8.3 Weak Acid and Base Equilibria

Weak acids and weak bases only partly ionize in water, so their pH depends on both the starting concentration and an equilibrium constant, $K_a$ or $K_b$, not just the concentration. To find pH, set up an ICE table, write the $K_a$ or $K_b$ expression, solve for hydronium or hydroxide concentration, and then convert to pH. For AP Chemistry, justify any small-$x$ approximation before using it.

Weak Acid and Base Equilibria Summary

Weak acid and base equilibria are equilibrium problems, not complete dissociation problems. A weak acid produces only a small amount of H3O+, and a weak base produces only a small amount of OH-, so you need Ka or Kb to find the equilibrium concentrations and pH.

For AP Chemistry, the usual setup is: write the acid or base reaction with water, build an ICE table, plug equilibrium values into Ka or Kb, solve for x, and then convert x into pH or pOH. The common mistake is treating a weak acid or base like a strong one, where the initial concentration would directly equal [H3O+] or [OH-].

Why This Matters for the AP Chemistry Exam

This topic connects the equilibrium reasoning from Unit 7 directly to acids and bases. You are expected to explain how pH, pOH, and the concentrations of every species in a monoprotic weak acid or weak base solution relate to each other. That means you should be comfortable working between Ka, pKa, Kb, pKb, percent ionization, and the actual concentrations at equilibrium.

On the exam, this shows up in calculations that ask you to find pH from a starting concentration and a Ka or pKa, in questions that compare how percent ionization changes with concentration, and in reasoning about why a weak acid solution has a higher pH than a strong acid of the same concentration. Getting fluent here also sets you up for buffers, titrations, and pH-pKa reasoning in later topics.

Key Takeaways

• Weak acids and bases ionize only partially, so [H3O+] is much less than the initial acid concentration (and [OH-] is much less than the initial base concentration).
• Ka = [H3O+][A-]/[HA] for a weak acid, and Kb = [OH-][HB+]/[B] for a weak base. Smaller Ka or Kb means a weaker acid or base.
• Use pKa = -log Ka and pKb = -log Kb to switch between constants and their log form.
• Set up an ICE table, then solve Ka = x^2/(C - x). The small-x approximation lets you treat C - x as C when x is tiny compared to C.
• Percent ionization depends on both the constant and the initial concentration. More dilute weak acids have a higher percent ionization.
• For any conjugate acid-base pair, Ka × Kb = Kw and pKa + pKb = pKw (14.0 at 25°C).

Strong vs Weak Acids and Bases

A strong acid or strong base ionizes nearly completely in water. For AP Chemistry, the strong acids to know are HCl, HBr, HI, HClO4, H2SO4, and HNO3, and the common strong bases are the group I and II hydroxides (such as NaOH, KOH, Ca(OH)2, and Sr(OH)2). When HCl dissolves, almost every molecule splits into H3O+ and Cl-, so [H3O+] equals the initial concentration of the acid.

Weak acids and bases ionize only partially. Most of the molecules stay in their un-ionized form at equilibrium. Acetic acid (CH3COOH) is a common weak acid with Ka = 1.8 × 10^-5, and ammonia (NH3) is a common weak base. Any acid that is not one of the strong acids behaves as a weak acid. On the exam, if a base is weak, the question will tell you (often by giving you a Kb or pKb).

One useful pattern: the conjugate of a strong acid is a negligible base, and the conjugate of a strong base is a negligible acid. Cl- does not meaningfully accept protons, so it does not raise the pH.

The Ka and Kb Expressions

A weak acid in water reaches equilibrium between the un-ionized acid and its conjugate base:

HA(aq) + H2O(l) ⇌ H3O+(aq) + A-(aq)

The equilibrium constant for this is the acid dissociation constant:

Ka = [H3O+][A-]/[HA]

A weak base in water reaches equilibrium between the un-ionized base and its conjugate acid:

B(aq) + H2O(l) ⇌ HB+(aq) + OH-(aq)

The base dissociation constant is:

Kb = [OH-][HB+]/[B]

You can report either constant in log form using pKa = -log Ka and pKb = -log Kb. A smaller Ka (larger pKa) means a weaker acid, because less of it ionizes.

Solving for pH of a Weak Acid

Example: Find the pH of a 2 M solution of CH3COOH (Ka = 1.8 × 10^-5).

Write the equilibrium and set up an ICE table:

CH3COOH ⇌ H3O+ + CH3COO-

Plug into the Ka expression:

Ka = x^2/(2 - x) = 1.8 × 10^-5

Because x is very small compared to 2, use the small-x approximation and treat 2 - x as 2:

x^2 = (1.8 × 10^-5)(2)

x = [H3O+] ≈ 6.0 × 10^-3 M

Then take the negative log:

pH = -log(6.0 × 10^-3) ≈ 2.22

Solving for pH of a Weak Base

Example: Find the pH of 1 M ammonia (NH3) (Kb = 1.8 × 10^-5).

Set up the base equilibrium with water:

NH3 + H2O ⇌ NH4+ + OH-

Plug into the Kb expression and use the small-x approximation:

Kb = x^2/(1 - x) ≈ x^2/1 = 1.8 × 10^-5

x = [OH-] ≈ 4.2 × 10^-3 M

Here is the step students miss: taking the negative log of x gives pOH, not pH.

pOH = -log(4.2 × 10^-3) ≈ 2.38

pH = 14 - pOH = 14 - 2.38 = 11.62

The answer makes sense because a basic solution should have a pH above 7.

Percent Ionization

Percent ionization tells you what fraction of the acid (or base) actually ionized:

percent ionization = (amount ionized at equilibrium / initial concentration) × 100

For the acetic acid example, that is (6.0 × 10^-3 / 2) × 100 ≈ 0.3 percent, which confirms it ionizes only slightly. You can calculate percent ionization from the constant and initial concentration, or from the initial concentration and the equilibrium concentration of any species. A key relationship to remember: as a weak acid or base gets more dilute, its percent ionization increases.

Linking Ka and Kb with Kw

For any conjugate acid-base pair, the acid and base constants are tied together through the autoionization of water:

Kw = Ka × Kb

pKw = pKa + pKb

At 25°C, Kw = 1.0 × 10^-14, so pKa + pKb = 14.0. This lets you find Kb for a conjugate base if you know the Ka of its acid, or the other way around. It is a fast way to switch between an acid and its conjugate base without re-deriving anything.

How to Use This on the AP Chemistry Exam

Problem Solving

• Start every weak acid or base problem by writing the balanced equilibrium with water and the matching Ka or Kb expression.
• Build an ICE table with the initial concentration, the -x and +x changes, and the equilibrium row.
• Use the small-x approximation (C - x ≈ C) when x is tiny compared to C. If x is not small relative to C, solve the full quadratic instead.
• After solving for x, check whether x is [H3O+] (acid problem) or [OH-] (base problem) before converting to pH.

Common Trap

For a weak base, x equals [OH-], so -log(x) gives pOH. You still have to use pH + pOH = 14 (at 25°C) to get pH. Skipping this gives an answer that is far too low for a basic solution.

Free Response

• Explain why a weak acid solution has a higher pH than a strong acid at the same concentration: only part of the weak acid ionizes, so [H3O+] is smaller.
• Use Ka × Kb = Kw to justify claims about the relative strength of a conjugate acid-base pair.
• Connect percent ionization to concentration when asked how dilution changes the system.

Common Misconceptions

• "Weak means low concentration." Strength refers to how completely an acid or base ionizes, not how much is dissolved. A concentrated weak acid is still weak.
• "[H3O+] equals the initial acid concentration." That is only true for strong acids. For weak acids, [H3O+] is much smaller because most molecules stay un-ionized.
• "Taking -log of x always gives pH." For a weak base, x is [OH-], so -log(x) gives pOH first.
• "A bigger Ka means a weaker acid." It is the opposite. A larger Ka (smaller pKa) means a stronger acid that ionizes more.
• "The small-x approximation always works." It is valid only when x is tiny compared to the initial concentration. For more concentrated answers or larger constants, you may need the quadratic formula.
• "Conjugates of strong acids matter for pH." The conjugate base of a strong acid (like Cl-) is so weak it does not affect pH.

Related AP Chemistry Guides

• Unit 8 Overview: Acids and Bases
• 8.1 Introduction to Acids and Bases
• 8.2 pH and pOH of Strong Acids and Bases
• 8.4 Acid-Base Reactions and Buffers
• 8.5 Acid-Base Titrations
• 8.7 pH and pKa