Boiling point of salt water

Depending on pressure $P$ and temperature $T$ , water is solid, liquid or gaseous. This can be represented in the form of a phase diagram:

The lines in the diagram represent the phase boundaries in which the different phases coexist. The boiling point of water thus corresponds to the boundary line between liquid and gaseous and depends on pressure. With increasing pressure, the boiling point increases as liquid water has a higher density than water vapor.

Since salt water consists of both water molecules, H $_2$ O, as well as sodium ions, Na $^+$ , and chlorine ions, Cl $^-$ , proportionately less water is contained in salt water. The partial pressure of the water therefore decreases. According to Rault's law, the partial pressures $P_i = x_i P$ are proportional to the molar fractions $x_i$ (with $\sum_i x_i = 1$ ) and add up to the total pressure $P$ : $\begin{aligned} P &= P_{\text{H}_2\text{O}} + P_{\text{Na}^+} + P_{\text{Cl}^-} \\ &= x_{\text{H}_2\text{O}} P + x_{\text{Na}^+} P + x_{\text{Cl}^-} P \\ P_{\text{H}_2\text{O}} &= x_{\text{H}_2\text{O}} P = (1 - 2 x_\text{NaCl}) P \\ \Delta P &= P_{\text{H}_2\text{O}} - P = - 2 x_\text{NaCl} P \end{aligned}$ The addition of salt therefore reduces the vapor pressure of the water, so that the vapor pressure curve in the phase diagram is shifted by $\Delta P$ to a lower value. The boiling point for the same external pressure $P =1 \,\text{bar}$ is then found at a higher temperature $T_b' > T_b = 100^\circ\, \text{C}$