OCR A-Level Chemistry Periodic table, elements and physical chemistry (01), June 2023: Question 19

✅ Correct Answer

Kp Expression: p(N₂O₄) / (p(NO₂)²)

Units: atm⁻¹

Final Value: 1.17 × 10⁻² (to 3 significant figures)

💡 Key Knowledge

• Kp is formulated using equilibrium partial pressures, omitting square brackets (use ordinary parentheses or species symbols).
• Mole fraction = (moles of gas / total moles).
• Partial pressure = (mole fraction × total pressure).

📐 Step-by-Step Calculation

1. Find equilibrium moles:
   Initial NO₂ = 6.00 mol. Eqm NO₂ = 5.40 mol.
   Moles of NO₂ reacted = 6.00 − 5.40 = 0.60 mol.
   By stoichiometry (2 NO₂ ⇌ N₂O₄), moles of N₂O₄ formed = 0.60 / 2 = 0.30 mol .
   Total moles at equilibrium = 5.40 + 0.30 = 5.70 mol .
2. Calculate mole fractions & partial pressures:
   Total pressure = 5.00 atm.
   p(NO₂) = (5.40 / 5.70) × 5.00 = 4.7368... atm
   p(N₂O₄) = (0.30 / 5.70) × 5.00 = 0.26315... atm
3. Substitute into Kp and evaluate:
   Kp = 0.26315 / (4.7368)² = 0.011685... = 1.17 × 10⁻² .

❌ Common Errors

• Stoichiometry trap: Forgetting to divide the reacted moles of NO₂ by 2 to find N₂O₄ moles (a major error giving 0.6 mol N₂O₄ instead of 0.3 mol).
• Unit blunders: Using square brackets [ ] in the Kp expression or writing incorrect units like atm instead of atm⁻¹ .
• Rounding too early: Rounding intermediate partial pressures before final substitution, leading to rounding errors.

✅ Correct Answer

Higher temperature shifts equilibrium to the left (decreases yield of N₂O₄) because the forward reaction is exothermic ( ΔH = −57.4 kJ mol⁻¹ ).

Higher pressure shifts equilibrium to the right (increases yield of N₂O₄) because there are fewer moles of gas on the right-hand side (1 mole vs 2 moles).

Conclusion: It is difficult to predict the net change because the two factors oppose each other and their relative magnitudes are unknown.

🧠 Exam Technique

When an exam question asks you to explain why a prediction is "difficult" or "ambiguous", you must systematically analyse both applied changes independently, state the direction each drives the equilibrium position, and explicitly conclude that they oppose one another.

❌ Common Errors

• Stating that both shifts work in the same direction.
• Vaguely stating "it's too complicated" without referencing Le Chatelier's principle, enthalpy sign, or gas mole stoichiometry.

✅ Correct Answer

Molar mass: 108 g mol⁻¹ (or 108.5)

Molecular formula: N₂O₅

📐 Step-by-Step Calculation

1. Rearrange the ideal gas equation:
   pV = nRT → n = pV / RT
2. Convert units carefully:
   Pressure (p) = 101 kPa = 101 × 10³ Pa
   Volume (V) = 74.0 cm³ = 74.0 × 10⁻⁶ m³
   Temperature (T) = 75.0 °C + 273.15 = 348.15 K (or 348 K)
   Gas constant (R) = 8.314 J mol⁻¹ K⁻¹
3. Calculate moles (n):
   n = (101 × 10³ × 74.0 × 10⁻⁶) / (8.314 × 348) = 2.583 × 10⁻³ mol
4. Calculate Molar Mass (M):
   M = mass / moles = 0.280 g / (2.583 × 10⁻³ mol) = 108.39 g mol⁻¹ → 108 g mol⁻¹
5. Deduce Molecular Formula:
   Stem states: N₂O₄ reacts fully with oxygen to form a different oxide of nitrogen, oxide A.
   Oxides of nitrogen containing at least one N: N₂O₅ has Mr = (2 × 14.0) + (5 × 16.0) = 108.0 g mol⁻¹ .

❌ Common Errors

• Volume conversion disaster: Failing to convert cm³ to m³ using ×10⁻⁶ (using 24 dm³ or forgetting multipliers entirely).
• Pressure conversion omission: Forgetting to convert kPa to Pa ( ×10³ ).
• Temperature units: Forgetting to convert Celsius to Kelvin by adding 273.