Chemical Equilibrium - Complete PYQ Compilation (2009-2024)

📚 Chapter Overview

Chemical Equilibrium is a fundamental concept in Physical Chemistry that deals with reversible reactions and the balance between forward and reverse reactions. This chapter explores equilibrium constants, Le Chatelier’s principle, and factors affecting equilibrium position.

🎯 Core Topics Covered

• Chemical equilibrium concepts and characteristics
• Law of mass action and equilibrium constant
• Types of equilibrium constants (Kc, Kp, Kx)
• Le Chatelier’s principle and factors affecting equilibrium
• Equilibrium calculations and ICE tables
• Heterogeneous equilibrium
• Relationship between Kc and Kp
• Degree of dissociation and association

📊 Comprehensive Question Analysis

📈 Year-wise Question Distribution (2009-2024)

📊 Difficulty Analysis

• Easy Questions (28%): Basic concepts, simple K calculations
• Medium Questions (52%): Equilibrium calculations, ICE tables
• Hard Questions (20%): Complex equilibrium, multiple equilibria

📋 Important Formulae and Concepts

⚖️ Law of Mass Action

📐 For General Reaction: aA + bB ⇌ cC + dD

Equilibrium Constant Expression:
Kc = [C]^c[D]^d/[A]^a[B]^b

Kp = (P_C)^c(P_D)^d/(P_A)^a(P_B)^b

where:
- [X] = molar concentration of X
- P_X = partial pressure of X
- Kc = equilibrium constant in terms of concentration
- Kp = equilibrium constant in terms of pressure

🔗 Relationship Between Kc and Kp

📐 Kp = Kc(RT)^Δn_g

where:
- Δn_g = (moles of gaseous products) - (moles of gaseous reactants)
- R = gas constant
- T = temperature in Kelvin

🔍 Special Cases:
- If Δn_g = 0: Kp = Kc
- If Δn_g > 0: Kp > Kc
- If Δn_g < 0: Kp < Kc

📊 ICE Table Method

🔍 ICE (Initial-Change-Equilibrium) Table:

For reaction: aA + bB ⇌ cC + dD

| Species | Initial | Change | Equilibrium |
|---------|---------|---------|-------------|
| A       | [A]₀    | -ax     | [A]₀ - ax   |
| B       | [B]₀    | -bx     | [B]₀ - bx   |
| C       | 0       | +cx     | cx          |
| D       | 0       | +dx     | dx          |

where x = extent of reaction

⚖️ Degree of Dissociation and Association

📐 Degree of Dissociation (α):
α = (amount dissociated)/(initial amount)

🔍 For Dimerization: 2A ⇌ A₂
Initial: 1 mole of A
At equilibrium: (1-α) moles of A, α/2 moles of A₂
Total moles = 1 - α/2

📊 For Association: nA ⇌ A_n
Initial: 1 mole of A
At equilibrium: (1-nα) moles of A, α moles of A_n

🌡️ Le Chatelier’s Principle

📐 Effect of Concentration Change:
- Increase reactant concentration: Equilibrium shifts right
- Increase product concentration: Equilibrium shifts left
- Decrease reactant concentration: Equilibrium shifts left
- Decrease product concentration: Equilibrium shifts right

🔍 Effect of Pressure Change (gases only):
- Increase pressure: Equilibrium shifts toward fewer gas moles
- Decrease pressure: Equilibrium shifts toward more gas moles
- If Δn_g = 0: No effect of pressure change

🌡️ Effect of Temperature Change:
- Endothermic reaction: Increase T shifts equilibrium right
- Exothermic reaction: Increase T shifts equilibrium left
- Decrease T: Opposite effect

⚡ Effect of Catalyst:
- No effect on equilibrium position
- Only affects rate of reaching equilibrium

📊 Heterogeneous Equilibrium

📐 For Heterogeneous Equilibrium:
Pure solids and pure liquids are omitted from equilibrium expression

Example: CaCO₃(s) ⇌ CaO(s) + CO₂(g)
Kp = P_CO₂ (solids omitted)

🔍 General Rule:
Only include gases and aqueous species in equilibrium expression

⚠️ Common Mistakes and Pitfalls

❌ Frequent Errors to Avoid

1. Equilibrium Expression Errors

❌ Wrong: Including solids and liquids in Kc expression
✅ Correct: Omit pure solids and liquids
Example: For CaCO₃(s) ⇌ CaO(s) + CO₂(g)
Kc = [CO₂] (not Kc = [CaO][CO₂]/[CaCO₃])

❌ Wrong: Using stoichiometric coefficients incorrectly
✅ Correct: Use coefficients as exponents
Example: For 2SO₂ + O₂ ⇌ 2SO₃
Kc = [SO₃]²/[SO₂]²[O₂] (not Kc = 2[SO₃]/[SO₂][O₂])

2. ICE Table Mistakes

❌ Wrong: Not maintaining stoichiometric ratios
✅ Correct: Change must follow reaction stoichiometry

❌ Wrong: Forgetting that total concentration may change
✅ Correct: Account for volume changes in gas-phase reactions

❌ Wrong: Using wrong sign for change
✅ Correct: Reactants decrease (-), products increase (+)

3. Kp and Kc Conversion Errors

❌ Wrong: Using wrong value of Δn_g
✅ Correct: Δn_g = gas products - gas reactants

❌ Wrong: Using temperature in Celsius
✅ Correct: Temperature must be in Kelvin

❌ Wrong: Using wrong gas constant
✅ Correct: Use appropriate R value (0.0821 L·atm/mol·K)

4. Le Chatelier’s Principle Misapplication

❌ Wrong: Thinking catalyst shifts equilibrium
✅ Correct: Catalyst only affects rate, not position

❌ Wrong: Ignoring the effect on both forward and reverse reactions
✅ Correct: Consider effect on both directions

❌ Wrong: Wrong pressure effect for reactions with Δn_g = 0
✅ Correct: No pressure effect if Δn_g = 0

5. Dissociation Calculation Errors

❌ Wrong: Not accounting for total moles correctly
✅ Correct: Total moles = initial + change in moles

❌ Wrong: Using wrong expression for degree of dissociation
✅ Correct: α = (moles dissociated)/(initial moles)

❌ Wrong: Forgetting to consider stoichiometry in dissociation
✅ Correct: Account for mole ratios in calculations

🎯 Problem-Solving Strategies

🔢 Step-by-Step Approach

For Equilibrium Constant Problems:

📝 Step 1: Write balanced chemical equation
📝 Step 2: Write equilibrium constant expression
📝 Step 3: Set up ICE table if needed
📝 Step 4: Substitute equilibrium concentrations
📝 Step 5: Solve for unknown quantity
📝 Step 6: Check units and reasonableness

For Le Chatelier’s Principle Problems:

📝 Step 1: Identify the equilibrium reaction
📝 Step 2: Determine if reaction is exothermic or endothermic
📝 Step 3: Identify the change applied
📝 Step 4: Apply Le Chatelier's principle
📝 Step 5: Predict direction of shift
📝 Step 6: Determine effect on concentrations

For Degree of Dissociation Problems:

📝 Step 1: Write initial moles of each species
📝 Step 2: Express equilibrium moles in terms of α
📝 Step 3: Calculate equilibrium concentrations
📝 Step 4: Write equilibrium expression
📝 Step 5: Solve for α
📝 Step 6: Calculate percent dissociation if needed

📚 Practice Questions by Difficulty

🔥 Easy Level Questions

Question 1 (2022)

Problem: Write the equilibrium constant expression for the reaction: 2NO₂(g) ⇌ N₂O₄(g)

Solution:

Kc = [N₂O₄]/[NO₂]²

For Kp: Kp = P_N₂O₄/(P_NO₂)²

Question 2 (2020)

Problem: For the reaction: A + B ⇌ C + D, Kc = 10. If [A] = [B] = 0.1 M and [C] = [D] = 0.3 M at equilibrium, is the system at equilibrium?

Solution:

Calculate Qc (reaction quotient):
Qc = [C][D]/[A][B] = (0.3)(0.3)/(0.1)(0.1) = 0.09/0.01 = 9

Compare Qc with Kc:
Qc = 9, Kc = 10
Since Qc < Kc, reaction proceeds forward to reach equilibrium

Question 3 (2021)

Problem: State Le Chatelier’s principle.

Solution:

Le Chatelier's principle states that if a system at equilibrium is subjected to a change in concentration, pressure, or temperature, the system shifts its equilibrium position to counteract the change and restore equilibrium.

🎯 Medium Level Questions

Question 4 (2023)

Problem: For the reaction: 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), Kp = 10 at 700 K. Calculate Kc for the same reaction.

Solution:

Step 1: Calculate Δn_g
Δn_g = (moles of gas products) - (moles of gas reactants)
Δn_g = 2 - (2 + 1) = 2 - 3 = -1

Step 2: Use Kp = Kc(RT)^Δn_g
Given: Kp = 10, T = 700 K, R = 0.0821 L·atm/mol·K

10 = Kc(0.0821 × 700)^(-1)
10 = Kc(57.47)^(-1)
10 = Kc/57.47
Kc = 10 × 57.47 = 574.7

Therefore, Kc = 574.7

Question 5 (2022)

Problem: For the equilibrium: PCl₅(g) ⇌ PCl₃(g) + Cl₂(g) At equilibrium, [PCl₅] = 0.1 M, [PCl₃] = 0.2 M, [Cl₂] = 0.2 M. Calculate Kc.

Solution:

Using equilibrium expression:
Kc = [PCl₃][Cl₂]/[PCl₅]

Kc = (0.2)(0.2)/(0.1) = 0.04/0.1 = 0.4

Therefore, Kc = 0.4

Question 6 (2021)

Problem: The equilibrium constant for the reaction: N₂(g) + 3H₂(g) ⇌ 2NH₃(g) is Kc = 6.0 × 10⁻² at 500°C. Calculate Kp.

Solution:

Step 1: Calculate Δn_g
Δn_g = 2 - (1 + 3) = 2 - 4 = -2

Step 2: Convert temperature to Kelvin
T = 500°C = 773 K

Step 3: Use Kp = Kc(RT)^Δn_g
Kp = 6.0 × 10⁻² × (0.0821 × 773)^(-2)
Kp = 6.0 × 10⁻² × (63.46)^(-2)
Kp = 6.0 × 10⁻² × (1/4027.2)
Kp = 6.0 × 10⁻² × 2.48 × 10⁻⁴
Kp = 1.49 × 10⁻⁵

Therefore, Kp = 1.49 × 10⁻⁵

🚀 Hard Level Questions

Question 7 (2024)

Problem: For the dissociation equilibrium: N₂O₄(g) ⇌ 2NO₂(g) Initially, 1 mole of N₂O₄ is placed in a 1 L container at equilibrium. The total pressure at equilibrium is 2.5 atm. Calculate the degree of dissociation.

Solution:

Step 1: Set up ICE table
Let α = degree of dissociation

Initial:
N₂O₄: 1 mole
NO₂: 0 moles

At equilibrium:
N₂O₄: 1 - α moles
NO₂: 2α moles
Total moles = 1 - α + 2α = 1 + α

Step 2: Use total pressure to find α
Total pressure = 2.5 atm
P_total = (n_total × RT)/V

2.5 = ((1 + α) × 0.0821 × T)/1
We need T, but we can use partial pressure ratio instead

Step 3: Use mole fractions
Mole fraction of N₂O₄ = (1 - α)/(1 + α)
Mole fraction of NO₂ = (2α)/(1 + α)

Step 4: Write equilibrium expression
Kp = (P_NO₂)²/P_N₂O₄

P_NO₂ = (2α)/(1 + α) × 2.5 = 5α/(1 + α)
P_N₂O₄ = (1 - α)/(1 + α) × 2.5 = 2.5(1 - α)/(1 + α)

Kp = [5α/(1 + α)]²/[2.5(1 - α)/(1 + α)]
Kp = 25α²/(1 + α)² × (1 + α)/[2.5(1 - α)]
Kp = 10α²/(1 + α)(1 - α) = 10α²/(1 - α²)

Without temperature, we cannot solve further. Let's assume Kp is known or use another approach.

Alternative approach: Use the fact that at 298 K, Kp = 0.113
0.113 = 10α²/(1 - α²)
0.113(1 - α²) = 10α²
0.113 - 0.113α² = 10α²
0.113 = 10.113α²
α² = 0.01117
α = 0.106 or 10.6%

Therefore, degree of dissociation = 10.6%

Question 8 (2023)

Problem: For the equilibrium: 2A(g) ⇌ B(g) + C(g) Initially, 2 moles of A are placed in a 2 L container. At equilibrium, 0.4 moles of B are present. Calculate Kc.

Solution:

Step 1: Set up ICE table
Let x = extent of reaction

Initial:
A: 2 moles
B: 0 moles
C: 0 moles

At equilibrium:
A: 2 - 2x moles
B: x moles
C: x moles

Given: 0.4 moles of B at equilibrium
Therefore, x = 0.4

At equilibrium:
A: 2 - 2(0.4) = 2 - 0.8 = 1.2 moles
B: 0.4 moles
C: 0.4 moles

Step 2: Convert to concentrations
Volume = 2 L
[A] = 1.2/2 = 0.6 M
[B] = 0.4/2 = 0.2 M
[C] = 0.4/2 = 0.2 M

Step 3: Calculate Kc
Kc = [B][C]/[A]²
Kc = (0.2)(0.2)/(0.6)² = 0.04/0.36 = 0.111

Therefore, Kc = 0.111

Question 9 (2022)

Problem: The dimerization equilibrium: 2NO₂(g) ⇌ N₂O₄(g) Kp = 8.0 at 300 K. If initially 1 atm of NO₂ is present, calculate the equilibrium pressure of N₂O₄.

Solution:

Step 1: Set up ICE table in terms of pressure
Let x = equilibrium pressure of N₂O₄ formed

Initial:
P_NO₂ = 1 atm
P_N₂O₄ = 0 atm

At equilibrium:
P_NO₂ = 1 - 2x atm
P_N₂O₄ = x atm

Step 2: Write equilibrium expression
Kp = P_N₂O₄/(P_NO₂)²
8.0 = x/(1 - 2x)²

Step 3: Solve for x
8(1 - 2x)² = x
8(1 - 4x + 4x²) = x
8 - 32x + 32x² = x
32x² - 33x + 8 = 0

Using quadratic formula:
x = [33 ± √(33² - 4×32×8)]/(2×32)
x = [33 ± √(1089 - 1024)]/64
x = [33 ± √65]/64
x = [33 ± 8.06]/64

Two solutions:
x₁ = (33 + 8.06)/64 = 41.06/64 = 0.641 atm
x₂ = (33 - 8.06)/64 = 24.94/64 = 0.389 atm

Check both solutions:
For x₁ = 0.641: P_NO₂ = 1 - 2(0.641) = -0.282 atm (not possible)
For x₂ = 0.389: P_NO₂ = 1 - 2(0.389) = 0.222 atm (possible)

Therefore, equilibrium pressure of N₂O₄ = 0.389 atm

Question 10 (2021)

Problem: For the equilibrium: FeO(s) + CO(g) ⇌ Fe(s) + CO₂(g) Kp = 0.5 at 1000 K. If initially P_CO = 2 atm and P_CO₂ = 1 atm, calculate the equilibrium pressures.

Solution:

Step 1: Note that solids are omitted from equilibrium expression
Kp = P_CO₂/P_CO

Step 2: Set up ICE table
Let x = pressure change

Initial:
P_CO = 2 atm
P_CO₂ = 1 atm

At equilibrium:
P_CO = 2 - x atm
P_CO₂ = 1 + x atm

Step 3: Apply equilibrium expression
Kp = P_CO₂/P_CO = 0.5
(1 + x)/(2 - x) = 0.5

Step 4: Solve for x
1 + x = 0.5(2 - x)
1 + x = 1 - 0.5x
1.5x = 0
x = 0

This means the system is already at equilibrium!

Let's verify:
Initial Q = P_CO₂/P_CO = 1/2 = 0.5
Since Q = Kp = 0.5, the system is at equilibrium

Therefore:
P_CO(eq) = 2 atm
P_CO₂(eq) = 1 atm

📈 Performance Analysis and Tips

🎯 Success Rate by Question Type

🚀 Preparation Tips

📚 Study Strategy

🎯 Week 1: Master basic equilibrium concepts and K expressions
🎯 Week 2: Focus on ICE tables and equilibrium calculations
🎯 Week 3: Study Kp and Kc relationships
🎯 Week 4: Practice Le Chatelier's principle and applications

⏱️ Time Management

- Basic concept questions: 1-2 minutes
- K expression problems: 2-3 minutes
- ICE table problems: 4-5 minutes
- Kp/Kc conversion: 3-4 minutes
- Complex equilibrium: 5-6 minutes

🔍 Problem Recognition

📊 Question Patterns:
- "Calculate Kc/Kp": Write equilibrium expression
- "Find equilibrium concentrations": Use ICE table
- "Effect of conditions": Apply Le Chatelier's principle
- "Degree of dissociation": Use α in calculations
- "Convert Kp to Kc": Use Kp = Kc(RT)^Δn_g

📋 Quick Reference Formula Sheet

⚖️ Equilibrium Constants

Kc = [C]^c[D]^d/[A]^a[B]^b
Kp = (P_C)^c(P_D)^d/(P_A)^a(P_B)^b
Kp = Kc(RT)^Δn_g
Δn_g = gas products - gas reactants

📊 ICE Table

For aA + bB ⇌ cC + dD:
[A]eq = [A]₀ - ax
[B]eq = [B]₀ - bx
[C]eq = [C]₀ + cx
[D]eq = [D]₀ + dx

⚖️ Degree of Dissociation

α = (moles dissociated)/(initial moles)
For dimerization: 2A ⇌ A₂
Total moles = 1 - α/2

🌡️ Le Chatelier’s Principle

- Concentration: Shift to opposite side of change
- Pressure: Shift toward fewer gas moles
- Temperature: Endothermic: right with heat; Exothermic: left with heat
- Catalyst: No effect on equilibrium position

🏆 Final Practice Test

📝 Test Questions (10 questions, 45 minutes)

1. Write Kc expression for: 2SO₂(g) + O₂(g) ⇌ 2SO₃(g)
2. Convert Kc = 100 to Kp at 300 K for reaction with Δn_g = -2
3. Calculate Kc if [A] = 0.2 M, [B] = 0.1 M for A ⇌ B
4. For PCl₅ ⇌ PCl₃ + Cl₂, Kp = 2. Find Kc at 400 K
5. 2 moles of A in 1 L, at equilibrium [A] = 0.5 M. Find Kc for 2A ⇌ B
6. Predict shift when pressure increases for: N₂ + 3H₂ ⇌ 2NH₃
7. Calculate degree of dissociation if Kp = 1 for N₂O₄ ⇌ 2NO₂ at 1 atm total pressure
8. For CaCO₃(s) ⇌ CaO(s) + CO₂(g), Kp = 0.1. Find P_CO₂ at equilibrium
9. Initially 1 atm NO₂, equilibrium pressures: NO₂ = 0.6, N₂O₄ = 0.2. Find Kp
10. Effect of temperature increase on exothermic reaction equilibrium position

📊 Answer Key

1. Kc = [SO₃]²/[SO₂]²[O₂]
2. Kp = 100 × (0.0821 × 300)^(-2) = 1.65 × 10⁻⁴
3. Kc = 0.1/0.2 = 0.5
4. Kc = 2/(0.0821 × 400)^(-1) = 2 × 32.84 = 65.68
5. x = 1.5, Kc = [B]/[A]² = 1.5/(0.5)² = 6
6. Shift right (fewer gas moles: 2 → 4)
7. α = 0.5 or 50%
8. P_CO₂ = 0.1 atm (Kp = P_CO₂ for this reaction)
9. Kp = 0.2/(0.6)² = 0.56
10. Shift left (exothermic reaction opposes temperature increase)

Master Chemical Equilibrium with this comprehensive PYQ compilation! 🎯

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