Faraday Electrolysis
Faraday's electrolysis laws
Deposited amount is directly proportional to transferred charge \(Q=I\cdot t\). With electron number \(z\) and molar mass \(M\), the deposited mass can be calculated.
\[ m = \frac{M\,I\,t}{zF} \]
This is fundamental for electroplating, process sizing, coating estimates, and electrochemical production planning.
- Metal deposition from electrolytes
- Required current for target mass
- Scaling from lab to production
Formulas (MathJax)
\[ Q = I\,t \]
\[ n = \frac{Q}{zF} = \frac{I\,t}{zF} \]
\[ n_\mathrm{real} = n_\mathrm{theo}\cdot\frac{\eta}{100} \]
\[ m = \frac{M\,I\,t}{zF}\cdot\frac{\eta}{100} \]
\[ I = \frac{m\,zF}{M\,t\,(\eta/100)} \]
Symbol legend
- \(m\): deposited mass [g]
- \(n\): amount of deposited substance [mol]
- \(M\): molar mass [g/mol]
- \(I\): current [A]
- \(t\): time [s]
- \(Q\): charge [C]
- \(z\): electrons transferred per ion
- \(F\): Faraday constant \(96485\,\mathrm{C\,mol^{-1}}\)
- \(\eta\): current efficiency in percent [%]
Detailed examples
Example 1 (copper deposition):
\(I=2.5\,A\), \(t=3600\,s\), \(M=63.546\), \(z=2\)
\(m\approx2.96\,g\)
\(I=2.5\,A\), \(t=3600\,s\), \(M=63.546\), \(z=2\)
\(m\approx2.96\,g\)
Example 2 (required current):
Target \(m=5\,g\) copper in 1 h
The calculator gives the required average current \(I\).
Target \(m=5\,g\) copper in 1 h
The calculator gives the required average current \(I\).
Example 3 (moles):
\(I=1.2\,A\), \(t=1800\,s\), \(z=2\)
Direct determination of deposited amount \(n\).
\(I=1.2\,A\), \(t=1800\,s\), \(z=2\)
Direct determination of deposited amount \(n\).
Practical note:
Real systems often have current efficiencies below 100%. For practical estimates, apply an efficiency factor.
Real systems often have current efficiencies below 100%. For practical estimates, apply an efficiency factor.
Practical depth
Current efficiency and side reactions
Part of the current may drive side reactions (e.g., gas evolution). Therefore, real deposited mass can be below theoretical values.
Engineering relevance
For plating processes, geometry, current density distribution, electrolyte flow, and temperature also matter. This calculator provides the electrochemical core estimate.
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