Relate Faraday, Avogadro and electron charge
Use F = Le to connect charge per mole of electrons, the Avogadro constant and the charge on one electron.
A Level; Cambridge International Chemistry 9701, 2028–2030 syllabus, Topic 24. Treat all tabulated electrode potentials as reduction potentials; state conditions, phases, signs and units. Written practice is self-checked
Before you begin
- Use AS redox half-equations, oxidation states, mole ratios, current and charge.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What does F represent?
What you will learn
- State the relationship F = Le
- Use the electron charge and Avogadro constant to calculate F
- Use consistent coulomb and mole units
One mole of electrons carries one Faraday of charge
The Faraday constant F is the charge carried by one mole of electrons. The Avogadro constant L counts electrons in one mole, and e is the magnitude of the charge on one electron, so F = Le.
Using L ≈ 6.02 × 10²³ mol⁻¹ and e ≈ 1.60 × 10⁻¹⁹ C gives F ≈ 9.63 × 10⁴ C mol⁻¹; the syllabus value is about 9.65 × 10⁴ C mol⁻¹. Keep the electron-charge magnitude positive when calculating F.
Rearrange before substituting
Use F = Le to find any one quantity when the other two are known: L = F/e and e = F/L. The unit check is C mol⁻¹ = mol⁻¹ × C.
F is not a current; it is charge per mole of electrons. Current I is charge per second, so a measured charge Q is connected to moles of electrons through Q/F.
Pause and explain
Which equation relates F, L and e?
Worked example
Calculate F using L = 6.02 × 10²³ mol⁻¹ and e = 1.60 × 10⁻¹⁹ C.
Show the worked solution
- Use F = Le.
- Multiply the powers of ten: 10²³ × 10⁻¹⁹ = 10⁴.
- Include coulombs per mole.
Answer F = (6.02 × 10²³)(1.60 × 10⁻¹⁹) = 9.63 × 10⁴ C mol⁻¹.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Calculate F from L = 6.02 × 10²³ mol⁻¹ and e = 1.60 × 10⁻¹⁹ C.
Give me a hint
Multiply L by the magnitude of e and combine powers of ten.
Compare my reasoning
- Multiply 6.02 by 1.60.
- Combine 10²³ and 10⁻¹⁹.
- State C mol⁻¹.
F = 9.63 × 10⁴ C mol⁻¹, approximately 9.65 × 10⁴ C mol⁻¹ at the syllabus precision.
Look for these in your work
- Values multiplied
- Power of ten correct
- Unit stated
Use F = 9.65 × 10⁴ C mol⁻¹ and e = 1.60 × 10⁻¹⁹ C to estimate L.
Give me a hint
Rearrange F = Le to make L the subject.
Compare my reasoning
- L = F/e.
- Substitute the values with units.
- Check that the result has units mol⁻¹.
L = (9.65 × 10⁴)/(1.60 × 10⁻¹⁹) ≈ 6.03 × 10²³ mol⁻¹.
Look for these in your work
- Formula rearranged
- Powers of ten handled
- Avogadro constant unit correct
A student says F = 9.65 × 10⁴ A because current is used in electrolysis. Explain the unit correction.
Give me a hint
Distinguish charge from charge per time.
Compare my reasoning
- F is charge per mole of electrons.
- Its unit is C mol⁻¹.
- Current I has unit A = C s⁻¹.
F is about 9.65 × 10⁴ C mol⁻¹, not amperes. Current is charge per second; the Faraday constant is charge per mole of electrons.
Look for these in your work
- Quantity distinguished
- Correct unit supplied
- Current unit contrasted
Common mistakes
- Using the negative sign of an electron's charge when calculating the magnitude F
- Confusing F with current
- Dropping the mol⁻¹ unit
- Using inconsistent powers of ten
What can you explain now?
What does F represent?
Compare with the explanation
Charge per mole of electrons
F is the charge carried by one mole of electrons.
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Make it stick
How do Avogadro's constant and the charge on one electron combine to give charge per mole of electrons?
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