Chemistry • Year 11 • Module 4 • Lesson 13

Gibbs Free Energy & Spontaneity

Lock in the ΔG = ΔH − TΔS equation, the spontaneity criteria, the 2×2 sign combinations, and the crossover temperature concept.

Build • Band 3–4 • Vocab & Core Concepts

1. Term–definition match

The ten definitions below are shuffled. In the right-hand column write the matching term from this list: Gibbs free energy (ΔG), spontaneous reaction, non-spontaneous reaction, equilibrium (ΔG = 0), enthalpy (ΔH), entropy (ΔS), crossover temperature (Tcross), TΔS term, standard conditions, thermodynamic favourability. 10 marks

#Definition (shuffled)Matching term
1.1A thermodynamic potential defined by ΔG = ΔH − TΔS that determines whether a process is thermodynamically favourable at constant temperature and pressure.
1.2A process that can occur without continuous external energy input; ΔG < 0.
1.3A process that requires a continuous input of energy to proceed; ΔG > 0 and the reverse reaction is thermodynamically favoured.
1.4The state at which forward and reverse reactions occur at equal rates; ΔG = 0 and there is no net change in composition.
1.5The heat energy exchanged with surroundings at constant pressure; negative for exothermic reactions, positive for endothermic.
1.6A measure of the dispersal of energy and matter in a system; increases (positive) when products are more disordered than reactants.
1.7The temperature at which ΔG changes sign; calculated as ΔH ÷ ΔS (with ΔS in kJ K−1 mol−1).
1.8The temperature-scaled entropy contribution in ΔG = ΔH − TΔS; this term grows larger at higher temperatures and can flip the sign of ΔG.
1.925°C (298 K) and 100 kPa — the reference state at which ΔG°, ΔH° and ΔS° values are tabulated.
1.10A property of a reaction that indicates whether it can proceed in the forward direction based solely on thermodynamics, independent of how fast it actually occurs.
Stuck? Review the Key Terms panel and Card 1 of Lesson 13.

2. True or false — correct the false statements

Decide whether each statement is True or False. If false, write a corrected version on the line provided. 12 marks

2.1 “Spontaneous means the reaction happens quickly.” 2 marks

T  /  F    Corrected statement:

2.2 “A reaction with ΔH < 0 and ΔS > 0 is spontaneous at all temperatures.” 2 marks

T  /  F    Corrected statement (if needed):

2.3 “When ΔG = 0 the reaction has stopped completely.” 2 marks

T  /  F    Corrected statement:

2.4 “The TΔS term becomes less important at very high temperatures.” 2 marks

T  /  F    Corrected statement:

2.5 “To calculate ΔG, the entropy value must be converted from J K−1 mol−1 to kJ K−1 mol−1 before substitution.” 2 marks

T  /  F    Corrected statement (if needed):

2.6 “A reaction with ΔH > 0 and ΔS < 0 can become spontaneous at very high temperatures.” 2 marks

T  /  F    Corrected statement:

3. Complete the ΔH / ΔS sign combination table

Fill in the missing cells in the table below. Use the formula ΔG = ΔH − TΔS to reason through each combination. 12 marks

Case ΔH sign ΔS sign Sign of TΔS term Spontaneous? Temperature effect
A Negative (exothermic) Positive (disorder increases)
B Positive (endothermic) Negative (disorder decreases)
C Negative (exothermic) Negative (disorder decreases)
D Positive (endothermic) Positive (disorder increases)
Hint: In case C and D the TΔS term changes size with temperature — that’s the key to both answers.

4. Cloze — fill the blanks

Complete the paragraph using words from the word bank below. Each word is used once only. 8 marks

Word bank: spontaneous  •  equilibrium  •  crossover  •  Kelvin  •  non-spontaneous  •  1000  •  negative  •  kinetics

The Gibbs free energy equation, ΔG = ΔH − TΔS, combines enthalpy and entropy into a single value that predicts whether a reaction is thermodynamically ______________. Before substituting, temperature must be converted to ______________ and ΔS must be divided by ______________ to convert from J K−1 mol−1 to kJ K−1 mol−1. If ΔG is ______________, the forward reaction is spontaneous. When ΔG = 0, the system is at ______________. If ΔG > 0, the reaction is ______________ in the forward direction. The temperature at which ΔG changes sign is called the ______________ temperature. Importantly, a negative ΔG says nothing about the rate of reaction — that depends on ______________.

5. Concept map — link the key terms

The six term chips below are drawn from Lesson 13. Draw labelled arrows between them to show how they are connected. Aim for at least six labelled connections. 6 marks

ΔG ΔH TΔS Spontaneous Tcross Temperature (K)

Draw your labelled arrows here or in your exercise book.

6. Function recall — short prose

Answer each prompt in 1–2 sentences. 6 marks

6.1 What does the TΔS term represent in ΔG = ΔH − TΔS, and why does it become more important at high temperatures? 2 marks

6.2 What is the crossover temperature, and what happens to the spontaneity of a reaction at exactly Tcross? 2 marks

6.3 Why do chemists say that “spontaneous does not mean fast”? Give a named example to support your answer. 2 marks

Answer Key

Section 1 — Term–definition match (10 marks, 1 mark each)

1.1 Gibbs free energy (ΔG)  •  1.2 Spontaneous reaction  •  1.3 Non-spontaneous reaction  •  1.4 Equilibrium (ΔG = 0)  •  1.5 Enthalpy (ΔH)  •  1.6 Entropy (ΔS)  •  1.7 Crossover temperature (Tcross)  •  1.8 TΔS term  •  1.9 Standard conditions  •  1.10 Thermodynamic favourability

Section 2 — True / False (2 marks each)

2.1 FALSE. Spontaneous means thermodynamically favourable (ΔG < 0), not fast. Rate is governed by kinetics and activation energy, not by ΔG. Example: diamond converting to graphite is spontaneous but takes millions of years.

2.2 TRUE. When ΔH < 0 and ΔS > 0, ΔG = ΔH − T(+) = (negative) − (positive) = always negative at any T. No correction needed.

2.3 FALSE. When ΔG = 0 the system is at equilibrium — forward and reverse reactions proceed at equal rates. The reaction has not stopped.

2.4 FALSE. At very high temperatures the TΔS term (= T × ΔS) grows larger, not smaller, because T is multiplied directly. The TΔS term dominates ΔG at high T.

2.5 TRUE. ΔS in J K−1 mol−1 must be divided by 1000 before substituting into ΔG (kJ mol−1) to avoid a 1000× error. No correction needed.

2.6 FALSE. When ΔH > 0 and ΔS < 0, ΔG = (+) − T(−) = (+) + (+) = always positive at every temperature. This combination is never spontaneous at any temperature.

Section 3 — 2×2 table (3 marks each case)

Case A (ΔH < 0, ΔS > 0): TΔS sign = positive; Spontaneous: Always spontaneous; Temperature effect: more spontaneous at higher T.

Case B (ΔH > 0, ΔS < 0): TΔS sign = negative; Spontaneous: Never spontaneous; Temperature effect: sign of ΔG never changes.

Case C (ΔH < 0, ΔS < 0): TΔS sign = negative; Spontaneous: Spontaneous at low T only; Temperature effect: becomes non-spontaneous above Tcross = ΔH/ΔS. Haber process is the key example.

Case D (ΔH > 0, ΔS > 0): TΔS sign = positive; Spontaneous: Spontaneous at high T only; Temperature effect: becomes spontaneous above Tcross. Limestone decomposition is the key example.

Section 4 — Cloze (1 mark each blank, 8 marks)

In order: spontaneous → Kelvin → 1000 → negative → equilibrium → non-spontaneous → crossover → kinetics

Section 5 — Concept map (1 mark per valid labelled arrow, 6 marks)

Accept any six of: ΔH + ΔS → “combined by ΔG formula” → ΔG; ΔG < 0 → “means” → Spontaneous; TΔS grows with → “increasing” → Temperature (K); Tcross = “ΔH divided by ΔS”; Tcross → “where ΔG = 0”; Spontaneous does NOT equal “fast kinetics”.

Section 6 — Function recall (2 marks each)

6.1 1 mark: TΔS is the entropy-temperature product that represents the energy dispersal contribution to ΔG. 1 mark: As T increases, TΔS grows larger (multiplied directly by T), so at high temperatures the entropy term dominates the sign of ΔG.

6.2 1 mark: Tcross = ΔH/ΔS is the temperature at which ΔG = 0. 1 mark: At exactly Tcross the system is at equilibrium — the reaction neither favours products nor reactants under standard conditions.

6.3 1 mark: ΔG predicts thermodynamic favourability; the rate of a reaction is controlled by kinetics (activation energy and collision frequency), which is independent of ΔG. 1 mark: Valid named example, e.g. diamond → graphite (ΔG < 0 but rate essentially zero), or Haber process at 25°C (spontaneous but kinetically frozen).