Key Learning Objectives
- Interpret linear ΔG = -ΔS(T) + ΔH plots to determine ΔH (y-intercept) and ΔS (-gradient).
- Calculate feasibility across varying temperatures and explain why some endothermic reactions occur spontaneously at high T.
- Avoid recurring unit pitfalls between Joules and kiloJoules.
Topic Summary & Core Notes
Walk through challenging AQA and Edexcel past paper exam questions on entropy changes, enthalpy of solution, lattice enthalpies, and Gibbs free energy graphs (ΔG vs T).
Key Rules, Formulas & Definitions
Gibbs Linear Form
ΔG = (-ΔS)T + ΔH [y = mx + c; y-intercept = ΔH; gradient = -ΔS]
2 Step-by-Step Worked Examples
Worked Example 1
Worked Example 1: Finding ΔS from a ΔG vs T Graph
Question: A plot of ΔG versus T has a negative gradient of -0.150 kJ K⁻¹ mol⁻¹. Determine the value and unit of ΔS.
Step-by-Step Solution:
- Step 1: Relate to y = mx + c: In ΔG = ΔH - TΔS, gradient m = -ΔS.
- Step 2: Solve for ΔS: -ΔS = -0.150 kJ K⁻¹ mol⁻¹ → ΔS = +0.150 kJ K⁻¹ mol⁻¹.
- Step 3: Convert to standard units: 0.150 × 1,000 = +150 J K⁻¹ mol⁻¹.
Final Answer: +150 J K⁻¹ mol⁻¹
Senior Examiner Insight: Remember gradient is -ΔS; a negative slope means a POSITIVE entropy change.
Worked Example 2
Worked Example 2: Spontaneous Endothermic Dissolution
Question: Explain why ammonium nitrate dissolves endothermically in water spontaneously at room temperature.
Step-by-Step Solution:
- Step 1: Enthalpy change: ΔH > 0 (endothermic; absorbs heat, cooling the beaker).
- Step 2: Entropy change: Solid ionic lattice dissociates into freely moving hydrated ions; ΔS > 0 (large increase in disorder).
- Step 3: Gibbs equation: At 298 K, the TΔS term is larger than ΔH, making ΔG = ΔH - TΔS negative (feasible).
Final Answer: The huge increase in disorder when the crystal lattice breaks into hydrated ions creates a large positive ΔS, so TΔS > ΔH, making ΔG negative.
Senior Examiner Insight: Explicitly state that TΔS outweighs ΔH at room temperature.
Common Pitfalls & Examiner Warnings
Common Mistake: Assuming gradient equals ΔS
The gradient of a ΔG vs T plot equals -ΔS (negative entropy).
Interactive Self-Check Quiz (3 Questions)
Question 1 of 3
On a graph of ΔG (y-axis) against Temperature (x-axis), what does the y-intercept represent?
Click to Reveal Answer & Mark Scheme
Correct Answer: A) Standard Enthalpy Change (ΔH)
Detailed Explanation: At T = 0 K, ΔG = ΔH - 0 = ΔH, so the y-intercept equals ΔH.
Mark Scheme & Scoring Points: 1 mark for Standard Enthalpy Change (ΔH).
Question 2 of 3
If a reaction becomes feasible only at temperatures ABOVE 500 K, what must be true of ΔH and ΔS?
Click to Reveal Answer & Mark Scheme
Correct Answer: A) ΔH > 0 and ΔS > 0
Detailed Explanation: When both are positive, ΔG is positive at low T but becomes negative at high T as TΔS exceeds ΔH.
Mark Scheme & Scoring Points: 1 mark for ΔH > 0 and ΔS > 0.
Question 3 of 3
What is the value of ΔG when a system is at dynamic equilibrium?
Click to Reveal Answer & Mark Scheme
Correct Answer: A) 0 kJ/mol
Detailed Explanation: At dynamic equilibrium, forward and reverse reaction rates are equal and ΔG = 0.
Mark Scheme & Scoring Points: 1 mark for 0 kJ/mol.
Created by Fiaraz Iqbal
Former Headteacher & Senior Science / Maths Examiner
Fiaraz produces structured video walkthroughs, Tier 3 literacy packs, and exam mark scheme breakdowns to help secondary students achieve top grades.
Accelerate Your Academic Progress
Join tailored 1-to-1 or masterclass revision programmes with senior examiner insights.
Book a Free Consultation