14.5 Polyprotic Acids

Acids are classified by the number of protons per molecule that they can give up in a reaction. Acids such as HCl, HNO₃, and HCN that contain one ionizable hydrogen atom in each molecule are called monoprotic acids. Their reactions with water are:

HCl (a q) + H_{2} O (l) ⟶ H_{3} O^{+} (a q) + Cl^{-} (a q) HNO_{3} (a q) + H_{2} O (l) ⟶ H_{3} O^{+} (a q) + NO_{3}^{-} (a q) HCN (a q) + H_{2} O (l) ⇌ H_{3} O^{+} (a q) + CN^{-} (a q)

Even though it contains four hydrogen atoms, acetic acid, CH₃CO₂H, is also monoprotic because only the hydrogen atom from the carboxyl group (COOH) reacts with bases:

This image contains two equilibrium reactions. The first shows a C atom bonded to three H atoms and another C atom. The second C atom is double bonded to an O atom and also forms a single bond to another O atom. The second O atom is bonded to an H atom. There is a plus sign and then the molecular formula H subscript 2 O. An equilibrium arrow follows the H subscript 2 O. To the right of the arrow is H subscript 3 O superscript positive sign. There is a plus sign. The final structure shows a C atom bonded the three H atoms and another C atom. This second C atom is double bonded to an O atom and single bonded to another O atom. The entire structure is in brackets and a superscript negative sign appears outside the brackets. The second reaction shows C H subscript 3 C O O H ( a q ) plus H subscript 2 O ( l ) equilibrium arrow H subscript 3 O ( a q ) plus C H subscript 3 C O O superscript negative sign ( a q ).

Similarly, monoprotic bases are bases that will accept a single proton.

Diprotic acids contain two ionizable hydrogen atoms per molecule; ionization of such acids occurs in two steps. The first ionization always takes place to a greater extent than the second ionization. For example, sulfuric acid, a strong acid, ionizes as follows:

First ionization: H_{2} SO_{4} (a q) + H_{2} O (l) ⇌ H_{3} O^{+} (a q) + HSO_{4}^{-} (a q) K_{a 1} = more than 10^{2}; complete dissociation Second ionization: HSO_{4}^{-} (a q) + H_{2} O (l) ⇌ H_{3} O^{+} (a q) + SO_{4}^{2 -} (a q) K_{a 2} = 1.2 \times 10^{- 2}

This stepwise ionization process occurs for all polyprotic acids. Carbonic acid, H₂CO₃, is an example of a weak diprotic acid. The first ionization of carbonic acid yields hydronium ions and bicarbonate ions in small amounts.

First ionization: H_{2} CO_{3} (a q) + H_{2} O (l) ⇌ H_{3} O^{+} (a q) + HCO_{3}^{-} (a q) K_{H_{2} CO_{3}} = \frac{[ H _{3} O ^{+} ] [ HCO _{3} ^{-} ]}{[ H _{2} CO _{3} ]} = 4.3 \times 10^{- 7}

The bicarbonate ion can also act as an acid. It ionizes and forms hydronium ions and carbonate ions in even smaller quantities.

Second ionization: HCO_{3}^{-} (a q) + H_{2} O (l) ⇌ H_{3} O^{+} (a q) + CO_{3}^{2 -} (a q) K_{HCO_{3}^{-}} = \frac{[ H _{3} O ^{+} ] [ CO _{3} ^{2 -} ]}{[ HCO _{3} ^{-} ]} = 4.7 \times 10^{- 11}

$K_{H_{2} CO_{3}}$ is larger than $K_{HCO_{3}^{-}}$ by a factor of 10⁴, so H₂CO₃ is the dominant producer of hydronium ion in the solution. This means that little of the formed by the ionization of H₂CO₃ ionizes to give hydronium ions (and carbonate ions), and the concentrations of H₃O⁺ and are practically equal in a pure aqueous solution of H₂CO₃.

If the first ionization constant of a weak diprotic acid is larger than the second by a factor of at least 20, it is appropriate to treat the first ionization separately and calculate concentrations resulting from it before calculating concentrations of species resulting from subsequent ionization. This approach is demonstrated in the following example exercise.

A triprotic acid is an acid that has three ionizable H atoms. Phosphoric acid is one example:

First ionization: H_{3} PO_{4} (a q) + H_{2} O (l) ⇌ H_{3} O^{+} (a q) + H_{2} PO_{4}^{-} (a q) K_{a 1} = 7.5 \times 10^{- 3} Second ionization: H_{2} PO_{4}^{-} (a q) + H_{2} O (l) ⇌ H_{3} O^{+} (a q) + HPO_{4}^{2 -} (a q) K_{a 2} = 6.2 \times 10^{- 8} Third ionization: HPO_{4}^{2 -} (a q) + H_{2} O (l) ⇌ H_{3} O^{+} (a q) + PO_{4}^{3 -} (a q) K_{a 3} = 4.2 \times 10^{- 13}

As for the diprotic acid examples, each successive ionization reaction is less extensive than the former, reflected in decreasing values for the stepwise acid ionization constants. This is a general characteristic of polyprotic acids and successive ionization constants often differ by a factor of about 10⁵ to 10⁶.

This set of three dissociation reactions may appear to make calculations of equilibrium concentrations in a solution of H₃PO₄ complicated. However, because the successive ionization constants differ by a factor of 10⁵ to 10⁶, large differences exist in the small changes in concentration accompanying the ionization reactions. This allows the use of math-simplifying assumptions and processes, as demonstrated in the examples above.

Polyprotic bases are capable of accepting more than one hydrogen ion. The carbonate ion is an example of a diprotic base, because it can accept two protons, as shown below. Similar to the case for polyprotic acids, note the ionization constants decrease with ionization step. Likewise, equilibrium calculations involving polyprotic bases follow the same approaches as those for polyprotic acids.

H_{2} O (l) + CO_{3}^{2 -} (a q) ⇌ HCO_{3}^{-} (a q) + OH^{-} (a q) K_{b1} = 2.1 \times 10^{- 4} H_{2} O (l) + H CO_{3}^{-} (a q) ⇌ H_{2} CO_{3} (a q) + OH^{-} (a q) K_{b2} = 2.3 \times 10^{- 8}

Key Concepts and Summary

An acid that contains more than one ionizable proton is a polyprotic acid. These acids undergo stepwise ionization reactions involving the transfer of single protons. The ionization constants for polyprotic acids decrease with each subsequent step; these decreases typically are large enough to permit simple equilibrium calculations that treat each step separately.

14.5 Polyprotic Acids

HCl (a q) + H_{2} O (l) ⟶ H_{3} O^{+} (a q) + Cl^{-} (a q) HNO_{3} (a q) + H_{2} O (l) ⟶ H_{3} O^{+} (a q) + NO_{3}^{-} (a q) HCN (a q) + H_{2} O (l) ⇌ H_{3} O^{+} (a q) + CN^{-} (a q)

Even though it contains four hydrogen atoms, acetic acid, CH₃CO₂H, is also monoprotic because only the hydrogen atom from the carboxyl group (COOH) reacts with bases:

Similarly, monoprotic bases are bases that will accept a single proton.

First ionization: H_{2} SO_{4} (a q) + H_{2} O (l) ⇌ H_{3} O^{+} (a q) + HSO_{4}^{-} (a q) K_{a 1} = more than 10^{2}; complete dissociation Second ionization: HSO_{4}^{-} (a q) + H_{2} O (l) ⇌ H_{3} O^{+} (a q) + SO_{4}^{2 -} (a q) K_{a 2} = 1.2 \times 10^{- 2}

First ionization: H_{2} CO_{3} (a q) + H_{2} O (l) ⇌ H_{3} O^{+} (a q) + HCO_{3}^{-} (a q) K_{H_{2} CO_{3}} = \frac{[ H _{3} O ^{+} ] [ HCO _{3} ^{-} ]}{[ H _{2} CO _{3} ]} = 4.3 \times 10^{- 7}

The bicarbonate ion can also act as an acid. It ionizes and forms hydronium ions and carbonate ions in even smaller quantities.

Second ionization: HCO_{3}^{-} (a q) + H_{2} O (l) ⇌ H_{3} O^{+} (a q) + CO_{3}^{2 -} (a q) K_{HCO_{3}^{-}} = \frac{[ H _{3} O ^{+} ] [ CO _{3} ^{2 -} ]}{[ HCO _{3} ^{-} ]} = 4.7 \times 10^{- 11}

A triprotic acid is an acid that has three ionizable H atoms. Phosphoric acid is one example:

First ionization: H_{3} PO_{4} (a q) + H_{2} O (l) ⇌ H_{3} O^{+} (a q) + H_{2} PO_{4}^{-} (a q) K_{a 1} = 7.5 \times 10^{- 3} Second ionization: H_{2} PO_{4}^{-} (a q) + H_{2} O (l) ⇌ H_{3} O^{+} (a q) + HPO_{4}^{2 -} (a q) K_{a 2} = 6.2 \times 10^{- 8} Third ionization: HPO_{4}^{2 -} (a q) + H_{2} O (l) ⇌ H_{3} O^{+} (a q) + PO_{4}^{3 -} (a q) K_{a 3} = 4.2 \times 10^{- 13}

H_{2} O (l) + CO_{3}^{2 -} (a q) ⇌ HCO_{3}^{-} (a q) + OH^{-} (a q) K_{b1} = 2.1 \times 10^{- 4} H_{2} O (l) + H CO_{3}^{-} (a q) ⇌ H_{2} CO_{3} (a q) + OH^{-} (a q) K_{b2} = 2.3 \times 10^{- 8}