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The second law of Faraday, also known as Faraday’s law of electrolysis, states that the amount of substance produced at an electrode during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte.

The mathematical expression of Faraday’s second law is:

m = (Q * M) / (n * F)

where: m = mass of substance produced Q = quantity of electricity passed through the electrolyte (in coulombs) M = molar mass of the substance n = number of electrons transferred in the reaction F = Faraday constant (96,485 coulombs per mole)

To perform calculations using Faraday’s second law, you need to know the values of Q, M, n, and F.

For example, suppose we want to calculate the mass of copper produced by passing 2.5 A of current through a solution of copper sulfate for 2 hours. The reaction equation for the electrolysis of copper sulfate is:

CuSO4(aq) → Cu(s) + SO4^2-(aq) + 2e^-

From the equation, we can see that each copper ion (Cu^2+) requires two electrons to be reduced to copper metal (Cu). Therefore, n = 2.

The molar mass of copper is 63.55 g/mol.

To calculate the quantity of electricity passed (Q), we need to convert the current from amperes to coulombs per second:

2.5 A = 2.5 C/s

The total quantity of electricity passed is:

Q = I * t = 2.5 C/s * 7200 s = 18,000 C

Now we can use Faraday’s second law to calculate the mass of copper produced:

m = (Q * M) / (n * F) = (18,000 C * 63.55 g/mol) / (2 * 96,485 C/mol) = 5.88 g

Therefore, passing 2.5 A of current through a solution of copper sulfate for 2 hours will produce 5.88 g of copper metal.

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