Chemical Equilibrium

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Chemical Equilibrium — Key Facts for MDCAT

Key Definitions:

• Reversible reaction: Can proceed in both forward and backward directions
• Equilibrium: Rate of forward reaction = Rate of reverse reaction; concentrations of reactants and products remain CONSTANT (not equal) with time
• Dynamic equilibrium: Both forward and reverse reactions continue indefinitely; macroscopic properties are static but microscopic processes continue

Law of Mass Action: For a general reaction: $aA + bB \rightleftharpoons cC + dD$ $$K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b} \text{ (at equilibrium)}$$ Where $[A]$, $[B]$, $[C]$, $[D]$ are molar concentrations at equilibrium.

Equilibrium Constant ($K_c$):

• $K_c >> 1$ (typically > 10³): Products are favoured; reaction lies to the right
• $K_c << 1$ (typically < 10⁻³): Reactants are favoured; reaction lies to the left
• $K_c ≈ 1$: Neither reactants nor products are strongly favoured

For gaseous reactions, use partial pressures: $$K_p = \frac{P_C^c \cdot P_D^d}{P_A^a \cdot P_B^b}$$ Relationship: $K_p = K_c(RT)^{\Delta n}$ where $\Delta n = (c+d) - (a+b)$

⚡ Exam tip: Only gaseous species and aqueous species appear in the $K$ expression. Pure solids and pure liquids are NOT included (their activities = 1). For the reaction $CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)$, $K_p = P_{CO_2}$ only. MDCAT commonly tests this distinction.

---

🟡 Standard — Regular Study (2d–2mo)

Standard content for students who want genuine understanding.

Chemical Equilibrium — Complete Study Guide

Le Chatelier’s Principle: If a system at equilibrium is subjected to a change in concentration, temperature, pressure, or volume, the system will shift to partially counteract the change and establish a new equilibrium.

Change	Effect
Increase [reactants]	Shift right (towards products)
Decrease [reactants]	Shift left (towards reactants)
Increase temperature (endothermic)	Shift right
Increase temperature (exothermic)	Shift left
Increase pressure (gas reactions)	Shift towards fewer moles of gas
Decrease pressure	Shift towards more moles of gas
Catalyst added	No shift — only speeds up attainment of equilibrium

Effect of Pressure on Equilibrium: For $N_2O_4(g) \rightleftharpoons 2NO_2(g)$:

• Reactant side: 1 mole gas; Product side: 2 moles gas
• Increasing pressure → shift LEFT (towards fewer gas moles)
• The equilibrium constant $K$ itself does NOT change with pressure — only the position shifts

Relation between $K$ and $K_{sp}$ (Solubility Product): For the dissolution equilibrium: $MX(s) \rightleftharpoons M^{n+}(aq) + X^{n-}(aq)$ $$K_{sp} = [M^{n+}][X^{n-}]$$ Precipitation occurs when the ion product (IP) > $K_{sp}$.

Reaction Quotient ($Q$): $$Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}$$

• If $Q < K$: Reaction shifts right (towards products) to reach equilibrium
• If $Q > K$: Reaction shifts left (towards reactants) to reach equilibrium
• If $Q = K$: System is at equilibrium

Important Equilibria in Industry:

• Haber process: $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$, $\Delta H = -92$ kJ/mol (exothermic)

  • Low temperature favours products BUT slow at low T → compromise at ~400–500°C with catalyst
  • High pressure favours products (4 → 2 moles) → high pressure (~200 atm)
  • Iron catalyst speeds up without affecting equilibrium position

• Contact process: $2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)$, $\Delta H = -197$ kJ/mol

  • V$_2$O$_5$ catalyst for sulfuric acid manufacture

⚡ Common mistakes: Thinking equilibrium means equal concentrations (wrong — only rates are equal). Adding a catalyst and expecting the equilibrium position to shift (it doesn’t — only speeds up reaching equilibrium). Confusing $K_c$ units with $K_p$ — $K_c$ has units of (mol/L)$^{\Delta n}$, $K_p$ has units of atm$^{\Delta n}$.

---

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Chemical Equilibrium — Advanced Notes

Thermodynamic Derivation of Equilibrium Constant: $$\Delta G = \Delta G^\circ + RT\ln Q$$ At equilibrium: $\Delta G = 0$, $Q = K$ $$\therefore \Delta G^\circ = -RT\ln K$$ Also: $\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$

This links thermodynamics (Gibbs energy) with the equilibrium constant. A negative $\Delta G^\circ$ means $K > 1$.

Van’t Hoff Equation (Temperature Dependence of $K$): $$\frac{d\ln K}{dT} = \frac{\Delta H^\circ}{RT^2}$$ Integrating: $\ln\frac{K_2}{K_1} = \frac{\Delta H^\circ}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)$

• For exothermic reactions ($\Delta H < 0$): Increasing $T$ → $K$ decreases
• For endothermic reactions ($\Delta H > 0$): Increasing $T$ → $K$ increases

Degree of Dissociation ($\alpha$): For $PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)$: Let initial moles of $PCl_5 = 1$, degree of dissociation = $\alpha$ At equilibrium: $[PCl_5] = (1-\alpha)V$, $[PCl_3] = \alpha/V$, $[Cl_2] = \alpha/V$ $$K_p = \frac{\alpha^2 P}{(1-\alpha)-\alpha^2} \text{ (for 1 atm initial)}$$

Simultaneous/Homogeneous vs Heterogeneous Equilibrium:

• Homogeneous: All species in same phase (usually gas)
• Heterogeneous: Species in different phases (e.g., solid + gas)
  • For $CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)$: $K_p = P_{CO_2}$
  • Activities of pure solids and liquids = 1, so they don’t appear in $K$ expression

Buffer Solutions and Equilibrium: The pH of a buffer containing a weak acid HA and its salt NaA: $$K_a = \frac{[H^+][A^-]}{[HA]} \Rightarrow [H^+] = K_a \frac{[HA]}{[A^-]}$$ Henderson-Hasselbalch: $pH = pK_a + \log\frac{[\text{salt}]}{[\text{acid}]}$

Salt Hydrolysis and $K_h$: For salt of weak acid and strong base (e.g., CH$_3$COONa): $$K_h = \frac{K_w}{K_a}$$ Degree of hydrolysis $h = \sqrt{\frac{K_h}{C}}$ where $C$ is concentration.

Common Ion Effect: The suppression of dissociation of a weak electrolyte by adding a strong electrolyte containing a common ion. Example: Adding NaOH (Na⁺, OH⁻) to NH₃/NH₄⁺ buffer shifts the equilibrium.

MDCAT Question Patterns: MDCAT Pakistan chemical equilibrium questions frequently test: (1) writing $K_c$ and $K_p$ expressions correctly (excluding solids/liquids), (2) Le Chatelier’s principle applications to Haber process, (3) calculating equilibrium concentrations, (4) relationship between $K_p$ and $K_c$, (5) using $Q$ to predict direction of shift, (6) van’t Hoff equation for temperature effects. 2–3 questions per paper. Le Chatelier’s principle in industrial contexts (ammonia synthesis) is very common.

---

Content adapted based on your selected roadmap duration. Switch tiers using the pill selector above.