Acids and Bases

There are three major frameworks for understanding acids and bases, each broader than the last:

Arrhenius definition: An acid produces H⁺ ions in water; a base produces OH^- ions in water. This is the simplest model but only works for aqueous solutions. HCl is an Arrhenius acid (produces H⁺), and NaOH is an Arrhenius base (produces OH^-).

Brønsted-Lowry definition: An acid is a proton (H⁺) donor; a base is a proton acceptor. This is more general — it explains acid-base behavior in any solvent, not just water. For example, NH₃ is a Brønsted-Lowry base because it accepts a proton from water: NH₃ + H₂O → NH₄⁺ + OH^-.

Lewis definition: An acid is an electron-pair acceptor; a base is an electron-pair donor. This is the broadest definition and includes reactions with no proton transfer at all, such as BF₃ + NH₃ → F₃B-NH₃.

Water is amphoteric — it can act as either an acid or a base depending on what it reacts with. With HF, water acts as a base (accepts H⁺). With NH₃, water acts as an acid (donates H⁺).

The concentration of H₃O⁺ (hydronium) ions in solution determines its acidity. Because these concentrations span many orders of magnitude, we use a logarithmic scale:

pH = −log[H₃O⁺]

pOH = −log[OH^-]

At 25 °C, these two values are always related by:

pH + pOH = 14.00

This comes from the ion-product constant of water: K_w = [H₃O⁺][OH^-] = 1.0 × 10^-14 at 25 °C.

To convert between pH and ion concentrations:

• [H₃O⁺] = 10^−pH
• [OH^-] = 10^−pOH

A neutral solution has pH = 7.00, acidic solutions have pH < 7, and basic solutions have pH > 7.

In every Brønsted-Lowry acid-base reaction, a proton is transferred from the acid to the base. This creates a conjugate pair: the acid loses a proton to become its conjugate base, and the base gains a proton to become its conjugate acid.

HF + H₂O ⇌ F^- + H₃O⁺

In this reaction:

• HF is the acid → F^- is its conjugate base
• H₂O is the base → H₃O⁺ is its conjugate acid

Key relationship: A strong acid has a very weak conjugate base, and a weak acid has a relatively stronger conjugate base. This inverse relationship is fundamental to understanding acid-base equilibrium.

Every acid-base reaction has two conjugate pairs — always identify both when analyzing a reaction.

Strong acids ionize completely in water — every molecule donates its proton. The common strong acids are HCl, HBr, HI, HNO₃, HClO₄, and H₂SO₄ (first proton).

For a strong acid, [H₃O⁺] equals the initial acid concentration:

Example: 0.025 M HCl → [H₃O⁺] = 0.025 M → pH = −log(0.025) = 1.60

Strong bases also dissociate completely. The common ones are Group 1 and 2 hydroxides: NaOH, KOH, Ca(OH)₂, Ba(OH)₂.

Example: 0.010 M NaOH → [OH^-] = 0.010 M → pOH = 2.00 → pH = 12.00

For bases with two OH^- per formula unit (like Ca(OH)₂), remember to double: 0.005 M Ca(OH)₂ → [OH^-] = 0.010 M.

Weak acids only partially ionize in water. The extent of ionization is quantified by the acid ionization constant, K_a:

HA + H₂O ⇌ A^- + H₃O⁺

K_a = [H₃O⁺][A^-] / [HA]

A larger K_a means a stronger weak acid (more ionization). To find pH from K_a and initial concentration:

1. Set up an ICE table (Initial, Change, Equilibrium)
2. Let x = [H₃O⁺] at equilibrium
3. Substitute into the K_a expression: K_a = x² / (C₀ − x)
4. If K_a is small relative to C₀, simplify: x ≈ √(K_a × C₀)
5. pH = −log(x)

Always verify the simplification: if x is more than 5% of C₀, solve the full quadratic instead.

A weak base only partially accepts protons from water, establishing an equilibrium:

B + H₂O ⇌ BH⁺ + OH⁻

The base-ionisation constant is K_b = [BH⁺][OH⁻] / [B]. A small K_b means the base ionises very little and the solution is only mildly basic.

Solving for pH follows the same ICE-table approach as weak acids, but you solve for [OH⁻] first:

1. Set up the ICE table with initial base concentration C₀, change −x for B and +x for BH⁺ and OH⁻.
2. If the small-x approximation is valid (x < 5% of C₀): x = [OH⁻] ≈ √(K_b · C₀).
3. Calculate pOH = −log[OH⁻], then pH = 14.00 − pOH.

Example: 0.50 M NH₃ with K_b = 1.8 × 10⁻⁵: x = √(1.8 × 10⁻⁵ × 0.50) = 3.0 × 10⁻³ M. Check: 3.0 × 10⁻³/0.50 = 0.6% < 5%, so the approximation holds. pOH = 2.52, pH = 11.48.

For any conjugate acid-base pair, the product of their ionization constants equals the ion-product constant of water:

K_a × K_b = K_w = 1.0 × 10^-14 (at 25 °C)

This means if you know K_a for an acid, you can calculate K_b for its conjugate base, and vice versa:

• K_b = K_w / K_a
• K_a = K_w / K_b

Example: Acetic acid has K_a = 1.8 × 10^-5. Its conjugate base (acetate, CH₃COO^-) has K_b = (1.0 × 10^-14) / (1.8 × 10^-5) = 5.6 × 10^-10.

A useful consequence: the stronger an acid, the weaker its conjugate base — and this is quantitatively precise, not just qualitative.

When a salt dissolves in water, its ions may react with water (hydrolyze) to produce an acidic or basic solution. The outcome depends on the parent acid and base:

• Strong acid + strong base → neutral salt. Example: NaCl from HCl + NaOH. Neither Na⁺ nor Cl^- hydrolyzes.
• Strong acid + weak base → acidic salt. Example: NH₄Cl from HCl + NH₃. The NH₄⁺ ion donates a proton to water.
• Weak acid + strong base → basic salt. Example: CH₃COONa from CH₃COOH + NaOH. The CH₃COO^- ion accepts a proton from water.
• Weak acid + weak base → depends on K_a vs K_b. Compare the ionization constants: if K_a > K_b, the solution is acidic; if K_b > K_a, it's basic.

To predict the pH, use K_a or K_b of the hydrolyzing ion (found via the K_a·K_b = K_w relationship).

Percent ionization measures how much of a weak acid or base actually ionizes in solution:

% ionization = ([H₃O⁺]_eq / [HA]_initial) × 100%

Key observations:

• Percent ionization increases as the solution is diluted. A 0.01 M weak acid is more ionized (percentage-wise) than a 1.0 M solution of the same acid.
• A larger K_a gives a higher percent ionization at any given concentration.
• For the 5% approximation used in ICE tables to be valid, the percent ionization must be ≤ 5%.

Example: If 0.10 M acetic acid gives [H₃O⁺] = 1.34 × 10^-3 M, then % ionization = (1.34 × 10^-3 / 0.10) × 100% = 1.34%.

Polyprotic acids have more than one ionizable proton. They ionize in successive steps, each with its own K_a value:

Diprotic acid (e.g., H₂SO₃):

H₂SO₃ + H₂O ⇌ HSO₃^- + H₃O⁺    K_a1

HSO₃^- + H₂O ⇌ SO₃^2- + H₃O⁺    K_a2

Triprotic acid (e.g., H₃PO₄) has three steps: K_a1 > K_a2 > K_a3.

Each successive ionization is always weaker (smaller K_a) because it's harder to remove a proton from a species that's already negatively charged. In practice, this means:

• The first ionization dominates the pH — you can usually ignore the second and third.
• Treat each step as a separate equilibrium, using the equilibrium concentrations from the previous step as the initial concentrations for the next.

When a solution contains both a weak acid and its conjugate base (a buffer), the pH can be calculated directly without an ICE table:

pH = pK_a + log([A^-] / [HA])

Where pK_a = −log(K_a), [A^-] is the conjugate base concentration, and [HA] is the acid concentration.

Key insights:

• When [A^-] = [HA], the log term is zero and pH = pK_a
• When [A^-] > [HA], pH > pK_a (more basic)
• When [A^-] < [HA], pH < pK_a (more acidic)

Example: A solution with 0.024 M HCO₃^- and 0.0012 M H₂CO₃ (K_a = 4.3 × 10^-7):

pH = −log(4.3 × 10^-7) + log(0.024/0.0012) = 6.37 + 1.30 = 7.67

This equation is most accurate when the acid/base ratio is between 0.1 and 10 (i.e., pH within ±1 of pK_a).

Oxides of elements show a clear pattern in their acid-base behavior that follows the periodic table:

• Metal oxides are typically basic. They react with water to form hydroxides: Na₂O + H₂O → 2NaOH. They react with acids to form salt + water.
• Nonmetal oxides are typically acidic. They react with water to form oxyacids: SO₃ + H₂O → H₂SO₄. They react with bases to form salt + water.
• Amphoteric oxides (like Al₂O₃ and ZnO) can react with both acids and bases.

The trend across a period: oxides become more acidic from left to right as metallic character decreases. Down a group, oxides of the same type become more basic as metallic character increases.

This is directly related to electronegativity: highly electronegative nonmetals form oxides where the O-H bond in the resulting oxyacid is highly polar and breaks easily, releasing H⁺.

Acid-base chapters feel broad because different equations apply to different regimes. Use this selection framework:

1. Strong acid/base only? Use direct stoichiometry, then pH/pOH from concentration.
2. Weak acid/base in water? Use K_a or K_b with ICE-table logic (small-x check).
3. Conjugate-pair mixture? Use Henderson–Hasselbalch (buffer region).
4. Salt solution? Identify parent acid/base strength, then hydrolysis behavior.

Quality checks: pH must be between 0 and 14 for standard aqueous problems, strong-acid solutions must yield pH below 7, and weak-acid pH should be higher than an equal-concentration strong acid. Include units and sig figs consistently when converting between [H⁺], [OH⁻], pH, and pOH.