Ionic Equilibrium: Acids, Bases, Salts, pH, Buffers & Solubility

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What is Ionic Equilibrium?

Ionic equilibrium refers to the dynamic balance between ions in a solution. When a substance dissolves in water, it breaks into ions (charged particles). These ions move freely, but their concentrations remain constant over time—this is called equilibrium.

Example: When sodium chloride (NaCl) dissolves in water:

NaCl (s) ⇌ Na⁺ (aq) + Cl⁻ (aq)

Here, the forward and backward reactions happen at the same rate, so the concentrations of Na⁺ and Cl⁻ stay the same.

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1. Acids and Bases: Definitions and Theories

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HCl+H₂OWaterH₃O⁺+Cl^-

A. Arrhenius Theory (Oldest Definition)

• Acid: A substance that releases H⁺ ions in water. Example: HCl → H⁺ + Cl⁻
• Base: A substance that releases OH⁻ ions in water. Example: NaOH → Na⁺ + OH⁻

Limitation: Only works for aqueous solutions.

B. Brønsted-Lowry Theory (More General)

• Acid: A proton (H⁺) donor.
• Base: A proton (H⁺) acceptor.

Example:

HCl + H₂O ⇌ H₃O⁺ + Cl⁻

Here, HCl donates H⁺ → acid, and H₂O accepts H⁺ → base.

C. Lewis Theory (Most General)

• Acid: An electron pair acceptor (e.g., BF₃).
• Base: An electron pair donor (e.g., NH₃).

Example:

BF₃ + NH₃ → BF₃:NH₃

BF₃ accepts electrons → Lewis acid, NH₃ donates electrons → Lewis base.

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2. Strength of Acids and Bases

acetic acidacetic acid

A. Strong vs. Weak Acids/Bases

B. Ionization Constant (Ka and Kb)

• Ka (Acid Dissociation Constant): For a weak acid HA:

  HA ⇌ H⁺ + A⁻
  Ka = [H⁺][A⁻] / [HA]
  

  Example: For acetic acid (CH₃COOH), Ka = 1.8 × 10⁻⁵.

Acetic acidAcetic acid

• Kb (Base Dissociation Constant): For a weak base B:

  B + H₂O ⇌ BH⁺ + OH⁻
  Kb = [BH⁺][OH⁻] / [B]
  

  Example: For ammonia (NH₃), Kb = 1.8 × 10⁻⁵.

Note: Strong acids/bases have very large Ka/Kb (almost complete dissociation).

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3. pH Scale and Hydrogen Ion Concentration

• pH = -log[H⁺]
  • pH < 7: Acidic (e.g., lemon juice, pH ≈ 2)
  • pH = 7: Neutral (pure water)
  • pH > 7: Basic (e.g., soap, pH ≈ 10)

Example Calculation: If [H⁺] = 1 × 10⁻³ M, then:

pH = -log(1 × 10⁻³) = 3

Relationship between pH and pOH:

pH + pOH = 14

Example: If pH = 5, then pOH = 9.

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A labelled pH scale from 0 to 14 with examples (lemon, water, soap) (Image: Piercetheorganist at English Wikipedia, Public domain, via Wikimedia Commons)

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4. Hydrolysis of Salts

When salts dissolve in water, their ions can react with water (hydrolysis), changing the pH.

NH₄⁺+H₂ONH₃+H₃O⁺

A. Cations from Weak Bases + Anions from Strong Acids → Acidic Solution

Example: NH₄Cl (from NH₄⁺ and Cl⁻)

NH₄⁺ + H₂O ⇌ NH₃ + H₃O⁺ (acidic)

B. Cations from Strong Bases + Anions from Weak Acids → Basic Solution

Example: CH₃COONa (from CH₃COO⁻ and Na⁺)

CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻ (basic)

C. Both Ions Hydrolyze → pH Depends on Ka/Kb

Example: CH₃COONH₄

• CH₃COO⁻ hydrolyzes to OH⁻ (basic)
• NH₄⁺ hydrolyzes to H⁺ (acidic)
• Net pH depends on Ka/Kb values.

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5. Buffer Solutions

A buffer resists changes in pH when small amounts of acid or base are added.

How Buffers Work

• Made from a weak acid + its conjugate base (or weak base + its conjugate acid).
• Example: CH₃COOH + CH₃COONa

Buffer Capacity

• Henderson-Hasselbalch Equation:

  pH = pKa + log([A⁻]/[HA])
  

  Example: For a buffer with pKa = 4.75 and [A⁻]/[HA] = 1:

  pH = 4.75 + log(1) = 4.75
  

Applications of Buffers

• Biological: Blood (pH ≈ 7.4, buffered by H₂CO₃/HCO₃⁻)
• Industrial: Soap, food preservation

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6. Solubility Product (Ksp)

When a sparingly soluble salt dissolves, it reaches equilibrium:

AgCl (s) ⇌ Ag⁺ (aq) + Cl⁻ (aq)

Solubility Product Constant (Ksp):

Ksp = [Ag⁺][Cl⁻]

Example: For AgCl, Ksp = 1.8 × 10⁻¹⁰.

Factors Affecting Solubility

• Temperature: Most solids become more soluble with heat.
• Common Ion Effect: Adding a common ion decreases solubility. Example: Adding NaCl to AgCl solution shifts equilibrium left → less AgCl dissolves.

Solubility vs. Ksp

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Exam Tip: How to Score Full Marks in NEB Exams

1. Memorize Key Formulas:

   • pH = -log[H⁺]
   • Ka = [H⁺][A⁻]/[HA]
   • Ksp = [cation][anion]
   • Henderson-Hasselbalch: pH = pKa + log([A⁻]/[HA])

2. Practice pH Calculations:

   • Always convert [H⁺] to pH and vice versa.
   • Example: If [OH⁻] = 1 × 10⁻², find pH.
     • pOH = -log(1 × 10⁻²) = 2
     • pH = 14 - pOH = 12

3. Understand Buffer Problems:

   • Identify weak acid/conjugate base pairs.
   • Use Henderson-Hasselbalch for pH calculations.

4. Solubility Questions:

   • Always write the dissociation equation first.
   • Use ICE (Initial-Change-Equilibrium) tables for Ksp problems.

5. Common Mistakes to Avoid:

   • Forgetting units (always use M for molarity).
   • Ignoring activity coefficients in simple problems.
   • Misapplying Ksp for miscible vs. insoluble salts.

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NEB Board-Style Questions (Solved Examples)

Question 1: pH Calculation

A solution has [H⁺] = 5 × 10⁻⁴ M. Calculate its pH and classify it as acidic or basic. Solution:

pH = -log(5 × 10⁻⁴) = -[log(5) + log(10⁻⁴)] = -[0.7 - 4] = 3.3

Since pH < 7 → acidic.

Question 2: Buffer pH

A buffer is made with 0.1 M CH₃COOH (Ka = 1.8 × 10⁻⁵) and 0.2 M CH₃COONa. Calculate its pH. Solution: Using Henderson-Hasselbalch:

pH = pKa + log([A⁻]/[HA]) = -log(1.8 × 10⁻⁵) + log(0.2/0.1)
pH = 4.75 + log(2) = 4.75 + 0.30 = 5.05

Question 3: Solubility Product

The Ksp of Ag₂CrO₄ is 1.1 × 10⁻¹². Calculate its solubility in mol/L. Solution:

Ag₂CrO₄ ⇌ 2Ag⁺ + CrO₄²⁻
Let s = solubility.
Ksp = [2s]² [s] = 4s³ = 1.1 × 10⁻¹²
s³ = 2.75 × 10⁻¹³ → s = 1.4 × 10⁻⁴ mol/L

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Summary Table: Key Concepts

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Final Note: Ionic equilibrium is everywhere—from stomach acid (HCl) to blood buffers (HCO₃⁻/CO₂). Master the definitions, formulas, and problem-solving steps, and you’ll ace NEB exams!

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