6.4: Acid-Base Strength

Last updated
Save as PDF

Page ID: 164766

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

Skills to Develop

Assess the relative strengths of acids and bases according to their ionization constants
Understand trends in the relative strengths of conjugate acid-base pairs and polyprotic acids and bases

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:

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

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

**Figure \(\PageIndex{1}\)**: 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

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, K_a. 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 we do not include [H₂O] in the equation. The larger the \(K_a\) of an acid, the larger the concentration of \(\ce{H3O+}\) and \(\ce{A^{−}}\) relative to the concentration of the nonionized acid, \(\ce{HA}\). Thus a stronger acid has a larger ionization constant than does a weaker acid. The ionization constants increase as the strengths of the acids increase.

The following data on acid-ionization constants indicate the order of acid strength: \(\ce{CH3CO2H} < \ce{HNO2} < \ce{HSO4-}\)

\[ \begin{aligned} \ce{CH3CO2H}(aq) + \ce{H2O}(l) &⇌\ce{H3O+}(aq)+\ce{CH3CO2-}(aq) \quad &K_\ce{a}=1.8×10^{−5} \\[4pt] \ce{HNO2}(aq)+\ce{H2O}(l) &⇌\ce{H3O+}(aq)+\ce{NO2-}(aq) &K_\ce{a}=4.6×10^{-4} \\[4pt] \ce{HSO4-}(aq)+\ce{H2O}(aq) &⇌\ce{H3O+}(aq)+\ce{SO4^2-}(aq) & K_\ce{a}=1.2×10^{−2} \end{aligned}\]

Another measure of the strength of an acid is its percent ionization. The percent ionization of a weak acid is the ratio of the concentration of the ionized acid to the initial acid concentration, times 100:

\[\% \:\ce{ionization}=\ce{\dfrac{[H3O+]_{eq}}{[HA]_0}}×100\% \label{PercentIon} \]

Because the ratio includes the initial concentration, the percent ionization for a solution of a given weak acid varies depending on the original concentration of the acid, and actually decreases with increasing acid concentration.

Example \(\PageIndex{1}\): Calculation of Percent Ionization from pH

Calculate the percent ionization of a 0.125-M solution of nitrous acid (a weak acid), with a pH of 2.09.

Solution

The percent ionization for an acid is:

\[\ce{\dfrac{[H3O+]_{eq}}{[HNO2]_0}}×100 \]

The chemical equation for the dissociation of the nitrous acid is:

\[\ce{HNO2}(aq)+\ce{H2O}(l)⇌\ce{NO2-}(aq)+\ce{H3O+}(aq). \]

Since 10^−pH = \(\ce{[H3O+]}\) , we find that \(10^{−2.09} = 8.1 \times 10^{−3}\, M\), so that percent ionization (Equation \ref{PercentIon}) is:

\[\dfrac{8.1×10^{−3}}{0.125}×100=6.5\% \]

Remember, the logarithm 2.09 indicates a hydronium ion concentration with only two significant figures.

Exercise \(\PageIndex{1}\)

Calculate the percent ionization of a 0.10 M solution of acetic acid with a pH of 2.89.

Answer: 1.3% ionized

We can rank the strengths of bases by their tendency to form hydroxide ions in aqueous solution. The reaction of a Brønsted-Lowry base with water is given by:

\[\ce{B}(aq)+\ce{H2O}(l)⇌\ce{HB+}(aq)+\ce{OH-}(aq)\]

Water is the acid that reacts with the base, \(\ce{HB^{+}}\) is the conjugate acid of the base \(\ce{B}\), and the hydroxide ion is the conjugate base of water. A strong base yields 100% (or very nearly so) of OH⁻ and HB⁺ when it reacts with water; Figure \(\PageIndex{1}\) lists several strong bases. A weak base yields a small proportion of hydroxide ions. Soluble ionic hydroxides such as NaOH are considered strong bases because they dissociate completely when dissolved in water.

As we did with acids, we can measure the relative strengths of bases by measuring their base-ionization constant (K_b) in aqueous solutions. In solutions of the same concentration, stronger bases ionize to a greater extent, and so yield higher hydroxide ion concentrations than do weaker bases. A stronger base has a larger ionization constant than does a weaker base. For the reaction of a base, \(\ce{B}\):

\[\ce{B}(aq)+\ce{H2O}(l)⇌\ce{HB+}(aq)+\ce{OH-}(aq),\]

we write the equation for the ionization constant as:

\[K_\ce{b}=\ce{\dfrac{[HB+][OH- ]}{[B]}}\]

where the concentrations are those at equilibrium. Again, we do not include [H₂O] in the equation because water is the solvent. The chemical reactions and ionization constants of the three bases shown are:

\[ \begin{aligned} \ce{NO2-}(aq)+\ce{H2O}(l) &⇌\ce{HNO2}(aq)+\ce{OH-}(aq) \quad &K_\ce{b}=2.17×10^{−11} \\[4pt] \ce{CH3CO2-}(aq)+\ce{H2O}(l) &⇌\ce{CH3CO2H}(aq)+\ce{OH-}(aq) &K_\ce{b}=5.6×10^{−10} \\[4pt] \ce{NH3}(aq)+\ce{H2O}(l) &⇌\ce{NH4+}(aq)+\ce{OH-}(aq) &K_\ce{b}=1.8×10^{−5} \end{aligned}\]

A table of ionization constants of weak bases appears in Table E2. As with acids, percent ionization can be measured for basic solutions, but will vary depending on the base ionization constant and the initial concentration of the solution.

Strengths of Conjugate Acid-Base Pairs

The acid/base strengths of a conjugate pair are related to each other. Consider the ionization reactions for a conjugate acid-base pair, HA − A⁻:

\[\ce{HA}(aq)+\ce{H2O}(l)⇌\ce{H3O+}(aq)+\ce{A-}(aq) \hspace{20px} K_\ce{a}=\ce{\dfrac{[H3O+][A- ]}{[HA]}}\]

\[\ce{A-}(aq)+\ce{H2O}(l)⇌\ce{OH-}(aq)+\ce{HA}(aq) \hspace{20px} K_\ce{b}=\ce{\dfrac{[HA][OH]}{[A- ]}}\]

Adding these two chemical equations yields the equation for the autoionization for water:

\[\cancel{\ce{HA}(aq)}+\ce{H2O}(l)+\cancel{\ce{A-}(aq)}+\ce{H2O}(l)⇌\ce{H3O+}(aq)+\cancel{\ce{A-}(aq)}+\ce{OH-}(aq)+\cancel{\ce{HA}(aq)}\]

\[\ce{2H2O}(l)⇌\ce{H3O+}(aq)+\ce{OH-}(aq)\]

As shown in the previous chapter on equilibrium, the K expression for a chemical equation derived from adding two or more other equations is the mathematical product of the other equations’ K expressions. Multiplying the mass-action expressions together and cancelling common terms, we see that:

\[K_\ce{a}×K_\ce{b}=\ce{\dfrac{[H3O+][A- ]}{[HA]}×\dfrac{[HA][OH- ]}{[A- ]}}=\ce{[H3O+][OH- ]}=K_\ce{w}\]

For example, the acid ionization constant of acetic acid (CH₃COOH) is 1.8 × 10⁻⁵, and the base ionization constant of its conjugate base, acetate ion (\(\ce{CH3COO-}\)), is 5.6 × 10⁻¹⁰. The product of these two constants is indeed equal to K_w:

\[K_\ce{a}×K_\ce{b}=(1.8×10^{−5})×(5.6×10^{−10})=1.0×10^{−14}=K_\ce{w}\]

The extent to which an acid, HA, donates protons to water molecules depends on the strength of the conjugate base, A⁻, of the acid. If A⁻ is a stronger base, most protons that are donated to water molecules are recaptured by A⁻. Thus there is relatively little A⁻ and \(\ce{H3O+}\) in solution, and the acid, HA, is weak. If A⁻ is a weaker base, water binds the protons more strongly, and the solution contains primarily A⁻ and H₃O⁺—the acid is stronger. Thus, the strengths of an acid and its conjugate base are inversely related, as shown in (Figure \(\PageIndex{2}\)).

<div data-mt-source="1"><img class="internal" alt="" style="width: 1300px; height: 450px;" data-cke-saved-src="http://chemwiki.ucdavis.edu/@api/deki/files/65684/CNX_Chem_14_03_strengths.jpg" src="http://chemwiki.ucdavis.edu/@api/deki/files/65684/CNX_Chem_14_03_strengths.jpg"></div> — **Figure \(\PageIndex{2}\)**: This diagram shows the relative strengths of conjugate acid-base pairs, as indicated by their ionization constants in aqueous solution.

A stronger acid has a weaker conjugate base. A weaker acid has a stronger conjugate base.

Figure \(\PageIndex{3}\) lists a series of acids and bases in order of the decreasing strengths of the acids and the corresponding increasing strengths of the bases. The acid and base in a given row are conjugate to each other.

The first six acids in Figure \(\PageIndex{3}\) are the most common strong acids. These acids are completely dissociated in aqueous solution. The conjugate bases of these acids are weaker bases than water. When one of these acids dissolves in water, their protons are completely transferred to water, the stronger base.

Those acids that lie between the hydronium ion and water in Figure \(\PageIndex{3}\) form conjugate bases that can compete with water for possession of a proton. Both hydronium ions and nonionized acid molecules are present in equilibrium in a solution of one of these acids. Compounds that are weaker acids than water (those found below water in the column of acids) in Figure \(\PageIndex{3}\) exhibit no observable acidic behavior when dissolved in water. Their conjugate bases are stronger than the hydroxide ion, and if any conjugate base were formed, it would react with water to re-form the acid.

The extent to which a base forms hydroxide ion in aqueous solution depends on the strength of the base relative to that of the hydroxide ion, as shown in the last column in Figure \(\PageIndex{3}\). A strong base, such as one of those lying below hydroxide ion, accepts protons from water to yield 100% of the conjugate acid and hydroxide ion. Those bases lying between water and hydroxide ion accept protons from water, but a mixture of the hydroxide ion and the base results. Bases that are weaker than water (those that lie above water in the column of bases) show no observable basic behavior in aqueous solution.

Example \(\PageIndex{2}\): The Product K_a × K_b = K_w

Use the K_b for the nitrite ion, \(\ce{NO2-}\), to calculate the K_a for its conjugate acid.

Solution

K_b for \(\ce{NO2-}\) is given in this section as 2.17 × 10⁻¹¹. The conjugate acid of \(\ce{NO2-}\) is HNO₂; K_a for HNO₂ can be calculated using the relationship:

\[K_\ce{a}×K_\ce{b}=1.0×10^{−14}=K_\ce{w} \]

Solving for K_a, we get:

\[K_\ce{a}=\dfrac{K_\ce{w}}{K_\ce{b}}=\dfrac{1.0×10^{−14}}{2.17×10^{−11}}=4.6×10^{−4} \]

This answer can be verified by finding the K_a for HNO₂ in Table E1

Exercise \(\PageIndex{2}\)

We can determine the relative acid strengths of \(\ce{NH4+}\) and HCN by comparing their ionization constants. The ionization constant of HCN is given in Table E1 as 4.9 × 10⁻¹⁰. The ionization constant of \(\ce{NH4+}\) is not listed, but the ionization constant of its conjugate base, NH₃, is listed as 1.8 × 10⁻⁵. Determine the ionization constant of \(\ce{NH4+}\), and decide which is the stronger acid, HCN or \(\ce{NH4+}\).

Answer: \(\ce{NH4+}\) is the slightly stronger acid (K_a for \(\ce{NH4+}\) = 5.6 × 10⁻¹⁰).

Polyprotic Acids and Bases

We can classify acids by the number of protons per molecule that they can give up in a reaction. Acids such as \(\ce{HCl}\), \(\ce{HNO3}\), and \(\ce{HCN}\) can only donate one proton per molecule. These are called monoprotic acids. Even though it contains four hydrogen atoms, acetic acid, \(\ce{CH3CO2H}\), is also monoprotic because only the hydrogen atom from the carboxyl group (\(\ce{-COOH}\)) reacts with bases:

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

However, certain acids are capable of donating more than a single proton per molecule in acid-base reactions. These are known as polyprotic acids ("many proton" acids). Polyprotic acids undergo more than one ionization equilibrium and therefore have more than one K_a value. For example, sulfuric acid, a strong acid, ionizes as follows:

First Ionization

\[ \ce{H2SO4}(aq)+\ce{H2O}(l)⇌\ce{H3O+}(aq)+\ce{HSO4-}(aq)\]

with \(K_{\ce a1} > 10^2;\: {complete\: dissociation}\).

Second Ionization

\[ \ce{HSO4-}(aq)+\ce{H2O}(l)⇌\ce{H3O+}(aq)+\ce{SO4^{2−}}(aq)\]

with \( K_{\ce a2}=1.2×10^{−2}\).

Notice that the first ionization has a much higher K_a value than the second. This illustrates an important point about polyprotic acids: the first ionization always takes place to a greater extent than subsequent ionizations.

In most cases, polyprotic acids lose their protons one at a time, with K_a1 >> K_a2 >> K_a3etc.

When we make a solution of a weak polyprotic acid, we get a solution that contains a mixture of acids. Carbonic acid, \(\ce{H2CO3}\), is an example of a weak diprotic acid ("diprotic" = two ionizable protons). The first ionization of carbonic acid yields hydronium ions and bicarbonate ions in small amounts.

First Ionization

\[\ce{H2CO3}(aq)+\ce{H2O}(l)⇌\ce{H3O+}(aq)+\ce{HCO3-}(aq)\]

with

\[K_{\ce{H2CO3}}=\ce{\dfrac{[H3O+][HCO3- ]}{[H2CO3]}}=4.3×10^{−7}\]

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

Second Ionization

\[\ce{HCO3-}(aq)+\ce{H2O}(l)⇌\ce{H3O+}(aq)+\ce{CO3^2-}(aq)\]

with

\[ K_{\ce{HCO3-}}=\ce{\dfrac{[H3O+][CO3^2- ]}{[HCO3- ]}}=4.7×10^{−11}\]

\(K_{\ce{H2CO3}}\) is larger than \(K_{\ce{HCO3-}}\) by a factor of 10⁴, so H₂CO₃ is the dominant producer of hydronium ion in the solution. This means that little of the \(\ce{HCO3-}\) formed by the ionization of H₂CO₃ ionizes to give hydronium ions (and carbonate ions), and the concentrations of H₃O⁺ and \(\ce{HCO3-}\) are practically equal in a pure aqueous solution of H₂CO₃.

This stepwise ionization process occurs for all polyprotic acids, as illustrated in Table \(\PageIndex{1}\).

Table \(\PageIndex{1}\). Common Polyprotic Acids with their Ionization Constants

Polyprotic Acids	Formula	Strong/Weak Acid	Number of Ionizable Hydrogens	K_a1	K_a2	K_a3
Sulfuric acid	H₂SO₄	Strong	2 (diprotic)	Very Large	1.1E-2
Sulfurous acid	H₂SO₃	Weak	2 (diprotic)	1.3E-2	6.2E-8
Phosphoric acid	H₃PO₄	Weak	3 (triprotic)	7.1E-3	6.3E-8	4.2E-13
Carbonic acid	H₂CO₃	Weak	2 (diprotic)	4.4E-7	4.7E-11
Hydrosulfuric acid or Hydrogen sulfide	H₂S	Weak	2 (diprotic)	1.0E-7	1E-19
Oxalic acid	H₂C₂O₄	Weak	2 (diprotic)	5.4E-2	5.3E-5
Malonic acid	H₂C₃H₂O₄	Weak	2 (diprotic)	1.5E-3	2.0E-6

The differences in the ionization constants of each polyprotic acid tell us that in each successive step the degree of ionization is significantly weaker. Successive ionization constants often differ by a factor of about 10⁵ to 10⁶. Practically speaking, if the first ionization constant is larger than the second by a factor of at least 20, it is appropriate to treat the first ionization separately when performing equilibrium calculations on polyprotic acids, which simplifies those calculations significantly.

Summary

The strengths of Brønsted-Lowry acids and bases in aqueous solutions can be determined by their acid or base ionization constants. Stronger acids form weaker conjugate bases, and weaker acids form stronger conjugate bases. Thus 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. Strong bases react with water to quantitatively form hydroxide ions. Weak bases give only small amounts of hydroxide ion. For polyprotic acids, successive ionizations become weaker in a stepwise fashion and can usually be treated as separate equilibria.

Key Equations

\(K_\ce{a}=\ce{\dfrac{[H3O+][A- ]}{[HA]}}\)
\(K_\ce{b}=\ce{\dfrac{[HB+][OH- ]}{[B]}}\)
\(K_a \times K_b = 1.0 \times 10^{−14} = K_w \,(\text{at room temperature})\)
\(\textrm{Percent ionization}=\ce{\dfrac{[H3O+]_{eq}}{[HA]_0}}×100\)

Glossary

acid ionization constant (K_a): equilibrium constant for the ionization of a weak acid

base ionization constant (K_b): equilibrium constant for the ionization of a weak base

leveling effect of water: any acid stronger than \(\ce{H3O+}\), or any base stronger than OH⁻ will react with water to form \(\ce{H3O+}\), or OH⁻, respectively; water acts as a base to make all strong acids appear equally strong, and it acts as an acid to make all strong bases appear equally strong

percent ionization: ratio of the concentration of the ionized acid to the initial acid concentration, times 100

Contributors

Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/85abf193-2bd...a7ac8df6@9.110).
Natalie Kania
Anna Christianson, Bellarmine University