D26.1 Reaction Between Amphiprotic Species

Acid-base reactions can occur between two amphiprotic species. For example, mixing a solution containing hydrogen sulfate ions (HSO4) and a solution containing hydrogen carbonate ions (HCO3) results in an acid-base reaction. However, if both reactants can act as either an acid or a base, which reactant is the acid and which is the base? In the example mixture, there are two possibilities:

possibility I:          HSO4(aq) + HCO3(aq) ⇌ SO42-(aq) + H2CO3(aq)
possibility II:          HSO4(aq) + HCO3(aq) ⇌ H2SO4(aq) + CO32-(aq)

Qualitatively, a product-favored acid-base reaction involves a stronger acid reacting with a stronger base to form a weaker acid and a weaker base. Acid and base strengths are comparable by Ka and Kb values.

In possibility I, the acids are HSO4 (Ka = 1.1 × 10-2) and H2CO3 (Ka = 4.3 × 10-7) and the bases are HCO3 (Kb = 2.3 × 10-8) and SO42− (Kb = 9.1 × 10-13). While all the species are weak acids/bases, the stronger acid and the stronger base are on the reactant side of the equation. Therefore, this reaction is product-favored at equilibrium.

In possibility II, the acids are H2SO4 (Ka = 4.0 × 103) and HCO3 (Ka = 4.7 × 10-11) and the bases are HSO4 (Kb = 2.5 × 10-18) and CO32− (Kb = 2.1 × 10-4). The stronger acid and the stronger base are on the product side of the equation, so this reaction is reactant-favored at equilibrium. This reaction also indicates the formation of a strong acid, H2SO4 (a relatively higher in energy reactive species), from a weak acid reacting with a weak base. This situation is not thermodynamically favorable.

Exercise: Acid-Base Reactions

We can also make use of the ionization constants to quantitatively determine which reaction occurs. In possibility I,

HSO4(aq) + H2O(ℓ) ⇌ SO42-(aq) + H3O+(aq)           K_1 = K_{\text{a, HSO}_4^-} = 1.1\;\times\;10^{-2}
HCO3(aq) + H3O+(aq) ⇌ H2CO3(aq) + H2O(ℓ)           K_2 = \dfrac{1}{K_{\text{a, H}_2\text{CO}_3}} = \dfrac{1}{4.3\;\times\;10^{-7}}

The sum of these two reactions gives the overall reaction for possibility I:

HSO4(aq) + H2O(ℓ) + HCO3(aq) + H3O+(aq) ⇌ SO42-(aq) + H3O+(aq) + H2CO3(aq) + H2O(ℓ)
HSO4(aq) + HCO3(aq) ⇌ SO42-(aq) + H2CO3(aq)

Therefore, the equilibrium constant for possibility I is:

 K_{\text{overall, possibility I}} = K_1 \times K_2 = \dfrac{1.1\;\times\;10^{-2}}{4.3\;\times\;10^{-7}} = 2.6\;\times\;10^{4}

Possibility I is product-favored at equilibrium because the equilibrium constant is much greater than 1.

In possibility II,

HSO4(aq) + H3O+(aq) ⇌ H2SO4(aq) + H2O(ℓ)           K_1 = \dfrac{1}{K_{\text{a, H}_2\text{SO}_4}} = \dfrac{1}{4.0\;\times\;10^{3}}
HCO3(aq) + H2O(ℓ) ⇌ CO32-(aq) + H3O+(aq)           K_2 = K_{\text{a, HCO}_3^-} = 4.7\;\times\;10^{-11}

The sum of these two reaction gives the overall reaction for possibility II:

HSO4(aq) + H3O+(aq) + HCO3(aq) + H2O(ℓ) ⇌ H2SO4(aq) + H2O(ℓ) + CO32-(aq) + H3O+(aq)
HSO4(aq) + HCO3(aq) ⇌ H2SO4(aq) + CO32-(aq)

Therefore, the equilibrium constant for possibility II is:

 K_{\text{overall, possibility II}} = K_1 \times K_2 = \dfrac{4.7\;\times\;10^{-11}}{4.0\;\times\;10^{3}} = 1.2\;\times\;10^{-14}

Possibility II is heavily reactant-favored at equilibrium (this reaction can be considered as not occurring). Therefore, of the two possibilities, the reaction that proceeds forward and produces products is possibility I, where HSO4 acts as an acid and HCO3 acts as a base.

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