1.
Introduction - reminders of what molarity is
- This page is all about a quantitative
chemical procedure called a
titration.
- We use a titration technique to find
out exactly, the concentration of a specified solute in
solution.
- e.g. you can find out precisely how much
of an acid solution (this volume is called the titre) is
needed to neutralise an accurately measured out volume of an
alkali, or the other way round.
- e.g. if you know the concentration of the
acid, together with this, and the two volumes of the solutions
required for neutralisation, you can calculate the unknown
concentration of the other alkaline solution.
- How to do titrations to find the
concentration of an acid or alkali from the relative volumes
used and the concentration of one of the two reactants are
described in the method and apparatus
sections of further down the page.
- Before studying this section you should
work your way through section 11.
Molarity, volumes and solution
concentrations
- You should be able to carry out calculations involving
neutralisation reactions in aqueous solution given the balanced equation or
from your own practical results.
- The examples in
section 7. moles and mass. and
section 11. concentration will
help you follow the calculations below.
-
Note again:
1dm3 = 1 litre = 1000ml = 1000 cm3, so dividing
cm3/1000 gives dm3.
-
and other useful formulae or relationships are:
- molarity (mol/dm3)
= mol / volume (dm3 = cm3/1000),
- moles = molarity
(mol/dm3) x volume (dm3 = cm3/1000),
- volume = moles / molarity
- 1 mole = formula mass
in grams.
- In most volumetric
calculations of this type, you first calculate the known
moles of one reactant from a volume and molarity.
- Then, from
the equation, you relate this to the number of moles of the
other reactant, and then with the volume of the unknown
concentration, you work out its molarity.
- I haven't quoted separately the
atomic masses used in the titration calculations, but they
quoted as part of the calculation and its pretty obvious what is
what!
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and sub-index
2.
Examples of how to do acid - alkali titration calculations
- Titration calculation
Example 12.1
- Given the equation:
NaOH(aq)
+ HCl(aq) ==> NaCl(aq) + H2O(l)
- This is read as 1 mol + 1 mol
reactants ===> 1 mol + 1 mol products
-
25.0 cm3 of a sodium hydroxide solution was
pipetted into a conical flask and titrated with a standard solution of 0.200 mol dm-3
(0.2M) hydrochloric acid (mol dm-3
means mol/dm3).
- Using phenolphthalein indicator
for the titration it was found that 15.0 cm3 of the acid was
required to neutralise the alkali. In the appendix this is titration
procedure 3.
- Calculate the molarity of the sodium
hydroxide and its concentration in g/dm3.
- moles = molarity x volume
(in dm3 = cm3/1000)
- moles HCl = 0.200 x (15.0/1000) = 0.003 mol
- moles HCl = moles NaOH (1 : 1 in equation)
- so there is 0.003 mol NaOH in 25.0 cm3
- scaling up to 1000 cm3
(1 dm3),
there are ...
-
0.003 x (1000/25.0) = 0.12 mol NaOH in 1 dm3
- molarity of NaOH is 0.120 mol
dm-3 (or 0.12M)
- since mass = moles x formula mass
- and Mr(NaOH)
= 23 + 16 + 1 = 40
- concentration in g/dm3
= molarity x formula mass
- concentration in g/dm3
is 0.12 x 40 = 4.80 g/dm3
- Titration calculation
Example 12.2
-
Given the equation:
2KOH(aq)
+ H2SO4(aq) ==> K2SO4 + 2H2O(l)
- This is read as 2 mol + 1 mol
reactants ===> 1 mol + 2 mol products
- 20.0 cm3 of a sulphuric acid solution was
titrated with a standardised solution of 0.0500 mol/dm3 (0.05M) potassium hydroxide.
- Using phenolphthalein indicator
for the titration, the acid required 36.0 cm3
of the alkali KOH for neutralisation what was the concentration of the acid?
In the appendix this is titration procedure 2.
- moles = molarity x volume
(in dm3 = cm3/1000)
- mol KOH = 0.0500 x (36.0/1000) = 0.0018 mol
- mol H2SO4
= mol KOH / 2 (because
of 2 : 1 ratio in equation above)
-
mol H2SO4
= 0.0018/2 = 0.0009 (in
20.0 cm3)
- scaling up to 1000 cm3
of solution = 0.0009
x (1000/20.0) = 0.0450 mol
- mol H2SO4 in 1 dm3 =
0.0450
-
so molarity of H2SO4
= 0.0450 mol dm-3 (0.045M)
- since mass = moles x formula mass
- and Mr(H2SO4)
= 2 + 32 + (4x16) = 98
- concentration in g/dm3
is 0.045 x 98 = 4.41 g/dm3
- -
- Titration Calculation
Example 12.3
-
Given the equation:
NaOH(aq)
+ HCl(aq) ==> NaCl(aq) + H2O(l)
- This is read as 1 mol + 1 mol
reactants ===> 1 mol + 1 mol products
- 25.00 cm3
portions of a dilute hydrochloric acid solution were titrated
with a standard solution of sodium hydroxide of concentration 0.250
mol/dm3 (mol dm-3). In the appendix this is titration procedure
2.
- Using phenolphthalein indicator
for the titration, it was found that the average titration was
18.50 cm3 of sodium hydroxide, calculate (i) the
molarity of the hydrochloric acid and (ii) its concentration in
g/dm3.
- moles NaOH = molarity
NaOH x volume of NaOH
(in dm3 = cm3/1000)
- moles NaOH = 0.250 x
(18.5 / 1000) = 0.004625
- In the equation 1 mole of HCl
reacts with 1 mole of HCl
-
therefore in the titration
reaction: moles HCl = moles NaOH
- therefore there were 0.004625
moles HCl in 25.00 cm3.
- molarity = moles / volume in
dm3 (1 dm3 =
1000 cm3)
- (i) molarity HCl =
0.004625 / (25.00/1000) = 0.004625/0.025 =
0.185 mol/dm3
- (ii) concentration =
molarity x formula mass
- formula mass HCl = 1 +
35.5 = 36.5
- = 0.185 x 36.5 =
6.75 g/dm3
- -
- Titration Calculation
Example 12.4
- Given the equation:
2NaOH(aq)
+ H2SO4(aq) ==> Na2SO4 + 2H2O(l)
- This is read as 2 mol + 1 mol
reactants ===> 1 mol + 2 mol products
- 25.00 cm3 portions of
a sodium hydroxide were titrated with a standardised solution of
0.75 mol/dm3 sulphuric acid solution using
phenolphthalein indicator. In the appendix this is titration
procedure 1.
- If the average titration was
17.70 cm3 of sulfuric acid, what is the molar
concentration of the sodium hydroxide?
-
moles H2SO4
in titration = molarity H2SO4 x volume in
dm3
- moles H2SO4
= 0.75 x (17.70/1000) = 0.013275 mol
- From the balanced equation, for
every mole of H2SO4, two moles of NaOH
react
- Therefore moles NaOH = 2 x moles
H2SO4
- moles NaOH = 0.013275 x 2 =
0.02655 mol
- molarity of NaOH = moles NaOH /
volume in dm3
- molarity NaOH = 0.02655 /
(25.00/1000) = 1.062 mol/dm3
- -
- Titration Calculation
Example 12.5
-
Given the equation:
NH3(aq) +
HCl(aq) ==> NH4Cl(aq)
- This is read as 1 mol + 1 mol
reactants ===> 1 mol products
- 5.00 cm3 portions of
household ammonia were titrated with a standard hydrochloric
acid solution of 1.00 mol/dm3. In the appendix this
is titration procedure 2.
- If the average titration, using
methyl orange indicator, was 22.5 cm3 of hydrochloric
acid, calculate ...
- (i) the molarity of the ammonia solution, and
its concentration in (ii) g/dm3 and (iii) g/cm3.
- (i) mol HCl in titration =
molarity HCl x volume of HCl in dm3
- mol HCl = 1.00 x (22.50/1000) =
0.0225 mol HCl
- From the equation, 1 mole of NH3
reacts with 1 mole of HCl
- Therefore mol HCl = mol
NH3 = 0.0225
-
molarity of NH3 = mol
NH3 / volume NH3in dm3
- molarity of NH3
= 0.0225 / (5.00/1000) =
4.50 mol/dm3
- (ii) concentration = formula
mass x molarity
- formula mass NH3 = 14
+ (3x1) = 17
- concentration of NH3
= 17 x 4.50 = 76.5 g/dm3
- (iii) since there are 1000 cm3
in 1 dm3
- concentration of NH3
= 76.5/1000 = 0.0765 g/cm3
- -
- Titration Calculation
Example 12.6
- Given the equation: CH3COOH(aq)
+ NaOH(aq) ==> CH3COONa(aq) + H2O(l)
- This is read as 1 mol + 1 mol
reactants ===> 1 mol + 1 mol products
-
25.00 cm3 portions of vinegar (ethanoic acid,
CH3COOH, 'acetic acid' solution) from a local supermarket were
pipetted into a conical flask and titrated with a standardised
solution of sodium hydroxide, of concentration 0.2000 mol/dm3
using phenolphthalein indicator. In APPENDIX 2 this is
titration is described in procedure 2.
- (i) If the average titration
value was 14.70 cm3 of the sodium hydroxide solution,
what is the molarity of the ethanoic acid in the vinegar?
-
moles NaOH in titration =
molarity x volume in dm3
- mole NaOH = 0.200 x (14.70/1000)
= 0.00294 moles
- from the equation moles NaOH =
moles CH3COOH = 0.00294
-
molarity CH3COOH =
mol CH3COOH/volume CH3COOH in dm3
-
molarity CH3COOH
= 0.00294 / (25.00/1000) =
0.1176 mol/dm3
-
(ii) What is the concentration of the ethanoic acid in
g/dm3?
- mass = moles x formula mass
- formula mass of CH3COOH = 12 +
3 + 12 + 16 + 16 + 1 = 60
- mass CH3COOH = 0.1176 x 60 =
7.056g (in 1 dm3, 1000 cm3)
- concentration =
7.06 g/dm3
(2dp, 3sf)
- for other mass/volume values ...
- eg if you were asked for the
concentration in g/100cm3,
- divide the g/dm3 by 10 giving
0.706g/100cm3
- or if you were asked for the
concentration in g/cm3,
- divide the g/dm3 by 1000
giving 0.00706 g/100cm3
- You can also work out the vinegar
concentration from the original moles and volume of the
titration eg
- mass = moles x formula mass
- mass = 0.00294 x 60 = 0.1764g in the 25
cm3 sample titrated.
- Since 25cm3 = 25/1000 = 0.025
dm3
- concentration = 0.1764 / 0.025 =
7.06g/dm3
- (iii) If a bottle of vinegar from
the super-market contained 250 cm3 of liquid, how
many grams of ethanoic acid are in the solution?
- concentration CH3COOH
= formula mass CH3COOH x molarity of CH3COOH
- formula mass CH3COOH
= 12 + (3x1) + 12 +(2x32) + 1 = 60
- concentration CH3COOH
= 60 x 0.1176 = 7.056 g/dm3
- Since 1 dm3 = 1000 cm3, there
must be proportionately
- 7.056 x (250/1000) =
1.76
g of CH3COOH in the bottle of vinegar
(3 sf)
- -
- Titration Calculation
Example 12.7
A titration to determine the solubility of calcium hydroxide in
water.
-
Approximately 250 cm3
of water was shaken with solid calcium hydroxide (slaked lime)
until no more appeared to dissolve and the solution filtered to
remove any excess undissolved solid. You now have a saturated
solution known as limewater.
- 25.00 cm3 of the
filtered calcium hydroxide solution (limewater) was pipetted
into a conical flask and titrated with standard hydrochloric
solution (0.100 mol/dm3) using phenolphthalein
indicator until the pink colour just disappeared (the
end-point). The experiment was repeated several times giving an
average HCl titration of 10.0 cm3.
- Calculate the concentration of
the calcium hydroxide in mol/dm3 and g/dm3.
- The equation for the titration
is: Ca(OH)2 + 2HCl ==> CaCl2 + 2H2O
- This is read as 1 mol + 2 mol
reactants ===> 1 mol + 2 mol products
-
moles = molarity x volume (dm3)
- mol HCl in titration = 0.10 x
10.0/1000 = 0.0010
- Therefore from the equation: mol
Ca(OH)2 = mol HCl/2 = 0.0005
-
Molarity of Ca(OH)2
= moles/volume = 0.0005 / (25.00/1000) = 0.0005 / 0.025 =
0.02 mol/dm3
-
concentration g/dm3 = molarity x
formula mass
- Atomic masses: Ca = 40, O = 16,
H = 1, Mr[CaOH)2] = 74
-
Concentration of Ca(OH)2
= 0.02 x 74 = 1.48 g/dm3
- -
NOTE:
If you have a question based on nitric acid
(HNO3), they are the same as for hydrochloric acid (HCl)
because both acids have one acidic proton (H), so balancing equations involves
the same numbers.
Self-assessment quizzes and questions on acid -
alkali titrations
Type in answer
Honly or
multiple choice
Honly
Advanced level
GCE-AS-A2 acid-alkali titration calculation questions
More questions
involving molarity in
section 11.
introducing molarity and
section 14.3
on dilution
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and sub-index
3. The
basic procedure for carrying out an acid - alkali titration
A variety of
apparatus you might come across, particularly
the pipette (1) for measuring accurately volumes of
solutions to be analysed by titration with a standard
solution in a burette (3)
with the chemicals mixing in a conical flask (4).
- The diagram above shows the typical
apparatus (1)-(6) used in manipulating liquids and on the left a brief three
stage description of titrating an acid with an alkali:
- (i) An accurate volume of acid is
pipetted into the conical flasks using a suction bulb and pipette for health and safety
reasons. Universal indicator is then added, which turns red in the
acid.
- The
alkali, of known accurate
concentration, is put in the burette and you can conveniently
level off the reading to zero (the meniscus on the liquid surface should
rest on the zero -- graduation mark).
- Note other
possibilities are:
- (ii) An accurate volume of alkali is
measured into a flask and titrated with an acid solution of known
concentration.
- (iii) A small amount of accurately
weighed solid acid is dissolved in water and titrated with alkali.
- (iv) A small amount of accurately
weighed solid alkali is dissolved in water and titrated with acid.
- This can procedure can be
used to compare the effectiveness of ant-acid indigestion
tablets, which are designed to neutralise excess acid in the
stomach. (more
details further down the page)
- A known and equal mass of each
brand of indigestion tablet is crushed and mixed with some water
eg 20 cm3 (fair test points).
- Make sure the mixture is gently
swirled to completely dissolve the crushed tablet powder.
- The burette is filled with a
standard solution of hydrochloric acid and zeroed to the top
calibration mark of 0.00 cm3.
- Universal indicator is added to
the flask and the indigestion powder should turn it blue -
alkaline.
- The acid is carefully and slowly
added until the indicator turns green - neutral at the end-point
of the titration.
- You then read the volume of acid
required to neutralise the ant-acid powder.
- The bigger the volume of acid
required for neutralisation, the more effective the indigestion
powder per mass of powder.
- Repeat the procedure with
another brand of indigestion powder using the same standard acid
solution (fair test).
- For (i) The alkali is then carefully added by
running it out of the burette in small quantities into the acid solution, controlling the flow
with the tap, until the indicator seems to be going yellow-pale green.
- The conical flask should be carefully swirled after each addition of alkali
to ensure all the alkali reacts.
- Near the end of the titration, the
alkali should added drop-wise until the universal indicator goes green.
- This is called the end-point of the titration and the
green means that all the acid has been neutralised.
- The volume of alkali
needed to titrate-neutralise the acid is read off from burette scale, again
reading the volume value on the underside of the meniscus.
- The calculation
can then be done to work out the concentration of the alkali.
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and sub-index
4. How
do you choose the right indicator for an acid - alkali
titration?
- Universal indicator, and most
other acid-base indicators, work for strong acid and alkali titrations, but
universal indicator is a somewhat crude indicator for other acid-alkali
titrations because it gives such a range of colours for different pH's. Examples of more accurate and 'specialised' indicators are:
-
titrating a strong alkali
with a strong acid (or vice versa):
- e.g. for sodium hydroxide (NaOH)
- hydrochloric/sulphuric acid (HCl/H2SO4)
titrations, use ...
- phenolphthalein indicator (pink
in alkali, colourless in acid-neutral solutions), the end-point is the
pink <==> colourless change.
- Litmus works too, the end point is the
red <==> purple/blue colour change AND with universal indicator you see green
at the endpoint, but these two indicators are NOT as accurate as
phenolphthalein.
- They are ok as simple demonstration to
illustrate the principles of a titration, BUT, they should not be used
for quantitative work.
-
titrating a weak alkali with
a strong acid:
- e.g. for titrating ammonia (NH3)
with hydrochloric/sulfuric acid (HCl/H2SO4), use
...
- methyl orange indicator (red in
acid, yellowish-orange in neutral-acid), the end-point is an 'orange'
colour, not easy to see without experience.
- screened methyl orange indicator
is a slightly different dye-indicator mixture that is reckoned to be
easier to see than methyl orange, the end-point is a sort of 'greyish
orange', but still not easy to do accurately.
-
titrating a weak acid with a strong alkali:
- e.g. for titrating ethanoic acid
(CH3COOH) with sodium hydroxide (NaOH), use ...
- phenolphthalein indicator (pink
in alkali, colourless in acid-neutral solutions, pink in alkali), the
end-point is the first permanent pink. when the solution just
becomes alkaline.
- methyl red indicator (red in
acid, yellow in neutral-alkaline), the end-point is 'orange'.
-
titrating a weak acid with a
weak alkali (or vice
versa):
- These are NOT practical
titrations because the pH changes at the end-point are not great
enough to give a sharp colour change with any indicator.
Indicator |
colour
in acid pH<7 |
colour
in neutral pH=7 |
colour
in alkali pH >7 |
litmus |
red |
'purple' |
blue |
phenolphthalein |
colourless |
colourless |
>9 pink |
methyl
orange |
<3.5 red,
orange
about pH 5, > 6 yellow |
yellow |
yellow |
methyl red |
<5 red,
orange, >6 yellow |
yellow |
yellow |
bromothymol
blue |
<6 yellow |
green |
>8 blue |
* Used in
titrations - see section 10, litmus is NOT a good indicator for use in
accurate titrations.
Summary: Three common indicators for titrations and their
colours:
litmus: red in acid, blue in alkali, doesn't give
that sharp a colour change except with moderately concentrated solutions, the
neutralisation end-point is a fairly sharp change red<=>blue
phenolphthalein: colourless in acid, pink in
alkali, the neutralisation end-point is the sharp change colourless<=>pink
methyl orange: red in acid, yellow in alkali, the
neutralisation end-point is an orange
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and sub-index
EXAMPLES OF
TITRATIONS
5.
An Antacid Indigestion Tablet
Investigation
This first titration
description also acts as an
introduction as how to do a TITRATION with a burette and conical flask etc. AND
it doesn't involve complex titration calculations, other titrations are
described in Appendix 2. which do involve calculations.
There is also a paragraph on
errors and reasons for repeating a titration several times.
Introduction
There are many
brands of antacid indigestion medications on the market and
through the following experimental investigation you can
check out their value for money. There are various ways you
can approach the investigation e.g. you can compare tablet
with tablet in terms of the recommended dose as to which
neutralises the most acid. You can compare the cost of each
tablet with the amount of acid it neutralises.
Experimentally, the investigation involves
titrating an indigestion tablet (weighed) with standardised hydrochloric acid
(in the burette, to represent stomach acid) using methyl orange indicator
to observe when the tablet has been completely neutralised,
that point is known as the end-point of the titration.
The apparatus, chemicals and indicator colours are
illustrated in the diagram on the left and the
procedure described in five stages below.
Preparing the sample and titration
procedure
Initially the burette
is clamped carefully in a vertical position and filled with
standard
hydrochloric acid of known concentration. A burette is a
long glass tube (open at the top), and accurately calibrated
for volume in cm3 an 1/10th
cm3 intervals, with a tap and tip at the lower
end.
For safety reasons wear safety
glasses, initially work below eye level, using a funnel, the acid is carefully added from the stock bottle down
in to the burette, avoid spillage, until the level is above
the 0.00 cm3 scale mark.
This burette filling is done below eye level in case of spillage down into
your eyes - goggles/safety glasses, which you should be wearing, do not protect from liquid falling onto
your forehead!
The acid is run through to
expel any air bubbles in the tip or tap until the reading
below the meniscus is 0.00 cm3 (the reading
on the above diagram is 7.00 cm3, which could represent
a small titration value).
All burette readings should be
made at eye level and taking the value exactly below the
meniscus on the burette scale.
The burette is usually
calibrated to a maximum 50.00 cm3 (only 10.00 cm3
in diagram - I couldn't fit rest of scale on!). Now we are
ready to take the antacid indigestion tablet!
The
weighed tablet is crushed up and dissolved in e.g. 25 cm3
or 50 cm3 of pure water (for other tablets keep
to the same volume of water as part of the fair test).
Add a few drops of methyl orange
indicator to the tablet solution and it should turn yellow
for an alkali. Carefully place the conical flask under the
tip of the burette so drops don't go astray!
The
titration: You carefully add small portions of the
hydrochloric acid, swirling after each addition and checking the colour
of the indicator (although not shown in the diagram, its good to
stand the flask on white tile to see the colour changes
better).
At the start of the
titration the methyl orange indicator is yellow.
As you add the acid you
get 'splurges' of reddish-orange colour until the mixture is
swirled in the conical flask and the yellow is temporarily
restored.
The swirling of the flask
contents is important, it ensures all the added hydrochloric
acid reacts with the antacid indigestion tablet solution
i.e. everything gets well mixed up and reacted.
Try
to add dropwise (to avoid overshooting) when you seem to be near the
orange colour
at the end-point as the yellow indicator colour begins
to fade.
The indicator colour at the end-point is orange
and indicates all the dissolved tablet has been neutralised.
At the end-point you take the titration reading by
carefully reading the burette scale under the meniscus
(think of the underside of the meniscus as sitting on your
reading - see diagram on the right illustrating a reading of
24.5 cm3).
To get the titration value you subtract the1st
reading from the 2nd.
The first reading might be zero (0.00
cm3) BUT you can do subsequent titrations without
refilling the burette every time, again you just subtract
the 1st reading from the 2nd.
You continue to use the
burette like this until in needs refilling for further
titrations.
If
you 'overshoot' the titration with excess acid, the
methyl orange indicator turns red and the result is
invalid.
The
first titration you do is likely to be the most inaccurate
until you 'get your eye in'. This is called the rough
titration and you can do the next titration quite
rapidly until near the end-point and then proceed slowly and
accurately to the end-point itself.
The
titration should be repeated several times with the same
brand of and the
average (mean) titration value calculated to use in any
subsequent calculations.
This makes the experimental results
more valid and reliable, as will any subsequent calculations
and conclusions based on the data recorded.
The procedure
should then be repeated with different brands of antacid
indigestion tablets and the results compared.
You should
keep to the same volumes of water and the same concentration
of hydrochloric acid throughout the whole class/individual
investigation.
Using a whole class you could amass quite a
bit of data by dividing the work up amongst the pupils.
Data and analysis of
the results
There are various ways in which
you can interpret the results, so here are a few ideas.
(a) Initially you can compare
the volume of acid needed to neutralise an individual
tablet, which is simply X cm3 of HCl
neutralised per tablet. This gives a straightforward
comparison, the bigger the titration the more stomach acid
would be neutralised.
(b) If you have weighed the
tablet, which I recommend you do, you can compare the
effectiveness of the antacid tablets in terms of acid per
mass of tablet i.e. X cm3 of HCl neutralised
per gram tablet (cm3/g). So this measure the
effectiveness of the tablet based on mass ('weight').
(c) If you know the cost of the
packet of indigestion tablets, you can work out the cost of
an individual tablet. Then you can calculate the 'cost
effectiveness' of the medication by dividing the titration
value by the cost per tablet e.g. X cm3 of HCl
neutralised per cost of tablet (cm3/p)
TOP OF PAGE
and sub-index
6.
Extra note - Why
repeat titrations several times?
-
To be
reasonably sure of your final result, you cannot
base it on one titration, no matter how perfectly
you think you have done it.
-
You need
repeated AND consistent burette readings.
-
There can
be many source of errors, some random, and, worst of
all, some systematic error to do with your
laboratory equipment or your titration technique.
Errors may
arise from ...
dirty
apparatus, grease in the burette can cause
traces of liquid to remain, so giving a
false larger than actual titration reading,
sometimes a
result doesn't fit in at all with the other
results (referred to as an 'outlier'), may
be due to carelessness in observing the
end-point or poor pipetting etc. - human
error,
apparatus may
be faulty,
-
If your
results are close together, this is a good sign -
consistent readings imply you have been accurate in
your titrations.
Your first
titration is very likely to be a bit inaccurate,
and is referred to as the initial rough
titration.
This gives you an
approximate value to aim for much more
accurately in subsequent titrations.
-
After
repeating the titrations accurately e.g. three
times, you then average your results and use the
average in your calculations.
You titration, at
best, is likely to be measured to the nearest
0.05 cm3, but you can use the average
to two decimal places because statistically,
that is the most probable value.
e.g. suppose you
got burette reading titration values of 21.45,
21.40, 21.45 (which would be impressive!),
the
average is 21.43 cm3, and
that goes into the calculation of ....
However, if a titration
reading seems way out, 'posh word', anomalous,
it should be ignored and not included in you
calculation e.g. if a titration value of 21.75
was obtained, its not close enough to the other
three values to be considered of value.
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and sub-index
APPENDIX 2 - More examples of HOW TO DO
TITRATIONS - apparatus and procedures
7.
Titration 1. The
titration of a weak base-alkali with a strong acid
e.g
titrating ammonia (pipetted) with standardised hydrochloric acid
(of known concentration in the burette) using methyl orange indicator
The apparatus, chemicals and indicator colours are
illustrated in the diagram on the left.
Initially the burette is clamped carefully in position and filled
with standard hydrochloric acid (e.g. 0.10 to 1.0 mol/dm3,
but accurately known, preferably to 4 sig. figs.).
You wear safety glasses and work below
eye level when filling the burette safely using a funnel
until a bit above the 0.00 cm3 mark.
The acid is run through until the reading
below the meniscus is 0.00 cm3 (the reading
in the diagram is 7.00 cm3, which could represent
a small titration value). The burette is usually
calibrated on the scale to 50.00 cm3 in
0.10 cm3 increments (only 10.00 cm3
in diagram - couldn't fit rest of scale on!)
The
ammonia solution is accurately measured out into the conical
flask with e.g. a 25 cm3 pipette and suction bulb
(see diagram further down).
You suck the ammonia solution up to a few
cm above the calibration mark and then let it run down until
the meniscus rests on the calibration mark (top of right
diagram).
Add a few drops of methyl orange
indicator to the ammonia solution and it should turn yellow
for an alkali. Carefully place the conical flask under the
tip of the burette so drops don't go astray!
The
titration: You carefully add small portions of the
acid, swirling after each addition and checking the colour
of the indicator (not shown in the diagram, but its good to
stand the flask on white tile).
At the start of the
titration the methyl orange indicator is yellow.
As you add the acid you
get 'splurges' of reddish-orange colour until the mixture is
swirled in the conical flask.
The swirling of the flask
contents is important, it ensures all the added hydrochloric
acid reacts with the ammonia solution.
Try
to add dropwise when you seem to be near the orange colour
at the endpoint.
The end-point is an orange colour
indicating when all the ammonia
is neutralised by which ever acid you are using.
You taking the reading of the
volume of the hydrochloric acid on the scale line the
meniscus lies on (see lower part of diagram above on the
right).
If
you 'overshoot' the titration with excess acid, the methyl
orange indicator turns red and the result is invalid.
The titration should be repeated
several times with other 25 cm3 portions and the
average (mean) titration value calculated to use in any
subsequent calculations.
How to calculate the
concentration of the weak alkali is explained in the top
half of the page.
The theory of which indicator
to use is explained on the
Changes in pH in a
neutralisation, choice and use of indicators page.
There is also a paragraph on
errors and reasons for repeating a titration several times.
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and sub-index
8.
Titration 2. The
titration of a weak/strong a strong acid with sodium
hydroxide solution
e.g
titrating ethanoic acid or hydrochloric acid (pipetted) with standardised
sodium hydroxide solution (of known concentration in burette) using
phenolphthalein indicator
The apparatus, chemicals and indicator colours are
illustrated in the diagram on the left.
Initially the burette is clamped carefully in position and
using a funnel, it is filled
with standard sodium hydroxide solution (e.g. 0.10 to 1.0
mol/dm3, but accurately known, preferably to 4
sig. figs.).
Wearing goggles, pour in using a
funnel and work below eye level.
The sodium hydroxide solution is run through until the reading
below the meniscus is 0.00 cm3 (the reading
in the diagram is 7.00 cm3, which could represent
a titration value). The burette is usually
calibrated on the scale to 50.00 cm3 in
0.10 cm3 increments (only 10.00 cm3
in diagram - couldn't fit rest of scale on!)
The
acid solution is accurately measured out into the conical
flask with e.g. a 25 cm3 pipette and suction bulb
(see diagram further down).
Add a few drops of
phenolphthalein
indicator to the acid solution and it should turn colourless
for an acid. Carefully place the conical flask under the tip
of the burette so drops don't go astray!
The
titration: You carefully add small portions of the
sodium hydroxide, swirling after each addition and checking the colour
of the indicator (not shown in the diagram, but its good to
stand the flask on white tile).
At the start of the
titration the phenolphthalein indicator is colourless.
As you add the alkali you
get 'splurges' of pink colour until the mixture is
swirled in the conical flask.
The swirling of the flask
contents is important, it ensures all the added sodium
hydroxide reacts with the acid in the flask.
Try
to add dropwise when you seem to be near the faint pink colour
of the endpoint.
The
end-point is the first faint, but permanent pink colour, that is when all the
acid is neutralised by the sodium hydroxide.
You taking the reading of the volume
of the sodium hydroxide on the scale line the meniscus lies
on (see lower part of diagram above on the right).
If
you 'overshoot' the titration with excess alkali, the
phenolphthalein indicator becomes an even deeper
pinkish-red and the result is invalid.
The titration should be repeated several times
with other 25 cm3 portions and the average (mean)
titration value calculated to use in any subsequent
calculations.
How to calculate the
concentration of the weak acid is explained in the top half
of the page.
The theory of which indicator
to use is explained on the
Changes in pH in a
neutralisation, choice and use of indicators page.
There is also a paragraph on
errors and reasons for repeating a titration several times.
|
TOP OF PAGE
and sub-index
9.
Titration 3. The
titration of a strong base-alkali with hydrochloric solution
e.g
titrating sodium hydroxide solution (pipetted) with standardised
hydrochloric solution (of known concentration in burette) using
phenolphthalein indicator
The apparatus, chemicals and indicator colours are
illustrated in the diagram on the left.
Initially the burette is clamped carefully in position and filled
with standard hydrochloric acid (e.g. 0.10 to 1.0 mol/dm3,
but accurately known, preferably to 4 sig. figs.).
Wear safety glasses and initially work
below eye level - so nothing can fall on your face!
Using a
funnel, the
hydrochloric acid is run through until the reading
below the meniscus is 0.00 cm3 (the reading
in the diagram is 7.00 cm3, which could represent
a titration value). The burette is usually
calibrated on the scale to 50.00 cm3 in
0.10 cm3 increments (only 10.00 cm3
in diagram - couldn't fit rest of scale on!)
The
alkali solution is accurately measured out into the conical
flask with e.g. a 25 cm3 pipette and suction bulb
(see diagram further down).
Add a few drops of
phenolphthalein indicator to the alkali solution and it should turn
deep pink
for an alkali. Carefully place the conical flask under the
tip of the burette so drops don't go astray!
The
titration: You carefully add small portions of the
acid, swirling after each addition and checking the colour
of the indicator (not shown in the diagram, but its good to
stand the flask on white tile).
At the start of the
titration the phenolphthalein indicator is a deep
reddish-pink in alkaline solution.
As you add the acid you
get 'splurges' of colourless solution until the mixture is
swirled in the conical flask.
The swirling of the flask
contents is important, it ensures all the added hydrochloric
acid reacts with the sodium hydroxide.
Try
to add dropwise when you seem to be near the faintest
pinkness left in the solution near the endpoint.
The
end-point is when the last trace of pink colour first
disappears from the solution.
You taking the reading of the
volume of the hydrochloric acid on the scale line the
meniscus lies on (see lower part of diagram above on the
right).
If
you 'overshoot' the titration with excess acid, it still
stays colourless and the result is invalid.
The titration should be repeated several
times with other 25 cm3 portions and the average
(mean) titration value calculated to use in any subsequent
calculations.
How to calculate the
concentration of the alkali is explained in the top half of
the page.
The theory of which indicator
to use is explained on the
Changes in pH in a
neutralisation, choice and use of indicators page.
There is also a paragraph on
errors and reasons for repeating a titration several times.
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and sub-index
10. Titration 4. Determination of the
concentration of calcium hydroxide in limewater
This almost the same experiment as APPENDIX 2.
Example 3. above
A practical exercise for
Advanced A level students
Calcium hydroxide is slightly
soluble in water and the resulting solution is commonly known as
'limewater.
It is a relatively strong alkali
and readily titrated with standardised hydrochloric acid using
phenolphthalein indicator.
Requirements
-
A bottle of water
shaken well for quite a few minutes with excess solid calcium hydroxide and left to
stand so that the excess solid settles out.
-
50 cm3
burette (with 0.1 cm3 graduations on the scale)
-
25.0 cm3
pipette (you can use a 10 cm3 pipette, but smaller and
less accurate titration)
-
250 cm3
conical flask and white tile
-
Squeezy wash bottle
of deionised/distilled water.
-
Standardised 0.1 or
0.05 mol dm-3 (M for short) hydrochloric acid.
-
Phenolphthalein
acid-base indicator solution (pink >pH 9, colourless <pH 9
Method-Procedure
-
Wear
safety glasses, initially work below eye level and use a funnel
to fill the burette.
-
Fill the burette
with the standard acid solution of known concentration and level off so that the bottom
of the meniscus rests on the 0.00 calibration mark.
-
Using a safe suction bulb,
suck the calcium hydroxide solution until its a few cm above the
calibration mark, then run it down until the meniscus rests on
the calibration mark (diagram on right).
-
Pipette 25.0 cm3 of
the clear liquid above the excess solid in the bottle of
limewater into the conical flask.
-
Add a few drops of
phenolphthalein indicator solution (it should turn pink -
alkaline)
-
Place the conical
flask on the white tile under the burette tip.
-
Carefully titrate
the limewater until ONE drop of the hydrochloric acid removes
the last of the pink colour (the end-point is pink to
colourless).
-
Take the reading of the
burette scale - the line on which the meniscus rests (right
diagram).
-
Repeat the procedure
at least twice to obtain good concordance of titration results.
-
Your results should
be over a maximum of 0.2 cm3 and +/- 0.1 cm3 range would be very
good.
-
In doing subsequent
titrations you do not have to keep on
Typical Results and
Calculations ('borrowed'
Q19 from one of
my volumetric titration calculation pages)
The solubility of calcium hydroxide in
water can be measured reasonably accurately to 3sf by titrating the saturated
solution with standard hydrochloric acid.
In the calculation below assume
the molarity of the standardised hydrochloric acid is 0.1005 mol dm-3.
At 25oC, a few grams
of solid calcium hydroxide was shaken with about 400 cm3 of
deionised water, and then filtered.
|
1st |
2nd |
3rd |
4th |
5th |
- |
2nd burette reading/cm3 |
|
|
|
|
|
average |
1st burette reading/cm3 |
|
|
|
|
|
titration |
titration value/cm3 |
|
|
|
|
|
|
titration value used in average |
|
|
|
|
|
- |
50.0 cm3 samples of the
'limewater' gave an average titration of 15.22 cm3 of 0.1005 mol
dm-3 hydrochloric acid using phenolphthalein indicator.
(a) The equation for
calcium hydroxide reacting with hydrochloric acid.
Ca(OH)2(aq) + 2HCl(aq) ==>
CaCl2(aq) + 2H2O(l)
(b) The reacting mole
ratio of Ca(OH)2 : HCl and hence calculate the moles of them
involved in the titration.
from equation,
mole ratio Ca(OH)2 : HCl is 1:2
and since moles
solute = molarity x volume in dm3 (dm3
= cm3/1000)
mol HCl used in
titration = 0.1005 x 15.22/1000 = 0.001530 mol HCl
therefore mol Ca(OH)2
= 0.001558/2 = 0.000765 mol Ca(OH)2
(c) Calculate the molarity of
the solution in terms of mol Ca(OH)2 dm-3.
Scaling up from mol
Ca(OH)2 in 50 cm3 to 1 dm3 (1000 cm3)
molarity Ca(OH)2
= 0.00765 x 1000/50 = 0.1558 =
0.153 mol dm-3 (to
3sf)
(d) What is the approximate
solubility of calcium hydroxide in g Ca(OH)2 per 100g water?
Mr[Ca(OH)2]
=74, mass = moles x formula mass
so solubility in g dm-3 = 0.153 x 74 =
1.13 g dm-3
(3 sf)
(If needed in another
question, this is equal to 1.13/1000 =
1.13 x 10-3
g/cm3 water)
Since density of
water is ~1.0 g cm-3, so the solubility per 100g is
1/10th of the solubility per dm3,
solubility of Ca(OH)2
is about 0.113 g/100 g H2O
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TOP OF PAGE
and sub-index
Self-assessment Quiz on titrations
type in titration answer
QUIZ or
multiple
choice
titration
QUIZ
See also
Advanced level
GCE-AS-A2 acid-alkali titration calculation questions
See also GCSE/IGCSE Acid & Alkalis revision notes
sub–index:
Index of all pH, Acids, Alkalis, Salts Notes 1.
Examples of everyday acids, alkalis,
salts, pH of
solution, hazard warning signs : 2.
pH scale, indicators, ionic theory of acids–alkali neutralisation : 4.
Reactions of acids with
metals/oxides/hydroxides/carbonates, neutralisation reactions : 5.
Reactions of bases–alkalis
like ammonia & sodium hydroxide : 6.
Four methods
of making salts : 7. Changes in pH in a
neutralisation, choice and use of indicators : 8.
Important formulae of
compounds, salt solubility and water of crystallisation :
10.
More on Acid–Base Theory and Weak and Strong Acids
OTHER CALCULATION PAGES
-
What is relative atomic mass?,
relative isotopic mass and calculating relative atomic mass
-
Calculating relative
formula/molecular mass of a compound or element molecule
-
Law of Conservation of Mass and simple reacting mass calculations
-
Composition by percentage mass of elements
in a compound
-
Empirical formula and formula mass of a compound from reacting masses
(easy start, not using moles)
-
Reacting mass ratio calculations of reactants and products
from equations
(NOT using
moles) and brief mention of actual percent % yield and theoretical yield,
atom economy
and formula mass determination
-
Introducing moles: The connection between moles, mass and formula mass - the basis of reacting mole ratio calculations
(relating reacting masses and formula
mass)
-
Using
moles to calculate empirical formula and deduce molecular formula of a compound/molecule
(starting with reacting masses or % composition)
-
Moles and the molar volume of a gas, Avogadro's Law
-
Reacting gas volume
ratios, Avogadro's Law
and Gay-Lussac's Law (ratio of gaseous
reactants-products)
-
Molarity, volumes and solution
concentrations (and diagrams of apparatus)
-
How to do acid-alkali titrations
and calculations, diagrams of apparatus,
details of procedures (this page)
-
Electrolysis products calculations (negative cathode and positive anode products)
-
Other calculations
e.g. % purity, % percentage & theoretical yield, dilution of solutions
(and diagrams of apparatus), water of crystallisation, quantity of reactants
required, atom economy
-
14.1
% purity of a product 14.2a
% reaction yield 14.2b
atom economy 14.3
dilution of solutions
-
14.4
water of crystallisation
calculation 14.5
how
much of a reactant is needed? limiting reactant
-
Energy transfers in physical/chemical changes,
exothermic/endothermic reactions
-
Gas calculations involving PVT relationships,
Boyle's and Charles Laws
-
Radioactivity & half-life calculations including
dating materials
-
Some Advanced A Level Practical Exercises and Calculations
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