Engineering
Faraday electrolysis yield and ideal van ’t Hoff osmotic pressure
Estimate deposited mass with a stated current efficiency and compare it with a separate ideal-solution osmotic-pressure calculation.
Charge balance and an ideal osmotic-pressure estimate
Constant current times elapsed seconds gives charge. Divide by electrons transferred per product unit and Faraday’s constant, then multiply by molar mass. The original11.85g result assumes100% current efficiency for copper deposition; competing reactions can reduce yield. B9 now supplies efficiency between0 and1. Variable current requires integrated charge instead of a single I*t.
The osmotic example is an idealized NaCl solution, not a seawater property model. The van ’t Hoff relation is a dilute ideal-solution approximation; actual electrolytes can deviate from complete dissociation behavior. Use molarity in mol/L and temperature in kelvin with the displayed gas constant.
Reverse osmosis depends on the osmotic-pressure difference across a membrane, not just one solution’s pressure. Nonzero permeate concentration, concentration polarization and hydraulic losses matter; this result is not a pump-sizing pressure or a prediction of water flux.
| Process Parameter | Cell | Copper Plating / Seawater RO | Engineering Output |
|---|---|---|---|
| Current I & Time t | B2 = 10 A, B3 = 3,600 s | Charge Q = 36,000 Coulombs | 0.3731 moles of electrons |
| Cu Molar Mass M & Valence n | B4 = 63.546 g/mol, B5 = 2 | (36000 * 63.546) / (2 * 96485) | 11.85 g Copper plated |
| Idealized NaCl solution | B6 = 2, B7 = 0.50 mol/L | 1.00 Osmolar total ions | Osmolarity = i * M |
| Temp 25 C (B8 = 298.15 K) | 2 * 0.50 * 0.083145 * 298.15 | Ideal solution osmotic pressure | Pi = 24.79 bar (359.5 psi) |
Faraday's Law electroplated mass m (grams)
Seconds times amperes gives coulombs. B5 is a positive integer electron stoichiometric number, B4 is positive molar mass in g/mol, and B9 is a fraction, not a percentage number.
=IF(OR(COUNT(B2:B5)<>4,COUNT(B9)<>1),"Invalid inputs",IF(OR(B2<0,B3<0,B4<=0,B5<1,B5<>INT(B5),B9<0,B9>1),"Invalid inputs",ROUND(B2*B3*B4*B9/(B5*96485),2)))Ideal osmotic pressure in bar
Use R = 0.083145 for bar (or R = 0.082057 for atmospheres: 24.47 atm).
=IF(OR(COUNT(B6:B8)<>3,B6<=0,B7<0,B8<=0),"Invalid inputs",ROUND(B6 * B7 * 0.083145 * B8, 2))Try the example
Use the original values or change them to test your understanding.