Acids, Bases, and Aqueous Ionic Equilibria: Study Guide

Ch. 17 Acids and Bases

Arrhenius and Brønsted Definitions of Acids and Bases

The Arrhenius and Brønsted-Lowry definitions are foundational for understanding acid-base chemistry. The Arrhenius definition classifies acids as substances that increase the concentration of H+ ions in aqueous solution, and bases as substances that increase the concentration of OH- ions. The Brønsted-Lowry definition expands this by defining acids as proton (H+) donors and bases as proton acceptors. The hydronium ion (H3O+) forms when H+ associates with water.

• Arrhenius Acid: Produces H+ in water (e.g., HCl → H+ + Cl-).

• Arrhenius Base: Produces OH- in water (e.g., NaOH → Na+ + OH-).

• Brønsted Acid: H+ donor.

• Brønsted Base: H+ acceptor.

• Hydronium Ion: $\mathrm{H_2O + H^+ \rightarrow H_3O^+}$

Conjugate Acid-Base Pairs

Every acid-base reaction involves two conjugate acid-base pairs. The conjugate acid is formed when a base gains a proton, and the conjugate base is formed when an acid loses a proton.

• Example: $\mathrm{NH_3 + H_2O \rightleftharpoons NH_4^+ + OH^-}$ NH3 (base) and NH4+ (conjugate acid); H2O (acid) and OH- (conjugate base).

Autoionization of Water; $K_w$; Calculating pH and pOH

Water can ionize to form H3O+ and OH-. The equilibrium constant for this process is $K_w$.

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

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

• pH: $\mathrm{pH = -\log[H_3O^+]}$

• pOH: $\mathrm{pOH = -\log[OH^-]}$

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

Strong and Weak Acids and Bases

There are seven strong acids; all others are weak. Strong bases are typically Group 1 and Group 2 metal hydroxides. Weak bases are less ionized in water.

• Strong Acids: HCl, HBr, HI, HNO3, HClO3, HClO4, H2SO4

• Strong Bases: NaOH, KOH, LiOH, Ca(OH)2, Sr(OH)2, Ba(OH)2

• Weak Acids/Bases: Partially ionize in water (e.g., CH3COOH, NH3).

Acid and Base Ionization Constants ($K_a$, $K_b$) and Their Significance

The magnitude of $K_a$ (acid dissociation constant) and $K_b$ (base dissociation constant) indicates acid or base strength. The larger the value, the stronger the acid or base.

• p$K_a$ and p$K_b$: $\mathrm{p}K_a = -\log K_a$; $\mathrm{p}K_b = -\log K_b$

• Relationship: $\mathrm{p}K_a + \mathrm{p}K_b = 14$ (for conjugate acid-base pairs at 25°C)

Ionization Reactions and pH Calculations for Weak Acids and Bases

Weak acids and bases do not fully ionize. Their ionization in water can be represented by equilibrium equations, and their pH can be calculated using $K_a$ or $K_b$.

• Example (Weak Acid): $\mathrm{HA + H_2O \rightleftharpoons H_3O^+ + A^-}$

• Percent Ionization: $\mathrm{\%\ Ionization = \frac{[H_3O^+]_{eq}}{[HA]_{initial}} \times 100}$

Acid-Base Properties of Salts

Salts can affect the pH of a solution through hydrolysis reactions. The pH depends on the strengths of the parent acid and base.

• Hydrolysis Reaction Example: $\mathrm{A^- + H_2O \rightleftharpoons HA + OH^-}$

• pH Calculation: Use $K_b$ for the anion or $K_a$ for the cation as appropriate.

Polyprotic Acids

Polyprotic acids can donate more than one proton. Each ionization step has its own $K_a$ value, with the first ionization being the strongest.

• Example: $\mathrm{H_2SO_4 \rightarrow H^+ + HSO_4^-}$ (first ionization, strong); $\mathrm{HSO_4^- \rightleftharpoons H^+ + SO_4^{2-}}$ (second ionization, weak)

• pH Calculation: Consider only the first ionization for strong polyprotic acids; for weak, use equilibrium calculations for each step.

Acid Strength and Molecular Structure

The strength of an acid depends on factors such as bond strength, polarity, and the stability of the conjugate base.

• Binary Acids: Acid strength increases down a group and across a period (e.g., HI > HBr > HCl > HF).

• Oxoacids: Acid strength increases with more electronegative central atoms and more oxygen atoms (e.g., HClO4 > HClO3 > HClO2 > HClO).

Ch. 18 Aqueous Ionic Equilibria

Buffers: Function, Components, and Blood Buffer

Buffers are solutions that resist changes in pH when small amounts of acid or base are added. They consist of a weak acid and its conjugate base, or a weak base and its conjugate acid. An important buffer in blood is the carbonic acid/bicarbonate system.

• Blood Buffer: $\mathrm{H_2CO_3/HCO_3^-}$

Buffer Action and Addition of Strong Acid or Base

When a strong acid or base is added to a buffer, the buffer components react to minimize pH change. The weak acid neutralizes added base, and the conjugate base neutralizes added acid.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation allows calculation of buffer pH:

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

Preparing Buffers and Buffer Calculations

To prepare a buffer, mix a weak acid with its salt (conjugate base) or a weak base with its salt (conjugate acid). Calculations involve determining the required amounts to achieve a desired pH.

• Example: To prepare a buffer at pH 5 using acetic acid ($K_a = 1.8 \times 10^{-5}$), use the Henderson-Hasselbalch equation to find the ratio of [A-] to [HA].

Buffer Capacity and Effective pH Range

Buffer capacity is the amount of acid or base a buffer can neutralize before pH changes significantly. Buffers are most effective within ±1 pH unit of the p$K_a$ of the acid.

Common Ion Effect

The common ion effect occurs when a solution contains two substances that share a common ion, suppressing the ionization of a weak acid or base. This affects pH and solubility.

• Example: Adding NaOAc to acetic acid solution decreases ionization of acetic acid.

Titrations: Equivalence Point and End Point

Titration is the gradual addition of one solution to another to determine concentration. The equivalence point is when moles of acid equal moles of base. The end point is when the indicator changes color.

Titration Curves

Titration curves plot pH versus volume of titrant added. They help identify the type of acid/base and key points:

• Strong Acid/Strong Base: Sharp pH change at equivalence point.

• Weak Acid/Strong Base: Buffer region before equivalence point; higher pH at equivalence point.

• Key Points: Initial pH, buffer region, half-equivalence point (pH = p$K_a$), equivalence point, post-equivalence region.

Calculating pH During Titrations

For weak monoprotic acids and bases, calculate pH at various stages using stoichiometry and equilibrium concepts. At half-equivalence, pH = p$K_a$.

Using Titration Curves

Titration curves can be used to determine unknown molar mass, $K_a$, or initial molarity by analyzing the volume at equivalence point and the shape of the curve.

Indicators

Indicators are chosen based on the expected pH at the equivalence point. The best indicator changes color near the equivalence point pH.

Solubility Equilibria of Salts

Solubility equilibria describe the dissolution of sparingly soluble salts in water. The equilibrium constant is the solubility product constant ($K_{sp}$).

• Example: $\mathrm{AgCl(s) \rightleftharpoons Ag^+(aq) + Cl^-(aq)}$

• $K_{sp}$ Expression: $K_{sp} = [Ag^+][Cl^-]$

Calculating $K_{sp}$ and Molar Solubility

Given molar solubility, $K_{sp}$ can be calculated, and vice versa.

• Example: If solubility of AgCl is $s$, then $K_{sp} = s^2$.

Solubility and the Common Ion Effect

The presence of a common ion decreases the solubility of a salt due to Le Chatelier's principle.

Precipitation and Ion Product $Q$

The ion product ($Q$) is calculated like $K_{sp}$ but with initial concentrations. If $Q > K_{sp}$, precipitation occurs; if $Q < K_{sp}$, more salt can dissolve.

Effect of pH on Solubility

pH can affect solubility, especially for salts containing basic or acidic ions. For example, increasing acidity increases solubility of salts with basic anions (e.g., CaCO3).