Chemical Equilibrium

Understanding Reversible Reactions

Reversible reactions are chemical reactions that can proceed in both forward and backward directions under suitable conditions. They are represented by double arrows (⇌) between reactants and products.

Types of Reversible Reactions

• Homogeneous Reversible Reactions: All reactants and products are in the same phase (e.g., all gases or all in solution)
• Heterogeneous Reversible Reactions: Reactants and products are in different phases (e.g., solid with gas, liquid with gas)

Equilibrium Constant (Kc)

The equilibrium constant (Kc) is the ratio of the concentrations of products to reactants, each raised to the power of their stoichiometric coefficients, at equilibrium.

Equilibrium Constant in Terms of Pressure (Kp)

For gaseous reactions, equilibrium constant can also be expressed in terms of partial pressures (Kp).

Characteristics of Equilibrium Constant

• Kc and Kp are constant at a given temperature
• Equilibrium constant changes with temperature
• Pure solids and liquids do not appear in equilibrium constant expression
• K > 1 indicates products are favored at equilibrium
• K < 1 indicates reactants are favored at equilibrium
• K = 1 indicates comparable amounts of reactants and products

Law of Mass Action

Proposed by Cato Guldberg and Peter Waage in 1864, the Law of Mass Action states that the rate of a chemical reaction is proportional to the product of the concentrations of the reactants, each raised to the power of their stoichiometric coefficients.

Derivation of Equilibrium Constant from Law of Mass Action

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

1. Forward reaction rate: R_f = k_f [A]ᵃ [B]ᵇ
2. Backward reaction rate: R_b = k_b [C]ᶜ [D]ᵈ
3. At equilibrium: R_f = R_b
4. Therefore: k_f [A]ᵃ [B]ᵇ = k_b [C]ᶜ [D]ᵈ
5. Rearranging: k_f/k_b = [C]ᶜ [D]ᵈ / [A]ᵃ [B]ᵇ = Kc

Applications of Law of Mass Action

• Derivation of equilibrium constant expressions
• Predicting the direction of reaction using reaction quotient (Q)
• Understanding how concentration changes affect equilibrium position
• Basis for all equilibrium calculations in chemistry

What is Heterogeneous Equilibrium?

Heterogeneous equilibrium involves reactants and products in two or more different phases (solid, liquid, gas, or aqueous). In such systems, the concentrations of pure solids and liquids remain constant and are not included in the equilibrium constant expression.

Rules for Writing Equilibrium Expressions for Heterogeneous Systems

1. Include only gaseous and aqueous species in the equilibrium expression
2. Omit pure solids and pure liquids from the expression
3. The concentrations of solids and liquids are constant and incorporated into K
4. For solutions, the solvent (if in large excess) is also omitted

Common Examples of Heterogeneous Equilibria

Reaction	Equilibrium Constant Expression	Notes
NH₄Cl(s) ⇌ NH₃(g) + HCl(g)	Kp = P(NH₃)·P(HCl)	Only gases appear in expression
H₂O(l) ⇌ H₂O(g)	Kp = P(H₂O)	Liquid water omitted
AgCl(s) ⇌ Ag⁺(aq) + Cl⁻(aq)	Kc = [Ag⁺][Cl⁻]	Solid omitted, ions included
C(s) + CO₂(g) ⇌ 2CO(g)	Kc = [CO]²/[CO₂]	Solid carbon omitted

Le Chatelier's Principle

Proposed by French chemist Henry Louis Le Chatelier in 1884, this principle states: "If a system at equilibrium is subjected to a change in concentration, temperature, or pressure, the equilibrium shifts in a direction that tends to counteract the effect of the change."

Effects of Various Changes on Equilibrium

1. Effect of Concentration Change

• Increase concentration of reactants: Equilibrium shifts to the RIGHT (toward products)
• Increase concentration of products: Equilibrium shifts to the LEFT (toward reactants)
• Decrease concentration of reactants: Equilibrium shifts to the LEFT
• Decrease concentration of products: Equilibrium shifts to the RIGHT

2. Effect of Pressure Change (for gaseous reactions)

• Increase pressure: Equilibrium shifts toward the side with FEWER moles of gas
• Decrease pressure: Equilibrium shifts toward the side with MORE moles of gas
• No effect: If Δn = 0 (equal moles on both sides), pressure change has no effect

3. Effect of Temperature Change

• Increase temperature: Equilibrium shifts in the ENDOTHERMIC direction
• Decrease temperature: Equilibrium shifts in the EXOTHERMIC direction

Detailed Analysis of Factors Affecting Equilibrium

While Le Chatelier's Principle gives qualitative predictions, understanding the quantitative effects requires deeper analysis of how equilibrium constants and reaction quotients respond to changes.

1. Effect of Concentration Changes

When concentration of a reactant is increased:

1. Q decreases (denominator increases)
2. Now Q < K
3. Reaction proceeds forward until Q = K again
4. Equilibrium shifts to the right

2. Effect of Pressure Changes

Pressure changes affect equilibrium ONLY if Δn ≠ 0 (different moles of gas on each side).

Mathematical Analysis:

For an ideal gas: PV = nRT → P = (n/V)RT = CRT

Increasing pressure increases concentration of ALL gaseous species proportionally.

For reaction: aA(g) + bB(g) ⇌ cC(g) + dD(g)

When pressure increases by factor x, partial pressures become xP_A, xP_B, etc.

New Qp = (xPc)ᶜ(xPd)ᵈ / (xPa)ᵃ(xPb)ᵇ = x^{Δn} × Kp

If Δn > 0 (more moles on right): Qp > Kp → shift left

If Δn < 0 (more moles on left): Qp < Kp → shift right

3. Effect of Temperature Changes

Temperature is the ONLY factor that changes the equilibrium constant K itself.

Van't Hoff Equation:

Where:

• K₁, K₂ = equilibrium constants at T₁, T₂
• ΔH° = standard enthalpy change
• R = gas constant (8.314 J/mol·K)

Temperature Dependence:

Reaction Type	ΔH	Effect of Increasing T	K vs T Relationship
Exothermic	Negative	K decreases	Equilibrium shifts left
Endothermic	Positive	K increases	Equilibrium shifts right

4. Effect of Catalyst

Important: A catalyst does NOT affect the equilibrium position or the equilibrium constant K.

• Catalyst increases BOTH forward and backward reaction rates equally
• Equilibrium is reached faster, but the equilibrium concentrations remain unchanged
• Catalyst lowers the activation energy for both forward and reverse reactions

Introduction to Ionic Equilibrium

Ionic equilibrium deals with the equilibrium established between unionized molecules and ions in solution of weak electrolytes. It's a special case of chemical equilibrium applied to electrolyte solutions.

Degree of Dissociation (α)

The fraction of total molecules that dissociate into ions.

For weak electrolytes: 0 < α < 1

For strong electrolytes: α ≈ 1 (complete dissociation)

Acid Dissociation Constant (Kₐ)

For a weak acid HA dissociating in water:

Base Dissociation Constant (Kբ)

For a weak base B dissociating in water:

Relation between Kₐ and Kբ

For a conjugate acid-base pair:

Where K_w = ionic product of water = 1 × 10⁻¹⁴ at 25°C

Factors Affecting Ionic Equilibrium

1. Nature of electrolyte: Strong vs weak electrolytes
2. Concentration: Degree of dissociation increases with dilution (Ostwald's Law)
3. Temperature: Dissociation is generally endothermic, so increases with temperature
4. Common ion effect: Adding a common ion suppresses dissociation
5. Solvent: Dielectric constant of solvent affects ion dissociation

Theories of Acids and Bases

1. Arrhenius Theory (1887)

• Acid: Substance that produces H⁺ ions in aqueous solution
• Base: Substance that produces OH⁻ ions in aqueous solution
• Limitation: Only applicable to aqueous solutions

2. Brønsted-Lowry Theory (1923)

• Acid: Proton (H⁺) donor
• Base: Proton (H⁺) acceptor
• Key Concept: Conjugate acid-base pairs

3. Lewis Theory (1923)

• Acid: Electron pair acceptor
• Base: Electron pair donor
• Advantage: Most general theory; includes non-proton reactions

Autoionization of Water

In pure water: [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ M

pH and pOH Scale

Solution Type	[H⁺] (M)	[OH⁻] (M)	pH	pOH	Nature
Strongly Acidic	1.0 × 10⁻¹	1.0 × 10⁻¹³	1	13	Acidic
Weakly Acidic	1.0 × 10⁻⁵	1.0 × 10⁻⁹	5	9	Acidic
Neutral	1.0 × 10⁻⁷	1.0 × 10⁻⁷	7	7	Neutral
Weakly Basic	1.0 × 10⁻⁹	1.0 × 10⁻⁵	9	5	Basic
Strongly Basic	1.0 × 10⁻¹³	1.0 × 10⁻¹	13	1	Basic

Salt Hydrolysis

Hydrolysis is the reaction of salt ions with water to produce acidic or basic solutions.

Types of Salts and Their Hydrolysis:

Salt Type	Formed From	Hydrolysis	pH of Solution	Example
Strong Acid + Strong Base	HCl + NaOH	No hydrolysis	pH = 7 (Neutral)	NaCl, KNO₃
Strong Acid + Weak Base	HCl + NH₄OH	Cation hydrolyzes	pH < 7 (Acidic)	NH₄Cl, CuSO₄
Weak Acid + Strong Base	CH₃COOH + NaOH	Anion hydrolyzes	pH > 7 (Basic)	CH₃COONa, KCN
Weak Acid + Weak Base	CH₃COOH + NH₄OH	Both ions hydrolyze	Depends on Kₐ & Kբ	CH₃COONH₄

Common Ion Effect

The suppression of dissociation of a weak electrolyte by adding a strong electrolyte containing a common ion.

Detailed pH Scale

The pH scale is a logarithmic scale used to specify the acidity or basicity of an aqueous solution. It ranges from 0 to 14, with 7 being neutral.

Buffer Solutions

A buffer solution resists changes in pH when small amounts of acid or base are added. It consists of a weak acid and its conjugate base, or a weak base and its conjugate acid.

Types of Buffer Solutions:

1. Acidic Buffer: Weak acid + salt of its conjugate base (e.g., CH₃COOH + CH₃COONa)
2. Basic Buffer: Weak base + salt of its conjugate acid (e.g., NH₃ + NH₄Cl)

Mechanism of Buffer Action:

For an acidic buffer (HA + A⁻):

• When acid (H⁺) is added: A⁻ + H⁺ → HA (conjugate base neutralizes added acid)
• When base (OH⁻) is added: HA + OH⁻ → A⁻ + H₂O (weak acid neutralizes added base)

Henderson-Hasselbalch Equation

For acidic buffer: HA ⇌ H⁺ + A⁻

For basic buffer: B + H₂O ⇌ BH⁺ + OH⁻

Buffer Capacity

Buffer capacity is the amount of acid or base that can be added before the buffer loses its ability to resist pH change.

Maximum buffer capacity occurs when [acid] = [salt] (or [base] = [salt]), i.e., when pH = pKₐ.

Applications of Buffer Solutions

• Biological systems: Blood (bicarbonate buffer), intracellular fluids
• Industrial processes: Fermentation, dyeing, photography
• Analytical chemistry: Calibration of pH meters
• Pharmaceuticals: Drug formulations to maintain stability
• Food industry: Preservation, flavor control

Solubility Product Constant (Ksp)

For a sparingly soluble salt, the solubility product constant (Ksp) is the equilibrium constant for the dissolution of the salt in water. It represents the maximum product of ion concentrations that can exist in a saturated solution.

Ionic Product (Qsp) and Precipitation

The ionic product Qsp has the same form as Ksp but is calculated using initial concentrations, not necessarily equilibrium concentrations.

Comparing Qsp and Ksp:

• If Qsp < Ksp: Solution is unsaturated. No precipitate forms. More salt can dissolve.
• If Qsp = Ksp: Solution is saturated. No net dissolution or precipitation.
• If Qsp > Ksp: Solution is supersaturated. Precipitation occurs until Qsp = Ksp.

Common Ion Effect on Solubility

The solubility of a sparingly soluble salt decreases in the presence of a common ion.

Factors Affecting Solubility

1. Common ion effect: Decreases solubility
2. Temperature: For endothermic dissolution, solubility increases with temperature; for exothermic dissolution, solubility decreases with temperature
3. Ionic strength: High ionic strength can increase solubility (salt effect)
4. pH: For salts of weak acids (like CaCO₃, Mg(OH)₂), solubility increases in acidic solutions
5. Complex formation: Formation of soluble complexes increases solubility (e.g., AgCl dissolves in NH₃ due to [Ag(NH₃)₂]⁺ formation)

Applications of Solubility Product

• Qualitative analysis: Separation and identification of cations in groups
• Purification of salts: By common ion effect
• Precipitation titrations: Argentometric titrations (Mohr's method)
• Preventing scale formation: In boilers and pipes
• Tooth decay prevention: Fluoride treatment forms less soluble CaF₂ on teeth
• Formation of stalactites and stalagmites: Due to solubility equilibrium of CaCO₃

Simultaneous Solubility and Selective Precipitation

When two salts share a common ion, they can be selectively precipitated by controlling the concentration of the common ion.