Given that M is the mass of a substance deposited during electrolysis and Q is the quantity of electricity…

Analysis

The question asks for the mathematical expression of Faraday’s First Law of Electrolysis, which relates the mass of a substance deposited at an electrode to the quantity of electricity passed through the electrolyte.

Concept Explanation

Faraday’s First Law of Electrolysis states that the mass ($M$) of a substance deposited or liberated during electrolysis is directly proportional to the quantity of electricity ($Q$) passed through the electrolyte.

Mathematically, this is expressed as: $M \propto Q$

To remove the proportionality sign, we introduce a constant of proportionality, $Z$, which represents the electrochemical equivalent of the substance. $M = ZQ$

In the context of this specific question, the symbol E is used to represent the electrochemical equivalent. Therefore, the formula becomes: $M = EQ$

Step-by-Step Solution

1. Identify the variables: • $M$ = Mass of the substance deposited. • $Q$ = Quantity of electricity. • $E$ = Electrochemical equivalent.
2. Apply the Law: According to Faraday's first law, the mass deposited is the product of the electrochemical equivalent and the quantity of electricity.
3. Formulate the equation: $M = E \times Q$ or $M = EQ$.

Conclusion

Comparing our derived formula ($M = EQ$) with the given options:

• Option A: $M = E/Q$ (Incorrect)
• Option B: $M = EQ$ (Correct)
• Option C: $M = Q/E$ (Incorrect)
• Option D: $M = E/2Q$ (Incorrect)

Exam Tip

Remember the mnemonic "MEQ" (like "Make" or "Me Q"). If you ever forget the formula, just remember that the mass ($M$) increases as you increase the quantity of electricity ($Q$), so they must be multiplied by the constant ($E$), not divided.