Acid–Base Equilibria: Classification, Strength, and Calculations

Chapter 16: Acid–Base Equilibria

16.1 Classifications of Acids and Bases

Acids and bases are fundamental chemical species with several definitions, each emphasizing different chemical properties. Understanding these classifications is essential for predicting their behavior in aqueous solutions.

• Arrhenius Definition: An acid increases the concentration of hydrogen ions (H+) in water, while a base increases the concentration of hydroxide ions (OH-).

• Brønsted–Lowry Definition: An acid is a proton (H+) donor; a base is a proton acceptor. A Brønsted–Lowry acid must have at least one removable (acidic) proton, and a base must have at least one nonbonding pair of electrons to accept a proton.

• Lewis Definition: A Lewis acid is an electron pair acceptor; a Lewis base is an electron pair donor. All Brønsted–Lowry acids and bases are also Lewis acids and bases.

Amphiprotic Substances: Some substances, such as water, can act as both an acid and a base, depending on the reaction context.

16.2 Conjugate Acid-Base Pairs

Acid–base reactions involve the transfer of a proton, resulting in the formation of conjugate acid–base pairs. These pairs differ by one proton.

• Conjugate Acid–Base Pair: An acid and a base that differ by a single proton.

• Reactions between acids and bases always yield their conjugate bases and acids.

• Relative Strengths: The stronger the acid, the weaker its conjugate base, and vice versa.

16.3 Autoionization of Water

Water is amphoteric, meaning it can act as both an acid and a base. In pure water, a small fraction of molecules autoionize:

• Autoionization: $2\mathrm{H_2O} \rightleftharpoons \mathrm{H_3O^+} + \mathrm{OH^-}$

• The equilibrium constant for this process is called the ion product constant for water ($K_w$).

Aqueous Solutions: Solutions can be acidic, basic, or neutral depending on the relative concentrations of H+ and OH-.

16.4 The pH Scale

The pH scale is a logarithmic method for reporting hydrogen ion concentration in aqueous solutions.

• Neutral pH: 7.00

• Acidic pH: Below 7.00

• Basic pH: Above 7.00

• Only digits after the decimal point are significant in logarithmic calculations.

pOH and Other “p” Scales: The "p" indicates the negative logarithm of a quantity (e.g., pH = -log[H+]).

Measuring pH

• pH Meter: Provides accurate measurements using electrodes sensitive to voltage changes.

• Indicators: Compounds that change color depending on pH; less accurate but quick.

16.5 Strong Acids and Bases

Strong acids and bases dissociate completely in aqueous solution, making them strong electrolytes.

• Strong Acids: The seven strong acids exist totally as ions in solution.

• Strong Bases: Soluble hydroxides of alkali and heavier alkaline earth metals; dissociate completely.

16.6 Weak Acids

Weak acids only partially dissociate in water, establishing an equilibrium between the acid and its ions.

• Acid-Dissociation Constant ($K_a$): Measures the strength of a weak acid. The larger the $K_a$, the stronger the acid.

• Equilibrium expression: $K_a = \frac{[\mathrm{H^+}][\mathrm{A^-}]}{[\mathrm{HA}]}$

Comparing Strong and Weak Acids: Strong acids dissociate completely; weak acids only partially.

Calculating $K_a$ from pH

• Write the dissociation equation.

• Set up an ICE (Initial, Change, Equilibrium) table.

• Use pH to find [H+], then calculate equilibrium concentrations.

• Substitute into the $K_a$ expression to solve.

Calculating Percent Ionization

• Percent ionization = $\frac{[\mathrm{H^+}]_{eq}}{[\mathrm{HA}]_{initial}} \times 100\%$

Calculating pH Using $K_a$

• Write the equilibrium equation and $K_a$ expression.

• Set up an ICE table and solve for x (change in concentration).

• Assume x is small if $K_a$ is much less than the initial concentration.

Polyprotic Acids

Polyprotic acids have more than one acidic proton. Each dissociation step has its own $K_a$ value, and the first proton is always easier to remove.

• If $K_a$ values differ by a factor of 1000, pH depends mainly on the first dissociation.

16.7 Weak Bases

Weak bases only partially accept protons in water, establishing an equilibrium.

• Base-Dissociation Constant ($K_b$): Measures the strength of a weak base. $K_b = \frac{[\mathrm{BH^+}][\mathrm{OH^-}]}{[\mathrm{B}]}$

• Many weak bases contain nitrogen with a lone pair (e.g., ammonia and amines).

Types of Weak Bases

• Neutral substances with a nonbonding pair of electrons (e.g., ammonia, amines).

• Anions of weak acids (conjugate bases).

Calculating pH Using $K_b$

• Write the equilibrium equation and $K_b$ expression.

• Set up an ICE table and solve for x.

• Calculate pOH, then pH: $\mathrm{pH} = 14 - \mathrm{pOH}$

16.8 Relationship Between $K_a$ and $K_b$

For a conjugate acid–base pair, $K_a$ and $K_b$ are related:

• $K_a \times K_b = K_w$ (ion-product constant for water)

• If you know one, you can calculate the other.

16.9 Acid–Base Properties of Salt Solutions

Many ions react with water (hydrolysis) to create acidic or basic solutions. The acid–base properties of a salt depend on its cation and anion.

• Cations can be acidic or neutral; anions can be acidic, basic, or neutral.

• Anions of strong acids are neutral; anions of weak acids are basic.

• Polyatomic cations are typically conjugate acids of weak bases and are acidic.

• Transition and post-transition metal cations are acidic due to Lewis acid–base reactions.

Salt Solutions—Acidic, Basic, or Neutral?

• If both ions do not react with water, the solution is neutral.

• If the anion reacts to produce OH- and the cation does not, the solution is basic.

• If the cation reacts to produce H+ and the anion does not, the solution is acidic.

• If both react, the larger equilibrium constant determines pH.

16.10 Acid–Base Behavior and Chemical Structure

The strength of an acid depends on several structural factors:

• Bond Polarity: The bond must be polarized with positive charge on H and negative on the other atom.

• Bond Strength: Acid strength increases as bond strength decreases.

• Stability of Conjugate Base: The more stable the conjugate base, the stronger the acid.

Binary Acids

• Consist of H and one other element.

• Within a group, bond strength is most important; within a period, bond polarity is most important.

Oxyacids

• Consist of H, O, and a nonmetal.

• Acidity increases with the electronegativity of the nonmetal and the number of O atoms.

• Higher oxidation number means higher acidity.

Carboxylic Acids

• Organic acids containing the carboxyl group (-COOH).

• Acidity is enhanced by electron-withdrawing O atoms and resonance stabilization of the conjugate base.