Polyprotic Acids

Polyprotic acids are acids that can donate more than one proton (H⁺ ion) per molecule in a stepwise manner. Each proton donation occurs with a distinct dissociation constant. These acids are also known as polybasic acids. Understanding polyprotic acids is crucial for predicting the pH of solutions, analyzing buffer systems, and understanding complex acid-base equilibria.

Characteristics of Polyprotic Acids

Stepwise Dissociation: Polyprotic acids dissociate in a stepwise process, with each step having its own equilibrium constant.
Sequential Dissociation Constants: The first dissociation constant (Ka1) is always larger than the second (Ka2), which in turn is larger than the third (Ka3), and so on. This is because it is energetically more favorable to remove the first proton from a neutral molecule than subsequent protons from an increasingly negatively charged ion.
pH Dependence: The pH of a solution containing a polyprotic acid depends on the concentration of the acid and its dissociation constants.
Buffering Capacity: Polyprotic acids can act as buffers in multiple pH ranges, each corresponding to a different dissociation step.

Dissociation of Polyprotic Acids

A general polyprotic acid, HₙA, can donate n protons. The dissociation can be represented as follows:

First dissociation: ( H_nA \rightleftharpoons H^{+} + H_{n-1}A^- ) with ( K_{a1} )
Second dissociation: ( H_{n-1}A^- \rightleftharpoons H^{+} + H_{n-2}A^{2-} ) with ( K_{a2} )
Third dissociation: ( H_{n-2}A^{2-} \rightleftharpoons H^{+} + H_{n-3}A^{3-} ) with ( K_{a3} )
... and so on until all protons are dissociated.

The dissociation constants are defined as:

[ K_{a1} = \frac{[H^{+}][H_{n-1}A^-]}{[H_nA]} ] [ K_{a2} = \frac{[H^{+}][H_{n-2}A^{2-}]}{[H_{n-1}A^-]} ] [ K_{a3} = \frac{[H^{+}][H_{n-3}A^{3-}]}{[H_{n-2}A^{2-}]} ] ... and so on.

Examples of Polyprotic Acids

Some common examples of polyprotic acids include:

Sulfuric acid (H₂SO₄)
Carbonic acid (H₂CO₃)
Phosphoric acid (H₃PO₄)
Oxalic acid (H₂C₂O₄)

Differences and Important Points

Property	Monoprotic Acids	Polyprotic Acids
Protons Donated	1 proton per molecule	More than 1 proton per molecule
Dissociation Steps	Single step	Multiple steps
Dissociation Constants	One dissociation constant (Ka)	Multiple dissociation constants (Ka1, Ka2, ...)
pH Calculation	Relatively simple	More complex due to multiple equilibria
Buffer Range	One pH range	Multiple pH ranges

Calculating pH of Polyprotic Acid Solutions

To calculate the pH of a polyprotic acid solution, one must consider the contribution of each dissociation step to the hydrogen ion concentration. Typically, the first dissociation has the most significant impact on the pH. Subsequent dissociations are often less impactful due to the much smaller dissociation constants.

For a diprotic acid (H₂A), the pH calculation involves these steps:

Calculate the concentration of H⁺ from the first dissociation using Ka1 and the initial concentration of H₂A.
Determine if the second dissociation needs to be considered. This is usually the case if the second dissociation constant (Ka2) is not negligible compared to the concentration of ( H_{n-1}A^- ).
If necessary, calculate the additional concentration of H⁺ from the second dissociation.
Sum the contributions of H⁺ from each dissociation to find the total [H⁺].
Calculate the pH as ( pH = -\log[H^+] ).

Example Calculation

Let's consider a 0.1 M solution of carbonic acid (H₂CO₃), a diprotic acid with ( K_{a1} = 4.3 \times 10^{-7} ) and ( K_{a2} = 5.6 \times 10^{-11} ).

Calculate the concentration of H⁺ from the first dissociation.
Since ( K_{a2} ) is much smaller than ( K_{a1} ), the second dissociation can often be ignored for a rough pH calculation.
Calculate the pH using the concentration of H⁺ from the first dissociation.

In practice, these calculations can become complex and often require iterative or approximate methods, especially when the concentrations are similar in magnitude to the dissociation constants.

Conclusion

Polyprotic acids are an important class of acids in chemistry, with unique properties and behaviors in solution. Understanding their stepwise dissociation and how to calculate the pH of their solutions is essential for students and professionals working with acid-base chemistry.