Solutions

Hydrochloric Acid
in Aqueous Solution
37.5%
HCI
Mole fraction If you know the number of moles of solute and solvent, you
can also express the concentration of a solution in what is known as a mole
fraction-the ratio of the number of moles of solute in solution to the total
number of moles of solute and solvent.
The symbol X is commonly used for mole fraction, with a subscript to indicate
the solvent or solute. The mole fraction for the solvent (X A ) and the mole
fraction for the solute (X B
) can be expressed as follows
X HC1 + X H 0 =1.000
2
0.229 + 0.771 =1.000
Figure 15-15
The mole fraction expresses the
number of moles of solvent and
solute relative to the total number
of moles of solution. Each
mole fraction can be thought of
as a percent. For example, the
mole fraction of water (X H 0) is
0.771, which is equivalent io
saying the solution contains
77.1 % water (on a mole basis).
where n A is the number of moles of solvent and nB is the number of moles
of solute. Why must the sum of the mole fractions for all components in a
solution equal one
Consider as an example the mole fraction of hydrochloric acid (HCI) in
the aqueous solution shown in Figure 15-15. For every 100 grams of solution,
37.5 g would be HCI and 62.5 g would be H 2 0. To convert these masses
to moles, you would use the molar masses as conversion factors.
1 mol HCI
nHCl = 37.5.g..Her X 36.5.g-Hef =
1.03 mol HCI
1 mol H 2 0
nH 2
0 = 62.5 .g.-I-f2O X 18.0.g.-H1J = 3.47 mol H 2 0
Thus, the mole fractions of hydrochloric acid and water can be expressed as
1.03 mol HCI
1.03 mol HCI + 3.47 mol H 2 0
X HC1 = 0.229
1.03 mol HCI + 3.47 mol H 2 0
X H20
= 0.771
PROBLEMS
26. What is the mole fraction of NaOH in an aqueous solution that contains
22.8% NaOH by mass
27. An aqueous solution of NaCI has a mole fraction of 0.21. What is the
mass of NaCI dissolved in 100.0 mL of solution
Assessment
28. Distinguish between a dilute solution and a concentrated
solution.
29. Compare and contrast five quantitative ways to
describe the composition of solutions.
30. Describe the laboratory procedure for preparing a
specific volume of a dilute solution from a concentrated
stock solution.
31. Thinking Critically Explain the similarities and
differences between a 1M solution of NaOH and a
1m solution of NaOH.
32. Using Numbers A can of chicken broth contains
450 mg of sodium chloride in 240.0 g of broth.
What is the percent by mass of sodium chloride in
the broth
470 Chapter 15 Solutions