Electroplating & Electrolysis Calculator

Electrolysis and Faraday's Laws Guide

What's the key thing to understand about Faraday's Laws of Electrolysis?

First law: the mass deposited is proportional to the charge passed. Second law: for the same charge, masses deposited are proportional to molar mass/charge number. Combined formula: m = (I × t × M) / (n × F). Where m = mass (g), I = current (A), t = time (s), M = molar mass (g/mol), n = number of electrons transferred per ion, F = Faraday constant (96,485 C/mol). Example: copper deposition (Cu²⁺ + 2e⁻ → Cu, n=2, M=63.5 g/mol) at 2A for 1 hour: m = (2 × 3600 × 63.5)/(2 × 96485) = 2.37g.

What's the key thing to understand about Electroplating Applications?

Electroplating deposits a thin metal layer onto a conducting surface. The object to be plated is the cathode (negative electrode). The plating metal or an inert electrode is the anode. The electrolyte contains ions of the plating metal. Uses: chromium plating (decorative and corrosion protection), gold plating (electronics, jewellery), silver plating (cutlery), zinc galvanising (steel protection), copper interconnects in PCB manufacture. Thickness control: precisely calculated current × time control (via Faraday's laws of electrolysis) allows platers to deposit a specified mass and thickness of metal reliably, since the amount deposited is directly proportional to the total charge passed (current × time) and inversely related to the ion's charge.

What's the key thing to understand about Products of Electrolysis?

At the cathode (reduction): positive ions gain electrons. Metals are deposited from metal salt solutions. From dilute H₂SO₄: H₂ gas produced (H⁺ + e⁻ → ½H₂). At the anode (oxidation): negative ions or water are oxidised. Chloride ions: Cl⁻ → ½Cl₂ + e⁻ (concentrated chloride). Sulphate ions in dilute H₂SO₄: water oxidised → O₂ + H⁺ + e⁻. Metal anodes dissolve: Cu → Cu²⁺ + 2e⁻ (used in copper refining where impure copper anode dissolves and pure copper deposits at cathode).

What do I need to know about Electrolysis in Industry?

Chlor-alkali industry: electrolysis of brine (NaCl solution) produces chlorine (Cl₂), hydrogen (H₂), and sodium hydroxide (NaOH). The Downs process: electrolysis of molten NaCl produces sodium metal and chlorine — the only commercial route to sodium metal. Aluminium production: electrolysis of aluminium oxide dissolved in cryolite — requires enormous electrical energy (approximately 14,000 kWh per tonne of aluminium — the reason aluminium recycling is so energy-efficient by comparison). Hydrogen production by water electrolysis is a growing industrial application too, particularly for 'green hydrogen' where the electricity comes from renewable sources — splitting water into hydrogen and oxygen gas at the electrodes, with the hydrogen used as a fuel or industrial feedstock.

What do I need to know about a Worked Faraday's Law Example?

Suppose a steel object is electroplated with copper using a current of 2.0 A for 30 minutes (1800 s), from a Cu2+ solution (n = 2 electrons per ion, Cu molar mass = 63.5 g/mol). Charge passed Q = I x t = 2.0 x 1800 = 3600 C. Moles of electrons = Q/F = 3600/96485 = 0.0373 mol. Moles of Cu deposited = 0.0373/2 = 0.0187 mol. Mass deposited = 0.0187 x 63.5 = 1.18g. Using the combined formula directly: m = (I x t x M)/(n x F) = (2.0 x 1800 x 63.5)/(2 x 96485) = 1.18g — matching. To instead find the time needed to deposit a target mass, rearrange: t = (m x n x F)/(I x M). This rearrangement is routinely used in industrial plating lines to calculate how long a part must remain in the bath to achieve a specified coating thickness.

What should I know about Choosing Current and Time in Practical Plating?

In real electroplating, current is normally expressed as current density (current per unit area of the object being plated), since deposition rate depends on local current density, not total current alone. Current density that is too low gives an impractically slow process; current density that is too high produces poor-quality deposits — rough, powdery, or poorly adherent coatings, because metal ions are reduced faster than they can arrange into an ordered crystal structure at the cathode. Industrial plating baths operate within a defined current density range specific to the metal and electrolyte, often combined with additives (brighteners, levelling agents) that improve deposit quality without changing the underlying Faraday's law mass calculation. Coating thickness relates to mass deposited via density and plated area: thickness = mass deposited / (density x area) — useful for converting a Faraday's law mass result into the micrometre thickness specification that plating standards actually require.

What do I need to know about Calculating Plating Thickness?

Faraday's law gives the mass of metal deposited during electroplating as m = ItM/(nF), where I is current, t is time, M is molar mass, n is the number of electrons transferred per metal ion, and F is Faraday's constant (96,485 C/mol). Converting that mass into a physical coating thickness requires dividing by the metal's density and the area being plated: thickness = m/(ρ × area). This two-step calculation — mass from Faraday's law, then thickness from density and area — is exactly how electroplating shops control coating thickness precisely by setting current and time rather than guessing.

What do I need to know about Faraday's Law Calculations for Common Plating Metals?

Faraday's first law of electrolysis states that the mass deposited at an electrode is directly proportional to the charge passed: m = (Q × M)/(n × F) = (I × t × M)/(n × F), where F = 96,485 C/mol is the Faraday constant, M is the molar mass of the metal, and n is the number of electrons needed to reduce one ion of that metal to the solid metal. Because n varies between metals — and sometimes between oxidation states of the same metal — it's the single most common source of error in plating calculations. Rearranging the law to find how much metal a fixed amount of charge deposits makes it easy to compare plating efficiency across metals:

Notice that chromium deposits the least metal per coulomb of any metal in the table, because each chromium atom needs six electrons rather than one or two. That's the chemical reason hard chrome plating takes so long and consumes so much current compared with silver or nickel plating of a similar thickness. It's also why some metals can be plated from more than one oxidation state — copper can deposit from either Cu⁺ (n=1) or Cu²⁺ (n=2) baths, and the two give different deposition rates for the same current, so the bath chemistry (not just the metal) determines which n value belongs in the calculation.

What do I need to know about a Worked Example — Silver-Plating a Spoon?

Worked example: electroplating a steel spoon with silver. A plating bath runs at a steady current of 2.0 A for 30 minutes (1,800 s), depositing silver from an Ag⁺ solution (n = 1, M = 107.87 g/mol). Step 1 — charge passed: Q = I × t = 2.0 A × 1,800 s = 3,600 C Step 2 — moles of electrons: moles e⁻ = Q/F = 3,600 ÷ 96,485 = 0.03732 mol Step 3 — moles of silver deposited (n = 1): 0.03732 mol Step 4 — mass deposited: m = 0.03732 mol × 107.87 g/mol = 4.02 g So a 2.0 A plating current for 30 minutes deposits about 4.02 g of silver onto the spoon. To convert that mass into a coating thickness, divide by the surface area being plated and the density of silver (10.49 g/cm³). For a spoon with roughly 20 cm² of plated surface: Volume deposited = 4.02 g ÷ 10.49 g/cm³ = 0.383 cm³ Average thickness = 0.383 cm³ ÷ 20 cm² = 0.0192 cm = 192 µm That's a notably thick coating by commercial standards — decorative silver plating on cutlery is typically only 10-40 µm thick, which means a real plating line would use a much lower current, a shorter time, or both, and would usually rotate or move the workpiece to keep the deposit even. The calculation also assumes 100% current efficiency, which real plating baths rarely achieve; side reactions such as hydrogen evolution at the cathode can divert 2-10% of the charge away from metal deposition, which is why practical plating times are usually a little longer than the theoretical Faraday's-law figure suggests.