Faraday's Law

Faraday's Law Michael Faraday (1791-1867) was an English scientist who conducted research in the areas of chemistry, electricity and magnetism. Faraday formulated several laws but the one that concerns us most is his law regarding the relationship between current, time and the weight of electroplated metal. Michael Faraday describes his law as follows: "What, then, follows as a necessary consequence of the whole experiment? Why, this: that the chemical action upon ... one equivalent of zinc, in this simple voltaic circle, was able to evolve such quantity of electricity in the form of a current, as , passing through water, should decompose ... one equivalent of that substance: and considering the definite relations of electricity as developed in the preceding parts of the present paper, the results prove that the quantity of electricity which, being naturally associated with the particles of matter, gives them their combining power, is able, when thrown into a current, to separate those particles from their state of combination; or, in other words, that the electricity which decomposes, and that which is evolved by the decomposition of, a certian quantity of matter, are alike."

This statement is usually reframed into the form of an equation in modern textbooks, like so:
Equation {1}:
W = (I*t*A)/(n*F)

where:

W = weight of plated metal in grams.
I = current in coulombs per second.
t = time in seconds.
A = atomic weight of the metal in grams per mole.
n = valence of the dissolved metal in solution in equivalents per mole.
F = Faraday's constant in coulombs per equivalent. F = 96,485.309 coulombs/equivalent.

The following illustration will describe how Faraday's Law can be used. Consider nickel electroplating. The electrochemical reaction at the cathode will be:
Equation {2}:
Ni(2+) + 2e(-) = Ni

Equation 2 means that nickel ions in solution will plate out as nickel metal on the cathode when two electrons per nickel ion are passed into solution. We might then ask ourselves: How much nickel will plate out onto the cathode if we pass a current of 1 ampere (1 coulomb/second) to the cathode for one hour (3600 seconds)? Using equation (1) the answer is: W = (1*3600*58.69)/(2*96485.309) = 1.09 grams. Usually though, we are more interested in the thickness of the electroplated metal. We can calculate this thickness using the following equation:
Equation {3}:
T = (W*10000)/(rho*S)

where:

T = thickness in microns.
rho = density in grams per cubic centimeter.
S = surface area of the plated part in square centimeters.
10,000 is a multiplicative constant to convert centimeters to microns.

If equations 1 and 3 are combined we have the following equation for plated thickness.
Equation {4}:
T = (I*t*A*10000)/(n*F*rho*S)

If we apply equation 3 to our earlier example of nickel plating we find that the thickness of plated metal is: W = (1*3600*58.69*10000)/(2*96485.309*8.90*22.1) = 55.67 microns. Here we have assumed that the surface area of the part is 22.1 cm2. Notice the importance of surface area in the equation. If all other parameters are kept the same, the plated thickness will increase as the surface area is decreased and vice versa.

At this point one might ask: How can I calculate the plating rate? This can be done by eliminating time from equation 4 like so:
Equation {5}:
R = (I*A*600000)/(n*F*rho*S)

where:

R = plating rate in microns per minute.
600,000 is a multiplicative constant used to make R come out in units of microns per minute.

Applying equation 5 to our nickel plating example we get: R = (1*58.69*600000)/(2*96485.309*8.90*22.1) microns/minute. This makes sense because if one multiplies 0.9278 microns/minute by 60 minutes (3600 seconds) one gets a thickness of 55.66 microns which matches the earlier calculation.