like dissolves like". The solubility of a solute in a solvent (that is, the extent of the mixing of the solute and solvent species) depends on a balance between the natural tendency for the solute and solvent species to mix and the tendency for a system to have the lowest energy possible.

Molecular solutions. Intermolecular forces between the same molecules in comparison with others. For example, VdW only interacting molecules and those with hydrogen bonding. I alcoholes, their miscibility with water declines with increasing length of a hydrocarbon chain.

Ionic solutions. Interacting between ion and water molecule is due an ion-dipole force. The attraction of ions for water molecules is called hydration. Hydration of ions can favor the dissolving of an ionic solid in water. That would be when energy of hydration of both ions exceeds the lattice energy which works against the solution process; ionic solids with relatively large lattice energy are usually insoluble. Remember that:

Lattice energy ~ (charge x charge)/distance

i.e. the smaller the size and the greater the charge on ions - the gretaer is the lattice energy. Compare it solubility table.

The solubility of a solute in both molecular solutions and ionic solutions is dependent on temperature and pressure.

Temperature. Most gases are less soluble at high T but solid compounds usually (but not always) are more soluble with T. Heat of solution could be either positive or negative. Depending on that - different applications. Dissolving of ammonium nitrate in water is the basis for instant cold packs used in hospitals and elsewhere (NH4NO3 crystals inside a bag of water). When the inner bag is broken, NH4NO3 dissolves in the water. Heat is absorbed, so the bag feels cold. Similarly, hot packs are available, containing either CaCl2, MgSO4 or sodium acetate, which dissolve in water with the evolution of heat.

Pressure. In general, pressure change has little effect on the solubility of a liquid or solid in water, except for gases. . Le Chatelier's principle - when a system in equilibrium is disturbed (by a change of temperature, pressure, or concentration variable), the system shifts in equilibrium composition in a way that tends to counteract this change of variable. CO2(g) --> CO2(aq) - solubility increases with P.

Henry's law: the solubility of a gas is directly proportional to the partial pressure of the gas above the solution, S = kHP , where S is the solubility of the gas (expressed as mass of solute per unit volume of solvent), kH is Henry's law constant for the gas for a particular liquid at a given temperature, and P is the partial pressure of the gas.


     The concentration of a solute is the amount of solute dissolved in a given quantity of solvent or solution. The quantity of solvent or solution can be expressed in terms of volume or in terms of mass or molar amount. The common expressions for concentration are: Molarity (M), Mass Percent, Mole Fraction (XA) and Molality (m)   

Molarity (M) Mass Percent
Molarity = moles of solute
liters of solution
Mass percentage
of solute =
mass of solute x100%
mass of solution
Mole Fraction (XA)  Molality (m)
XA = moles of substance A
total moles of solution
Molality = moles of solute
kilograms of solvent

The conversion of concentration units from one to another is critical when solving problems. Let's see an example:

Example: What is the molality of 9.79 M solution of H2O2? We have to know density of the solution in order to answer this question. The density of the solution is 1.11 g/mL.

Raoult's law, the partial pressure of solvent, PA, over a solution equals the vapor pressure of the pure solvent, PA, times the mole fraction of solvent, XA, in the solution: PA = PAXA

Ideal Solution is the one that follows Raoult's law.

Colligative Properties

Colligative properties of solutions are properties that depend on the concentration of solute molecules or ions in solution but not on the chemical identity of the solute. For example, the vapor pressure of a solvent above a solution is lowered by addition of a nonvolatile solute. Raoult's law is used to relate the vapor pressure of the solution to the vapor pressure of the pure solvent using the mole fraction. Another example of colligative properties is boiling point elevation and freezing point depression. The change in temperature observed for each of these processes can be related to a constant multiplied by the molality of the solution.

Colligative properties have a number of practical applications including antifreeze for automobiles, spreading salt on icy roads, and determining the molecular weight of unknown substances.

The boiling-point elevation, DTb, is found to be proportional to the molal concentration, cm, of the solution (for dilute solutions).

DTb = Kbcm

The constant of proportionality, Kb (called the boiling-point-elevation constant), depends only on the solvent.

Boiling-Point-Elevation Constants (Kb) and Freezing-Point-Depression Constants (Kf)

 Solvent                             Formula           Boiling Point (C)    Freezing Point (C)     Kb (C/m)             Kf (C/m)
Acetic acid 
Carbon disulfide

[Data taken from Landolt-Bornstein, 6th ed., Zahlenwerte und Functionen aus Physik, Chemie, Astronomie,
Geophysik, und Technik,
Vol. II, Part IIa (Heidelberg: Springer-Verlag, 1960), pp. 844-849 and pp. 918-919.]

The freezing-point depression, DTf, is a colligative property of a solution equal to the freezing point of the pure solvent minus the freezing point of the solution. (DTf is shown in the figure below.) Freezing-point depression, DTf, like boiling-point elevation, is proportional to the molal concentration, cm (for dilute solutions).

DTf = Kfcm

Here Kf is the freezing-point-depression constant and depends only on the solvent.
To explain the colligative properties of ionic solutions, you must realize that it is the total concentration of ions, rather than the concentration of ionic substance, that is important. For example, the freezing-point depression of 0.100 m sodium chloride solution is nearly twice that of 0.100 m glucose solution because ach formula unit of NaCl gives two particles, Na+ and Cl-, upon dissolving in water. You can write the freezing-point lowering more generally as

DTf = iKfcm

where i is the number of ions resulting from each formula unit and cm is the molality computed on the basis of the formula of the ionic compound. The equations for the other colligative properties must be similarly modified by the factor i.
Actually, the freezing points of ionic solutions agree with the previous equation only when the solutions are quite dilute. The i values calculated from the freezing-point depression are usually smaller than the number of ions obtained from the formula unit. The Debye - Hckel theory (1923) suggests to use activities (or effective concentrations) of the ions which are less than their actual concentrations as a result of the electrical interactions of the ions in solution. When DH theory applied, it gives an excellent agreement with experiment for dilute solutions.

Try drill problems on colligative properties.


Osmosis is the phenomenon of solvent flow through a semipermeable membrane to equalize the solute concentrations on both sides of the membrane. The osmotic pressure is the amount of pressure necessary to just stop osmosis from occurring and is equal to p = MRT where p is the osmotic pressure and M is the molarity.  

Osmotic pressure varies over several orders of magnitude and is important in many biological processes. A cell might be thought of (simplistically) as an aqueous solution enclosed by a semipermeable membrane. The solution surrounding the cell must have an osmotic pressure equal to that within the cell.

The process of reverse osmosis has been applied to the problem of purifying water. By applying a pressure P > p, the osmotic process can be reversed. Then, solvent flows from the concentrated solution (which could be ocean water) through a membrane to the more dilute solution (which could be more or less pure water).

Try drill problems on osmosis



A colloid is a dispersion of (relatively large) particles of one substance (the dispersed phase) throughout another substance or solution (the continuous phase). Fog is an example of a colloid: it consists of very small water droplets (dispersed phase) in air (continuous phase). A colloid differs from a true solution in that the dispersed particles are larger than normal molecules, though they are too small to be seen with a microscope. The particles range from about 1 x 103 pm to about 2 x 105 pm in size.

Types of Colloids

 Continuous Phase     Dispersed Phase      Name                        Example
  Solid sol 
  Fog, mist 
  Whipped cream 
  Mayonnaise (oil dispersed in water) 
  AgCl(s) dispersed in H2O
  Pumice, plastic foams 
  Jelly, opal (mineral with liquid inclusions)
  Ruby glass (glass with dispersed metal) 

Hydrophilic and Hydrophobic Colloids

Colloids in which the continuous phase is water are divided into two major classes: hydrophilic colloids and hydrophobic colloids. A hydrophilic colloid is a colloid in which there is a strong attraction between the dispersed phase and the continuous phase (water). Many such colloids consist of macromolecules (very large molecules) dispersed in water. Except for the large size of the dispersed molecules, these colloids are like normal solutions. Protein solutions, such as gelatin in water, are hydrophilic colloids. Gelatin molecules are attracted to water molecules by London forces and hydrogen bonding.

A hydrophobic colloid is a colloid in which there is a lack of attraction between the dispersed phase and the continuous phase (water). Hydrophobic colloids are basically unstable. Given sufficient time (could be years), the dispersed phase aggregates into larger particles. In this behavior, they are quite unlike true solutions and hydrophilic colloids.

Hydrophobic sols are often formed when a solid crystallizes rapidly from a chemical reaction or a supersaturated solution. When crystallization occurs rapidly, many centers of crystallization (called nuclei) form at the same time. Ions are attracted to these nuclei, and very small crystals form. These small crystals are prevented from settling out by the random thermal motion of the solvent molecules, which continue to buffet them.

You might expect these very small crystals to aggregate into larger crystals because the aggregation would bring ions of opposite charge into contact. However, sol formation appears to happen when, for some reason, each of the small crystals gets a preponderance of one kind of charge on its surface. For example, iron(III) hydroxide forms a colloid because an excess of iron(III) ion (Fe3+) is present on the surface, giving each crystal an excess of positive charge. These positively charged crystals repel one another, so aggregation to larger particles is prevented.


An iron(III) hydroxide sol can be made to aggregate by the addition of an ionic solution, particularly if the solution contains anions with multiple charges (such as phosphate ions, PO43-). Coagulation is the process by which the dispersed phase of a colloid is made to aggregate and thereby separate from the continuous phase.

Association Colloids

When molecules or ions that have both a hydrophobic and a hydrophilic end are dispersed in water, they associate, or aggregate, to form colloidal-sized particles, or micelles. A micelle is a colloidal-sized particle formed in water by the association of molecules or ions that each have a hydrophobic end and a hydrophilic end. The hydrophobic ends point inward toward one another, and the hydrophilic ends are on the outside of the micelle facing the water. A colloid in which the dispersed phase consists of micelles is called an association colloid.

Eaxample - ordinary soap in water which consists of compounds such as sodium stearate, C17H35COONa. The stearate ion has a long hydrocarbon end that is hydrophobic (because it is nonpolar) and a carboxyl group (COO-) at the other end that is hydrophilic (because it is ionic).

Soap and sodium lauryl sulfate (synthetic detergent present in toothpastes and shampoos):

sodium lauryl sulfate

are examples of "anionics" - they have a negative charge at the hydrophilic end. Other detergent molecules are "cationics," because they have a positive charge at the hydrophilic end:

Many cationic detergents also have germicidal properties and are used in hospital disinfectants and in mouthwashes.