Weak Acid and | AP Chem Unit 8 Study Guide

Getting Started

Most discussions of acids and bases begin with strong acids, which are assumed to ionize completely in water. However, the vast majority of acids and bases are weak, meaning they only partially react with water. This chapter explores the dynamic equilibrium that a weak acid or base establishes in solution, focusing on how to quantify the concentrations of all species present and determine the resulting pH.

What You Should Be Able to Do

By the end of this section, you should be able to:

Write the equilibrium reaction for a weak acid or weak base in water.
Use the equilibrium constant (Ka or Kb) and initial concentration to calculate the pH and pOH of the solution.
Calculate the percent ionization of a weak acid or base.
Explain the inverse relationship between the strength of an acid and its conjugate base using the ion-product constant for water (Kw).

Key Concepts & Analysis: The Process of Reaching Equilibrium

The behavior of weak acids and bases is governed by the process of establishing a chemical equilibrium in water. We can analyze this by examining the inputs, the steps to reach and quantify the equilibrium state, and the resulting outputs.

Inputs & Preconditions

Reactants: A weak acid (a general monoprotic acid, HA) or a weak base (B) and the solvent, water (H₂O).
Initial Conditions: The initial molar concentration of the weak acid, [HA]₀, or weak base, [B]₀.
System Constant: The acid-dissociation constant, Ka, or the base-dissociation constant, Kb. These temperature-dependent constants quantify the intrinsic strength of the acid or base.

Key Steps / Mechanism

The core of understanding weak electrolytes is a two-part process: the chemical reaction itself and the mathematical procedure to solve for the final state.

1. The Chemical Process: Reversible Ionization

Weak Acid: A weak acid, HA, donates a proton to water in a reversible reaction. This establishes a dynamic equilibrium where the rate of the forward reaction equals the rate of the reverse reaction.
HA(aq) + H₂O(l) ⇌ H₃O⁺(aq) + A⁻(aq)
At equilibrium, the solution contains significant amounts of the un-ionized acid (HA) as well as the hydronium ion (H₃O⁺) and the conjugate base (A⁻). Because only a small fraction of HA molecules ionize, the equilibrium concentration of hydronium, [H₃O⁺], is always much less than the initial concentration of the acid, [HA]₀.
Weak Base: A weak base, B, accepts a proton from water in a similar reversible reaction.
B(aq) + H₂O(l) ⇌ BH⁺(aq) + OH⁻(aq)
This equilibrium mixture contains the un-ionized base (B), its conjugate acid (BH⁺), and hydroxide ions (OH⁻). As with weak acids, only a small percentage of base molecules react, so the equilibrium [OH⁻] is much less than the initial base concentration, [B]₀.

2. The Calculation Process: The I.C.E. Table Method

To find the pH of a weak acid or base solution, we must calculate the equilibrium concentration of H₃O⁺ or OH⁻. The most common tool for this is the I.C.E. table, which stands for Initial, Change, and Equilibrium.

Example: Calculating the pH of a 0.10 M Acetic Acid Solution (Ka = 1.8 x 10⁻⁵)

Step 1: Write the balanced equilibrium equation.
HC₂H₃O₂(aq) + H₂O(l) ⇌ H₃O⁺(aq) + C₂H₃O₂⁻(aq)
Step 2: Set up the I.C.E. table. Let 'x' be the change in concentration as the system moves to equilibrium.

Concentration (M)	HC₂H₃O₂	H₃O⁺	C₂H₃O₂⁻
Initial	0.10	~0	0
Change	-x	+x	+x
Equilibrium	0.10 - x	x	x

Step 3: Write the Ka expression and substitute equilibrium values.
Ka = ([H₃O⁺][C₂H₃O₂⁻]) / [HC₂H₃O₂]
1.8 x 10⁻⁵ = (x)(x) / (0.10 - x)
Step 4: Solve for x, using an approximation if valid. Because Ka is very small, we can often assume that 'x' is negligible compared to the initial concentration. This is the "5% rule": if x is less than 5% of the initial concentration, the approximation is valid.
Assume 0.10 - x ≈ 0.10.
1.8 x 10⁻⁵ ≈ x² / 0.10
x² ≈ 1.8 x 10⁻⁶
x ≈ 1.34 x 10⁻³ M
(Check assumption: (1.34 x 10⁻³ / 0.10) * 100% = 1.34%, which is < 5%. The approximation is valid.)
Step 5: Calculate the pH.
x = [H₃O⁺] = 1.34 x 10⁻³ M
pH = -log[H₃O⁺] = -log(1.34 x 10⁻³) = 2.87

The same five-step process applies to weak bases, but you solve for x = [OH⁻] using the Kb expression and then calculate pOH, which can be converted to pH (pH = 14.00 - pOH).

Outputs & Effects

Equilibrium Concentrations: The final concentrations of all aqueous species (e.g., [HA], [A⁻], and [H₃O⁺]).
pH and pOH: The ultimate measure of the solution's acidity or basicity.
Percent Ionization: A way to express the extent of dissociation. It is the fraction of the initial acid/base molecules that have ionized, expressed as a percentage.
Percent Ionization = ([H₃O⁺] at eq / [HA] initial) × 100%
For the acetic acid example above, the percent ionization is 1.34%.

Controls & Limiting Factors

Magnitude of Ka/Kb: This is the primary factor controlling the position of the equilibrium. A larger Ka or Kb value means a stronger acid or base, respectively, leading to greater ionization and a more significant change in pH.
Initial Concentration: For a given weak acid, a more dilute solution will have a higher percent ionization. While the concentration of H₃O⁺ will be lower in the dilute solution, a greater fraction of the acid molecules will have ionized.

Key Models & Representations

This flowchart outlines the general problem-solving approach for determining the pH of a weak acid solution. A nearly identical process is used for weak bases, substituting B, BH⁺, OH⁻, and Kb.

Flowchart: Calculating pH of a Weak Acid Solution


graph TD

    A[Start: Given Initial Concentration [HA]₀ and Ka] --> B{Write the equilibrium reaction:\nHA + H₂O ⇌ H₃O⁺ + A⁻};

    B --> C{Set up an I.C.E. Table};

    C --> D{Write the Ka expression:\nKa = [H₃O⁺][A⁻]/[HA]};

    D --> E{Substitute equilibrium concentrations from I.C.E. table into Ka expression};

    E --> F{Solve for x, where x = [H₃O⁺]};

    F --> G{Check 5% rule approximation if used};

    G --> H[Calculate pH = -log(x)];

    H --> I[End: Final pH];

Key Terms, Quantities, & Concepts

Weak Acid/Base: An acid or base that only partially ionizes in aqueous solution, establishing an equilibrium.
Acid-Dissociation Constant (Ka): The equilibrium constant for the ionization of a weak acid. A larger Ka indicates a stronger weak acid.
Base-Dissociation Constant (Kb): The equilibrium constant for the reaction of a weak base with water. A larger Kb indicates a stronger weak base.
pKa and pKb: The negative base-10 logarithm of Ka and Kb, respectively (pKa = -log(Ka)). A smaller pKa/pKb value indicates a stronger acid/base.
Conjugate Acid-Base Pair: Two species that differ by a single proton (H⁺), such as HA (acid) and A⁻ (conjugate base).
Percent Ionization: The percentage of dissolved acid or base molecules that have separated into ions at equilibrium.
Relationship between Ka, Kb, and Kw: For any conjugate acid-base pair, the product of their dissociation constants equals the ion-product constant for water: Ka × Kb = Kw = 1.0 x 10⁻¹⁴ (at 25°C). This implies that a strong acid must have a very weak conjugate base, and vice versa.

Skill Snapshots

Causation

A larger Ka value causes the equilibrium to lie further to the right, resulting in a higher [H₃O⁺] and a lower pH for a given initial concentration.
Adding a weak base to water causes the production of OH⁻ ions through proton abstraction from water, raising the solution's pH above 7.
Diluting a weak acid solution causes the percent ionization to increase, as the equilibrium shifts to favor the side with more particles (Le Châtelier's principle).

Comparison

Strong vs. Weak Acids: A 0.1 M solution of a strong acid (like HCl) has a [H₃O⁺] of 0.1 M, whereas a 0.1 M solution of a weak acid (like HF) has a [H₃O⁺] significantly less than 0.1 M.
Ka vs. Kb: Ka measures an acid's ability to donate a proton to water, while Kb measures a base's ability to accept a proton from water. For a conjugate pair, they are inversely related.
pH vs. pKa: pH is a property of a specific solution that depends on concentration, while pKa is an intrinsic property of a specific acid that measures its inherent strength.

Change and Continuity Over Time

Baseline: Pure water has a neutral pH of 7.00, with [H₃O⁺] = [OH⁻] = 1.0 x 10⁻⁷ M.
Change 1: Upon adding a weak acid like acetic acid, the system establishes a new equilibrium. The [H₃O⁺] increases and the pH drops below 7.
Change 2: If a strong base is later added to this solution, it will neutralize the H₃O⁺ and react with the acetic acid, causing the equilibrium to shift and the pH to rise.
Continuity: Throughout these changes in concentration and pH, the value of Ka for acetic acid remains constant as long as the temperature does not change.

Common Misconceptions & Clarifications

Misconception: The [H₃O⁺] in a weak acid solution is equal to the initial concentration of the acid.
Clarification: This is only true for strong acids. For weak acids, [H₃O⁺] is always much less than the initial acid concentration because the ionization is incomplete. You must use an I.C.E. table to find the true value.
Misconception: A "dilute" acid is the same as a "weak" acid.
Clarification: "Dilute" refers to concentration (moles per liter), while "weak" refers to the intrinsic degree of ionization (the value of Ka). You can have a concentrated weak acid or a dilute strong acid.
Misconception: The formula Ka × Kb = Kw applies to any acid and any base.
Clarification: This crucial relationship applies only to a conjugate acid-base pair. For example, it relates the Ka of acetic acid (HC₂H₃O₂) to the Kb of its conjugate base, the acetate ion (C₂H₃O₂⁻).
Misconception: Water is just a solvent and can be ignored in the equilibrium expression for bases.
Clarification: Water is a direct reactant in the weak base equilibrium (B + H₂O ⇌ BH⁺ + OH⁻). While its concentration is omitted from the Kb expression because it is a pure liquid, its role as the proton source is essential to the reaction.

One-Paragraph Summary

Weak acids and bases engage in a reversible reaction with water, establishing a dynamic equilibrium that leaves most of the initial substance un-ionized. The extent of this ionization is quantified by the equilibrium constants Ka and Kb, which, along with the initial concentration, are the key inputs for calculating the solution's pH. By using an I.C.E. table, we can determine the equilibrium concentrations of all species, including the hydronium or hydroxide ions that define the pH. The strength of an acid and its conjugate base are inversely related through the constant Kw, illustrating a fundamental principle of acid-base chemistry: the weaker the acid, the stronger its conjugate base.

Weak Acid and Base Equilibria - AP Chemistry Study Guide