VOLUMETRIC ANALYSIS
We have already established that the number of moles of a substance can be obtained
by dividing the mass of a substance by the mass of one mole of it.
Often in chemistry chemical reactions are carried out in solution and we need to know
the number of moles of the substances present so that the reaction will take place in
the correct reacting quantities as determined by the equation for the reaction.
Concentration means the number of moles dissolved in 1000 cm3 (1 dm3) of a solvent,
usually water.
For example if we dissolve 58.5g of sodium chloride in 1dm3 of water then we have a
solution whose concentration is 1mole per dm3 (1mol dm-3)
If we dissolve 29.25g of sodium chloride in 1dm3 of water, what would be the
concentration in mol dm-3?
If we dissolved 5.85g of sodium chloride in 1 dm3 of water what would be the
concentration?
If we dissolve 5.85g of sodium chloride in 100cm3 of water what would be the
concentration?
If we dissolve 58.5g of sodium chloride in 2dm3 of water what would be the
concentration?
So, knowing the number of moles of a substance dissolved in a given volume we can
scale up or down to find the number of moles present in 1 dm3, which is the
concentration.
Sometimes we might express concentration in terms of the mass of a substance
dissolved in 1 dm3. For example, the concentration of a solution of sodium chloride is
0.25 moldm-3, what is its concentration in terms of mass?
1 mole of sodium chloride is 58.5g, therefore 0.25 mole is 14. 625g therefore the mass
concentration is 14.625g dm-3
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The concentration of a solution of sulphuric acid (H2 SO4 is 0.1 moldm-3, what is its
mass concentration?
Often, given the concentration of a solution, we may want to determine the number of
moles present in a given volume of the solution.
A solution of sulphuric acid has a concentration of 0.5 moldm-3 how many moles are
present in 25cm3 ?
How many moles are present in 1000cm3?
How many moles are present in 1 cm3?
So, how many moles are present in 25 cm3 ?
Use this method to answer the following questions:
A solution of nitric acid has a concentration of 0.1 moldm-3 calculate the number of
moles present in 15 cm3
A solution of sodium hydroxide (NaOH) has a mass concentration of 2.0g dm-3,
calculate the number of moles present in 25 cm3
How many moles of a 0.75 mol dm-3 solution of calcium hydroxide will be present in
35 cm3 of solution?
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We often need to perform these types of calculations when we carry out reactions in
solution, particularly if we want to calculate the concentration of one of the reactants
or products.
Often we would perform these reactions via a titration in a process known as
volumetric analysis.
In this process a solution of a reactant, A, whose concentration is usually known, is
added from an instrument called a burette (see below) to an accurately measured
volume of another reactant, B whose concentration is usually unknown. Some kind of
indicator previously added to B or another measuring instrument immersed in B tells
us when enough of A has been added to completely react with B.
An indicator is a solution whose colour changes when enough of one reactant has
been added to completely react with the other reactant.
The entire process is shown below:
a) Accurate delivery of a volume of B to a conical flask using a pipette
Pipette containing B
Conical flask
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b) Accurate delivery of reactant A to reactant B to which a few drops of indicator
have been added
Reactant A in a burette
Reactant B + indicator
Supposing we wanted to determine the concentration of B by reacting it with A,
whose concentration was known.





The volume of A needed to react with B would be determined.
The number of moles of A needed to react with B would be worked out.
The equation for the reaction would be consulted to see in what mole ratio A
reacts with B.
The number of moles of B would be worked out.
The concentration of B would be determined.
We can represent this process by a U- turn calculation chart. The U- turn template
for calculations is a series of operation boxes arranged like a flow chart in the
shape of a letter U. The rules of use of the template are:

The top left or right hand box contains the information you have been given.

The operation boxes that follow down a leg of the U are operations you
perform on the information you have been given.
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
The operation box at the bottom of the U contains the equation and mole ratio
of the substances you are interested in.

The operation boxes on the opposite leg of the U help you to work out the
mass or moles of the substance you need to produce an answer for.
Concentration of
A is known
Concentration of
B worked out
Volume of A added to
completely react with
B is determined
This number of
moles is present in
the volume of B
Work out the
number of moles
of B = y/n x
number of moles
of A
Number of moles of A
added is worked out
Equation consulted
nA + y B zC
Ratio of A:B = n:y
We can use the U- turn chart to perform volumetric calculations for example
complete the U- turn chart for the following reaction.
20 cm3 of a solution of sulphuric acid whose concentration was 0.2 mol dm-3 was
required to completely neutralise 25 cm3 of a solution of sodium hydroxide.
Calculate the concentration of sodium hydroxide:
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Concentration of sulphuric
acid = ___ mol dm-3
Therefore the
concentration of NaOH
= ___mol dm-3
___moles NaOH present in
___cm3 NaOH used in the
titration.
Volume of sulphuric acid added
to completely react with sodium
hydroxide =___ cm3
Number of moles of
NaOH reacted = ___x
__moles H2SO4; this is
___moles
Number of moles of sulphuric
acid present in this volume =
___moles
Equation consulted
H2SO4 + 2NaOH Na2 SO4 + 2H2O
Ratio = 1mole H2SO4 : __ mole NaOH
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The U- turn calculation can be extended to have as many steps as you want, for
example
Number of moles NaOH in
1000 cm3 = ______moles. So,
concentration = ___mol dm-3
Concentration of sulphuric
acid = ___ mol dm-3
Therefore the number of
moles NaOH in 1 cm3=
____moles
___moles NaOH present in 25
cm3 NaOH used in the
titration.
Number of moles H2SO4 present
in 1 cm3 = ____ moles
Number of moles of
NaOH reacted = ___x
__moles H2SO4; this is
___moles
Number of moles of sulphuric
acid present in volume added
(20cm3) = _____ moles
Equation consulted
H2SO4 + 2NaOH Na2 SO4 + 2H2O
Ratio = 1mole H2SO4 : __ mole NaOH
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Use a similar U- turn template as the one above but fill it in yourself for the
following problem:
30cm3 of aqueous ammonia was neutralised by 14 cm3 of a solution of sulphuric
acid whose concentration was 0.2 mol dm-3. Calculate the concentration of the
ammonia solution
Equation consulted:
H2SO4 + 2NH3 (NH4)2 SO4
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We will use U- turn calculations to solve other types of chemical problems to do with
the mole as well. We will meet these in the next chapter.
HOMEWORK
Use the U- turn template above to calculate the following:
The concentration of:
1) A solution of calcium hydroxide, when 20 cm3 of it was neutralised by 20 cm3 of a
solution of hydrochloric acid whose concentration was 0.5 moldm-3.
2) A solution of sulphuric acid, when 25 cm3 of it was used to neutralise a 15 cm3 of a
solution of sodium hydroxide whose concentration was 0.4 mol dm-3.
3) Consider the following reaction when a solution of 2.0mol dm-3 sodium hydroxide
was reacted with hydrochloric acid. Hydrochloric acid was added from a burette to 25
cm3 of the sodium hydroxide in 1 cm3 increments and the temperature measured after
each 1 cm3 had been added. The results are shown below:
VOLUME OF HCl / cm3
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
TEMPERATURE/C
22.0
26.5
30.1
33.9
37.2
35.3
32.3
29.1
26.0
23.2
20.1
a) Use a graphical method to determine the volume of HCl required to neutralise
the NaOH.
b) Use a U- turn calculation and template to determine the concentration of the
HCl.
4) A small corrie (upland lake) had a pH of 3 as a result of acid deposition which can
be regarded as H2SO4 . The concentration of hydrogen ions was 10-3 mol dm-3.
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What would be the concentration of the sulphuric acid?
The lake is approximately circular of diameter 200m and has an average
depth of 12 m.
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In order to restore the lake to pH 7 it has been decided to drop calcium
hydroxide from a light aircraft to neutralise the sulphuric acid.
Write a balanced equation for the reaction.
Use a U- turn calculation and template to calculate the mass of calcium
hydroxide that would need to be used to restore the lake to pH 7.
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