D37.2 Predicting the Extent of an Acid Base Reaction

In the previous section, we considered the extent of an acid-base reaction qualitatively: we can predict whether an acid-base reaction is reactant- or product-favored by considering which side has the weaker acid and base.

Specifically, the reaction

is product-favored because there is a weak acid and a strong base on the reactant side and only a weak base on the product side. In other words, the presence of the reactive hydroxide base raises the overall energy of the reactants relative to the products.

In more quantitative terms, the equilibrium constant of this reaction can be calculated from the known K_a and K_b values. To simplify things a little, let’s use the net ionic reaction equation:

we can obtain this reaction equation by combining the reaction equations associated with K_a of acetic acid and K_w (Hess’s law):

	CH3COOH(aq) + H2O(ℓ)	⇌	CH3COO–(aq) + H3O+(aq)	K1 = Ka = 1.8 × 10-5
	H3O+(aq) + OH–(aq)	⇌	H2O(ℓ) + H2O(ℓ)	K2 = = 1.0 × 1014
Sum:	CH3COOH(aq) + OH–(aq)	⇌	CH3COO–(aq) + H2O(ℓ)

Therefore, the overall reaction equilibrium constant is

which shows that this reaction is indeed product-favored.

What if we instead mix acetic acid with ammonia, a weak base?  Is the reaction

reactant-favored or product-favored?

Qualitatively, there is a weak acid (CH₃COOH) and a weak base (NH₃) on the reactant-side, and a weak acid (NH₄⁺) and a weak base (CH₃COO¯) on the product-side. The prediction is not straightforward, so we need to know their K_a and K_b values.

Now, we can see that CH₃COOH is a stronger acid than NH₄⁺, and NH₃ is a stronger base than CH₃COO¯. The weaker (and therefore more stable) acid and base are both on the product-side, therefore, this reaction is product-favored.

Quantitatively, we can again apply Hess’s law to calculated the K for this reaction using the known K_a and K_b values.

	CH3COOH(aq) + H2O(ℓ)	⇌	CH3COO–(aq) + H3O+(aq)	K1 = Ka, CH3COOH = 1.75 × 10-5
	NH3(aq) + H3O+(aq)	⇌	NH4+(aq) + H2O(ℓ)	K2 = = 1.77 × 109
Sum:	CH3COOH(aq) + NH3(aq)	⇌	CH3COO–(aq) + NH4+(aq)	K = K1K2 = 3.10 × 104

The overall reaction equilibrium constant agrees with the qualitative analysis that this reaction is product-favored.

Left-click here for optional information: application to amphiprotic species

Acid-base reactions can occur between two amphiprotic species, where both reactants can act as either an acid or a base.

For example, two reactions are possible when mixing together a sodium bisulfate solution (NaHSO₄(aq), which contains the HSO₄^– ion) and a sodium bicarbonate solution (NaHCO₃(aq), which contains the HCO₃^– ion):

possibility I:          HSO₄^–(aq) + HCO₃^–(aq) ⇌ SO₄^2-(aq) + H₂CO₃(aq)

possibility II:          HSO₄^–(aq) + HCO₃^–(aq) ⇌ H₂SO₄(aq) + CO₃^2-(aq)

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

In possibility II, there is a weak acid and a weak base on the reactant-side, and a strong acid (H₂SO₄) and a weak base on the product-side. The presence of the strong acid would drive the reaction to be reactant-favored. (the exact values are: the acids: H₂SO₄ (K_a = 4.0 × 10³) and HCO₃^– (K_a = 4.7 × 10^-11), the bases: HSO₄^– (K_b = 2.5 × 10^-18) and CO₃²⁻ (K_b = 2.1 × 10^-4).)

We can also make use of the known K_a values to quantitatively determine which reaction occurs. In possibility I,

	HSO4–(aq) + H2O(ℓ)	⇌	SO42-(aq) + H3O+(aq)	K1 = Ka, HSO4¯ = 1.1 × 10-2
	HCO3–(aq) + H3O+(aq)	⇌	H2CO3(aq) + H2O(ℓ)	K2 = = 2.3 × 106
Sum:	HSO4–(aq) + HCO3–(aq)	⇌	SO42-(aq) + H2CO3(aq)	K = K1K2 = 2.6 × 104

In possibility II,

	HSO4–(aq) + H3O+(aq)	⇌	H2SO4(aq) + H2O(ℓ)	K1 = = 2.5 × 10-4
	HCO3–(aq) + H2O(ℓ)	⇌	CO32-(aq) + H3O+(aq)	K2 = Ka, HCO3¯ = 4.7 × 10-11
Sum:	HSO4–(aq) + HCO3–(aq)	⇌	H2SO4(aq) + CO32-(aq)	K = K1K2 = 1.2 × 10-14

K_{possibility I} >> K_{possibility II}, therefore, the reaction that occurs (proceeds forward and produces products) is possibility I, where HSO₄^– acts as an acid and HCO₃^– acts as a base.