Elevation of Boiling Point

A liquid's boiling point is the temperature at which its vapour pressure becomes equal to the atmospheric (external) pressure, conventionally 1 atm. When a nonvolatile solute is added to a pure solvent, at what was the solvent's normal boiling point the solution's vapour pressure is now lower than 1 atm (section 9.7.2). To bring the vapour pressure back up to 1 atm, the temperature must be raised further -- so the solution boils at a higher temperature, $T_b$, than the pure solvent's boiling point, $T_b^\circ$. This increase is called the elevation of boiling point:

Plotting vapour pressure against temperature for pure water and for a solution (Figure 9.11): the pure-water curve reaches $P=1$ atm exactly at $100^\circ$C ($T_b^\circ$); the solution's curve, sitting below water's at every temperature (lower vapour pressure throughout), only reaches $P=1$ atm at the higher temperature $T_b$. The horizontal gap between where the two curves cross the $P=1$ atm line is the elevation of boiling point.

Experimentally, this elevation is found to be directly proportional to the solute's molal concentration:

where $K_b$ is the molal boiling-point-elevation constant (also called the ebullioscopic constant) of the solvent. If $m=1$ (a one-molal solution), then $\Delta T_b=K_b$ -- so $K_b$ is numerically the elevation produced by dissolving exactly one mole of solute per kilogram of solvent. $K_b$ itself can be derived from the solvent's own thermodynamic properties:

Table 9.3 -- $K_b$ values for common solvents (K kg mol$^{-1}$): water 0.52; ethanol 1.20; benzene 2.53; chloroform 3.63; ether 2.02; carbon tetrachloride 5.03; carbon disulphide 2.42; acetic acid 2.93; cyclohexane 2.79.

Determining molar mass from boiling point elevation. For $w_B$ g of solute dissolved in $w_A$ g of solvent, the molality is

so the elevation is

$\Delta T_b = \frac{K_b\,w_B\times1000}{M_B\,w_A} \qquad (9.29)$ …