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Lesson 33 · Time to plate
Sizing the job
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Sizing the job

A plating shop never asks for a mass. It asks for a setting: how many amperes, for how many minutes, to land the thickness the drawing calls for. That question is this chapter's last two formulas welded end to end, Q=I tQ = I\,t feeds m=QMnFm = \dfrac{QM}{nF} — and the weld holds in both directions.

Forwards, from the setting: seconds times amperes give coulombs, and coulombs give grams. Backwards, from the drawing: Q=mnFMQ = \dfrac{mnF}{M} prices the wanted mass in coulombs, and then I=QtI = \dfrac{Q}{t} or t=QIt = \dfrac{Q}{I} splits that bill between the dial and the clock. The cast is unchanged, mm in grams, QQ in coulombs, II in amperes, tt in seconds, MM in g/mol, and nn a bare count of electrons per ion — and whichever one the question leaves blank is the one you solve for.

Push the units through every rearrangement you write. C⋅g/molC/mol\dfrac{\mathrm{C} \cdot \mathrm{g/mol}}{\mathrm{C/mol}} cancels to grams, which is precisely why Faraday's law is shaped the way it is. If your units refuse to cancel into the answer's units, the rearrangement is wrong — no appeal. Units that DO work out never prove you right; the check is a one-way street.

One wink before you start. The current 9.65 A9.65\ \mathrm{A} turns up in these problems the way 3-4-5 turns up in triangles: held for 1000 s it delivers 9650 C, which is exactly a tenth of a mole of electrons. Examiners are not being random there. They are being kind.

QmMn

m=QMnFm = \frac{Q M}{n F}

  • mm= Mass deposited or dissolved (mass)
  • QQ= Charge passed (electric charge)
  • MM= Molar mass of the deposited element (molar mass)
  • nn= Electrons transferred per ion
Faraday's Law of Electrolysis (m = QM/nF) solver →
IQt

Q=ItQ = I t

  • QQ= Charge (electric charge)
  • II= Current (electric current)
  • tt= Time (time)
Electric Charge (Q = It) solver →