# 5.3: Relative Strengths of Acids

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

##### Learning Objectives
• Distinguish between strong and weak acids
• Assess the relative strengths of acids according to their ionization constants

We can rank the strengths of acids by the extent to which they ionize in aqueous solution. The reaction of an acid with water is given by the general expression:

$\ce{HA}(aq)+\ce{H2O}(l)⇌\ce{H3O+}(aq)+\ce{A-}(aq)$

In these reactions, water is the base that reacts with the acid $$\ce{HA}$$, $$\ce{A^{−}}$$ is the conjugate base of the acid $$\ce{HA}$$, and the hydronium ion is the conjugate acid of water.

## Strong Acid Ionization

A strong acid yields 100% (or very nearly so) of $$\ce{H3O+}$$ and $$\ce{A^{−}}$$ when the acid ionizes in water; Table $$\PageIndex{1}$$ lists several strong acids. A weak acid gives small amounts of $$\ce{H3O+}$$ and $$\ce{A^{−}}$$.

Table $$\PageIndex{1}$$: Some of the common strong acids and bases are listed here.
Six Strong Acids Six Strong Bases
$$\ce{HClO4}$$ perchloric acid $$\ce{LiOH}$$ lithium hydroxide
$$\ce{HCl}$$ hydrochloric acid $$\ce{NaOH}$$ sodium hydroxide
$$\ce{HBr}$$ hydrobromic acid $$\ce{KOH}$$ potassium hydroxide
$$\ce{HI}$$ hydroiodic acid $$\ce{Ca(OH)2}$$ calcium hydroxide
$$\ce{HNO3}$$ nitric acid $$\ce{Sr(OH)2}$$ strontium hydroxide
$$\ce{H2SO4}$$ sulfuric acid $$\ce{Ba(OH)2}$$ barium hydroxide

Because strong acids ionize completely in water, the pH of a strong acid solution can be found using the acid concentration.

$\ce{[HA]}=\ce{[H3O+]}$

##### Example $$\PageIndex{1}$$

What is the pH of concentrated hydrochloric acid, a 12.1 M solution?

Solution

Because hydrochloric acid is a strong acid, we know that $$\ce{[HCl]}$$ is equal to the hydronium concentration $$\ce{[H3O+]}$$.

$\ce{[HCl]}=\ce{[H3O+]}=12.1 \:M$

$pH=-log(12.1) = -1.083$

The pH of concentrated HCl is -1.083.

##### Exercise $$\PageIndex{1}$$

What is the pH of a 0.075 M solution of nitric acid?

pH = 1.12

## The Ionization of Weak Acids

Many acids are weak; that is, they do not ionize fully in aqueous solution. A solution of a weak acid in water is a mixture of the non-ionized acid, hydronium ion, and the conjugate base of the acid, with the non-ionized acid present in the greatest concentration. The relative strengths of acids may be determined by measuring their equilibrium constants in aqueous solutions. In solutions of the same concentration, stronger acids ionize to a greater extent, and so yield higher concentrations of hydronium ions than do weaker acids. The equilibrium constant for an acid is called the acid-ionization constant, Ka. For the reaction of an acid $$\ce{HA}$$:

$\ce{HA}(aq)+\ce{H2O}(l)⇌\ce{H3O+}(aq)+\ce{A-}(aq)$

we write the equation for the ionization constant as:

$K_\ce{a}=\ce{\dfrac{[H3O+][A- ]}{[HA]}}$

where the concentrations are those at equilibrium. Although water is a reactant in the reaction, it is the solvent as well, so its activity has a value of 1, which does not change the value of $$K_a$$.

Acetic acid ($$\ce{CH3CO2H}$$) is a familiar example of a weak acid. When we add acetic acid to water, it ionizes to a small extent according to the equation:

$\ce{CH3CO2H}(aq)+\ce{H2O}(l)⇌\ce{H3O+}(aq)+\ce{CH3CO2-}(aq) \nonumber$

giving an equilibrium mixture with most of the acid present in the non-ionized (molecular) form. This equilibrium, like other equilibria, is dynamic; acetic acid molecules donate hydrogen ions to water molecules and form hydronium ions and acetate ions at the same rate that hydronium ions donate hydrogen ions to acetate ions to reform acetic acid molecules and water molecules. We can tell by measuring the pH of an aqueous solution of known concentration that only a fraction of the weak acid is ionized at any moment (Figure $$\PageIndex{1}$$). The remaining weak acid is present in the non-ionized form.

For acetic acid, at equilibrium:

$K_\ce{a}=\ce{\dfrac{[H3O+][CH3CO2- ]}{[CH3CO2H]}}=1.8 \times 10^{−5} \nonumber$

Table $$\PageIndex{2}$$ gives the ionization constants for several weak acids; additional ionization constants can be found in the appendix of this text. Notice that all of the $$K_a$$ values for weak acids are smaller than 1, indicating that the reactants side of the equilibrium reaction is favored. This is consistent with our definition of a weak acid: an acid that only partially ionizes in solution.

The strength of weak acids can be compared through their $$K_a$$ values. The larger the $$K_a$$ of an acid, the larger the concentration of $$\ce{H3O+}$$ and $$\ce{A^{−}}$$ relative to the concentration of the non-ionized acid, $$\ce{HA}$$. Thus a stronger acid has a larger ionization constant than does a weaker acid.

Table $$\PageIndex{2}$$: Ionization Constants of Some Weak Acids

Ionization Reaction Ka at 25 °C
$$\ce{HSO4- + H2O ⇌ H3O+ + SO4^2-}$$ 1.2 × 10−2
$$\ce{HF + H2O ⇌ H3O+ + F-}$$ 3.5 × 10−4
$$\ce{HNO2 + H2O ⇌ H3O+ + NO2-}$$ 4.6 × 10−4
$$\ce{HNCO + H2O ⇌ H3O+ + NCO-}$$ 2 × 10−4
$$\ce{HCO2H + H2O ⇌ H3O+ + HCO2-}$$ 1.8 × 10−4
$$\ce{CH3CO2H + H2O ⇌ H3O+ + CH3CO2-}$$ 1.8 × 10−5
$$\ce{HCIO + H2O ⇌ H3O+ + CIO-}$$ 2.9 × 10−8
$$\ce{HBrO + H2O ⇌ H3O+ + BrO-}$$ 2.8 × 10−9
$$\ce{HCN + H2O ⇌ H3O+ + CN-}$$ 4.9 × 10−10
##### Example $$\PageIndex{2}$$: Determination of Ka from Equilibrium Concentrations

Acetic acid is the principal ingredient in vinegar; that's why it tastes sour. At equilibrium, a solution contains [CH3CO2H] = 0.0787 M and $$\ce{[H3O+]}=\ce{[CH3CO2- ]}=0.00118\:M$$. What is the value of $$K_a$$ for acetic acid?

Solution

We are asked to calculate an equilibrium constant from equilibrium concentrations. At equilibrium, the value of the equilibrium constant is equal to the reaction quotient for the reaction:

$\ce{CH3CO2H}(aq)+\ce{H2O}(l)⇌\ce{H3O+}(aq)+\ce{CH3CO2-}(aq) \nonumber$

\begin{align*} K_\ce{a} &=\ce{\dfrac{[H3O+][CH3CO2- ]}{[CH3CO2H]}} \\[4pt] &=\dfrac{(0.00118)(0.00118)}{0.0787} \\[4pt] &=1.77×10^{−5} \end{align*}

##### Exercise $$\PageIndex{2}$$

What is the equilibrium constant for the ionization of the $$\ce{HSO4-}$$ ion, the weak acid used in some household cleansers:

$\ce{HSO4-}(aq)+\ce{H2O}(l)⇌\ce{H3O+}(aq)+\ce{SO4^2-}(aq) \nonumber$

In one mixture of NaHSO4 and Na2SO4 at equilibrium, $$\ce{[H3O+]}$$ = 0.027 M; $$\ce{[HSO4- ]}=0.29\:M$$; and $$\ce{[SO4^2- ]}=0.13\:M$$.

$$K_a$$ for $$\ce{HSO_4^-}= 1.2 ×\times 10^{−2}$$

## Summary

The strengths of Brønsted-Lowry acids and bases in aqueous solutions can be determined by their acid ionization constants. Strong acids are completely ionized in aqueous solution because their conjugate bases are weaker bases than water. Weak acids are only partially ionized because their conjugate bases are strong enough to compete successfully with water for possession of protons. S

## Key Equations

• $$K_\ce{a}=\ce{\dfrac{[H3O+][A- ]}{[HA]}}$$

## Glossary

acid ionization constant (Ka)
equilibrium constant for the ionization of a weak acid

This page titled 5.3: Relative Strengths of Acids is shared under a CC BY license and was authored, remixed, and/or curated by OpenStax.