96,485
C
31.773
g
5.000000e-1
mol
31.773
g/equiv
1.000000e+0
mol e−
26.801389
Ah
96,485
C
31.773
g
5.000000e-1
mol
31.773
g/equiv
1.000000e+0
mol e−
26.801389
Ah
Faraday's Law Calculator applies Michael Faraday's quantitative laws of electrolysis to determine the mass of substance produced at an electrode for a given amount of electric charge. You can enter charge directly in coulombs or calculate it from current and time. The calculator also computes the moles deposited and the equivalent mass (molar mass divided by valence). Faraday's laws, formulated in 1833–1834, established the first quantitative link between electricity and chemical change. They remain foundational in analytical electrochemistry, coulometry, electroplating process control, battery capacity calculations, and determining the Faraday constant itself. These laws are exact within the assumption that all charge participates in the desired electrode reaction.
Faraday's laws combine into a single quantitative relationship:
$$m = \frac{QM}{zF}$$
where m is mass deposited (g), Q is total charge (C), M is molar mass (g/mol), z is the valence (electrons per ion), and F = 96,485 C/mol is the Faraday constant.
If charge is not directly measured, it can be calculated from:
$$Q = I \times t$$
The number of moles deposited is:
$$n_{mol} = \frac{Q}{zF}$$
The equivalent mass (or electrochemical equivalent per Faraday) is:
$$E = \frac{M}{z}$$
This represents the mass deposited per Faraday of charge. For example, Cu (M = 63.55, z = 2) has an equivalent mass of 31.77 g/equiv, meaning one Faraday deposits 31.77 g of copper.
The mass deposited is directly proportional to the total charge. One Faraday (96,485 C) deposits exactly one equivalent of any substance. The equivalent mass lets you quickly compare how much mass different metals yield per unit charge — silver (107.87/1 = 107.87 g/equiv) yields much more mass per Faraday than aluminum (26.98/3 = 8.99 g/equiv). In coulometric analysis, the precise relationship between charge and mass allows determination of unknown concentrations with very high accuracy, often better than gravimetric or volumetric methods.
Inputs
Results
One Faraday (96,485 C) deposits M/(z) = 63.546/2 = 31.773 g of copper. This is exactly 0.5 mol Cu, because Cu²⁺ requires 2 electrons per ion. The equivalent mass equals the mass deposited per Faraday.
Inputs
Results
Q = 10 A × 7200 s = 72,000 C. m = (26.982 × 72000)/(3 × 96485) = 6.71 g Al. Despite high charge, the trivalent Al³⁺ (z = 3) yields relatively little mass per coulomb compared to monovalent ions.
The mass of substance altered at an electrode during electrolysis is directly proportional to the quantity of electricity transferred at that electrode: m ∝ Q. This means doubling the charge doubles the deposited mass.
For a given quantity of electricity, the mass of an element deposited is proportional to its equivalent weight (M/z). Elements with higher equivalent weights deposit more mass per coulomb.
Equivalent mass (E = M/z) is the molar mass divided by the valence. It represents the mass of substance deposited by one Faraday (96,485 C) of charge. For Cu²⁺: E = 63.55/2 = 31.77 g/equiv.
In coulometric analysis, the total charge consumed in completely reacting an analyte is measured precisely. Using Faraday's law, the mass (and therefore concentration) of the analyte is calculated. Coulometry is an absolute method requiring no calibration standards.
F = 96,485.33212 C/mol (CODATA 2018 value) is the charge of one mole of electrons. It equals Avogadro's number × elementary charge: F = Nₐ × e = 6.022 × 10²³ × 1.602 × 10⁻¹⁹ C.
Yes. First calculate moles using Faraday's law, then apply the ideal gas law (V = nRT/P). For water electrolysis, 2 Faradays produce 1 mol H₂ at the cathode (22.4 L at STP) and 0.5 mol O₂ at the anode.
Current (I, in amperes) is the rate of charge flow — coulombs per second. Total charge Q = I × t. A higher current deposits mass faster, but the total mass depends on the total charge passed.
Battery capacity (in Ah or C) determines how much active material is consumed. Faraday's law calculates the mass of electrode material needed for a desired capacity. A 1 Ah lithium battery requires m = (6.941 × 3600)/(1 × 96485) = 0.259 g Li.
The total charge splits among competing reactions. The fraction going to the desired reaction is the current efficiency. Faraday's law gives the theoretical maximum; actual yield is reduced by side reactions like solvent decomposition.
Michael Faraday (1791–1867) was a British scientist who discovered electromagnetic induction, the laws of electrolysis, and the Faraday effect. His electrolysis laws (1833–1834) established the quantitative foundation of electrochemistry and contributed to understanding atomic theory.
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