Page 231 - Theory and Problems of BEGINNING CHEMISTRY

220 SOLUTIONS [CHAP. 15

a solution. The symbol for molality is m. Its unit is molal. Carefully note the differences between molality and
molarity:
1. Molality is defined in terms of kilograms, not liters.
2. Molality is defined in terms of solvent, not solution.
3. The symbol for molality is a lowercase m, not capital M.
Take great care not to confuse molality and molarity.

EXAMPLE 15.3. Calculate the molality of a solution prepared by adding 0.300 mol of solute to 225 g of water.
0.300 mol
Ans. = 1.33 m
0.225 kg
EXAMPLE 15.4. What mass of H 2 O is required to make a 2.50 m solution with 0.511 mol NaCl?
1.00 kg H O

Ans. 0.511 mol NaCl 2 = 0.204 kg H O
2.50 mol NaCl 2
EXAMPLE 15.5. What mass of 1.25 m CH 3 OH solution in water can be prepared with 50.0 g of CH 3 OH?
1 mol CH 3 OH 1.00 kg solvent

Ans. 50.0gCH OH = 1.25 kg solvent
3
32.0gCH OH 1.25 mol CH 3 OH
3
50.0gCH OH + 1250 g H O = 1300 g solution
3 2
Note the importance of keeping track of what materials you are considering, in addition to their units.

EXAMPLE 15.6. Calculate the molarity of a 1.85 m solution of NaCl in water if the density of the solution is 1.04 g/mL.
Ans. Since neither concentration depends on the quantity of solution under consideration, let us work with a solution
containing 1.000 kg H 2 O. Then we have

58.5 g NaCl
1.85 mol NaCl = 108 g NaCl
1 mol NaCl
The total mass of the solution is therefore 1108 g, and its volume is

1mL
1108 g = 1070 mL = 1.07 L
1.04 g
The molarity is
1.85 mol NaCl
= 1.73 M
1.07 L

15.3. MOLE FRACTION
The other temperature-independent concentration unit introduced in this chapter is the mole fraction. The
mole fraction of a substance in a solution is the ratio of the number of moles of that substance to the total number
of moles in the solution. The symbol for mole fraction of A is usually X A , although some texts use the symbol
N A . Thus, for a solution containing x mol of A, y mol of B, and z mol of C, the mole fraction of A is
x mol A
X A =
x mol A + y mol B + z mol C
EXAMPLE 15.7. What is the mole fraction of CH 3 OH in a solution of 12.0 g CH 3 OH and 25.0 g H 2 O?

1 mol CH 3 OH
Ans. 12.0gCH OH = 0.375 mol CH 3 OH
3
32.0gCH OH
3