Chapter 15
Concentration of solutions
15.1 Concentration of solutions in g dm–3 and in
mol dm–3 (molarity/molar concentration)
15.2 Calculations related to the concentration of
solutions
Key terms
Progress check
Summary
Concept map
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15.1 Concentration of solutions in g dm–3
and in mol dm–3 (molarity/molar
concentration)
The concentration of a solution is the amount of
solute in a unit volume of the solution.
It is usually expressed in two ways:
in g dm–3 ;
in mol dm–3.
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Concentration of a solution in g dm–3
The concentration of a solution can be expressed
in grams of solute per dm3 of the solution (g dm–3).
Learning tip
1 dm = 10 cm; 1 dm3 = 1000 cm3
Key point
Concentration of a solution (g dm–3)
=
mass of solute (g)
volume of solution (dm3)
15.1 Concentration of solutions in g dm–3 and in mol dm–3
(molarity/molar concentration)
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Concentration of a solution in mol dm–3
(molarity/molar concentration)
The molarity (or molar concentration) of a
solution is the number of moles of solute per dm3
of the solution.
The unit of molarity is mol dm–3 or M.
Learning tip
‘M’ is pronounced as ‘molar’ but not ‘mole’.
Key point
Molarity of a solution (mol dm–3 or M)
number of moles of solute (mol)
________________________________________
=
volume of solution (dm3)
15.1 Concentration of solutions in g dm–3 and in mol dm–3
(molarity/molar concentration)
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E.g. one molar (1 M) solution contains 1 mole of
solute per dm3 of the solution.
The concentrations of aqueous bench reagents
are usually stated in molarity (mol dm–3).
Figure 15.1 The concentrations of
aqueous bench reagents are
usually stated in molarity (M).
15.1 Concentration of solutions in g dm–3 and in mol dm–3
(molarity/molar concentration)
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Converting molar concentration of a solution to
g dm–3
To convert the molar concentration of a solution to
g dm–3, substitute the following equation,
mass of solute (g)
Number of moles of solute (mol) =
molar mass of solute (g mol–1)
into the equation below:
Molarity of a solution number of moles of solute (mol)
=
(mol dm–3)/(M)
volume of solution (dm3)
15.1 Concentration of solutions in g dm–3 and in mol dm–3
(molarity/molar concentration)
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mass of solute (g)
(
)
–1
∴ molarity of a solution
molar mass of solute (g mol )
=
(mol dm–3)/(M)
volume of solution (dm–3)
Rearranging the above equation,
mass of solute (g)
volume of solution (dm3)
= molarity of a solution (mol dm–3) × molar mass of solute (g mol–1)
Key point
Concentration of a solution (g dm–3)
= molarity of a solution (mol dm–3) × molar mass of solute (g mol–1)
15.1 Concentration of solutions in g dm–3 and in mol dm–3
(molarity/molar concentration)
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Mass of
solute (g)
divided by molar
mass of solute
(g mol–1)
Number of moles
of solute (mol)
divided by
volume of the
solution (dm3)
Concentration
of the solution
in g dm–3
multiplied by
molar mass of
solute (g mol–1)
divided by
volume of the
solution (dm3)
Molarity of the
solution
(mol dm–3 or M)
Figure 15.2 Relationship between the amount of solute (in mass or in
number of moles), molarity of the solution and concentration of the
solution in g dm–3.
15.1 Concentration of solutions in g dm–3 and in mol dm–3
(molarity/molar concentration)
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15.2 Calculations related to the
concentration of solutions
Concentration of solutions
The concentration of a solution can be calculated
if the volume of the solution and the amount
of solute it contains are given;
if the density of the solution and the
percentage by mass of the solute in solution
are known.
Example 15.1
Example 15.2
Example 15.3
Class practice 15.1
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Number of moles of solute in a solution
The number of moles of solute in a solution can
be calculated from the molar concentration and
volume of the solution.
Example 15.4
Volume of solution
The volume of a solution can be calculated if the
specific amount of solute it contains and the molar
concentration of the solution are known.
Example 15.5
15.2 Calculations related to the concentration of solutions
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Mass of solute
The mass of solute present in a specific volume
can be calculated from a solution of known molar
concentration.
Example 15.6
Class practice 15.2
15.2 Calculations related to the concentration of solutions
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Dilution
A solution can be diluted (made less concentrated)
using water.
The process is called dilution.
During the dilution process,
only water is added to the concentrated
solution;
the volume of the solution increases;
the number of moles of solute remains
unchanged.
Think about
15.2 Calculations related to the concentration of solutions
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Learning tip
When a solution is concentrated by evaporation, the
number of moles of solute also remains unchanged.
As the same amount of solute dissolves in a
larger volume of solution, the concentration of
the solution decreases.
number of moles of solute = number of moles of solute
(before dilution)
or,
(after dilution)
M1V1 = M2V2
15.2 Calculations related to the concentration of solutions
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Before dilution
After dilution
adding water
Molarity of solution 1 = M1
Volume of solution 1 = V1
Molarity of solution 2 = M2
Volume of solution 2 = V2
Figure 15.3 Dilution of a solution. The amount of solute in the solution
remains unchanged after addition of water.
Example 15.7
15.2 Calculations related to the concentration of solutions
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Example 15.8
Concentration of constituent ions in a solution
The molar concentration of constituent ions in a
solution can be found if the molar concentration of
the solution is known.
Class practice 15.3
Example 15.9
15.2 Calculations related to the concentration of solutions
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Key terms
1.
2.
3.
concentration 濃度
dilution 稀釋
molarity/molar concentration 摩爾濃度
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Progress check
1. How do we define concentration?
2. What is the unit of concentration and molarity (or
molar concentration)?
3. How can molar concentration of a solution be
converted to g dm–3?
4. What is dilution? How do volume and
concentration of the solution change during
dilution?
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Summary
15.1 Concentration of solutions in g dm–3 and
mol dm–3 (molarity/molar concentration)
1.
The concentration of a solution is the amount of
solute in a unit volume of the solution. It is
usually expressed in g dm–3 or mol dm–3.
2.
Molarity of a solution (mol dm–3 or M)
number of moles of solute (mol)
=
volume of solution (dm3)
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3.
Concentration of a solution (g dm–3)
= molarity of a solution (mol dm–3) × molar mass
of solute (g mol–1)
15.2 Calculations related to the concentration of
solutions
4.
5.
Number of moles of solute (mol)
= molarity of solution (mol dm–3) × volume of
solution (dm3)
Volume of solution (dm3)
number of moles of solute (mol)
=
molarity of solution (dm3)
Summary
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6.
7.
Mass of solute (g)
= volume of solution (dm3) × molarity of solution
(mol dm–3) × molar mass of solute (g mol–1)
Dilution is the process of adding water to a
concentrated solution to reduce its
concentration. In diluting a solution, the number
of moles of solute remains unchanged:
M1V1
= M2V2
(before dilution)
(after dilution)
where M1 = molarity of solution 1;
V1 = volume of solution 1;
M2 = molarity of solution 2;
V2 = volume of solution 2
Summary
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Concept map
CONCENTRATION OF SOLUTION
Concentrated
solution
dilution
__________
Diluted
solution
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CONCENTRATION OF SOLUTION
can be calculated as
Mass of solute (g)
__________________
Number
of moles of solute (mol)
______________________
Volume of solution (dm3)
Volume of solution (dm3)
with unit
g
dm–3
molar mass of
______________
×
solute (g mol−1)
______________
Molarity
Molar concentration
(or ________________)
with unit
mol dm–3 (or M)
Concept map
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