Editing Colligative properties (section)

=== Boiling point elevation (ebullioscopy) ===
{{Main|Boiling point elevation}}
The [[boiling point]] of a liquid at a given external pressure is the temperature (<math>T_{\rm b}</math>) at which the vapor pressure of the liquid equals the external pressure. The ''normal boiling point'' is the boiling point at a pressure equal to 1 [[atmosphere (unit)|atm]].

The boiling point of a pure solvent is increased by the addition of a non-volatile solute, and the elevation can be measured by [[ebullioscopy]]. It is found that 
    
:<math>\Delta T_{\rm b} = T_{\rm b,\text{solution}} - T_{\rm b,\text{pure solvent}} = i\cdot K_b \cdot m </math><ref name=":0">{{Cite book|last=Tro|first=Nivaldo J.|title=Chemistry; Structure and Properties|publisher=[[Pearson Education]]|year=2018|isbn=978-0-134-52822-9|edition=2nd|pages=563–566|type=Textbook.}}</ref>

Here ''i'' is the [[van 't Hoff factor]] as above, ''K''<sub>b</sub> is the [[ebullioscopic constant]] of the solvent (equal to 0.512&nbsp;°C kg/mol for water), and ''m'' is the [[molality]] of the solution.

The boiling point is the temperature at which there is equilibrium between liquid and gas phases.  At the boiling point, the number of gas molecules condensing to liquid equals the number of liquid molecules evaporating to gas. Adding a solute dilutes the concentration of the liquid molecules and reduces the rate of evaporation. To compensate for this and re-attain equilibrium, the boiling point occurs at a higher temperature.

If the solution is assumed to be an [[ideal solution]], ''K''<sub>b</sub> can be evaluated from the [[thermodynamic]] condition for liquid-vapor equilibrium. At the boiling point, the [[chemical potential]] μ<sub>A</sub> of the solvent in the solution phase equals the chemical potential in the pure vapor phase above the solution.

:<math>\mu _A(T_b)  = \mu_A^{\star}(T_b)  + RT\ln x_A\  = \mu_A^{\star}(g, 1 \,\mathrm{atm}),</math>

The asterisks indicate pure phases. This leads to the result <math>K_b = RMT_b^2/\Delta H_{\mathrm{vap}}</math>, where R is the [[molar gas constant]], M is the solvent [[molar mass]] and Δ''H''<sub>vap</sub> is the solvent molar [[enthalpy of vaporization]].<ref name=Engel>T. Engel and P. Reid, Physical Chemistry (Pearson Benjamin Cummings 2006) p.204-5</ref>