11.4 Colligative properties  (Page 3/30)

where P _A is the partial pressure exerted by component A in the solution, $P_{\text{A}}^{°}$ is the vapor pressure of pure A, and X _A is the mole fraction of A in the solution. (Mole fraction is a concentration unit introduced in the chapter on gases.)

Recalling that the total pressure of a gaseous mixture is equal to the sum of partial pressures for all its components (Dalton’s law of partial pressures), the total vapor pressure exerted by a solution containing i components is

A nonvolatile substance is one whose vapor pressure is negligible ( P ° ≈ 0), and so the vapor pressure above a solution containing only nonvolatile solutes is due only to the solvent:

Elevation of the boiling point of a solvent

As described in the chapter on liquids and solids, the boiling point of a liquid is the temperature at which its vapor pressure is equal to ambient atmospheric pressure. Since the vapor pressure of a solution is lowered due to the presence of nonvolatile solutes, it stands to reason that the solution’s boiling point will subsequently be increased. Compared to pure solvent, a solution, therefore, will require a higher temperature to achieve any given vapor pressure, including one equivalent to that of the surrounding atmosphere. The increase in boiling point observed when nonvolatile solute is dissolved in a solvent, Δ T _b , is called boiling point elevation    and is directly proportional to the molal concentration of solute species:

where K _b is the boiling point elevation constant    , or the ebullioscopic constant and m is the molal concentration (molality) of all solute species.

Boiling point elevation constants are characteristic properties that depend on the identity of the solvent. Values of K _b for several solvents are listed in [link] .