1. Boiling-Point Elevation and Freezing-Point Depression Boiling-Point Elevation (∆T b ): The boiling point of the solution (T b ) minus the boiling point of the pure solvent (T ° b ): ∆T b = T b – T ° b –∆T b is proportional to concentration: ∆T b = K b m K b = molal boiling-point elevation constant.

2. Boiling-Point Elevation and Freezing-Point Depression Freezing-Point Depression (∆T f ): The freezing point of the pure solvent (T ° f ) minus the freezing point of the solution (T f ). ∆T f = T ° f – T f –∆T f is proportional to concentration: ∆T f = K f m K f = molal freezing-point depression constant.

3. Boiling-Point Elevation and Freezing-Point Depression

5. The phase diagram shows a close-up of the liquid–vapor phase transition boundaries for pure chloroform. a)Estimate the boiling point of pure chloroform. a)Estimate the molal concentration of the nonvolatile solute.

6. Boiling-Point Elevation and Freezing-Point Depression van’t Hoff Factor, i: This factor equals the number of ions produced from each molecule of a compound upon dissolving. –i = 1 for CH 3 OHi = 3 for CaCl 2 –i = 2 for NaCli = 5 for Ca 3 (PO 4 ) 2 For compounds that dissociate on dissolving, use: ∆T b = i  K b m ∆T f = i  K f m ∆P = i  x 2 P ° 1