§ C-6 Chemical Equilibrium & Le Chatelier’s Principle (N₂O₄ ⇄ 2NO₂) (Grade 9–11 · Chemistry)
Dynamic equilibrium N₂O₄ ⇄ 2NO₂, equilibrium constant Kₚ & shifts under T and P. When a system at chemical equilibrium is subjected to an external change in temperature or pressure, the equilibrium shifts in the direction that counteracts the imposed change.
Theory Summary & Scientific Mechanism
Reversible chemical reactions proceed simultaneously in both forward and reverse directions. For the dinitrogen tetroxide / nitrogen dioxide system N₂O₄(g, colorless) ⇄ 2NO₂(g, brown) (Δ H^° = +57.2 kJ/mol), the law of mass action gives forward dissociation rate r_fwd = k₁[N₂O₄] and reverse dimerization rate rᵣev = k₂[NO₂]². Dynamic chemical equilibrium is reached when r_fwd = rᵣev > 0: macroscopic concentrations remain constant while molecular interconversion continues unabated.
The ratio of rate constants defines the equilibrium constant K_c(T) = (k₁)/(k₂) = ([NO₂]²)/([N₂O₄]), whose temperature dependence follows the Van ’t Hoff equation: (dln K)/(dT) = (Δ H^°)/(RT²). Because dissociation of N₂O₄ is endothermic (Δ H^° > 0), heating increases K_c(T) and shifts equilibrium toward brown paramagnetic NO₂ gas.
Le Chatelier’s principle states that when an equilibrium system is subjected to an external perturbation (change in T, P, or concentration), the system shifts in the direction that counteracts the perturbation. Since 1 mol of N₂O₄ gas produces 2 mol of NO₂ gas, increasing total pressure P shifts equilibrium to the left (toward fewer gas moles, lightening the mixture).
Everyday Analogy
Le Chatelier’s principle acts like a smart thermostat: heat the equilibrium mixture and it shifts toward the heat-absorbing endothermic reaction; compress the gas and it pairs molecules up (2NO₂ → N₂O₄) to relieve the pressure!
Interactive Question & Derivation
The forward dissociation N₂O₄(g) ⇄ 2NO₂(g) is endothermic (Δ H > 0) and increases gas moles (1 mol → 2 mol). Under what conditions does the gas mixture turn darkest brown (maximum NO₂ yield)?
- A: At higher temperature T (shifting equilibrium toward endothermic dissociation) and lower total pressure P (shifting equilibrium toward the side with more gas moles)
- B: At low temperature in an ice bath under high compression
- C: Neither temperature nor pressure affects the degree of dissociation α
Study Hint: Since N₂O₄ ⇄ 2NO₂ is endothermic (Δ H > 0) and doubles the number of gas molecules (1 mol → 2 mol), what combination of temperature T and pressure P maximizes brown NO₂ yield?
Proof & Explanation: By Le Chatelier’s principle, heating shifts the equilibrium in the endothermic direction (Δ H = +57.2 kJ/mol > 0), increasing Kₚ(T) via the van ’t Hoff equation. Lowering total pressure P favors the side with more gas molecules (2NO₂), increasing the dissociation degree α = √((Kₚ)/(Kₚ + 4P)) and deepening the brown color.
Key Equations & 3D Simulation Parameters
Kₚ(T) = exp ≤ft(-(Δ H^° - TΔ S^°)/(RT) ), α = √((Kₚ(T))/(Kₚ(T) + 4P))
- Thermostat temperature T (273 K = ice, 373 K = boiling): 260 … 390 K (default: 315 K)
- Total system pressure P: 0.25 … 4 atm (default: 1 atm)
- Initial N₂O₄ amount ν₀: 0.5 … 2 mol (default: 1 mol)