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K-Chemistry.com: Acid-Base Equilibrium - Ka and Kb

Introduction: What are Ka and Kb?

Ka and Kb are equilibrium constants that help us understand how strong acids and bases are. They're like the "power ratings" for acids and bases!

Ka - Acid Dissociation Constant

• Measures how completely an acid dissociates in water

• HA + H₂O ⇌ H₃O⁺ + A⁻

• Ka = [H₃O⁺][A⁻] / [HA]

Kb - Base Dissociation Constant

• Measures how completely a base dissociates in water

• B + H₂O ⇌ BH⁺ + OH⁻

• Kb = [BH⁺][OH⁻] / [B]

Why Do We Care?

• 🧪 Predict Reactions: Helps us predict how acids and bases will behave in solutions

• 📊 Calculate pH: Allows us to calculate the pH of solutions accurately

• 🔬 Lab Applications: Essential for designing experiments and understanding results

Ka - Acid Dissociation Constant

When an acid (HA) dissolves in water, it can donate a proton (H⁺) to water, forming hydronium ions (H₃O⁺) and its conjugate base (A⁻).

HA + H₂O ⇌ H₃O⁺ + A⁻

The Ka Formula

Ka = [H₃O⁺][A⁻] / [HA]

The larger the Ka value, the stronger the acid!

Ka Values and Acid Strength

| Acid | Ka | Strength | |------|-------|----------| | HCl (Hydrochloric acid) | Very large (>10⁶) | Strong acid | | H₂SO₄ (Sulfuric acid) | Very large (>10³) | Strong acid | | CH₃COOH (Acetic acid) | 1.8 × 10⁻⁵ | Weak acid | | HCN (Hydrocyanic acid) | 4.9 × 10⁻¹⁰ | Very weak acid |

Using Ka to Calculate pH

For a weak acid, we can use Ka to find the pH of a solution:

1. Write the equilibrium expression: Ka = [H⁺][A⁻] / [HA]

2. Use the ICE table (Initial, Change, Equilibrium) to track concentrations

3. Solve for [H⁺]

4. Calculate pH = -log[H⁺]

Kb - Base Dissociation Constant

When a base (B) dissolves in water, it can accept a proton (H⁺) from water, forming hydroxide ions (OH⁻) and its conjugate acid (BH⁺).

B + H₂O ⇌ BH⁺ + OH⁻

The Kb Formula

Kb = [BH⁺][OH⁻] / [B]

The larger the Kb value, the stronger the base!

Kb Values and Base Strength

| Base | Kb | Strength | |------|-------|----------| | NaOH (Sodium hydroxide) | Very large | Strong base | | NH₃ (Ammonia) | 1.8 × 10⁻⁵ | Weak base | | C₅H₅N (Pyridine) | 1.7 × 10⁻⁹ | Very weak base |

The Relationship Between Ka and Kb

For a conjugate acid-base pair, there's an important relationship: Ka × Kb = Kw = 1.0 × 10⁻¹⁴ (at 25°C)

This means:

• If an acid is strong (large Ka), its conjugate base is weak (small Kb)

• If a base is strong (large Kb), its conjugate acid is weak (small Ka)

Practice Problems

Practice Problem 1

Calculate the pH of a 0.05 M solution of acetic acid (Ka = 1.8 × 10⁻⁵).

Solution: Step 1: Write the equilibrium expression CH₃COOH ⇌ H⁺ + CH₃COO⁻ Ka = [H⁺][CH₃COO⁻] / [CH₃COOH]

Step 2: Set up ICE table | | CH₃COOH | H⁺ | CH₃COO⁻ | |---|---|---|---| | Initial | 0.05 | 0 | 0 | | Change | -x | +x | +x | | Equilibrium | 0.05-x | x | x |

Step 3: Substitute into Ka expression 1.8 × 10⁻⁵ = (x)(x) / (0.05-x) For weak acids, we can assume x << 0.05, so 0.05-x ≈ 0.05 1.8 × 10⁻⁵ = x² / 0.05 x² = 1.8 × 10⁻⁵ × 0.05 = 9.0 × 10⁻⁷ x = 9.49 × 10⁻⁴

Step 4: Calculate pH pH = -log[H⁺] = -log(9.49 × 10⁻⁴) = 3.02

The pH of the solution is 3.02

Practice Problem 2

If the Kb of ammonia (NH₃) is 1.8 × 10⁻⁵, what is the Ka of its conjugate acid (NH₄⁺)?

Solution: Using the relationship: Ka × Kb = Kw = 1.0 × 10⁻¹⁴ Ka(NH₄⁺) × Kb(NH₃) = 1.0 × 10⁻¹⁴ Ka(NH₄⁺) × (1.8 × 10⁻⁵) = 1.0 × 10⁻¹⁴ Ka(NH₄⁺) = 1.0 × 10⁻¹⁴ / (1.8 × 10⁻⁵) Ka(NH₄⁺) = 5.56 × 10⁻¹⁰

The Ka of NH₄⁺ is 5.56 × 10⁻¹⁰

Quiz

1. Which of the following statements is true about Ka?

   • A) A larger Ka value indicates a weaker acid

   • B) A larger Ka value indicates a stronger acid ✓

   • C) Ka values are typically greater than 1 for most acids

   • D) Ka is the same as pH

2. If the Ka of an acid is 1.0 × 10⁻⁴, what is the Kb of its conjugate base?

   • A) 1.0 × 10⁻⁴

   • B) 1.0 × 10⁻⁷

   • C) 1.0 × 10⁻¹⁰ ✓

   • D) 1.0 × 10⁻¹⁴

3. Which of the following acids has the highest Ka value?

   • A) Acetic acid (Ka = 1.8 × 10⁻⁵)

   • B) Hydrofluoric acid (Ka = 6.8 × 10⁻⁴) ✓

   • C) Carbonic acid (Ka = 4.3 × 10⁻⁷)

   • D) Hydrocyanic acid (Ka = 4.9 × 10⁻¹⁰)

4. What is the relationship between Ka and Kb for a conjugate acid-base pair?

   • A) Ka + Kb = 1

   • B) Ka - Kb = 0

   • C) Ka / Kb = 10⁻¹⁴

   • D) Ka × Kb = 10⁻¹⁴ ✓

5. If a 0.1 M solution of a weak acid has a pH of 3.5, what is the approximate Ka of the acid?

   • A) 3.5 × 10⁻⁴

   • B) 1.0 × 10⁻⁵ ✓

   • C) 3.2 × 10⁻⁷

   • D) 1.0 × 10⁻¹⁰

     
     

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