You have probably heard of phosphoric acid before. Phosphoric acid is an acid that is widely used in fertilizers, detergents, and even as an acidity regulator in cereal bars and jams! Phosphoric acid is considered a polyprotic acid. So, if you are interested to know about titrations of polyprotic acids, keep reading!
- This article is about titrations of polyprotic acids.
- First, we will take a look at what a polyprotic acid titration curve looks like.
- Then, we will learn the attributes of a weak polyprotic acid titration curve.
- Next, we will look at polyprotic acid titration calculation and problems.
- Lastly, we will look at some examples of polyprotic acid titration graphs.
Polyprotic Acid Titration Curve
First, let's review monoprotic acids. Monoprotic acids are acids that can yield only one H+ (also written as, H3O+) per molecule of acid. They possess a single ionizable hydrogen atom in each molecule.
$$HA\rightleftharpoons H^{+}+A^{-}$$
where, A-, symbolizes the anionic (negatively charged) species. Examples of monoprotic acids include HCl, HClO4, and HNO3.
$$HCl_{(aq)}+H_{2}O_{(l)}\rightarrow H_{3}O^{+}+Cl^{-}_{(aq)}$$
$$HClO_{4\ (aq)}+H_{2}O_{(l)}\rightarrow H_{3}O^{+}_{(aq)}+ClO_{4\ (aq)}^{-}$$
$$HNO_{3\ (aq)}+H_{2}O_{(l)}\rightarrow H_{3}O^{+}_{(aq)}+NO_{3\ (aq)}^{-}$$
Where all of the above three different reactions produce the same cationic (positively charged) species, H3O+ (also written as, H+) but yield different anionic species. The first reaction produces the, Cl-, anion, the second reaction produces the ClO4-, anion and the last reaction produces the NO3-, anion.
Now, let's define what a polyprotic acid is.
A polyprotic acid is an acid that has more than one ionizable hydrogen (H) atom.
In other words, they have more than one acidic proton, so they can undergo more than one dissociation reaction Examples of polyprotic acids include H2SO4 and H3PO4. Let's look at the dissociation of H3PO4(aq). Phosphoric acid has three acidic protons, and therefore, its ionization happens in three steps.
$$Dissociation\ 1: H_{3}PO_{4\ (aq)}+H_{2}O_{(l)}\rightleftharpoons H_{3}O^{+}_{(aq)}+H_{2}PO_{4\ (aq)}^{-}$$
$$Dissociation\ 2: H_{2}PO_{4\ (aq)}^{-}+H_{2}O_{(l)}\rightleftharpoons H_{3}O^{+}_{(aq)}+HPO_{4\ (aq)}^{2-}$$
$$Dissociation\ 3: HPO_{4\ (aq)}^{2-}+H_{2}O_{(l)}\rightleftharpoons H_{3}O^{+}_{(aq)}+PO_{4\ (aq)}^{3-}$$
Notice in this case, that these three dissociation steps are part of a single reaction.
pH, Ka, and pKa
The acid dissociation constant measures the degree of dissociation of hydrogens in an acid. Scientists use the acid dissociation constant (Ka) to determine the strength of acids. We can use the equations below to find Ka and pKa, which is the -log10 of Ka.
$$K_{a}=\frac{Concentration\ of\ products}{Concentration\ of\ reactants}=\frac{[Products]}{[Reactants]}=\frac{[H^{+}][A^{-}]}{[HA]}$$
$$pK_{a}-log_{10}(Ka)$$
Ka is sometimes called acid ionization constant or acidity constant!
Let's look at the Ka equations for a polyprotic acid H3A (also called a triprotic acid). What is happening here is that water gains a proton (H+) to become a hydronium ion (H3O+), whereas phosphoric acid loses a proton and becomes a conjugate base! Since this is a triprotic acid, we have three ionizations that occur:
$$H_{3}A_{(aq)}+H_{2}O_{(l)}\rightarrow H_{2}A^{-}_{(aq)}+H_{3}O^{+}_{(aq)}$$
$$K_{a1}=\frac{[H_{2}A^{-}][H^{+}]}{[H_{3}]A}$$
$$H_{2}A_{(aq)}^{-}+H_{2}O_{(l)}\rightarrow HA^{2-}_{(aq)}+H_{3}O^{+}_{(aq)}$$
$$K_{a2}=\frac{[HA^{2-}][H^{+}]}{[H_{3}]A}$$
$$HA_{(aq)}^{2-}+H_{2}O_{(l)}\rightarrow A^{3-}_{(aq)}+H_{3}O^{+}_{(aq)}$$
$$K_{a2}=\frac{[A^{3-}][H^{+}]}{[H_{3}]A}$$
Now that we know what monoprotic and polyprotic acids are, let's jump into the titrations! Titrations are used by chemists to determine the unknown concentration of an acid or base. Then, we can use the data gathered from the titration to draw a titration curve.
A titration curve (sometimes called a pH curve) is a graph that shows how the pH of a solution changes when an acid or base is added to it.
You can learn more about titrations by checking out "Types of Acid-Base Titrations".
Titration curves are also used to find out the number of acidic protons in an acid. A typical titration curve for a weak polyprotic acid looks like this:
This pH curve has three different acid dissociation constants, meaning that the acid has three acidic protons. For now, just take the time to familiarize yourself with what it looks like. We will learn how to interpret them in a bit.
Attributes of a Weak Polyprotic Acid Titration Curve
Let's go back to our previous example showing the dissociation of phosphoric acid. H3PO4 is a weak polyprotic acid that is capable of losing three protons per molecule. In H3PO4, the values for Ka are:
- Ka1 = 7.1·10-3
- Ka2 = 8.1·10-8
- Ka3 = 4.8·10-13
For each successive dissociation, the acid dissociation constant (Ka) value gets smaller because it becomes more difficult to remove the ionizable hydrogen (Ka1 > Ka2 > Ka3).
If we calculated the pKa values for each Ka, we would get:
$$pK_{a1})-log_{10}(7.1\cdot 10^{-3})=2.15$$
$$pK_{a2})-log_{10}(8.1\cdot 10^{-8})=7.09$$
$$pK_{a3})-log_{10}(4.8\cdot 10^{-13})=12.32$$
The titration curve below shows the titration of H3PO4 with a strong base.
Fig. 2: Titration curve of weak phosphoric acid with a strong base, Isadora Santos - Vaia Original.
Let's interpret this pH curve. The graph shows the changes in pH that occur when phosphoric acid is titrated with a strong base, adding OH- ions to the solution. So, before adding any strong base (such as NaOH), all we have is a solution of a weak acid (in this case, H3PO4). The arrows point to the half-equivalence point.
The half-equivalence point is the point in a titration where there are equal concentrations of the acid and its conjugate base. For a weak acid, [HA] = [A-] , at the half-equivalence point; where [HA], is the concentration of the acid and [A-], is the concentration of the conjugate base.
The Conjugate Base is the anionic species A-, which results from dissolving an acid HA, in water.
In this titration curve, there are three different half-equivalence points. At the half-equivalence point, the pH is equal to the pKa value. For example, if the value for pKa at the first half-equivalence point is equal to 2.15, then pH at that point will also be 2.15.
The titration curve also shows three equivalence points. At this point, moles of H+ = moles of OH-.
The equivalence point is the point where the number of moles of titrant added is equal to the number of moles of analyte that was originally present.
In our case, the titrant is the base OH-, added and the analyte is acid H+.
Polyprotic Acid Titration Calculations
Have you heard the quote "practice makes perfect"? This also applies here! So, let's take a look at a calculation problem involving a polyprotic acid!
Find the pH of a 0.1 M solution of carbonic acid (H2CO3). The Ka values are: Ka1 = 4.3 x 10-7, and Ka2 = 4.8 x 10-11.
To calculate the pH of a polyprotic acid, we need to consider all the dissociation reactions involved. In this case, carbonic acid is a diprotic acid, so it has two dissociation reactions.
$$First\ dissociation: H_{2}CO_{3\ (aq)}+H_{2}O_{(l)}\rightleftharpoons H_{3}O^{+}+HCO_{3\ (aq)}^{-}$$
$$Second\ dissociation: HCO_{3\ (aq)}^{-}+H_{2}O_{(l)}\rightleftharpoons H_{3}O^{+}+CO_{3\ (aq)}^{2-}$$
Since we are dealing with a weak acid, first we need to make an ICE chart for the first dissociation. The acronym "ICE" stands for "Initial concentration, "Change in concentration" and "Equation for concentration". This is important because we must figure out the concentration of HCO3- before making an ICE chart for the second dissociation reaction! Once we find the total concentration of protons, then we can calculate pH!
- Add the initial concentration of carbonic acid (0.1 M) to the ICE chart.
- Next, we add the change in concentration in terms of x.
- Then, we write the equation for concentration at equilibrium.
Fig. 4: ICE chart for the first ionization reaction of carbonic acid, Isadora Santos - Vaia Originals.
Now, we can calculate the value of x by adding the terms in lines "I" and "C" and then substituting the terms in line "E" into the equation for Ka1.
$$K_{a1}=\frac{[H^{+}][HCO_{3}^{-}]}{[H_{2}CO_{3}]}=\frac{x^{2}}{0.1-x}\approx \frac{x^{2}}{0.1}$$
$$4.3\cdot 10^{-7}=\frac{x^{2}}{0.1}$$
$$x=2.1\cdot 10^{-4}$$
Now that we have the value of x, we can use it as the values for the initial concentration of HCO3- and H+ at the second dissociation reaction. So, let's make another ICE chart.
Fig. 5: ICE chart for the second dissociation reaction of carbonic acid, Isadora Santos - Vaia Original.
Now, we can calculate the value of y using the equation of Ka2.
$$K_{a1}=\frac{[H^{+}][CO_{3}^{2-}]}{[HCO_{3}^{-}]}=\frac{(2.1\cdot 10^{-4}+y)(y)}{(2.1\cdot 10^{-4})}\approx\frac{(2.1\cdot 10^{-4})(y)}{(2.1\cdot 10^{-4})} $$
$$4.8\cdot 10^{-11}=\frac{(2.1\cdot 10^{-4})(y)}{(2.1\cdot 10^{-4})} $$
$$y=4.8\cdot 10^{-11}$$
Finally, we can calculate the total concentration of protons and use it to find pH. In the first ICE chart, we found the concentration of H+ to be 2.1 x 10-4. But, since the second Ka is tiny compared to the first Ka, we can completely neglect it!
So, in this case, pH will be equal to -log10 (2.1 x 10-4), which gives us a pH of 3.68
Polyprotic Acid Titration Problems
In some exam problems, you might be asked to find the pKa values of a polyprotic acid by looking at a titration curve. For example, let's say that you are given the titration curve for the titration of 0.1 M citric acid, H3C6H5O7 with a 0.1 M solution of a strong base (NaOH).
The pH of the three equivalence points is given. But, to find pKa, we need to first figure out the pH at the half-equivalence points. Remember that at the half-equivalence point, pH = pKa.
- The pH at the first half-equivalence point is 3.13. So, pKa1 = 3.13
- The pH at the second half-equivalence point is 4.76. Therefore, pKa2 = 4.76
- The pH at the third half-equivalence point is 6.40. Therefore, pKa3 = 6.40
Now, if a question asks you to calculate the Ka values, use the pKa values that you found and use the following equation to calculate Ka for each pKa!
$$K_{a}=10^{-pKa}$$
Polyprotic Acid Titration Graph
Lastly, let's look at an example of a polyprotic acid titration graph. The titration graph for 0.1 M of maleic acid (C4H4O4) with 0.1 M sodium hydroxide shows two equivalence points. In this titration curve, the pKa1 = 1.83, where the pKa2 = 6.07.
Now, I hope that you are feeling more confident in your ability to some problems involving titrations of polyprotic acids!
Titrations of Polyprotic Acids - Key takeaways
- Monoprotic acids are acids that have can yield one H+ per molecule of acid.
- A polyprotic acid is an acid that has more than one ionizable hydrogen (H) atom.
- In polyprotic acids, for each successive dissociation, the acid dissociation constant (Ka) value gets smaller because it becomes more difficult to remove the ionizable hydrogen (Ka1 > Ka2 > Ka3).
References
- Moore, John T, and Richard Langley. McGraw Hill : AP Chemistry, 2022. New York, Mcgraw-Hill Education, 2021.
- Theodore Lawrence Brown, et al. Chemistry : The Central Science. 14th ed., Harlow, Pearson, 2018.
- “Titration of a Polyprotic Acid.” Www.chem.fsu.edu, Bluedoor Labs Chemistry, www.chem.fsu.edu/chemlab/bluedoor_background.html.
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