Key Points

A solution is a homogeneous mixture of two or more components. Solutions can be gaseous (air), liquid (saltwater), or solid (alloys like brass), depending on the physical state of the solvent.

Molarity (M) is moles of solute per liter of solution, $M = \frac{\text{moles of solute}}{\text{volume of solution (L)}}$. Molality (m) is moles of solute per kilogram of solvent, $m = \frac{\text{moles of solute}}{\text{mass of solvent (kg)}}$. Molality is independent of temperature.

Mole fraction (x) of a component is the ratio of its moles to the total moles in the solution. For a binary solution with components A and B, $x_A = \frac{n_A}{n_A + n_B}$, and the sum of all mole fractions is always 1.

Henry's law states that the partial pressure of a gas in the vapor phase (p) is proportional to its mole fraction (x) in the solution. The formula is $p = K_H x$, where $K_H$ is Henry's law constant.

For a solution of volatile liquids, Raoult's law states the partial vapor pressure of each component ($p_i$) is the product of its mole fraction ($x_i$) and its vapor pressure in the pure state ($p_i^0$). The formula is $p_i = p_i^0 x_i$.

Ideal solutions obey Raoult's law over the entire concentration range. For ideal solutions, the enthalpy of mixing ($\Delta_{mix}H$) and volume of mixing ($\Delta_{mix}V$) are both zero.

Solutions showing positive deviation from Raoult's law have a higher vapor pressure than predicted. This occurs when solute-solvent interactions (A-B) are weaker than solute-solute (A-A) and solvent-solvent (B-B) interactions, and $\Delta_{mix}H > 0$.

Solutions showing negative deviation have a lower vapor pressure than predicted. This happens when solute-solvent interactions (A-B) are stronger than A-A and B-B interactions, and $\Delta_{mix}H < 0$.

Azeotropes are binary mixtures with the same composition in liquid and vapor phases, boiling at a constant temperature. They cannot be separated by fractional distillation and can be minimum-boiling (positive deviation) or maximum-boiling (negative deviation).

Colligative properties are properties of solutions that depend on the number of solute particles, not their identity. The four main colligative properties are relative lowering of vapor pressure, elevation of boiling point, depression of freezing point, and osmotic pressure.

The relative lowering of vapor pressure is equal to the mole fraction of the non-volatile solute ($x_2$). The formula is $\frac{p_1^0 - p_1}{p_1^0} = x_2$.

The elevation of boiling point ($\Delta T_b$) is directly proportional to the molal concentration (m) of the solute. The formula is $\Delta T_b = K_b m$, where $K_b$ is the ebullioscopic constant.

The depression of freezing point ($\Delta T_f$) is directly proportional to the molal concentration (m) of the solute. The formula is $\Delta T_f = K_f m$, where $K_f$ is the cryoscopic constant.

Osmosis is the flow of solvent through a semipermeable membrane from a dilute to a concentrated solution. Osmotic pressure ($\Pi$) is the external pressure required to stop osmosis, given by $\Pi = CRT$, where C is molarity, R is the gas constant, and T is temperature.

Two solutions with the same osmotic pressure are isotonic. If a solution has a higher osmotic pressure than another, it is hypertonic; if it has a lower pressure, it is hypotonic. Blood cells shrink in a hypertonic solution and swell in a hypotonic solution.

Solutes that associate or dissociate in solution show an experimental molar mass different from the normal value, called abnormal molar mass. The van't Hoff factor (i) corrects for this effect.

The van't Hoff factor is the ratio of observed colligative property to the calculated property, or $i = \frac{\text{Normal Molar Mass}}{\text{Abnormal Molar Mass}}$. For dissociation, $i > 1$; for association, $i < 1$; for non-electrolytes, $i = 1$.

To account for association or dissociation, the colligative property formulas are modified by the van't Hoff factor (i). For example, $\Delta T_b = i K_b m$, $\Delta T_f = i K_f m$, and $\Pi = i CRT$.