Successive Ka Values of Multiple Ionizations — Overview

We've been studying acids and bases. We've covered a lot of material! So far, we can distinguish between Arrhenius, Bronstead-Lowery, and Lewis acids and bases. We learned that acids and bases affect a solution's pH or pOH. Changes in hydrogen or hydroxide ion concentrations alter the solution's acidity or basicity.

After we learned the basics, we examined strong acids and bases. Stong acid and bases were easy! They fully dissociate. So, their ion concentration equals the molarity. Then we investigated weak acids. They are more challenging because they are in equilibrium. So, we applied our knowledge about equilibrium constants and calculation. Acids and bases have their own constants. Chemists are super creative! So, we call them the acid or base dissociation or ionization constants. We write them as either, $pK_{a/b}$ or $K_{a/b}$. We can work with either one.

Dissociation Constants of Polyprotic Acids

We've started to study polyprotic acids. They are molecules that can lose multiple ions. A few acids can even lose three hydrogen ions! So, they have many $K_{a}$ values. Below, I made a table of some common polyprotic acids. You can see that for each dissociation, $K_{a}$ lessens. Often, it reduces by many orders of magnitude.

But, why? Let's say we have a diprotic acid. So, for the first dissociation, it lost a hydrogen ion. Now we have a hydrogen ion and the conjugate base. The base is an anion. It's going to be very challenging to remove the second hydrogen. We have to pull a second cation from an anion. It's analogous to lattice energy. It is very tough to rip apart ionic bonds because of the electrostatic attraction. When we already have an anion, it's like an ionic bond. The anion wants to hold on to its cation! It takes more and more energy to remove each cation.

But, we can also think about the solvent interactions. Let's say we did lose a second hydrogen ion. Now, we have a dianion. The solvent now has to balance two charges! That's going to take a lot of energy! So, the more hydrogen ions we lose, the less likely something is to dissociate.

Common Polyprotic Acids

$$\begin{array}{c|c|c|c} Acid & K_{a1} & K_{a2} & K_{a3} \\ \hline Citric\,Acid\, (C_{6}H_{8}O_{7}) & 7.4\times10^{-4} & 1.7\times 10^{-5} & 4.0 \times10^{-7} \\ Phosporic\,Acid\, (H_{3}PO_{4}) & 6.9\times10^{-3} & 6.2\times 10^{-8} & 4.8 \times10^{-13} \\ Phosporous\,Acid\, (H_{3}PO_{3}) & 5.0\times10^{-2} & 2.0\times 10^{-7} & - \\ Carbonic\,Acid \,(H_{2}CO_{3}) & 4.5\times10^{-7} & 4.7\times 10^{-11} & - \\ Oxalic\,Acid \,(C_{2}H_{2}O_{4}) & 5.6\times10^{-2} & 1.5\times 10^{-4} & - \end{array}$$

Are There Bases with Multiple Dissociations?

We spend a lot of time looking at polyprotic acids. They are far more common. But, polybasic compounds do exist. There are two common types. The first are compounds with multiple hydroxide groups. For example, the alkaline-earth hydroxides each have two hydroxides. From our qualitative solubility rules, we know they have a low solubility. So, we would expect two small $K_{b}$'s.

The other type is the conjugate bases of polyprotic acids. For example, phosphoric acid is a triprotic acid. So, the phosphate anion, $PO_{4}^{3-}$, is a base. It can take on three hydrogen ions. How would we introduce phosphate into a solution? Typically, we would add its salt. For example, we could add sodium phosphate, $Na_{3}PO_{4}$.

Another common example is carbonate, $CO_{3}^{2-}$. Calcium Carbonate is the active ingredient in antacids. When you've eaten a greasy meal, your stomach produces more acid. The carbonate anion absorbs excess hydrogen ions. Your stomach feels a lot better!

(Video) 15.5 Polyprotic Acids

By Michael Evans

This video is an introduction to polyprotic acids. But, it does an excellent job of explaining their successive $K_{a}$ values. He explains the general trend and the reasoning behind the trend. This video will help you feel more confident about polyprotic acid dissociations!