UNIT 6: EQUILIBRIUM Meaning of equilibrium, the concept of dynamic equilibrium. Equilibria involving physical processes: Solid-liquid, liquid - gas and solid-gas equilibria, Henry's law. General characteristics of equilibrium involving physical processes. Equilibrium involving chemical processes: Law of chemical equilibrium, equilibrium constants (Kp and Kc) and their significance, the significance of G and G in chemical equilibrium, factors affecting equilibrium concentration, pressure, temperature, the effect of catalyst; Le Chatelier’s principle. Ionic equilibrium: Weak and strong electrolytes, ionization of electrolytes, various concepts of acids and bases (Arrhenius. Bronsted - Lowry and Lewis) and their ionization, acid-base equilibria (including multistage ionization) and ionization constants, ionization of water. pH scale, common ion effect, hydrolysis of salts and pH of their solutions, the solubility of sparingly soluble salts and solubility products, buffer solutions.
Reading File
This is a chemistry topic (Unit 6: Equilibrium), not a medical topic — the medical library skill doesn't apply here. I'll answer this comprehensively from my training knowledge.
UNIT 6: EQUILIBRIUM — Complete Study Notes
1. MEANING OF EQUILIBRIUM
Equilibrium is the state of a system in which all measurable properties (concentration, pressure, temperature, density, colour) remain constant over time, provided external conditions do not change.
Concept of Dynamic Equilibrium
In chemistry, equilibrium is dynamic, not static:
- Both the forward and reverse reactions continue to occur simultaneously.
- The rate of the forward reaction equals the rate of the reverse reaction.
- There is no net change in concentrations of reactants or products.
Key features:
- Only attainable in a closed system (no exchange of matter with surroundings).
- Equilibrium can be approached from either direction.
- At equilibrium, ΔG = 0 (Gibbs free energy change is zero).
2. EQUILIBRIA INVOLVING PHYSICAL PROCESSES
2.1 Solid–Liquid Equilibrium
Example: Ice ⇌ Water at 273 K (0°C) and 1 atm
$$\text{H}_2\text{O(s)} \rightleftharpoons \text{H}_2\text{O(l)}$$
- At the melting point, rate of melting = rate of freezing.
- Temperature remains constant as long as both phases coexist.
- This is the normal melting/freezing point.
2.2 Liquid–Gas Equilibrium
Example: Water ⇌ Water vapour in a closed container
$$\text{H}_2\text{O(l)} \rightleftharpoons \text{H}_2\text{O(g)}$$
- Vapour pressure builds up until the rate of evaporation = rate of condensation.
- At this point, saturated vapour pressure (SVP) is established.
- SVP depends only on temperature, not on the amount of liquid.
2.3 Solid–Gas Equilibrium
Example: Sublimation of iodine in a closed container
$$\text{I}_2\text{(s)} \rightleftharpoons \text{I}_2\text{(g)}$$
Another common example: Camphor sublimation.
Henry's Law
Governs the dissolution of gases in liquids:
"The mass of a gas dissolved in a given volume of solvent at constant temperature is directly proportional to the partial pressure of the gas above the solution."
$$p = K_H \cdot x$$
Where:
- $p$ = partial pressure of gas
- $x$ = mole fraction of gas in solution
- $K_H$ = Henry's law constant (specific to each gas-solvent pair at a given temperature)
Applications:
- Carbonated beverages (CO₂ dissolved under pressure).
- Deep-sea diving — N₂ dissolves in blood at high pressure → decompression sickness ("the bends").
- Oxygen supply from dissolved O₂ in aquatic systems.
Limitations: Valid only at low pressures and concentrations (ideal dilute solutions).
General Characteristics of Physical Equilibria
| Property | Description |
|---|---|
| System | Must be closed |
| Properties | Constant and measurable at macro level |
| Nature | Dynamic at molecular level |
| Temperature | Fixed (for a given equilibrium) |
| Equilibrium constant | Has a definite value at constant temperature |
3. EQUILIBRIUM INVOLVING CHEMICAL PROCESSES
3.1 Law of Chemical Equilibrium
For a general reversible reaction:
$$aA + bB \rightleftharpoons cC + dD$$
At equilibrium, the Law of Mass Action states:
$$K_c = \frac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b}$$
- $K_c$ = equilibrium constant in terms of molar concentrations
- Square brackets denote molar concentrations
- $K_c$ depends only on temperature
3.2 Equilibrium Constants: Kc and Kp
Kp is used when dealing with gases (concentrations expressed as partial pressures):
$$K_p = \frac{(p_C)^c(p_D)^d}{(p_A)^a(p_B)^b}$$
Relationship between Kc and Kp:
$$K_p = K_c(RT)^{\Delta n}$$
Where:
- $R$ = 0.0821 L·atm·mol⁻¹·K⁻¹
- $T$ = temperature in Kelvin
- $\Delta n$ = (moles of gaseous products) − (moles of gaseous reactants)
| Condition | Relationship |
|---|---|
| Δn = 0 | K |
| Δn > 0 | K |
| Δn < 0 | K |
Significance of Kc and Kp
- Large K (K >> 1): Equilibrium lies to the right; products are favoured.
- Small K (K << 1): Equilibrium lies to the left; reactants are favoured.
- K ≈ 1: Significant amounts of both reactants and products present.
- K predicts the direction a reaction will proceed and the extent of reaction.
- K is independent of initial concentrations and catalyst.
3.3 Reaction Quotient (Qc)
$$Q_c = \frac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b} \quad \text{(at any point, not necessarily equilibrium)}$$
| Comparison | Implication |
|---|---|
| Q | Reaction proceeds forward (→) |
| Q | Reaction proceeds backward (←) |
| Q | System is at equilibrium |
3.4 Significance of ΔG and ΔG°
Standard Gibbs free energy change (ΔG°):
$$\Delta G° = -RT \ln K$$
Or equivalently:
$$K = e^{-\Delta G°/RT}$$
| ΔG° | K | Implication |
|---|---|---|
| ΔG° < 0 | K > 1 | Products favoured at standard state |
| ΔG° > 0 | K < 1 | Reactants favoured at standard state |
| ΔG° = 0 | K = 1 | Neither strongly favoured |
Gibbs free energy change (ΔG) during reaction:
$$\Delta G = \Delta G° + RT \ln Q$$
At equilibrium, Q = K and ΔG = 0:
$$0 = \Delta G° + RT \ln K$$
$$\Delta G° = -RT \ln K$$
- ΔG < 0: Reaction is spontaneous in the forward direction.
- ΔG > 0: Reaction is non-spontaneous (reverse is spontaneous).
- ΔG = 0: System is at equilibrium — no net driving force.
4. FACTORS AFFECTING EQUILIBRIUM — LE CHATELIER'S PRINCIPLE
Le Chatelier's Principle: "If a system at equilibrium is subjected to a change in concentration, pressure, or temperature, the equilibrium shifts in the direction that tends to oppose the change and re-establish equilibrium."
4.1 Effect of Concentration
| Change | Shift Direction |
|---|---|
| Add reactant | Forward (→) |
| Remove reactant | Backward (←) |
| Add product | Backward (←) |
| Remove product | Forward (→) |
Note: K remains unchanged; only the position of equilibrium shifts.
4.2 Effect of Pressure (for gaseous reactions)
| Change | Shift Direction |
|---|---|
| Increase pressure (decrease volume) | Towards side with fewer moles of gas |
| Decrease pressure (increase volume) | Towards side with more moles of gas |
| Δn = 0 | No effect on equilibrium position |
Example:
$$\text{N}_2\text{(g)} + 3\text{H}_2\text{(g)} \rightleftharpoons 2\text{NH}_3\text{(g)} \quad (\Delta n = 2 - 4 = -2)$$
Increasing pressure → shifts right (fewer gas moles) → more NH₃.
4.3 Effect of Temperature
Uses Van't Hoff's equation:
$$\ln\frac{K_2}{K_1} = \frac{\Delta H°}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)$$
| Reaction Type | Increase Temperature | Decrease Temperature |
|---|---|---|
| Exothermic (ΔH < 0) | K decreases (←) | K increases (→) |
| Endothermic (ΔH > 0) | K increases (→) | K decreases (←) |
Unlike concentration and pressure changes, temperature changes alter the value of K.
4.4 Effect of Catalyst
- A catalyst lowers the activation energy of both forward and reverse reactions equally.
- It does not change K, the position of equilibrium, or the equilibrium concentrations.
- It only speeds up the attainment of equilibrium.
4.5 Addition of Inert Gas
- At constant volume: No effect (partial pressures of reactants/products unchanged).
- At constant pressure: Total pressure maintained by inert gas → partial pressures of reactants/products decrease → shifts towards more moles of gas.
5. IONIC EQUILIBRIUM
5.1 Electrolytes
| Type | Description | Examples |
|---|---|---|
| Strong electrolytes | Completely dissociate in water | HCl, H₂SO₄, HNO₃, NaOH, KOH, NaCl |
| Weak electrolytes | Partially dissociate; exist in equilibrium | CH₃COOH, NH₄OH, H₂CO₃, HF |
5.2 Concepts of Acids and Bases
Arrhenius Concept (1884)
- Acid: Substance that produces H⁺ ions in water.
- Base: Substance that produces OH⁻ ions in water.
- Limitation: Restricted to aqueous solutions; cannot explain NH₃ as a base.
Brønsted–Lowry Concept (1923)
- Acid: Proton (H⁺) donor.
- Base: Proton (H⁺) acceptor.
- Introduces the concept of conjugate acid-base pairs.
$$\underbrace{\text{HCl}}{\text{acid}} + \underbrace{\text{H}2\text{O}}{\text{base}} \rightleftharpoons \underbrace{\text{H}3\text{O}^+}{\text{conj. acid}} + \underbrace{\text{Cl}^-}{\text{conj. base}}$$
Conjugate pair: Acid and its conjugate base differ by one H⁺.
| Acid | Conjugate Base |
|---|---|
| HCl | Cl⁻ |
| CH₃COOH | CH₃COO⁻ |
| H₂O | OH⁻ |
| NH₄⁺ | NH₃ |
Lewis Concept (1923)
- Acid: Electron pair acceptor (Lewis acid).
- Base: Electron pair donor (Lewis base).
- Broadest concept — covers reactions without proton transfer.
Examples:
- BF₃ (Lewis acid) + NH₃ (Lewis base) → BF₃·NH₃
- Cu²⁺ + 4NH₃ → [Cu(NH₃)₄]²⁺
5.3 Ionization of Weak Acids
For a weak acid HA:
$$\text{HA} \rightleftharpoons \text{H}^+ + \text{A}^-$$
$$K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}$$
Degree of ionization (α): Fraction of acid molecules that ionize.
For a weak acid at concentration C:
$$[\text{H}^+] = \sqrt{K_a \cdot C}$$
$$\alpha = \sqrt{\frac{K_a}{C}}$$
Ostwald's Dilution Law: α increases with dilution.
$$K_a \approx C\alpha^2 \quad (\text{when } \alpha << 1)$$
5.4 Ionization of Weak Bases
For a weak base BOH (e.g., NH₄OH):
$$\text{BOH} \rightleftharpoons \text{B}^+ + \text{OH}^-$$
$$K_b = \frac{[\text{B}^+][\text{OH}^-]}{[\text{BOH}]}$$
$$[\text{OH}^-] = \sqrt{K_b \cdot C}$$
5.5 Ionization of Water
$$\text{H}_2\text{O} \rightleftharpoons \text{H}^+ + \text{OH}^-$$
$$K_w = [\text{H}^+][\text{OH}^-] = 1.0 \times 10^{-14} \text{ at } 25°C$$
- Pure water: [H⁺] = [OH⁻] = 10⁻⁷ mol/L
- K
wincreases with temperature (ionization is endothermic).
Relationship:
$$pK_w = pH + pOH = 14 \text{ at } 25°C$$
Relation between Ka, Kb, and Kw:
$$K_a \times K_b = K_w$$
$$pK_a + pK_b = pK_w = 14$$
5.6 pH Scale
$$\text{pH} = -\log_{10}[\text{H}^+]$$
$$\text{pOH} = -\log_{10}[\text{OH}^-]$$
| Solution | pH |
|---|---|
| Neutral (at 25°C) | pH = 7 |
| Acidic | pH < 7 |
| Basic | pH > 7 |
Quick pH calculations:
- Strong acid: [H⁺] = C → pH = −log C
- Strong base: [OH⁻] = C → pOH = −log C → pH = 14 − pOH
- Weak acid: [H⁺] = √(K
a·C) → pH = ½(pKa− log C)
5.7 Multi-stage (Polyprotic) Ionization
Example: H₂SO₄, H₃PO₄, H₂CO₃
For H₂CO₃:
$$\text{H}_2\text{CO}_3 \rightleftharpoons \text{H}^+ + \text{HCO}3^- \quad K{a1} = 4.3 \times 10^{-7}$$
$$\text{HCO}_3^- \rightleftharpoons \text{H}^+ + \text{CO}3^{2-} \quad K{a2} = 4.8 \times 10^{-11}$$
- K
a1>> Ka2>> Ka3: Each successive ionization is much weaker. - [H⁺] is primarily determined by the first ionization step.
5.8 Common Ion Effect
The suppression of ionization of a weak electrolyte by adding a strong electrolyte with a common ion.
Example: Adding NaCl to a CH₃COOH solution:
$$\text{CH}_3\text{COOH} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}^+$$
Adding CH₃COONa (→ CH₃COO⁻) shifts equilibrium left → less ionization → lower [H⁺] → higher pH.
Applications:
- Buffer solutions
- Precipitation of ions
- Salting out of soaps
5.9 Hydrolysis of Salts
Reaction of the cation or anion of a salt with water:
| Salt Type | Composition | Hydrolysis | pH |
|---|---|---|---|
| Strong acid + Strong base | NaCl | No hydrolysis | 7 |
| Weak acid + Strong base | CH₃COONa | Anionic hydrolysis | > 7 (basic) |
| Strong acid + Weak base | NH₄Cl | Cationic hydrolysis | < 7 (acidic) |
| Weak acid + Weak base | CH₃COONH₄ | Both hydrolyse | ≈ 7 (depends on K |
For salt of weak acid + strong base (e.g., CH₃COONa):
$$\text{CH}_3\text{COO}^- + \text{H}_2\text{O} \rightleftharpoons \text{CH}_3\text{COOH} + \text{OH}^-$$
$$K_h = \frac{K_w}{K_a}$$
$$\text{pH} = 7 + \frac{1}{2}(\text{p}K_a + \log C)$$
For salt of strong acid + weak base (e.g., NH₄Cl):
$$\text{NH}_4^+ + \text{H}_2\text{O} \rightleftharpoons \text{NH}_4\text{OH} + \text{H}^+$$
$$\text{pH} = 7 - \frac{1}{2}(\text{p}K_b + \log C)$$
5.10 Solubility Product (Ksp)
For a sparingly soluble salt MxAy:
$$\text{M}_x\text{A}_y\text{(s)} \rightleftharpoons x\text{M}^{n+} + y\text{A}^{m-}$$
$$K_{sp} = [\text{M}^{n+}]^x[\text{A}^{m-}]^y$$
Relationship between solubility (s) and Ksp:
| Salt | Equilibrium | K |
|---|---|---|
| AB (e.g., AgCl) | [A⁺][B⁻] = s·s | s² |
| AB₂ (e.g., PbCl₂) | [A²⁺][B⁻]² = s·(2s)² | 4s³ |
| A₂B₃ (e.g., Bi₂S₃) | [A³⁺]²[B²⁻]³ | 108s⁵ |
Precipitation condition:
- If ionic product (IP) > K
sp→ precipitation occurs. - If IP < K
sp→ solution is unsaturated (no precipitate). - If IP = K
sp→ saturated solution (equilibrium).
Effect of common ion on solubility:
Adding a common ion decreases the solubility of the sparingly soluble salt (common ion effect).
Example: AgCl solubility in 0.1 M NaCl:
$$s = \frac{K_{sp}}{[\text{Cl}^-]} = \frac{1.8 \times 10^{-10}}{0.1} = 1.8 \times 10^{-9} \text{ mol/L}$$
5.11 Buffer Solutions
A buffer resists change in pH on addition of small amounts of acid or base.
Types:
- Acidic buffer: Weak acid + its conjugate base (salt with strong base)
- Example: CH₃COOH + CH₃COONa
- Basic buffer: Weak base + its conjugate acid (salt with strong acid)
- Example: NH₄OH + NH₄Cl
Henderson–Hasselbalch Equation:
$$\text{pH} = \text{p}K_a + \log\frac{[\text{Salt}]}{[\text{Acid}]}$$
$$\text{pOH} = \text{p}K_b + \log\frac{[\text{Salt}]}{[\text{Base}]}$$
Buffer capacity: Maximum when [Salt] = [Acid] → pH = pKa. Effective range: pH = pKa ± 1.
Applications:
- Blood pH maintenance (carbonate-bicarbonate buffer, pH ≈ 7.4).
- Industrial and pharmaceutical processes.
- Enzymatic reactions in biological systems.
SUMMARY TABLE: KEY CONSTANTS
| Quantity | Formula | Notes |
|---|---|---|
| K | [products]/[reactants] | Molar concentrations |
| K | (partial pressures) | K |
| K | [H⁺][OH⁻] | 10⁻¹⁴ at 25°C |
| K | [H⁺][A⁻]/[HA] | Acid dissociation |
| K | [B⁺][OH⁻]/[BOH] | Base dissociation |
| K | [M^n+^]^x^[A^m-^]^y^ | Sparingly soluble salts |
| K | K | Salt hydrolysis |
| K | p/x | Henry's law |
These notes cover the complete syllabus for Unit 6. Let me know if you'd like deeper worked examples, numerical problems, or a focus on any specific subtopic.
This is a shared conversation. Sign in to Orris to start your own chat.