The amount of radium formed by the passage of electric current through an electrolytic cell can be calculated using Faraday’s laws of electrolysis.
The first law states that the amount of substance produced at an electrode is directly proportional to the amount of electric charge passed through the cell.
The second law states that the amount of substance produced by a given amount of electric charge is proportional to the equivalent weight of the substance.
The equivalent weight of radium is its atomic weight divided by its valence, which is 226/2 = 113 g/mol.
The electric charge passed through the cell is equal to the current multiplied by the time, which is (2.81 A) x (2.47 hours) x (3600 s/hour) = 24,104 C.
Therefore, the amount of radium produced is equal to (24,104 C) / (96,485 C/mol) x (113 g/mol) = 28.2 g.
So, 28.2 grams of radium may be formed by the passage of 2.81 amps for 2.47 hours through an electrolytic cell that contains a molten radium salt.