PER CENT BY MASS
SECTION I
One of the methods of expressing the concentration of solutions is per cent by mass. This refers to
a given weight of solute in 100 g of solution. For example. a 10% sodium chloride solution contains 10 g
NaCl in 100 g of solution, i.e. the solution is composed of 10 g of NaCl and 90 g of water.
If the mass of solute and the weight of the solution are given, then it is possible to calculate the per
cent of the solute by weight.
EXAMPLE I
A solution contains 2 g of NaCl in 40 g of solution. Calculate the per cent of NaCl by mass.
SOLUTION
2 g of NaCl were dissolved to give 40 g of solution
? g of NaCl were dissolved to give 100 g of solution
10  2
= 5%
40
Using ratio and proportion 2g NaCl ≈ 40 g of solution
x ≈ 100 g of solution
(x) (40) = (100) (2)
x=
(100)(2)
 5%
40
EXAMPLE 2
What mass of NaNO3 is contained in 170 g of a 15% solution of NaNO3 by mass?
SOLUTION
In 100 g of solution there are 15 g of NaNO3
In 170 g of solution there are ? g of NaNO3
170  15
= 25.5 g
100
Using ratio and proportion:
15 g NaNO3 ≈ 100 g solution
? ≈ 170 g solution
(100)(x) = (15)(170)
x=
(15)(170)
= 25.5
100
The mass of water in this solution is the difference between the mass of solution and the mass of
the solute 170 - 25.5 = 144.5 g.
EXAMPLE 3
How many grams of H2SO4 are contained in 65 ml of sulfuric acid solution of 1.82 g/ml density
and containing 38.5% H2SO4 by mass?
Since the density of the H2SO4 solution is given, then the mass of the solution is obtained from:
M = DV
M = 1.82 g/ml  65 ml = 118.3 g weight of solution
H2SO4 is 38.5% by mass, then the weight of H2SO4 is obtained by multiplying the per cent of
H2SO4 by the mass of solution.
38.5
 118.3 = 45.5 g of H2SO4
100
Using ratio and proportion:
38.5
x

100 118.3
(100)(x) = (118.3)(38.5)
x=
118.3  38.5
 455
.
100
SECTION II
1.
10 g of NaCl are dissolved in 70 g of water. Calculate the per cent of NaCl in the solution.
2.
How many grams of NaOH are there in 50 g of 15 per cent solution of NaOH by mass?
3.
How many grams of water and how many grams of salt would you use to prepare 50 g of a 5 per
cent solution of NaCl?
4.
The mass of 16 ml of a solution is 11 g. Calculate the density of the solution.
5.
The density of a solution is 1.2 g/ml. Calculate the mass of 150 ml of the solution.
6.
15 g of KCl are dissolved in 90 ml of solution. The density of the solution is 1.2 g/ml. Calculate
the per cent of KCl in the solution.
ANSWERS TO SECTION II
1.
2.
3.
4.
5.
6.
12.5%
7.5 g NaOH
2.5 grams of salt and 47.5 grams of water
.69 g/ml
180 g
13.9%