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Introduction
So far, we have been going through a series of posts on acids and bases. However, we have yet to discuss one important aspect, which is that of titrations and the solubility product. We will explain these concepts in this article.
For titrations, we will look at what they are, their function, and the different types of graphs one might obtain from a titration (spoiler: these graphs include strong acid-strong base, weak acid-weak base, strong acid-weak base, and of course weak acid-strong base).
As for the solubility product, we will also look at what it refers to and how we can use it when we are answering questions for acids and bases.
Why did I begin discussing titration, even after I seemingly finished with the topic of acids and bases a few articles ago? Well, it is because of the question I had posed in the previous two articles, as follows:
“A 20mM histidine monohydrochloride solution (Mr = 209.63) is prepared. 20ml of it is used in a titration with 0.05M NaOH. It has an initial pH of 4.00. In a previous experiment, 2 pKa values of histidine were determined: 6.00 and 9.35. Calculate the pH of the solution after addition of 12ml of 0.05M NaOH.”
Although we did indeed manage to arrive at the correct answer, I realised that underlying this question was the concept of titration, which I failed to explain in the previous posts. As such, we will be going through these concepts today. Particularly, it was this section of the question:
“In a previous experiment, 2 pKa values of histidine were determined: 6.00 and 9.35.”
Technically, one can still solve the question without knowledge of titration, but it’s easier for us to understand if we know the concept of titration. So, let us jump straight into the content!
Titrations
First, let us understand what a titration is in the first place. A titration refers simply to a kind of setup used to find out the concentration of a solution of known volume. This solution is placed in a conical flask while the second reactant, known as the titrant, will be slowly added into the conical flask through a suspended burette (Fig. 1).
Fig. 1: Setup for titrations.
A pH meter is also used to measure the pH as the titrant is added in. The point of slowly adding the titrant in is so that a highly precise value for the volume of titrant needed to cause the pH to become 7 (i.e. all the HCl has reacted).
We can understand this a bit better by citing an example. For example, a HCl solution of unknown concentration but known volume is placed in the conical flask. The titrant is NaOH which is of known concentration and volume. How do we figure out the concentration of HCl?
Titration will help, naturally. We can know the concentration of HCl if we know the volume of NaOH added to the solution to make it pH = 7, because that would mean all the HCl had reacted away. Furthermore, the acid-base reaction is also in a 1:1 molar ratio, there would be an equal number of moles of HCl and NaOH.
This means that we are able to calculate the concentration of HCl, since we already know the number of moles of NaOH from the volume taken for the solution to reach pH = 7 and the concentration of NaOH.
At the end of this titration, when the pH reaches 14 (which indicates that only NaOH is left in the solution, since that is its pH), a graph can be recorded, and it will look something like Fig. 2. At the equivalence point (pH = 7), there are no OH- or H+ ions in the mixture (except for those from the autoionization of water, which is negligible), resulting in a neutral pH.
This means that at the equivalence point, all of the solution has reacted with all of the titrant (that has been added into the mixture so far).
Fig. 2: Strong acid-strong base titration graph.
What about something more interesting, like a weak acid-strong base titration? One example of this would be CH3COOH and NaOH. In that case, the graph would look slightly different as can be seen in Fig. 3.
Let us take note of the similarities and differences from Fig. 1. Since CH3COOH is still acidic, the graph still begins at pH < 7. However, as we can see from Fig. 3, the rate of pH increase slows down all of a sudden after a while of rapid pH increase! Why is this?
Well, we have to remember that a weak acid and its conjugate base may make a buffer solution. In this case, it does make the buffer solution which slows down the rate of pH increase. The most effective buffer solution is produced at the maximum buffering capacity, a point on the graph. Why? An ideal buffer solution has a 1:1 ratio of weak acid and conjugate base.
As such, at the maximum buffering capacity, [CH3COOH] = [CH3COO-], and because of this, pH = pKa (but only at the maximum buffering capacity) as proven by the Henderson-Hasselbalch equation (Fig. 4).
We note that in the weak acid-strong base graph, the equivalence point becomes pH > 7, indicating that the solution has become basic. Why? This is because CH3COOH reacts with a base such as NaOH to produce CH3COONa, which dissociates into the weakly basic CH3COO- ion.
Finally, we introduce something known as the half-equivalence point. At this point, exactly half of the solution has reacted with all the titrant added.
The graph in Fig. 3 is very significant because it is related to the question discussed in the previous two articles (reaction between weak CH3COOH and strong NaOH). The question states that pKas of 6.00 and 9.35 were determined.
We can infer that these pKas were determined at the equivalence points (there is more than one equivalence point here because there is more than one acidic / basic site on histidine).
As such, at 6.00 and 9.35, there should theoretically only be a pure solution of histidine (depending on the pH, the form could be different). Note that at the equivalence point, pH = pKa.
Fig. 3: Weak acid-strong base titration graph.
pH = pKa + lg([A-]/[HA])
pH = pKa + lg 1 (since [A-] = [HA])
pH = pKa
Fig. 4: The composition of an ideal buffer solution.
We also have the direct opposite kind of titration, the strong acid-weak base titration (Fig. 5). We won’t talk much about this graph as it is simply the reverse of the weak acid-strong base titration (starting at a basic pH, with the half-equivalence point forming also at a basic pH).
Fig. 5: Strong acid-weak base titration graph.
Finally, we have the last type of curve, which is the weak acid-weak base titration (Fig. 6). Nothing impressive about the graph here; it is almost the same as the strong acid-strong base graph, except that the starting point is higher and the ending point is lower (since the acid and base are weak).
Fig. 6: Weak acid-weak base titration graph.
For acids that can donate more than one proton, there will be two equivalence points as well as two half-equivalence points (simply the double of a typical titration graph). Such a graph, known as a polybasic acid-strong base graph, is shown in Fig. 7.
Fig. 7: Polybasic acid-strong base titration graph.
The direct opposite of Fig. 7 is a carbonate-strong acid titration graph, since a carbonate is a diprotic base (it gains a proton to form HCO3-, then gains another to form water and carbon dioxide). The graph in this case would basically be the opposite of Fig. 7 (Fig. 8).
Fig. 8: Carbonate-strong acid titration graph.
That’s all for now. If you feel there’s anything I missed out, please feel free to voice it out in the comments. Goodbye for now!