Faraday's Law of Electrolysis Mass & Tafel Electrode Overpotential

Two separate electrochemistry calculations

For a specified electrode reaction, charge Q = I t at constant current corresponds to Q/(n F) moles of product at 100% current efficiency. Multiply by molar mass M and a current-efficiency fraction to estimate product mass. Use amperes, seconds and grams per mole. The rounded Faraday constant used here is 96485.33 C/mol. For changing current, use integrated charge rather than one instantaneous current multiplied by time.

This workbook does not size a bath, electrolyzer or battery. Current efficiency describes the share of charge producing the specified product, not its purity. Reaction stoichiometry, side reactions and operating conditions must be established separately.

Mass for one specified electrode reaction

B2 is current magnitude in A, B3 time in seconds, B4 molar mass in g/mol, B5 the positive integer electron count per product unit, and B6 current efficiency from 0 to 1. E2 retains the unrounded result. For Cu2+ + 2e− → Cu, 15 A for 3600 s at efficiency 1 gives approximately 17.782 g. At 0.8 efficiency it gives approximately 14.226 g. Zero current, time or efficiency gives zero mass.

=IF(COUNT(B2:B6)<>5,"Enter numeric mass inputs",IF(OR(B2<0,B3<0,B4<=0,B5<=0,B5<>INT(B5),B6<0,B6>1),"Invalid mass inputs",B2*B3*B4*B6/(B5*96485.33)))

Anodic Tafel approximation

The anodic Tafel limit of Butler–Volmer neglects the cathodic contribution: eta = b LOG10(j/j0). B7 is a positive slope in V per decade; B8 and B9 are positive anodic and exchange current densities in the same units. With slope 0.12 and ratio 100, E3 is 0.24 V. This is a separate anodic kinetic example, not a signed copper-deposition model.

Do not add an arbitrary intercept when j0 already denotes exchange current density in this expression. An empirical intercept form instead needs its own explicitly defined reference current and fitted parameters. The workbook is not a full Butler–Volmer solver and does not include mass-transfer or ohmic losses.

For this exercise only, ratios below 10 are rejected to keep away from equilibrium. That threshold is a teaching guard, not proof that the neglected branch is small enough for a particular reaction. Establish the applicable kinetic regime and fitted slope independently.

=IF(COUNT(B7:B9)<>3,"Enter numeric kinetic inputs",IF(OR(B7<=0,B8<=0,B9<=0),"Invalid kinetic inputs",IF(B8/B9<10,"Outside this Tafel exercise",B7*LOG10(B8/B9))))

Try controlled changes

Double B2: the mass doubles while E3 stays unchanged. Set B6 to 0.8 to model 80% current efficiency. Multiply B8 by ten: E3 increases by B7. Multiply both B8 and B9 by the same positive factor: E3 stays unchanged. Invalid or missing inputs produce an explanation rather than a plausible-looking result.

Further reading

• NIST — Fundamental Physical Constants
• COMSOL — Modeling Electrochemical Reactions