1. Chemical Equilibrium

Introduction: Understanding Chemical Changes

Chemical reactions are fundamental processes occurring continuously in our environment. These reactions can be classified based on their completeness and reversibility:

• Irreversible reactions: Proceed in one direction only until completion
• Reversible reactions: Can proceed in both forward and reverse directions simultaneously

The key distinction lies in :
1. Whether the reaction goes to completion
2. It reaches a state of balance where both forward and reverse processes occur at equal rates.

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Reversible Reactions (Incomplete Reaction)

1. Definition
   A reaction in which the products can react to form the original reactants under the same conditions.
2. Bidirectional
   Represented by a double arrow (⇌) indicating both forward and backward reactions occur.
3. Dynamic Equilibrium
   After some time, the forward and backward reactions proceed at the same rate, establishing equilibrium.
4. Incomplete Reaction
   Reactants are never completely converted into products; a mixture of reactants and products remains at equilibrium.
5. Examples
   • N₂ + 3H₂ ⇌ 2NH₃ (Haber process)
   • CaCO₃ ⇌ CaO + CO₂

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Irreversible Reactions (Complete Reaction)

1. Definition
   A reaction that proceeds in one direction only, and products do not revert to reactants under normal conditions.
2. Unidirectional
   Represented by a single arrow (→) indicating only forward reaction occurs.
3. Complete Conversion
   Reactants are almost completely converted into products.
4. No Equilibrium
   These reactions do not establish dynamic equilibrium.
5. Conditions Have Limited Effect
   Changing temperature or pressure does not make the products revert back.
6. Examples
   • C + O₂ → CO₂
   • 2Mg + O₂ → 2MgO

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Rate of Reaction

Rate of reaction is how fast a chemical reaction happens.

Think of it like a race: some reactions are super fast, like an explosion, while others are very slow, like rust forming

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Chemical Equilibrium

Chemical equilibrium is the state of a reversible reaction where the rates of the forward and backward reactions are equal. At this point, there is no net change in the concentrations of the reactants and products

At equilibrium: Rate of forward reaction = Rate of reverse reaction

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What is Dynamic Equilibrium?

Dynamic equilibrium occurs when the forward and reverse reactions proceed at equal rates, creating a state of balance where:

• No net change occurs in concentrations
• Both reactions continue simultaneously
• The system appears static but is actually dynamic (Molecular activity continues)

• • Physical Example: Water-Ice System
  • At 0°C:
  • Ice melts to form water (forward process)
  • Water freezes to form ice (reverse process)
  • Rates are equal → no net change in amounts
  • System appears static but is molecularly active
• • Chemical Example: Formation and Decomposition
  • 2NaHCO₃ ⇌ Na₂CO₃ + CO₂ + H₂O
  • Forward: Sodium bicarbonate decomposes
  • Reverse: Products recombine
  • At equilibrium: Both processes occur at equal rates

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Understanding Forward and Reverse Reactions

Forward Reaction

A forward reaction proceeds from reactants → products (left to right in a chemical equation)

Key Characteristics:

• Always proceeds from left to right in the chemical equation
• Cannot produce reactants (only converts reactants to products)
• Initially proceeds at a fast rate but gradually slows down as reactants are consumed

Reverse Reaction

A reverse reaction proceeds from products → reactants (right to left in a chemical equation)

Key Characteristics:

• Always proceeds from right to left in the chemical equation
• Cannot produce products (only converts products back to reactants)
• Initially proceeds slowly but gradually speeds up as products accumulate

Forward Reaction Characteristics in Equilibrium Context

Definition: The reaction that converts reactants → products (left to right)

Behavioral Characteristics:

• Directional constraint: Always proceeds from left to right in the chemical equation
• Product limitation: Cannot produce reactants (only converts reactants to products)
• Rate behavior during equilibrium approach:
  • Initially proceeds at a fast rate when reactant concentration is high
  • Gradually slows down as reactants are consumed and their concentration decreases
  • At equilibrium: Maintains a constant rate equal to the reverse reaction rate

Reverse Reaction Characteristics in Equilibrium Context

Definition: The reaction that converts products → reactants (right to left)

Behavioral Characteristics:

• Directional constraint: Always proceeds from right to left in the chemical equation
• Reactant limitation: Cannot produce products (only converts products back to reactants)
• Rate behavior during equilibrium approach:
  • Initially proceeds slowly when product concentration is low
  • Gradually speeds up as products accumulate and their concentration increases
  • At equilibrium: Maintains a constant rate equal to the forward reaction rate

Why These Characteristics Matter in Equilibrium

Understanding these characteristics helps explain:

1. How equilibrium is reached – the changing rates eventually balance
2. Why equilibrium is dynamic – both reactions continue at equal rates
3. How the system responds to changes – rate changes drive equilibrium shifts

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Law of Mass Action and Chemical Equilibrium

Understanding Active Mass

Active Mass: The concentration of reacting substance is called Active mass. The unit of active mass is mol dm⁻³ and its value is expressed in square brackets.

For example, if we have substance A, its active mass is represented as [A].

Active Mass in General Terms

Active mass refers to the effective chemical presence of a substance in a reaction, meaning how much of it is truly available and capable of influencing the reaction rate or equilibrium.

It goes beyond just the measured amount (like grams or molarity) because not every particle contributes equally under real conditions. Interactions, phase, and freedom to react matter.

• For gases, active mass is expressed as partial pressure, because the tendency to react depends on the number of collisions in a given volume.
• For dilute solutions, active mass is approximately the molar concentration, as particles are free to interact.
• For pure solids and pure liquids, active mass is considered constant (taken as 1), since their effective contribution does not change with more or less quantity.
• In advanced terms, active mass relates to activity, which accounts for non-ideal behavior, where the “effective concentration” differs from the actual concentration due to particle interactions.

In short:
Active mass = how strongly a substance effectively participates in a chemical process, not just how much of it is physically present.

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The Fundamental Principle: Law of Mass Action

Now that we understand active mass, let’s explore the basic principle that governs chemical reactions.

The Law of Mass Action states that:

• The rate at which a substance reacts is directly proportional to its active mass
• The rate of reaction is directly proportional to the product of the active masses of the reacting substances

This law also suggests that the ratio of the reactant concentration and the product concentration is constant at a state of equilibrium.

Applying Mass Action to Forward and Reverse Reactions

Let’s consider a general reversible reaction and see how the law of mass action applies:

For a general reaction: aA + bB ⇌ cC + dD

Where:

• A and B are reactants
• C and D are products
• a, b, c, d are the number of moles needed to balance the chemical reaction

Forward Reaction Rate

For the forward reaction: aA + bB → cC + dD

According to the law of mass action: Rf = kf[A]ᵃ[B]ᵇ

Where:

• Rf = rate of forward reaction
• kf = rate constant for forward reaction
• [A]ᵃ[B]ᵇ = product of active masses raised to their stoichiometric coefficients

Reverse Reaction Rate

Similarly, for the reverse reaction: cC + dD → aA + bB

The rate of reverse reaction is directly proportional to product concentrations: Rr = kr[C]ᶜ[D]ᵈ

Where:

• Rr = rate of reverse reaction
• kr = rate constant for reverse reaction

The Equilibrium Condition

At equilibrium, a crucial condition is met: the rate of forward reaction equals the rate of reverse reaction.

At equilibrium: Rf = Rr

Therefore: kf[A]ᵃ[B]ᵇ = kr[C]ᶜ[D]ᵈ

Deriving the Equilibrium Constant Expression

From the equilibrium condition, we can derive the equilibrium constant:

Rearranging the equation: kf[A]ᵃ[B]ᵇ = kr[C]ᶜ[D]ᵈ

kf/kr = [C]ᶜ[D]ᵈ/[A]ᵃ[B]ᵇ

Since kf and kr are constants, their ratio is also constant.

The Equilibrium Constant (Kc)

We define this constant ratio as the equilibrium constant (Kc):

Kc = kf/kr = [C]ᶜ[D]ᵈ/[A]ᵃ[B]ᵇ

Alternatively, this can be written as:

Kc = [Product]/[Reactant]

Where Kc is called the equilibrium constant.

Key Insights and Applications

The derivation shows us that:

1. The law of mass action provides the theoretical foundation for understanding how reaction rates depend on concentrations
2. At equilibrium, opposing reactions balance – the forward and reverse rates become equal
3. The equilibrium constant expression emerges naturally from applying mass action principles to both directions of a reversible reaction
4. All chemical equilibria can be expressed in this form – the equilibrium constant relates the concentrations of products and reactants at equilibrium

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Equilibrium Constant and Its Units

Understanding Equilibrium Constants

Building on the equilibrium condition, we can define the equilibrium constant.

Key Concept:It is a value that shows the relationship between the amounts of products and reactants when a chemical reaction reaches equilibrium. In simple terms, it’s a number that tells you how far a reaction has gone before it stops changing.

What Does the Equilibrium Constant Tell Us?

The equilibrium constant provides crucial information about:

• The position of equilibrium (whether products or reactants are favored)
• How far a reaction proceeds before reaching equilibrium
• The relative concentrations of reactants and products at equilibrium

The Mathematics Behind Equilibrium Constants

Basic Principle

You have to figure out the ratio of product to reactant concentrations.

For any general reaction: aA + bB ⇌ cC + dD

The equilibrium constant expression is: Kc = [C]ᶜ[D]ᵈ/[A]ᵃ[B]ᵇ

Important Mathematical Rules

Rule 1: It represents the equilibrium concentration of the reactant and product in mol dm⁻³

Rule 2: Kc indicates reactant and product concentration

Rule 3: Kc varies with temperature

Understanding Units of Equilibrium Constants

Now that we understand the basic expression, let’s explore how units work.

When Do Equilibrium Constants Have Units?

Case 1: When Units Cancel Out

Consider the reaction: CO₍g₎ + H₂O₍g₎ ⇌ CO₂₍g₎ + H₂O₍l₎

Kc = [CO₂][H₂O]/[CO][H₂O]

Since we have equal numbers of moles on both sides of the equation, the concentration units cancel:

Kc = [mol dm⁻³][mol dm⁻³]/[mol dm⁻³][mol dm⁻³] = no unit

Case 2: When Units Don’t Cancel Out

For reactions where the number of moles of reactants and products are not equal, Kc has units.

Example: N₂₍g₎ + 3H₂₍g₎ ⇌ 2NH₃₍g₎

Kc = [NH₃]²/[N₂][H₂]³

Calculating the units: Kc = [mol dm⁻³]²/[mol dm⁻³][mol dm⁻³]³ = [mol dm⁻³]²/[mol dm⁻³]⁴ = mol⁻² dm⁶

Practical Guidelines for Working with Equilibrium Constants

Temperature Dependence

• It is impossible to change a given reaction’s equilibrium constant since concentration can be measured at equilibrium
• The temperature is the single factor affecting the equilibrium constant value
• At different temperatures, the same reaction will have different Kc values

Reaction Direction and Equilibrium Position

Rule 5: Kc represents equilibrium position. If Kc is larger than 1, the reaction is forward.

Rule 6: If Kc is less than 1, the reaction is a reverse reaction.

Rule 7: Remember that equilibrium constant Kc is ratio of reactant to product that is utilized to define chemical behavior.

Key Takeaways for Understanding Equilibrium Constants

1. Foundation: Equilibrium occurs when forward and reverse reaction rates are equal
2. Expression: The equilibrium constant is always the ratio of products to reactants, with concentrations raised to their stoichiometric coefficients
3. Units: Units depend on whether the total moles of reactants equal the total moles of products
4. Temperature: Only temperature affects the value of the equilibrium constant
5. Interpretation: The magnitude of Kc tells us which direction is favored and how complete the reaction is at equilibrium

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Understanding What the Equilibrium Constant Really Means

Before exploring its applications, it’s essential to understand the fundamental nature of the equilibrium constant.

Key Insight: The value of Kc varies depending on the response. Kc isn’t only a calculating constant. It affects both the direction and the extent of a chemical reaction.

This dual role makes the equilibrium constant one of the most powerful tools in chemistry for predicting and understanding chemical behavior.

First Application: Predicting the Direction of Chemical Reactions

Now that we understand Kc’s importance, let’s see how it helps us predict which way a reaction will proceed.

The Concept of Reaction Quotient (Qc)

When dealing with concentrations at any given time (not necessarily at equilibrium):

• Reaction Quotient (Qc) helps make predictions about reaction direction
• Qc has the same mathematical structure as Kc but uses current concentrations instead of equilibrium concentrations
• Qc is calculated as the ratio of product to reactant concentrations at any given moment

Using Qc vs Kc to Predict Direction

By comparing the current state (Qc) with the equilibrium state (Kc), we can predict what will happen:

Case 1: System at Equilibrium
If Qc = Kc: The actual product and reactant concentrations are equal to the equilibrium concentrations, and the system is stable.

Case 2: Forward Reaction Favored
If Qc < Kc: There is an increase in product concentration for equilibrium. So the forward reaction forming more products occurs.

Case 3: Reverse Reaction Favored
If Qc > Kc: There is a decrease in product concentration to achieve equilibrium. As a result, the process reverses, forming more reactants.

Visual Understanding

The relationship can be visualized as:

• Qc < Kc → Forward reaction (more products needed)
• Qc = Kc → Equilibrium (no change)
• Qc > Kc → Reverse reaction (fewer products needed)

3. Second Application: Determining the Extent of Chemical Reactions

Beyond predicting direction, the equilibrium constant tells us how far a reaction will proceed.

What Does “Extent” Mean?

At a certain temperature, the extent of a reaction is measured. The magnitude of an equilibrium constant can predict the scope of a chemical reaction. As magnitude may be very high, very low, or moderate, so complete extent of chemical reaction varies.

Interpreting Kc Values: Three Categories

Category 1: Very Small Kc Values

Kc is very small (Kc << 1)

Characteristics:

• Reactions with low Kc never finish
• Maximum reactant concentration and minimum product concentration
• These are called “reverse or backward reactions”

Example: F₂⇌2F(g) Kc= 7.4 × 10⁻¹³ at 227°C

Interpretation: The reaction barely proceeds forward; reactants are heavily favored.

Category 2: Very Large Kc Values

Kc is very large (Kc >> 1)

Characteristics:

• Reactions with high Kc values are virtually complete
• Maximum product concentration and minimum reactant concentration
• This type of reaction is known as “forward reaction”

Example: 2H₂(g)+O₂(g)⇌2H₂O(g) Kc= 2.4 × 10⁴⁷ at 227°C

Interpretation: The reaction goes almost completely to products.

Category 3: Moderate Kc Values

Kc is neither very small nor very large (Kc ≈ 1)

Characteristics:

• Reactions which have moderate value of Kc are considered to be at equilibrium
• The concentration of reactants and products is almost same

Example: N₂O₄(g)⇌2NO₂(g) Kc= 0.36 at 25°C

Interpretation: Significant amounts of both reactants and products are present at equilibrium.

Practical Applications and Special Cases

Industrial and Biological Applications

Do You Know? Equilibrium constants exist for certain groups of equilibria, such as for:

• Weak acids and weak bases
• The autoionization of water
• Slightly soluble salts

These specialized equilibrium constants have specific names and applications in different fields of chemistry.

Real-World Significance

Understanding Kc values helps chemists and engineers:

1. Optimize Industrial Processes: Choose conditions that maximize desired product formation
2. Predict Reaction Feasibility: Determine if a reaction is worth pursuing commercially
3. Control Reaction Conditions: Adjust temperature and concentration to shift equilibrium
4. Understand Biological Systems: Predict how biological reactions will respond to changing conditions

Key Takeaways: The Power of Equilibrium Constants

The equilibrium constant serves as a fundamental tool that provides:

1. Predictive Power: Tells us which direction a reaction will proceed under given conditions
2. Quantitative Analysis: Gives us numerical insight into how much product we can expect
3. Process Optimization: Helps in designing efficient chemical processes
4. Universal Application: Works for all types of chemical equilibria, from simple gas reactions to complex biochemical processes

By mastering the concept of equilibrium constants, you gain the ability to predict and control chemical reactions, making it one of the most practical and powerful concepts in chemistry.

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Book-5 Test Yourself

Write down Forward and Reverse reactions

1. N₂(g) + O₂(g) ⇌ 2NO(g)

Forward Reaction: N₂(g) + O₂(g) → 2NO(g)

• Nitrogen gas and oxygen gas combine to form nitrogen monoxide gas

Reverse Reaction: 2NO(g) → N₂(g) + O₂(g)

• Nitrogen monoxide gas decomposes to form nitrogen gas and oxygen gas

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2. 2SO₂(g) + O₂(g) ⇌ 2SO₃(g)

Forward Reaction: 2SO₂(g) + O₂(g) → 2SO₃(g)

• Sulfur dioxide gas and oxygen gas combine to form sulfur trioxide gas

Reverse Reaction: 2SO₃(g) → 2SO₂(g) + O₂(g)

• Sulfur trioxide gas decomposes to form sulfur dioxide gas and oxygen gas

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3. COCl₂(g) ⇌ CO(g) + Cl₂(g)

Forward Reaction: COCl₂(g) → CO(g) + Cl₂(g)

• Phosgene gas (carbonyl chloride) decomposes to form carbon monoxide gas and chlorine gas

Reverse Reaction: CO(g) + Cl₂(g) → COCl₂(g)

• Carbon monoxide gas and chlorine gas combine to form phosgene gas (carbonyl chloride)

Book-7 Test Yourself

Define the term “active mass”

Active mass is the molar concentration of a substance that is actively participating in a chemical reaction at a given temperature. It is expressed in mol/L (molarity) and represents the effective concentration of reactants and products that influence the rate and equilibrium of a chemical reaction.

Key points:

• Active mass = Molar concentration = [substance] in mol/L
• Only substances in solution (aqueous) or gas phase have active mass
• Pure solids and liquids have constant active mass (usually taken as 1)
• Active mass directly affects reaction rates and equilibrium constants

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Figure out coefficients for the hypothetical reaction

Given: 9X(g) + Y₃(g) ⇌ 3X₃Y(g)

Step-by-step balancing:

1. Count atoms on each side:
   • Left side: 9 X atoms + 3 Y atoms
   • Right side: 9 X atoms + 3 Y atoms
2. Verification:
   • X atoms: 9 (left) = 3 × 3 = 9 (right) ✓
   • Y atoms: 3 (left) = 3 × 1 = 3 (right) ✓

The equation is already balanced as given: 9X(g) + Y₃(g) ⇌ 3X₃Y(g)

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Write down Kc equations for given reactions

a) S(s) + O₂(g) ⇌ SO₂(g)

Kc equation: K_c = \frac{[SO_2]}{[O_2]}

Note: [S] is not included because it’s a pure solid

b) SO₂(g) + NO₂(g) ⇌ NO(g) + SO₃(g)

Kc equation: K_c = \frac{[NO][SO_3]}{[SO_2][NO_2]}

c) NH₄Cl(s) ⇌ NH₃(g) + HCl(g)

Kc equation: K_c = [NH_3][HCl]

Note: [NH₄Cl] is not included because it’s a pure solid

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EXERCISE

SECTION A : MULTIPLE CHOICE QUESTIONS

Question 1: Which one of the following statements is false about dynamic equilibrium?

Answer: d. Equilibrium cannot be disturbed by any external stress

Explanation:
A dynamic equilibrium is characterized by:

• It must occur in a closed system (a closed container) to prevent reactants or products from escaping (Statement a is true).
• The concentrations of reactants and products remain constant (not necessarily equal, but unchanged) (Statement b is true).
• This constant concentration is because the rate of the forward reaction equals the rate of the reverse reaction (Statement c is true).
• According to Le Chatelier’s Principle, a system at equilibrium will shift to counteract any change imposed on it (e.g., changes in concentration, pressure, or temperature). Therefore, equilibrium can be disturbed by an external stress (Statement d is false).

Question 2: Indicate the equilibrium constant expression Kc for 4NH₃ + 5O₂ ⇌ 4NO + 6H₂O

Answer: c. K_c = \frac{[NO]^4[H_2O]^6}{[NH_3]^4[O_2]^5}

Question 3: Reversible reaction is represented by:

Answer: c. Double arrow (⇌)

Question 4: When the magnitude of Kc is small, it indicates:

Answer: a. Reaction mixture contains most of the reactant

Question 6: The unit of Kc for reaction N2+O2⇌2NON2​+O2​⇌2NO

Answer: d. no unit

Question 7: The system is stable in equilibrium when:

Answer: a. Qc=Kc​

Question 8: Qc can be defined as:

Answer: b. ratio of molar concentration of product and reactant at specific time

Question 10: The value of Kc increases when:

Answer: b. [Product] is more

Explanation:
The equilibrium constant, Kc, is a ratio of the concentrations of products to reactants at equilibrium: Kc = [Products] / [Reactants].

SECTION-B: SHORT QUESTIONS

1. Define chemical equilibrium with example.

Answer:
Chemical equilibrium is the state in a reversible reaction where the rate of the forward reaction equals the rate of the reverse reaction. As a result, the concentrations of reactants and products remain constant over time, though both reactions continue to occur.

Example: The synthesis of ammonia via the Haber process:
N₂(g) + 3H₂(g) ⇌ 2NH₃(g)
In a closed container, the reaction reaches a point where the amounts of nitrogen, hydrogen, and ammonia no longer change.

2. Why chemical equilibrium is dynamic?

Answer:
Chemical equilibrium is dynamic because the reactions do not stop at equilibrium. The forward and reverse reactions continue to occur at equal rates. The constancy in concentrations is due to the fact that products are formed from reactants and reactants are formed from products at the same rate, not because the reactions have ceased.

3. When writing an equation, how is a reversible reaction distinguished from irreversible reaction?

Answer:
A reversible reaction is denoted by a double arrow (⇌ or ≡) pointing in both directions between reactants and products. An irreversible reaction is denoted by a single arrow (→ or =) pointing only from reactants to products.

4. Write an equilibrium equation of monoatomic carbon and a molecule of oxygen as reactant and carbon monoxide as product.

Answer:
C(g) + O₂(g) ⇌ 2CO(g)

5. Outline the characteristics of reversible reaction.

Answer:

• They do not go to completion and instead reach a state of equilibrium.
• They are represented by a double arrow (⇌).
• They occur in a closed system.
• At equilibrium, the concentrations of all species remain constant.
• The equilibrium can be approached from either direction (starting with reactants or products).

. Distinguished between reversible and irreversible reaction.

Answer:

Feature	Reversible Reaction	Irreversible Reaction
Arrow	Double arrow (⇌)	Single arrow (→)
Completion	Never goes to completion	Goes to completion
System	Occurs in a closed system	Can occur in an open or closed system
State	Reaches dynamic equilibrium	Goes to a final state where reactants are consumed

7. State law of mass action. How is the active mass represented?

Answer:
The law of mass action states that the rate of a chemical reaction is directly proportional to the product of the active masses (concentrations) of the reactants, each raised to the power of their stoichiometric coefficient in the balanced chemical equation.

Active mass is represented by the molar concentration (in mol dm⁻³) of a substance, denoted by square brackets, e.g., [A] for the concentration of A.

8. Why equilibrium constant may or may not have unit? Justify with example.

Answer:
The equilibrium constant (Kc) may or may not have units depending on the change in the number of moles (Δn) of the reaction.

• Δn = (moles of gaseous products) - (moles of gaseous reactants)
• The units of Kc are (mol dm⁻³)^Δn.

Example with units:
For N₂(g) + 3H₂(g) ⇌ 2NH₃(g)
Δn = 2 - 4 = -2.
Units of Kc: (mol dm⁻³)⁻² = mol⁻² dm⁶

Example without units:
For H₂(g) + I₂(g) ⇌ 2HI(g)
Δn = 2 - 2 = 0.
Units of Kc: (mol dm⁻³)⁰ = 1 (No unit)

9. How direction of a reaction can be predicted if Kc is known to you.

Answer:
The direction of a reaction is predicted by comparing the reaction quotient (Qc) to the known equilibrium constant (Kc).

• If Qc < Kc: The forward reaction is favored to reach equilibrium.
• If Qc = Kc: The system is at equilibrium; no net change.
• If Qc > Kc: The reverse reaction is favored to reach equilibrium.

10. Write equilibrium constant expression for the following equations:

i) N_2(g) + 2O_2(g) \leftrightharpoons 2NO_2(g)
Answer: K_c = \frac{[NO_2]^2}{[N_2][O_2]^2}

ii) N_2(g) + 3H_2(g) \leftrightharpoons 2NH_3(g)
Answer: K_c = \frac{[NH_3]^2}{[N_2][H_2]^3}

iii) H_2(g) + Br_2(g) \leftrightharpoons 2HBr(g)
Answer: ]K_c = \frac{[HBr]^2}{[H_2][Br_2]}

SECTION-C: DETAILED QUESTIONS

1. Describe dynamic equilibrium with two examples.

Answer:
Dynamic equilibrium is a state of balance within a system where two opposing processes occur at the same rate, resulting in no net change in the system’s properties.

Example 1: A Closed Soda Bottle
In a sealed soda bottle, carbon dioxide gas (CO₂) dissolved in the liquid is in equilibrium with CO₂ gas in the space above the liquid.
CO₂(aq) ⇌ CO₂(g)
The rate at which CO₂ molecules escape from the liquid (forward reaction) is equal to the rate at which CO₂ molecules dissolve back into the liquid (reverse reaction). The concentration of CO₂ in both phases remains constant.

Example 2: The Haber Process
As mentioned earlier: N₂(g) + 3H₂(g) ⇌ 2NH₃(g)
In a closed reactor, nitrogen and hydrogen gases combine to form ammonia at the same rate that ammonia decomposes back into nitrogen and hydrogen. The amounts of all three gases remain unchanged, signaling a dynamic equilibrium.

2. State law of mass action. Derive an expression for equilibrium constant.

Answer:
Law of Mass Action: 

Derivation:
Consider a general reversible reaction at equilibrium:
aA + bB ⇌ cC + dD

• According to the law of mass action:
  • \text{Rate of forward reaction: } R_f \propto [A]^a [B]^b \;\Rightarrow\; R_f = k_f [A]^a [B]^b
  • \text{Rate of reverse reaction: } R_r \propto [C]^c [D]^d \;\Rightarrow\; R_r = k_r [C]^c [D]^d
• At equilibrium, the rates are equal: R_f = R_r
• Therefore:k_f [A]^a [B]^b = k_r [C]^c [D]^d
• Rearranging this equation to group the constants and concentrations:
  \frac{k_f}{k_r} = \frac{[C]^c [D]^d}{[A]^a [B]^b}
• The ratio k_f / k_r is a constant, which is the equilibrium constant, K_c.
  K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}

3. Describe the characteristics of equilibrium constant.

Answer:

• Constant at Constant Temperature: Kc is fixed for a given reaction at a specific temperature. It changes only if the temperature changes.
• Independent of Initial Concentrations: The value of Kc is the same regardless of whether you start with reactants or products; it depends only on the equilibrium concentrations.
• Independent of Catalyst: A catalyst speeds up both the forward and reverse reactions equally, so it helps the system reach equilibrium faster but does not change the value of Kc.
• Dependent on the Reaction Stoichiometry: The form of the Kc expression and its value depend on how the balanced chemical equation is written. If the equation is multiplied by a factor n, the new Kc’ is (Kc)^n.
• Predicts Reaction Extent: The magnitude of Kc indicates whether the products or reactants are favored at equilibrium.

4. How can you predict the following stages of a reaction by comparing the values of Kc and Qc:

Answer:
The reaction quotient (Qc) is calculated using the same formula as Kc but with initial (non-equilibrium) concentrations.

• i) Net reaction proceeds in forward direction:
  This happens when Qc < Kc. The system has too many reactants and too few products compared to the equilibrium state. To achieve equilibrium, the reaction must proceed in the forward direction to produce more products.
• ii) Net reaction proceeds in reverse direction:
  This happens when Qc > Kc. The system has too many products and too few reactants compared to the equilibrium state. To achieve equilibrium, the reaction must proceed in the reverse direction to produce more reactants.

5. Predict which system at equilibrium will contain maximum amount of product and which system will contain maximum amount of reactant?

Analysis: The magnitude of Kc tells us the position of equilibrium. A very large Kc (>> 1) means products are favored. A very small Kc (<< 1) means reactants are favored.

a) 2CO₂(g) ⇌ 2CO(g) + O₂(g) 
K_{c (927°C)} = 3.1 × 10⁻¹⁸ mol.dm⁻³

• Kc is very small (<< 1). Therefore, the system at equilibrium will contain the maximum amount of reactant (CO₂).

b) 2O₃(g) ⇌ 3O₂(g) 
K_{c (298K)} = 5.9 × 10³⁵ mol.dm⁻³

• Kc is very large (>> 1). Therefore, the system at equilibrium will contain the maximum amount of product (O₂).

c) Kc = 3.1 × 10⁻¹⁸ mol.dm⁻³

• This Kc value is the same as in (a). It is very small. Therefore, the system at equilibrium will contain the maximum amount of reactant.

d) Kc = 5.9 × 10³⁵ mol.dm⁻³

• This Kc value is the same as in (b). It is very large. Therefore, the system at equilibrium will contain the maximum amount of product.

Final Answer:

• Maximum amount of product: Systems (b) and (d).
• Maximum amount of reactant: Systems (a) and (c).

SECTION-D: Numerical

1. Dinitrogen tetroxide (N₂O₄) decomposes into nitrogen dioxide (NO₂).
Derive the Kc expression and interpret its unit.

Step 1: Write the balanced reversible reaction.N₂O₄(g) \leftrightharpoons 2NO₂(g)

Step 2: Derive the equilibrium constant expression (Kc).
According to the law of mass action, Kc is the ratio of the product of the concentrations of the products to the product of the concentrations of the reactants, each raised to the power of their stoichiometric coefficients.
K_c = \frac{[NO_2]^2}{[N_2O_4]}

Step 3: Interpret the unit of Kc.

• The unit for concentration is mol dm⁻³.
• For the reaction: N_2O_4(g) \leftrightharpoons 2NO_2(g)
• Change in the number of moles, Δn=(2)−(1)=1Δn=(2)−(1)=1
• The unit of Kc is (mol dm−3)Δn=(mol dm−3)1(mol dm−3)Δn=(mol dm−3)1

Final Answer:

• Kc Expression: K_c = \frac{[NO_2]^2}{[N_2O_4]}
• Unit of Kc: mol dm⁻³

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2. Calculate Kc for the reaction: PCl₅ ⇌ PCl₃ + Cl₂

Given:

• Temperature = 500 K
• [PCl₅]=0.8×10⁻³ mol dm⁻³
• [PCl₃]=1.2×10⁻³ mol dm⁻³
• [Cl₂]=1.2×10⁻³ mol dm⁻³

Step 1: Write the balanced equation and the Kc expression.
PCl_5(g) \leftrightharpoons PCl_3(g) + Cl_2(g)

K_c = \frac{[PCl_3][Cl_2]}{[PCl_5]}

Step 2: Substitute the given concentrations into the Kc expression.
Kc=(1.2×10⁻³)×(1.2×10⁻³) / (0.8×10⁻³)

Step 3: Perform the calculation.
Kc= (1.2×10⁻³)×(1.2×10⁻³) / 0.8×10⁻³
K_c= (1.44×10⁻⁶) x (0.8×10⁻³)
Kc= (1.44×10⁻⁶) x (8.0×10⁻⁴)
Kc​= 1.8×10−3

Step 4: Determine the unit of Kc.

• For the reaction: PCl_5(g) ⇌ PCl_3(g)+Cl_2(g)​
• Unit of Kc = mol dm⁻³
• Unit =mol dm⁻³

Final Answer:Kc=1.8×10⁻³ mol dm^−3​

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3. Predict the direction of the reaction: 2HI(g) ⇌ H₂(g) + I₂(g)

Given:

• Kc=1×10⁻⁴
• Concentrations:
  • [HI]=2×10⁻⁵ mol dm⁻³
  • [H₂]=1×10⁻⁵ mol dm⁻³
  • [I₂]=1×10⁻⁵ mol dm⁻³

Step 1: Write the reaction quotient (Qc) expression.
The expression for Qc is the same as for Kc but uses the initial concentrations.
Q_c=[H₂][I₂] / [HI]²​

Step 2: Calculate the value of Qc.
Qc = (1×10⁻⁵)×(1×10⁻⁵) / (2×10⁻⁵)²
Qc = (1×10⁻¹⁰) / (4×10⁻¹⁰)
Qc = 0.25

Step 3: Compare Qc to Kc to predict the direction.

• Kc = 1×10⁻⁴ = 0.0001
• Qc=0.25

Since Qc(0.25) > Kc( 0.0001)
The reaction will proceed in the reverse direction to decrease the concentration of products (H₂ and I₂) and increase the concentration of the reactant (HI) until Qc=Kc.

Final Answer:
The reaction will proceed in the reverse direction.