Calculating the pKa of an Acid Using the Half-Neutralization Method
Introduction
Acid-base reactions involve neutralization between an acid and a base. The ability of an
acid to donate its proton is dependent on the strength of the acid. Strong acids will
completely dissociate – the concentration of [H+] in a 0.1 M solution of HCl is 0.1 M.
However, weak acids only partially dissociate and will only form a smaller concentration
of H+ relative to the HA present.
As with any equilibrium constant for any reaction, the constant is a ratio of the
concentration of the products to the concentration of the reactants.
For the weak acid reaction
HA (aq)   H+(aq) + A-(aq)
the equilibrium constant Ka is
Ka = [H+][A-]/[HA]
The value of Ka lets us determine whether the equilibrium lies to the left or to the
right, and thus the strength of the acid.
If you take a weak acid and titrate it with a strong base such as NaOH, partway through
the titration, you will reach what is known as the half-equivalence point. This is the point
where the concentration of acid and deprotonated acid are equal to each other – also
equal to half an equivalent of base having been added (by definition, at the endpoint of
the titration, you will have mixed one equivalent of base and one equivalent of acid).
At the half-equivalence point:
[HA] = [A-]
Thus in the equation Ka = [H+][A-]/[HA], [A-]/[HA] = 1
and at this particular point, Ka = [H+]
and pKa = pH
We care about this because it allows us to experimentally determine Ka through titration!
Thus, one can determine the pKa of a weak monoprotic acid by titrating the acid with a
base, monitoring the pH, and graphing pH vs. volume base added.
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Procedure
1. You will receive two burets. Rinse each 2-3 times with distilled water. Rinse and fill
one with your assigned acid; rinse and fill the other with your assigned base. Make sure
there are no air bubbles at the bottom, and that they don’t leak. (If there are bubbles, try
to release some of the extra liquid)
2. Using the acid buret, deliver 25.00.1 mL of your assigned acid to a 150 mL beaker.
Record the exact volume of acid used. Add 4-5 drops of phenolphthalein. Also, add 75
mL of distilled water. Swirl to stir.
3. Set up your base buret with your acid beaker underneath, so that you can place a stir
plate underneath your beaker, and that there is room to place a pH probe in the beaker as
well.
4. Carefully insert the pH probe into the solution so that it is immersed at least 0.5 cm
above the bottom of the solution. Do not let it sink too far down – the stirring action
may break the tip of the probe.
5. Measure the pH of your solution, and record this value in your notebook as “initial
pH”. Place a stir bar in the solution, and gently start stirring. Arrange your equipment so
that you can measure the pH and add NaOH at the same time.
6. For the first titration you will do a rough estimate. Add NaOH in 2.0 mL increments,
recording volume to the nearest 0.1 mL and pH to the nearest 0.1 pH unit in a table with
each addition. Also record any color changes, and keep adding NaOH until the pH
reaches 11.
7. For both of the acids we use in class, the equivalence point should be somewhere
around the color change for phenolphthalein (but not exactly). Make a quick plot of pH
vs. amount of NaOH used. This should give you an idea of the inflection point of your
titration curve, which is your equivalence point – this is the region where you will be
more precise on the second titration.
8. For the second titration you will be more precise. Set up the same way you did for the
first titration (same amount and type of acid) but you will take more readings near the
equivalence point – this is the middle of the pH curve, where it increases in pH
dramatically. You should be able to estimate this region from your first titration. When
you reach this region, add NaOH dropwise until you reach the equivalence point – this
will give you the most accurate volume.
9. Repeat step 8. You will be calculating an average of your two more precise titrations
in your postlab.
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There is no prelab for this experiment (other than the writeup in your notebook as usual)
Postlab
1. Attach graphs of pH vs. NaOH concentration from your last two titrations (the more
precise ones).
2. From the graph, determine the volume of NaOH needed to reach the equivalence point
in each titration.
3. Given the answer to 2, what volume of NaOH is needed to reach the half-equivalence
point in each titration?
4. What is the corresponding pH to the half-equivalence point on each graph?
5. Use the pH value from each graph to calculate a Ka value for each titration. Then,
average your two values.
6. Using either your textbook or the web, look up the true Ka value for your acid.
Determine the percent error for your experiment.
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