First law: The amount of the substance liberated or deposited or dissolved at an electrode during electrolysis of an electrolyte is directly proportional to the quantity of electricity passing through the solution of electrolyte or melt. Mathematically Faraday’s first law is \(m \propto q\) or \(m = eq\) or \(m = ect\), where m is the mass of the substance liberated or deposited or dissolved, q is the quantity of electricity in coulomb, t is the time in seconds, c is the strength of current in amperes and e is the electrochemical equivalent of the ion or metal or molecule deposited or liberated or dissolved at the electrode.
Chemical equivalent of a substance is the amount of substance deposited or liberated or dissolved or had undergone electrode reaction at an electrode during the passage of one Faraday of electricity during the electrolysis of electrolyte solution or melt.
\(\text{Chemical equivalent of an element or ion = }\frac{\text{Atomic weight}}{\text{Valency or charge of the ion}}\)
Second law of Faraday states that if same quantity of electricity is passed through different electrolyte solutions or melts, the amount of the different substances liberated or deposited or dissolved or had undergone reaction at electrode is directly proportional to their chemical equivalents.
\( \displaystyle \frac{W_1}{E_1} = \frac{W_2}{E_2} = \frac{W_3}{E_3} \)
According to Faraday’s second law of electrolysis, a given quantity of electricity produces
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → the same number of equivalents of any substance in electrolysis
The passage states the second law: when the same quantity of electricity is passed through different electrolytes, the amounts of the substances liberated or deposited are directly proportional to their chemical equivalents:
\( \displaystyle \frac{W_1}{E_1}=\frac{W_2}{E_2}=\frac{W_3}{E_3} \)
W/E is the number of equivalents of each substance. Since this ratio is the same for every substance, a given quantity of electricity produces the same number of equivalents of each.
Why the other options are incorrect
Option (1) the same number of moles of any substance in electrolysis — Incorrect. Ions of different charge need different numbers of electrons per mole. One mole of electrons deposits 1 mol of Ag from \( \ce{Ag^+} \) but only 0.5 mol of Cu from \( \ce{Cu^2+} \).
Option (2) the same number of atoms of any substance in electrolysis — Incorrect. The number of atoms follows the number of moles, so it too differs with the charge on the ion: one \( \ce{Ag^+} \) takes one electron, one \( \ce{Cu^2+} \) takes two.
Option (4) the same volume of any gas in electrolysis — Incorrect. Gases also need different numbers of electrons per molecule: one \( \ce{H2} \) molecule needs 2 electrons but one \( \ce{O2} \) molecule needs 4, so the same charge gives twice as much hydrogen as oxygen by volume.