Acids, Bases, and Aqueous Equilibria: Definitions, Calculations, and Applications

Acids and Bases: Definitions and Properties

Arrhenius, Brønsted-Lowry, and Lewis Definitions

Acids and bases can be defined in several ways, each broadening the scope of what substances qualify as acids or bases.

• Arrhenius Definition: An acid produces H+ ions in aqueous solution; a base produces OH- ions.

• Brønsted-Lowry Definition: An acid is a proton (H+) donor; a base is a proton acceptor.

• Lewis Definition: An acid is an electron pair acceptor; a base is an electron pair donor.

Example: NH3 is not an Arrhenius base (does not produce OH- directly), but it is a Brønsted-Lowry and Lewis base.

Identifying Acids and Bases by Definition

• To determine if a substance is an acid or base under each definition, consider the reaction context and the species' ability to donate/accept protons or electron pairs.

• Some substances may qualify under one definition but not another.

Conjugate Acid-Base Pairs

In Brønsted-Lowry theory, acids and bases exist in conjugate pairs, differing by one proton.

• Conjugate Acid: The species formed when a base gains a proton.

• Conjugate Base: The species formed when an acid loses a proton.

• Example: For NH3 + H2O → NH4+ + OH-, NH3 is the base, NH4+ is its conjugate acid.

Identifying Acid/Base Reactions and Amphoteric Substances

• Acid/base reactions involve proton transfer (Brønsted-Lowry) or electron pair transfer (Lewis).

• Amphoteric substances can act as either acids or bases (e.g., H2O, HCO3-).

Acid Strength and Molecular Structure

Binary Acids (HX)

• Acid strength increases with increasing bond polarity and decreasing bond strength.

• For HX, acid strength increases down a group (e.g., HF < HCl < HBr < HI).

Oxyacids

• For oxyacids with the same central atom, acid strength increases with more oxygen atoms (e.g., HClO < HClO2 < HClO3 < HClO4).

• For oxyacids with the same number of oxygens, acid strength increases with increasing electronegativity of the central atom (e.g., HClO3 > HBrO3).

Ordering Acids by Strength

• Use molecular structure and periodic trends to rank acids.

Acid-Base Equilibria and Calculations

Direction of Acid/Base Reactions

• The reaction favors the side with the weaker acid and base.

pH, pOH, and Ion Concentrations

• pH Equation: $\mathrm{pH} = -\log_{10}[\mathrm{H_3O^+}]$

• pOH Equation: $\mathrm{pOH} = -\log_{10}[\mathrm{OH^-}]$

• Relationship: $\mathrm{pH} + \mathrm{pOH} = 14$ (at 25°C)

• Ion Product of Water: $K_w = [\mathrm{H_3O^+}][\mathrm{OH^-}] = 1.0 \times 10^{-14}$ (at 25°C)

Example: If [H3O+] = 1.0 × 10-3 M, pH = 3.

Acidic and Basic Solutions

• pH < 7: Acidic; pH > 7: Basic; pH = 7: Neutral (at 25°C).

Strong vs. Weak Acids and Bases

• Strong acids/bases dissociate completely in water.

• Weak acids/bases only partially dissociate.

• For strong acids/bases, [H3O+] or [OH-] equals the initial concentration.

Calculations for Strong and Weak Acids/Bases

• For strong acids/bases: Direct calculation using initial concentration.

• For weak acids/bases: Use equilibrium expressions and $K_a$ or $K_b$.

• Acid Dissociation Constant: $K_a = \frac{[\mathrm{H_3O^+}][\mathrm{A^-}]}{[\mathrm{HA}]}$

• Base Dissociation Constant: $K_b = \frac{[\mathrm{BH^+}][\mathrm{OH^-}]}{[\mathrm{B}]}$

Example: Calculate pH of 0.10 M acetic acid (weak acid) given $K_a$.

Ranking Acids and Bases by $K_a$ and $K_b$

• Larger $K_a$ or $K_b$ values indicate stronger acids or bases.

Polyprotic Acids

Definition and Dissociation Steps

• Polyprotic acids can donate more than one proton (e.g., H2SO4, H3PO4).

• Dissociation occurs in steps, each with its own $K_a$ value: $K_{a1} > K_{a2} > K_{a3}$.

Example: For H2SO4:

• First dissociation: $\mathrm{H_2SO_4} \rightarrow \mathrm{H^+} + \mathrm{HSO_4^-}$

• Second dissociation: $\mathrm{HSO_4^-} \rightarrow \mathrm{H^+} + \mathrm{SO_4^{2-}}$

Salts, Hydrolysis, and Solution pH

Hydrolysis of Ions

• Some ions react with water to produce acidic or basic solutions.

• Write hydrolysis equations to show this process.

Example: $\mathrm{NH_4^+} + \mathrm{H_2O} \rightarrow \mathrm{NH_3} + \mathrm{H_3O^+}$ (acidic solution)

Predicting Salt Solution pH

• Salts from strong acid + strong base: Neutral solution.

• Salts from strong base + weak acid: Basic solution.

• Salts from strong acid + weak base: Acidic solution.

Calculating pH of Salt Solutions

• Use hydrolysis reactions and $K_a$, $K_b$ values to determine pH.

Relationship Between $K_a$ and $K_b$

• For a conjugate acid-base pair: $K_a \times K_b = K_w$

Buffers and the Common Ion Effect

Common Ion Effect

• The presence of a common ion suppresses the ionization of a weak acid or base, affecting pH.

• Mathematical explanation: Use equilibrium expressions to show decreased ionization.

Buffer Solutions

• Buffer: A solution that resists changes in pH when small amounts of acid or base are added.

• Made from a weak acid and its conjugate base, or a weak base and its conjugate acid.

• To make a buffer of specified pH, choose a weak acid/base with $pK_a$ close to the desired pH.

Buffer Calculations

• Henderson-Hasselbalch Equation:

$\mathrm{pH} = \mathrm{p}K_a + \log_{10}\left(\frac{[\mathrm{A^-}]}{[\mathrm{HA}]}\right)$

• Calculate pH given buffer composition, or determine required quantities for a target pH.

Buffer Capacity

• Buffer capacity is the amount of acid or base a buffer can neutralize before pH changes significantly.

Buffer Action: Chemical Equations

• Show how a buffer reacts with added acid or base to minimize pH change.

Example: Acetate buffer: CH3COO- + H3O+ → CH3COOH + H2O

Titrations and Indicators

Titration Calculations

• Determine molar mass, unknown concentration, or volume of titrant needed for equivalence point.

• Calculate pH at half-equivalence and equivalence points.

• For weak acid/strong base titrations, the equivalence point pH > 7; for strong acid/strong base, pH = 7.

Choosing Indicators

• Select an indicator whose color change range includes the equivalence point pH.

Indicator	pH Range	Suitable Titration Type
Methyl Orange	3.1 - 4.4	Strong acid/weak base
Bromothymol Blue	6.0 - 7.6	Strong acid/strong base
Phenolphthalein	8.3 - 10.0	Weak acid/strong base

Additional info: Table inferred from standard indicator ranges (see Table 17.1 in most textbooks).