1. Calculations & Colligative Properties
Chapter 16.4

2. Learning Objectives Know the difference between molality and molarity
Be able to calculate molality
Can use molality to calculate freezing point depression or boiling point elevation
Understand how ionic compounds affect colligative properties
Can calculate mole fractions

3. Molarity vs Molality Molarity (M) moles of solute M =
liters of solution
Molality (m)
m =
moles of solute
mass of solvent (kg)

4. Molarity vs Molality
so 3.2 M means we have 3.2 moles in 1 liter of solution
so 3.2 m means we have 3.2 moles in 1 kg of solvent

5. Why do we need to know molality?
Colligative properties …..
We use molality to make calculations for boiling point elevation or freezing point depression

6. Boiling Point Elevation
DTb = Kb x m x i
Van’t Hoff factor
Change in boiling point
Molality of solution
Molal boiling point constant
(0.51 oC/m for water)

7. Freezing Point Depression
DTf = Kf x m x i
Van’t Hoff factor
Change in freezing point
Molality of solution
Molal freezing point constant
(-1.86 oC/m for water)

8. Important note about these calculations!
The calculations change depending on whether you have a nonelectrolyte or electrolyte solution
Why?
1 C12H22O11 (s)  1 C12H22O11 (aq) (i =1)
Sugar does not dissociate into ions!
1 Ba(NO3)2 (s)  1 Ba2+(aq) NO3-1(aq) (i =3)
Barium nitrate will lower the freezing point of its solvent
three times as much as sugar of the same molality

9. Sample Calculation: Freezing Point Depression: Electrolyte
What is the freezing point depression of water in a solution of 62.5 g of barium nitrate, Ba(NO3)2, in 800. g of water?
DTf = Kf •m•i
137.3(1) 14(2)
16(6)_____
261.3g/mol
800. g = kg
Let’s calculate m first
m = moles of Ba(NO3)2 / kg solvent
m = moles / kg water
62.5 g
261.3 g/mol
m = mol/kg
DTf = (-1.86 oC/m)(0.299 m)(3)  Van’t Hoff factor (i)
DTf = oC

10. Mole Fraction
Mole fractions have no units
XA XB = 1

11. Mole Fraction Calculation
A solution has 1.43 moles of vanadium oxide in 3.45 moles of chloroform. What is the mole fraction of each component in the solution?
XA = 1.43 /
XA = 0.293
XA = 3.45 /
XA = 0.707
= 1