2.8: Acid and Base Strength

Different acids differ in their ability to donate H⁺. Stronger acids, such as HCl, react almost completely with water, whereas weaker acids, such as acetic acid (CH₃CO₂H), react only slightly. The exact strength of a given acid HA in water solution is described using the acidity constant (K_a) for the acid-dissociation equilibrium.

\[\ce{HA(aq) + H2O(l) <=> H3O^{+}(aq) + A^{-}(aq)} \nonumber \]

the acid ionization constant is written

\[K_{ a }=\frac{[\ce{H3O^{+}}] [\ce{A^{-}}]}{[\ce{HA}]} \nonumber \]

Recall from general chemistry that the solvent concentration does not appear in the equilibrium expression, and that brackets [ ] around a substance refer to the concentration of the enclosed species in moles per liter (molarity).

Note

Equilibrium constant expressions are actually ratios of activities, and the value of K is determined at the limit of infinite dilution of the solutes. In these very dilute solutions, the activity of the solvent has a value of unity (1) and the activity of each solute can be approximated by its molar concentration.

Stronger acids have their equilibria toward the right and thus have larger acidity constants, whereas weaker acids have their equilibria toward the left and have smaller acidity constants. The range of K_a values for different acids is enormous, running from about 10¹⁵ for the strongest acids to about 10^–60 for the weakest. Common inorganic acids such as H₂SO₄ , HNO₃ , and HCl have K_a ’s in the range of 10¹ to 10⁹ , while organic acids generally have K_a ’s in the range of 10^–5 to 10^–15 . As you gain experience, you’ll develop a rough feeling for which acids are “strong” and which are “weak” (always remembering that the terms are relative, not absolute).

Acid strengths are normally expressed using pK_a values rather than K_a values, where the pK_a is the negative common logarithm of the K_a:

pK_a=−log K_a

A stronger acid (larger K_a) has a smaller pK_a, and a weaker acid (smaller K_a) has a larger pK_a. Table \(\PageIndex{1}\) lists the pK_a’s of some common acids in order of their strength, and a more comprehensive table is given in Appendix B.

Notice that the pK_a value shown in Table \(\PageIndex{1}\) for water is 14.00, which results from the following calculation.

\[\ce{H2O(l) + H2O(l) <=> H3O^{+}(aq) + OH^{-}(aq)} \label{autoionization} \]

with

\[K_w=K_a =[\ce{H3O^{+}}][\ce{OH^{-}}] \label{Kw} \]

As explained above, because the water is the solvent and has an activity of unity (1), water is not shown explicitly in the equilibrium constant expression for K_w

Notice also in Table \(\PageIndex{1}\) that there is an inverse relationship between the acid strength of an acid and the base strength of its conjugate base. A strong acid has a weak conjugate base, and a weak acid has a strong conjugate base. To understand this inverse relationship, think about what is happening to the acidic hydrogen in an acid–base reaction. A strong acid is one that loses H⁺ easily, meaning that its conjugate base holds the H⁺ weakly and is therefore a weak base. A weak acid is one that loses H⁺ with difficulty, meaning that its conjugate base holds the proton tightly and is therefore a strong base. The fact that HCl is a strong acid, for example, means that Cl^– does not hold H⁺ tightly and is thus a weak base. Water, on the other hand, is a weak acid, meaning that OH^– holds H⁺ tightly and is a strong base.

Table \(\PageIndex{1}\): Relative Strengths of Some Common Acids and Their Conjugate Bases

	Acid	Name	pKa	Conjugate base	Name
	CH3CH2OH	Ethanol	16.00	CH3CH2O^–	Ethoxide ion
	H2O	Water	14.00	HO^–	Hydroxide ion
	HCN	Hydrocyanic acid	9.31	CN^–	Cyanide ion
	H2PO4^–	Dihydrogen phosphate ion	7.21	HPO4^2^–	Hydrogen phosphate ion
	CH3CO2H	Acetic acid	4.76	CH3CO2^–	Acetate ion
	H3PO4	Phosphoric acid	2.16	H2PO4^–	Dihydrogen phosphate ion
	H3O^+	Hydronium ion	0.0	H2O	Water
	HNO3	Nitric acid	–1.3	NO3^–	Nitrate ion
	HCl	Hydrochloric acid	–7.0	Cl^–	Chloride ion

Exercise \(\PageIndex{1}\)

The amino acid phenylalanine has pK_a = 1.83, and tryptophan has pK_a = 2.83. Which is the stronger acid?

Answer

Phenylalanine is stronger.

Exercise \(\PageIndex{2}\)

Amide ion, H₂N^–, is a much stronger base than hydroxide ion, HO^–. Which is the stronger acid, NH₃ or H₂O? Explain.

Answer

Water is a stronger acid.