Titration curves

During acid-base titrations, the pH changes in characteristic ways. We can follow these changes using a pH meter or the pH probe of a data logger.

Burette contains base pH probe Beaker contains acid Magnetic stirrer

Strong acid-strong base We put NaOH in the burette and use a pipette to measure 20.0 mL of dilute HCl. We’re going to measure the pH as we slowly add NaOH to the beaker. First the pH of the solution is measured before any NaOH goes in.

Then 1.0 mL of NaOH is added, and the pH recorded. We carry on adding mL after mL of NaOH, and recording the pH each time. The data recorder makes this a simple task and plots the graph while we wait.

Volume of NaOH added (mL) Strong acid-strong base pH of solution Volume of NaOH added (mL)

This is the typical shape of a strong acid-strong base titration curve. Notice the long flat bit at the beginning, as the pH barely changes. Where the titration would normally be stopped, the graph is almost vertical. As excess NaOH is added the graph levels out again. We can read off the equivalence point, where the amounts of HCl and NaOH are equal, by finding the point on the graph that is most vertical.

Equivalence point? During a titration we find the volume of the reagent in the burette which is required to exactly react with the volume of reagent in the flask or beaker. We call this the equivalence point. We often refer to the end-point of a titration, however, the endpoint is indicated when the indicator used changes colour. As you will see later on, different indicators change colour at different pHs. If the wrong indicator is chosen, then it will not change colour at the equivalence point.

When NaOH reacts with HCl, forming NaCl, we can say that the equivalence point is where the NaOH exactly neutralises the HCl. However, if NaOH reacts with CH3COOH, the final solution formed (CH3COONa) is not neutral. So we can’t always say ‘neutralise’ and we can’t say ‘endpoint’, which is why we have this new term: equivalence point. The equivalence point is the stage in a titration when the reactants and products are present in equivalent amounts according to the balanced equation for the reaction. It is the point on a pH titration curve where the curve is the most vertical.

26.5 mL We use the data logger to find the tangent to the curve. It is its most vertical when V(NaOH) = 26.5 mL.

NaOH(aq) + HCl(aq) → NaCl(aq) + H2O(l) The NaOH was 0.0250 mol L–1, and we used 20.0 mL of HCl, so we can calculate the concentration of the HCl. NaOH(aq) + HCl(aq) → NaCl(aq) + H2O(l)

No-one would choose to do an acid-base titration this way if they didn’t have to: its much easier to use an indicator if you can. However, if acid-base indicators aren’t working – perhaps because one of the solutions is strongly coloured – then plotting graphs like this will work. But there is more to pH titration curves than just the equivalence point, especially if weak acids or bases are involved.

Weak acid – strong base The experiment is repeated using the same NaOH in the burette, but with 20.0 mL of dilute ethanoic acid in the beaker. As before, we take the pH reading before NaOH is added, and then every mL or 0.5 mL during the titration.

Weak acid-strong base pH Volume of NaOH added

As before, we use the computer to find the point on the curve that is most vertical. The equivalence point is at 16.5 mL.

Patterns in titration curves Strong acid-strong base Weak acid-strong base What similarities and differences can you see in these two graphs?

* * Strong acid-strong base Weak acid-strong base 8.2 7 Look at the pH at the equivalence points (EP). On the left the pH at the EP is 7, but on the right the pH is just over 8. The solution is neutral at the EP of a strong acid-strong base titration, but it is alkaline at the EP of a weak acid-weak base titration.

We knew that already: sodium chloride solution (formed when NaOH reacts with HCl) is neutral, while sodium ethanoate (formed when CH3COOH reacts with NaOH) is alkaline. Salts formed when strong acids react with strong bases are neutral. The EP of strong acid-strong base titrations are neutral. Salts formed when weak acids react with strong bases are alkaline. The EP of weak acid-strong base titrations are alkaline.

Strong acid-strong base Weak acid-strong base Vertical region Vertical region Notice the length of the vertical region of the graphs: the one on the left has a much longer vertical region than the one on the right.

The vertical region is that zone where a very small change in volume of base added has a large change in the pH of the solution. The length of this region in important in the choice of acid-base indicator for a traditional titration. We need to use an indicator which changes colour within the pH range of the vertical region of the graph. Since a strong acid-strong base titration has a long vertical region, a wide range of indicators are suitable. On this example, anything changing colour between a pH of 4 and a pH of 9. Because weak acid-strong base curves have a short vertical region, the choice of indicator is much more critical. Only those which change colour between 7 and 9 will be suitable.

Strong acid-strong base Weak acid-strong base Notice the pH at the start and finish of each graph. The pH at the start is the pH of the acid we used. The strong acid has a lower pH than the weak acid. The pH at the end is related to the pH of the base used. Since we used the same base, the pH at the end is roughly the same.

The final pH, when excess base has been added, is not equal to the pH of the base, because the solution has been diluted. To estimate the pH at some point after the equivalence point: calculate the volume of excess base added calculate the total volume of the solution treat it as a simple dilution problem to find the concentration of base at that point calculate the pH of this concentration of base.

Strong acid-strong base Weak acid-strong base The general shape of these graphs is different. The graph on the left has a very gentle slope up, then a sharp, almost vertical rise, then it levels off. The graph on the right rises a little, then is almost flat, then has a short vertical section, and finally levels off.

This almost flat region near the start of the weak acid graph is very important. At this point the pH remains almost constant even though quite large amounts of base are added. The mixture is acting as a buffer. Why? Because around this region the concentrations of acid (CH3COOH) and the conjugate base of this acid (CH3COO–) are nearly equal. When these concentrations are exactly equal, the pH of the solution will equal the pKa of the acid. That will be the point when the volume of base added is exactly half the equivalence volume.

The EP for this graph was at 16.5 mL. Halfway to this is 8.25 mL. Weak acid-strong base pH = pKa The EP for this graph was at 16.5 mL. Halfway to this is 8.25 mL. At this point the pH = 4.75, which is equal to the pKa of ethanoic acid.

* Equivalence point pH = pKa Buffer zone Weak acid-strong base * Equivalence point pH = pKa Buffer zone You’ll be expected to label a titration curve with its key points.

Weak base-strong acid A weak base-strong acid curve is similar in principle to the weak acid-strong base curve. The buffer zone occurs when half the weak base remains unreacted, and the other half has been converted into the conjugate base. Thus, we must put the weak base in the beaker and acid in the burette.

Weak base-strong acid Here we have 20.0 mL of ammonia solution in beaker, and HCl solution in the burette.

* pKa(NH4+) = 9.75 Buffer zone pH = pKa Equivalence point = 13.5 mL Weak base-strong acid pKa(NH4+) = 9.75 Buffer zone pH = pKa * Equivalence point = 13.5 mL

Weak base-strong acid * Notice that the pH at the equivalence point for this reaction is about 5.5, and that the vertical zone is short. We will need to use an indicator which changes colour between about 4.5 and 7 for this titration.

You will be asked to label key points on titration curves (especially involving weak acids or weak bases) to read off the pKa and/or the equivalence point to use the equivalence point to calculate the concentration of one of the reagents to select the appropriate indicator for a titration You may also be asked to calculate the pH at any point on the graph to sketch (usually without calculations) the pH curve for a given titration.