Other Ways of Expressing the
Concentration of Solutions
percent concentration,
ppm, ppb
Percentage Concentration
Can be expressed as:
1. % mass/volume, or % m/v;
2. % mass/mass, or % m/m;
3. % volume/volume, or % v/v.
1. % mass/volume, or % m/v
% m/v = mass of solute (g)
100 mL solution1
—or—
mass of solute (g) * 100%
vol of solution (mL)
1solution
=
solute + solvent
sample problem 1
What is the % concentration when 4.52 g
KNO3 is dissolved in 250 mL of solution?
Answer:
(4.52 g/250 mL) * 100% = 1.81%
—or—
4.52 g
=
?g
250 mL
100 mL
? = 1.81 g/100 mL or 1.81 %
.
sample problem 2
Na3PO4 is sold in hardware stores under the
(incorrect) name “Trisodium phosphate”,
or TSP.
A 1.7% (m/v) solution of TSP is
recommended for cleaning walls before
painting or putting up wallpaper.
What mass of TSP is needed to make 2.0 L
of solution?
Answer:
1.7% (m/v) means
1.7 g per 100 mL or
? g per 2000 mL
cross-multiplying gives
? = (1.7 g * 2000 mL)/100 mL
= 34 g
Use 34 g TSP to make 2.0 L of cleaning sol’n.
NB. Solutions of TSP are VERY BASIC.
Wear Gloves!!
2. % mass/mass, or % m/m
% m/m = mass of solute (g)
100 g solution1
—or—
mass of solute (g) * 100%
mass of solution (g)
1solution
=
solute + solvent
sample problem 3
CaCl2 is often used as an ice-melter.
If 45.3 g of slush (snow, ice, CaCl2) was
evaporated to yield 6.37 g CaCl2, calculate
the % m/m CaCl2 in the slush.
Here, the slush represents the
solution.
Answer:
% CaCl2 = (6.37 g CaCl2/45.2 g slush)*100%
CaCl2 = 14.1 % (m/m)
3. % volume/volume, or % v/v
% v/v =
volume of solute (mL)
100 mL solution1
—or—
volume of solute (mL) * 100%
volume of solution (mL)
1solution
=
solute + solvent
sample problem 4
Rubbing alcohol is a 70% (v/v) solution of
isopropyl alcohol in water.
What volume of isopropyl alcohol is required
to prepare 350 mL of rubbing alcohol?
Answer:
70 mL isopropyl alcohol =
? mL
100 mL rubbing alcohol
350 mL
? = (70 mL * 350 mL)/100 mL
= 245 mL isopropyl alcohol in 350 mL
Practical Application
The concentration of alcohol (ethanol) in
alcoholic beverages is stated as % (v/v).
Regular beer is 5.0% (v/v) ethanol;
“lite” beer is 4.0% (v/v).
Express the % ethanol in “lite” beer as % (m/v).
What information do you need?
Density of ethanol = 0.80 g/mL.
Answer:
4.0% (v/v) =
4.0 mL ethanol/100 mL
We need to convert 4.0 mL ethanol  mass.
4.0 mL*(0.80 g·mL-1) = 3.2 g ethanol/100 mL
% ethanol (m/v) in “lite” beer = 3.2%
If you were the brewer, would you label %
ethanol in “lite” beer as m/v or v/v?
ppm concentration*
ppm =
mass of solute * 106
mass of solution
or
mass of solute
=
mass of solution
(*parts per million—106)
?g
106 g solution
.
.
ppb concentration*
ppb =
mass of solute * 109
mass of solution
or
mass of solute
=
mass of solution
(*parts per billion—109)
?g
109 g solution
.
.
sample problem 5
Symptoms of mercury poisoning become
apparent after the ingestion of more than
20 mg of Hg. For a 70 kg person, convert
this to
a) % m/m
b) ppm
c) ppb
Answer:
a) % m/m = (20 x 10-3 g/70 x 103 g) * 100%
= 2.9 x 10-5 is percent Hg in body
b) ppm = (20 x 10-3 g/70 x 103 g) * 106
= 0.29 ppm Hg
c) ppb = (20 x 10-3 g/70 x 103 g) * 109
= 2.9 x 102 ppb Hg
HW
P 371 to 377, do several problems from
each set.