Electroplating Surface Finishing, Watts Nickel / Hard Chrome Baths & Faraday’s Law
Faraday Electroplating Thickness & Cathode Efficiency Formula
Calculate Cathode Current Density J (A/dm²), Ideal 100%-Faradaic Deposited Mass (g), Cathode-Efficiency-Adjusted Metal Mass (g), and Mean Electroplated Coating Thickness (um).
Why hard-chrome plating builds microns 14x slower than Watts nickel at the same amperage—valence n=6 AND 82% hydrogen gas loss!
By Michael Faraday’s First and Second Laws of Electrolysis (`F = 96,485.33` C/mol), passing DC Rectifier Current `I` (A) for Immersion Time `t` (min -> `Q = 60 * I * t` coulombs) theoretically reduces `m_ideal = (Q * M_mol) / (n * 96,485.33)` grams of metal of Molar Mass `M_mol` (g/mol) and Ionic Oxidation Valence `n` (`n = 2` for `Ni^2+`, `Cu^2+`, `Zn^2+` vs `n = 6` for hexavalent chromic acid `Cr^6+`!). In real industrial plating tanks, parasitic cathode `2H+ + 2e- -> H2` hydrogen gas evolution steals `1 - eta_c` of the current—leaving Cathode Current Efficiency `eta_c` near `92%–97%` in Watts nickel or acid copper baths, yet ONLY `15%–22%` in hexavalent hard-chrome tanks! Dividing Actual Metal Mass `m_act = m_ideal * (eta_c / 100)` by Metal Density `rho` (g/cm³) and Wetted Part Surface Area `A_dm2 * 100` (cm²) yields Mean Coating Build `delta_um = (m_act / (rho * A_cm2)) * 10,000` micrometers!
Verify on a Watts Bright-Nickel Rack Plating Bath—Rectifier_Current `I` = 180.0 A (B2), Immersion_Time `t` = 45.0 min (B3), Cathode_Efficiency `eta_c` = 94.0% (B4), Nickel_Molar_Mass `M` = 58.69 g/mol (B5), Nickel_Valence `n` = 2 (B6), Nickel_Density `rho` = 8.90 g/cm³ (B7), and Rack_Part_Area = 30.0 dm² (`3,000` cm², B8 -> Current Density `J = 6.00` A/dm² in E2): `100%` Faradaic Mass is `147.81` g (E3), Actual Plated Nickel is `138.94` g (E4), and Mean Coating Thickness hits `52.04` um (E5)!
| Faraday Electroplating KPI (180 A x 45 min on 30 dm²: Watts Ni2+ vs Cr6+ Hard Chrome) | Formula | Verified Output |
|---|---|---|
| Cathode Current Density (A/dm²) | Rectifier_Current_A / Part_Area_dm2 | 6.00 A/dm² (`600` A/m²) |
| 100% Faradaic Ideal Mass (g) | (I * t_min * 60 * M_g_mol) / (n * 96485.33) | 147.81 g Ni (43.65 g @ Cr n=6!) |
| Actual Deposited Metal Mass (g) | Ideal_Mass_g * (Cathode_Eff_Pct / 100) | 138.94 g Ni (7.86 g @ Cr 18% eff!) |
| Mean Plated Thickness (um) | (Actual_Mass_g / (rho * Area_dm2*100))*1e4 | 52.04 um Ni (3.64 um Cr—14.3x slower!) |
Faraday’s Electrolysis Law & Cathode Efficiency Micron Coating Formula
Validate `Current > 0` A, `Time > 0` min, `Cathode_Eff` in `(0%, 100%]`, `Molar_Mass > 0` g/mol, integer `Valence n` in `[1, 8]`, `Density > 0.5` g/cm³, and `Surface_Area > 0` dm²!
=LET(ia_m, B2, tm_m, B3, ef_c, B4, mm_g, B5, vn_i, B6, rh_g, B7, ar_d, B8, IF(OR(ia_m <= 0, tm_m <= 0, ef_c <= 0, ef_c > 100, mm_g <= 0, vn_i < 1, vn_i > 8, rh_g <= 0.5, ar_d <= 0), "Invalid Plating Input", LET(mi_g, (ia_m * tm_m * 60 * mm_g) / (vn_i * 96485.33), ma_g, mi_g * (ef_c / 100), ROUND((ma_g / (rh_g * ar_d * 100)) * 10000, 2))))Hexavalent Hard-Chrome Tank Comparison Check (Set Eff = 18%, M = 52.00, n = 6, rho = 7.19 g/cm³)
Run the exact same `180` A x `45` min charge in a hexavalent hard-chrome tank (`B4 = 18`, `B5 = 52.00`, `B6 = 6`, `B7 = 7.19`): `6`-electron reduction cuts Ideal Mass E3 to `43.65` g, `82%` hydrogen evolution slashes Actual Chromium E4 to `7.86` g, and Thickness E5 reaches only `3.64` um—explaining why hard-chrome hydraulic rods require `30–50` A/dm² and multi-hour tank cycles!
=IF(ISTEXT(E5), E5, ROUND(((B2 * B3 * 60 * B5) / (B6 * 96485.33)) * (B4 / 100), 2))Try the example
Use the original values or change them to test your understanding.