Faraday's Law Calculator

Calculate the mass of substance deposited or liberated during electrolysis

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Parameters

A
s
g/mol
C/mol
Common Elements

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Fill in the values on the left and click "Calculate Mass"

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Faraday's Law Guide

Faraday's First Law of Electrolysis

The mass of a substance deposited or liberated during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte.

m ∝ Q

Where Q is the total electric charge passed through the substance.

Faraday's Second Law of Electrolysis

For a given quantity of electricity, the mass of elements deposited is proportional to their chemical equivalent weights.

m ∝ M/n

Where M is the molar mass and n is the valency number of ions of the element.

Combined Faraday's Law Equation

The combined equation from both laws is:

m = (M × I × t) / (n × F)

Where:

  • m = mass of the substance (grams)
  • M = molar mass of the substance (g/mol)
  • I = current (amperes)
  • t = time (seconds)
  • n = number of electrons in the redox reaction
  • F = Faraday's constant (96,485 C/mol)
Example Calculation

Calculate the mass of copper deposited when a current of 2.5 A flows through a copper sulfate solution for 1 hour (3600 seconds).

Given:

  • Molar mass of copper (M) = 63.55 g/mol
  • Number of electrons (n) = 2 (Cu²⁺ + 2e⁻ → Cu)
  • Faraday's constant (F) = 96,485 C/mol

Calculation:

m = (63.55 × 2.5 × 3600) / (2 × 96485) ≈ 2.96 g

Tip: Use the preset buttons for common elements to quickly fill in molar mass and electrons.

Faraday's Law Formula

m = M × I × t⁄n × F

Electrochemical Theory & Academic Context

Fundamental Principle

Faraday's Laws of Electrolysis (1833) establish the quantitative relationship between electric charge and chemical change during electrolysis. The calculator implements the combined law derived from Michael Faraday's experimental work, which remains foundational to electrochemistry and industrial electrochemical processes. For a deeper understanding of the underlying thermodynamics, explore the Gibbs Free Energy Calculator which connects electrochemical cell potential to spontaneity.

Scientific Variables & Units

Symbol Variable Name SI Unit Physical Meaning
m Mass deposited grams (g) Amount of substance liberated at electrode
I Current ampere (A) Rate of charge flow: 1 A = 1 C/s
t Time seconds (s) Duration of electrolysis
Q = I·t Total charge coulomb (C) Total electricity passed: 1 C = 1 A·s
M Molar mass g/mol Mass of one mole of substance
n Number of electrons unitless Stoichiometric coefficient in half-reaction. Determining this correctly is crucial, and tools like the Redox Reaction Balancer can help ensure your half-reactions are properly balanced.
F Faraday constant C/mol Charge of 1 mole electrons: 96,485 C/mol

Laboratory & Industrial Applications

  • Electroplating: Thickness control in metal coating
  • Electrowinning: Metal extraction from ores (Cu, Al, Zn)
  • Battery Technology: Capacity calculations and electrode design
  • Analytical Chemistry: Coulometric titrations and electrogravimetry
  • Environmental: Electrochemical wastewater treatment

Common Student Considerations

Avoid These Common Mistakes:
  • Using atomic mass instead of molar mass for correct species
  • Incorrect "n" value from unbalanced half-reactions
  • Time unit inconsistencies (hours vs seconds)
  • Assuming 100% current efficiency in real systems
  • Confusing mass deposited with moles deposited

Theoretical Derivation & Formula Context

The combined Faraday's Law equation derives from fundamental relationships:

  1. Charge relationship: Q = I × t (definition of current)
  2. Mole-electron relationship: moles of electrons = Q/F. This calculation is made simple using the Avogadro's Number Calculator, which helps relate macroscopic charge to the number of elementary entities.
  3. Stoichiometry: moles of substance = (moles of electrons)/n
  4. Mass relationship: m = M × moles of substance

Combining these yields: m = M × (Q/F) × (1/n) = (M × I × t)/(n × F)

Electrochemical Equivalent (Z): Alternative form: m = Z × Q, where Z = M/(nF) represents mass deposited per coulomb.

Accuracy & Limitations

Tool Assumptions
  • Ideal Conditions: 100% current efficiency
  • Pure Substances: No competing reactions
  • Constant Current: Steady DC current
  • Uniform Deposition: Homogeneous electrode surface
  • SI Units: Strict adherence to SI definitions
Real-World Deviations
  • Current efficiencies typically 90-98% in industry
  • Side reactions may consume charge
  • Electrode polarization effects
  • Solution resistance and temperature variations

Calculation Examples

Silver Plating Example

Goal: Deposit 5.00 g of silver (Ag⁺ + e⁻ → Ag)

Given: M = 107.87 g/mol, n = 1, I = 2.00 A

Calculate required time:

Rearrange: t = (m × n × F)/(M × I)

t = (5.00 × 1 × 96485)/(107.87 × 2.00) ≈ 2236 s ≈ 37.3 min

This demonstrates reverse calculation capability using the same formula.

Constants & Standards Reference

Faraday Constant

F = 96,485.33212 C/mol (CODATA 2018)
Derived from: F = Nₐ × e
Nₐ = Avogadro constant, e = elementary charge

Unit Relationships

1 ampere = 1 coulomb/second
1 faraday = 1 mole of electrons
1 mole electrons = 6.022×10²³ electrons
Elementary charge: e = 1.602×10⁻¹⁹ C

Precision Notes

Calculator uses 4 decimal places for mass
Charge displayed to 2 decimal places
Default F = 96485 C/mol (educational standard)
For research: Use CODATA 96,485.33212 C/mol

Educational FAQ

Each Al³⁺ ion requires 3 electrons for reduction (Al³⁺ + 3e⁻ → Al), while Ag⁺ requires only 1. For the same charge (same number of electrons), you get 1 mole of Al versus 3 moles of Ag. Since molar mass also differs, the mass ratio is: m_Al/m_Ag = (M_Al/3)/(M_Ag/1) ≈ (26.98/3)/(107.87) ≈ 0.083.

Industrial processes account for current efficiency (CE) factors. Actual mass = theoretical mass × CE/100. Typical CEs: copper electrowinning (85-95%), aluminum production (85-90%), chrome plating (10-25% due to side reactions). This calculator provides theoretical maximum yield.

For complex ions or organic compounds, determine "n" from the balanced half-reaction. Example: MnO₄⁻ reduction to Mn²⁺ requires 5 electrons (n=5). For water electrolysis: 2H₂O → O₂ + 4H⁺ + 4e⁻ (n=4 per O₂ molecule). Always balance both mass and charge in the half-reaction. You can use a Redox Reaction Balancer to assist with this step.

No. Faraday's Law applies to direct current (DC) only. AC causes reversible reactions with no net deposition. For pulsating DC, use average current over time. The calculator assumes steady DC as specified in the original 1833 experiments.
Academic Integrity & Verification

This calculator implements the standard combined Faraday's Law formula as taught in undergraduate chemistry curricula worldwide. All constants use IUPAC-recommended values for educational contexts. Calculations are verified against textbook examples from:

  • Atkins' Physical Chemistry (11th ed.)
  • Bard & Faulkner: Electrochemical Methods (2nd ed.)
  • CRC Handbook of Chemistry and Physics

Last formula verification: October 2025. Next review scheduled: November 2026.

This tool is designed for educational and planning purposes. Laboratory applications require consideration of experimental conditions, overpotentials, and current efficiencies. Always consult primary literature for research-grade calculations.