6.2.13Additional lessons
Gibbs Energy and Standard Cell Potential — IB Chemistry HL Revision Notes & Topical Questions
5 min read 5 parts Lesson 144 of 172
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Part 1 of 5The Link
The electrical work a cell can do is the maximum useful energy from the reaction.
Energy and voltage
- Energy and voltage A positive cell potential corresponds to a negative Gibbs energy change, so both show a spontaneous reaction.
Formula
- Formula ΔG° = −nFE°, where n is the number of moles of electrons transferred and F is 96 500 C mol⁻¹.
Units
- Units With E° in volts and F in C mol⁻¹ the answer is in joules per mole, and it is usually quoted in kJ mol⁻¹.
Meaning of n
- Meaning of n n is taken from the balanced equation, so a reaction transferring two electrons has n = 2.
Part 2 of 5Linking to Equilibrium
1
The Gibbs energy change also relates to the equilibrium constant by ΔG° = −RT ln K.
2
Combine this with ΔG° = −nFE° to obtain nFE° = RT ln K.
3
A large positive E° therefore gives a large K, and the position of equilibrium lies far to the right.
4
A negative E° gives a K smaller than one, so the reactants are favoured at equilibrium.
5
When E° is zero, ΔG° is zero and K equals one.
| E°cell | ΔG° | K | Reaction |
|---|---|---|---|
| Positive | Negative | Greater than 1 | Spontaneous |
| Zero | Zero | Equal to 1 | At equilibrium |
| Negative | Positive | Less than 1 | Not spontaneous |
Part 3 of 5Applying the Relationship
Applying the Relationship
Data booklet
- Data booklet F = 96 500 C mol⁻¹ and R = 8.31 J K⁻¹ mol⁻¹ are given, with T taken as 298 K for standard values.
Unit care
- Unit care Convert kJ to J before using ΔG° in ΔG° = −RT ln K, because R is in joules.
Many electrons
- Many electrons More electrons transferred means a larger magnitude of ΔG° for the same E°.
Reversal
- Reversal Reversing a reaction changes the sign of E° and of ΔG°, and K becomes its reciprocal.
Part 4 of 5Worked Example
Question
- Calculate ΔG° for the cell reaction Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s), where E°cell = +1.10 V, and estimate K at 298 K.
- (F = 96 500 C mol⁻¹;
- R = 8.31 J K⁻¹ mol⁻¹)
- Two electrons are transferred, so n = 2.
- ΔG° = −nFE° = −2 × 96 500 × 1.10 = −212 300 J mol⁻¹ = −212 kJ mol⁻¹.
- ln K = −ΔG°/RT = 212 300 ÷ (8.31 × 298) = 85.7, so K = e85.7 ≈ 1.7 × 10³⁷.
Answer ΔG° = −212 kJ mol⁻¹ and K ≈ 1.7 × 10³⁷, so the reaction goes essentially to completion.
Part 5 of 5Exam Checklist & Tips
6.2.13 – Key Points for the Exam
- Gibbs energy change The energy change that determines spontaneity, ΔG, with ΔG° at standard conditions.
- Faraday constant The charge of one mole of electrons, 96 500 C mol⁻¹.
- Equilibrium constant K, the ratio of product to reactant concentrations at equilibrium.
- Moles of electrons The number n of electrons transferred in the balanced equation.
Common Mistakes
- Forgetting the negative sign in ΔG° = −nFE° and getting a positive ΔG° for a feasible cell.
- Mixing kJ and J when using ΔG° with the gas constant.
- Using the wrong n, for instance one electron when two are transferred.
- Believing a large E° means the reaction rate is large rather than K.
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Cambridge 9700 AS Biology
Core Formula
Magnification Triangle & Unit Conversion
Formula: M = I / A ⇔ A = I / M ⇔ I = M × A
Units: 1 mm = 1,000 μm = 1,000,000 nm.
Rule: Convert Image size (ruler mm) to μm by ×1,000 before dividing by Actual size.