Chemistry
Sensors:
Loggers:
pH, Drop / Bubble counter
Any EASYSENSE
Logging time: EasyLog
Teacher’s notes
37 Acid base titration: Polyprotic acids,
phosphoric acid with sodium hydroxide
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Many of the common acids such as hydrochloric acid and ethanoic acid have only one hydrogen, which is
easily transferred to water to form H3O+. These acids are called monoprotic acids. Acids such as
carbonic acid and phosphoric acid have more than one ionisable proton. These acids are called
polyprotic and they show the release of protons in step wise manner. Phosphoric acid can release 3
protons in the following steps. Each successive proton released with more difficulty.
•
Ka1 H3PO4(aq) + H2O(l) Ù H3O+(aq) + H2PO4-(aq)
•
Ka2 H2PO4-(aq) + H2O(l) Ù H3O+(aq) + HPO42-(aq)
•
Ka3 HPO42-(aq) + H2O(l) Ù H3O+(aq) + PO43--(aq)
Reaction Ka2 will not take place until reaction Ka1 has finished.
⎡⎣ H 3O + ⎤⎦ ⎡⎣ H 2 PO -4 ⎤⎦
= 7.5 × 10 −3
Ka1 =
[ H 3PO 4 ]
⎡⎣ H 3O + ⎤⎦ ⎡⎣ HPO 2-4 ⎤⎦
= 6.2 × 10−8
Ka 2 =
⎡⎣ H 2 PO-4 ⎤⎦
⎡⎣ H 3O + ⎤⎦ ⎡⎣ PO3-4 ⎤⎦
= 4.8 × 10−13
Ka3 =
⎡⎣ HPO 2-4 ⎤⎦
Ka1 is much larger than Ka2 which in turn is much larger than Ka3. This tells us that the first proton is
more easily lost from the phosphoric acid than the second and third protons. It can be assumed
therefore that the majority of protons donated come from the first ionisation.
The Ka values listed after each calculation above are the acid ionisation constants. They indicate the
relative ease with which each reaction takes place. A small Ka value indicates a reaction that will not
take place easily.
In the experiment, the titration of phosphoric acid with sodium hydroxide will reveal the successive
ionisations as a set of steps in the change in pH as the sodium hydroxide is added. The change in pH vs.
volume of base can be produced and the Ka values determined.
L3 Chemistry
T37 - 1(V2)
Apparatus
1.
An EASYSENSE logger.
2. A Smart Q pH sensor
3. A Smart Q Drop / Bubble counter set to the correct volume range (see calibrating the Drop
counter) with alignment adapter fitted.
4. The drop counter reagent reservoir fitted with two stopcocks and tip.
5. 3 x 200 ml beakers.
6. Magnetic stirrer and follower.
7. 90 cm3 of 0.2 mol dm-3 Sodium hydroxide (NaOH).
8. 30 cm3 of 0.1 mol dm-3 Phosphoric acid (H3PO4).
9. Measuring cylinders (50 ml capacity).
Set up of the software
The time for the experiment will depend upon the drop rate. To account for variation of this in
individual experiments use EasyLog which is open ended.
When testing the experiment with the solutions suggested, the titration was complete in 20 minutes.
Notes
Hazard information
0.2 mol dm-3 Sodium Hydroxide is suggested as it represents a compromise between accuracy and a
reasonable time span for the experiment to run to completion.
Sodium Hydroxide
Corrosive 0.5 M or
higher
Precautions
Goggles and
gloves should
be worn
Irritant
Phosphoric acid
Precautions
Goggles and
gloves should
be worn
Corrosive
The solid hydroxide should not be
allowed to come into contact with
skin, if it does it should be washed
away with plenty of running cold
water
Burns and irritates the skin and
eyes. If swallowed causes serious
internal injuries
Irritant
Phosphoric acid: Refer to local guidance for regulations concerning this reagent.
Stock solutions can be referenced by specific gravity or molar concentration.
• Mass = Volume x specific gravity.
•
Molecular mass of Phosphoric acid is 98.00
L3 Chemistry
T37 - 2(V2)
For example a 500 cm3 bottle of SG1.75 phosphoric acid will contain 500 x 1.75 = 875 g of the acid
which is a molar concentration of 1750/98 = 17.87 mol dm-3 (note the volume has been corrected to
give a 1 litre equivalent).
For SG1.75 Phosphoric acid
A dilution of 1:10 will give a molarity of 1.787 mol dm-3
A dilution of 1:100 will give a molarity of 0.1787 mol dm-3
It may be worth considering using volumetric analysis grade Sodium hydroxide and back calculating to
find the true molarity of the Phosphoric acid that was used
Calibrating the Drop counter
This investigation uses the Drop counter with one of its preset calibrated ranges e.g. 27 drops/cm3 so
the drops counted are automatically converted and displayed as volume in cm3.
If accuracy is not critical and you are using the reagent reservoir and tip supplied with a low viscosity
liquid (like water) and the flow rate set to: • Fast e.g. 10 plus drops per second, use the 24 drops/cm3 range.
• Medium e.g. between 5 – 10 drops per second, use the 25 drops/cm3 range.
• Slow e.g. between 1.5 – 5 drops per second, use the 26 drops/cm3 range.
• Very Slow e.g. less than 1.5 drops per second, use the 27 drops/cm3 range
When used with a pH Sensor, the flow rate is best set very slow (less than 1.5 drops per second) to
allow the pH Sensor time to settle to a new reading after addition of the titrant.
Results and analysis
Advanced
To calculate the pKa values you need to find the equivalence points and then find the point halfway
between them. Finding pKa2 is relatively straightforward but the other values will need to be
calculated from information on the graph.
Finding pKa2
Produce the first derivative for the pH curve.
Use the Smoothing tool if necessary to remove any artefacts from the derivative line, producing the
derivative does amplify small changes in the rate of pH change.
Use Values to produce a line that intersects the highest point of the first peak on the derivative
curve. Note down the volume of titrant and the pH at this point. Repeat for the second peak, if the
derivative peaks are wide and produce a set of points with the same value try to use the central value.
Refer to the diagram below
L3 Chemistry
T37 - 3(V2)
5
4
3
2
1
From your results you can you can find the values for
•
pH = (pKa1 + pKa2)/2 (point 2)
•
pH = (pKa2 +pKa3)/2 (point 4).
You now need to calculate the pKa2 (3).
•
Take the volume at (2) and add it to the volume at (4). Divide by two.
•
Use Values to find the pH at this volume. The pH at this value is pKa2.
The values of the pH at points 2, 3 and 4 are now known.
Using the values you have and pH = (pKa1 + pKa2)/2 and pH = (pKa2 + pKa3)/2 calculate the values for
pKa1 and pKa3.
Extension
Try the following titration and compare the results
•
0.1 mol dm-3 sodium hydroxide vs. 0.1 mol dm-3 sulphuric acid.
•
Using pKa values to determine the phosphoric acid content of cola
L3 Chemistry
T37 - 4(V2)
Data for phosphoric acid
pKa1 = 2.17
pKa2 = 7.21
pKa3 = 12.7
Note: these are an average of values from several sources.
Molecular mass = 98.00
Worked example
Values collected from titration curve
(2) pH = ( pKa1+ pKa2)/2 = 4, Volume of NaOH = 21.26
(4) pH = ( pKa2+ pKa3)/2 = 9.0, Volume NaOH = 42.67
(3) pH = pKa2
Difference in volume from (2) to (4) = 42.67 - 21.26 = 21.41
Volume at pKa2 = 21.26 + (21.41/2) = 21.26 + 10.7 = 31.96
pH at NaOH volume of 31.96 (from table and graph using values) = 6.5
pKa2 = 6.5
(1) pH pKa1
•
(2) = pH = ( pKa1+ pKa2)/2 = 4.0
•
Substituting known values (2) = (pKa1 + 6.5)/2 = 4.0
•
(pKa1+6.4) = 8.0
•
pKa1 = 8.0 - 6.5
•
pKa1 = 1.5
(5) pKa3
•
(4) pH = ( pKa2+ pKa3)/2 = 9.0.
•
Substituting known values (2) = (6.5 + pKa3)/2 = 9.0
•
(pKa3+6.5) = 18
•
pKa3 = 18.0 - 6.5
L3 Chemistry
T37 - 5(V2)
•
pKa3 = 11.5
Relationship between Ka and pKa
pKa = - log Ka
Ka = 10-pKa
if pKa = 2.14
Ka = 10-2.14 = 7.24 x 10-3
Applying this to the experimental results we get
pKa1 = 1.5 = 3.2 x10-2
(2.17 = 6.76 x10-3)
pKa2 = 6.5 = 3.2 x10-7
(7.21 = 3.16 x10-7)
pKa3 = 11.5 =3.2 x 10-12 (12.7 = 2.0 x10-13)
Potential sources of error:
•
Temperature of the titration was not controlled.
•
Concentration of the titrants could be different from calculated values.
•
Acidity in the water is not accounted for.
L3 Chemistry
T37 - 6(V2)