Faraday’s Law - Quantitative Electrochem

Core Concept

The mass of a substance changed at an electrode during electrolysis is directly proportional to the quantity of electricity (total charge) transferred. Essentially, if you want to plate more gold onto a ring or produce more hydrogen gas, you must pass more electrons through the system.

$$m = \left( \frac{Q}{F} \right) \left( \frac{M}{z} \right)$$

m: Mass of the substance (grams)
Q: Total electric charge (Q = I x t, where I is current and t is time)
F: Faraday’s constant (96,485 C/mol), representing the charge of 1 mole of electrons
M: Molar mass of the substance
z: electrons transferred per ion

Key Tips

Always convert minutes or hours to seconds before multiplying by current.
Double-check the half-reaction — the number of electrons transferred (nₑ) is critical.
Use dimensional analysis to track units: coulombs → mol e⁻ → mol substance → grams.
Memorize Faraday’s constant (96,485 C/mol e⁻) or keep it on your formula sheet.
Think stoichiometrically — the logic is the same as any mass-to-mass problem, just with electricity.

Test Yourself

Assorted Multiple Choice

A constant current of $2.00\text{ amperes}$ is passed through an aqueous solution of $\text{CuSO}_4$ for $965\text{ seconds}$. How many moles of solid copper ($\text{Cu}$) will be plated out at the cathode? (Faraday's constant $\approx 96,500\text{ C/mol }e^-$)

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Faraday's Law — Quantitative Electrochemistry

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01

Fundamental Charge and Mole Relationships

Faraday's constant, charge-to-mole conversions.

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Mass-to-Current Calculations

The "forward" path — mass → charge → current.

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Current-to-Product Calculations

The "reverse" path — current → moles → mass.

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Stoichiometry and the "n" Factor

Valence dependence and electron transfer count.

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Mixed and edge-case questions.

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Assorted Multiple Choice

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Electric Charge (Q)

Definition: The total electric charge transferred during an electrochemical reaction.

Formula: Q = I ⋅ t where:

Q: Charge (Coulombs (C))
I: Current (Amperes (A))
t: Time (seconds (s))

Faraday's Constant (F): Represents the charge of one mole of electrons: F=96,485 C/mol

Moles of Electrons (n): The amount of charge relates to the moles of electrons transferred: $n_{\text{e}^-} = \frac{Q}{F}$

Faraday’s Laws of Electrolysis

First Law: The mass (m) of a substance deposited or liberated at an electrode is proportional to the charge passed through the electrolyte. m = Z ⋅ Q Where:

Z = Electrochemical equivalent (g/C)
Q = I ⋅ t

Second Law: For the same amount of charge, the mass of different substances produced is proportional to their molar masses (M) divided by the number of electrons (n) transferred. $m \propto \frac{M}{n}$

Quantitative Relationships

Mass of Product: m = $\frac{M \cdot Q}{n \cdot F}$

m: Mass of the product (g)
M: Molar mass (g/mol)
n: Number of electrons in the half-reaction

Volume of Gas: For gases produced at electrodes, use the ideal gas law: V = $\frac{nRT}{P}$ Where:

V: Volume (L)
R: Ideal gas constant (0.0821 L·atm/mol·K).
T: Temperature (K).
P: Pressure (atm).

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