m = (M × I × t)/(n × F). Calculate mass deposited.

Faraday's Laws of Electrolysis

Question

A current of 2 A is passed through a solution of copper sulphate (CuSO₄) for 30 minutes. Calculate the mass of copper deposited at the cathode.

(Atomic mass of Cu = 63.5 g/mol, n-factor of Cu²⁺ = 2, Faraday constant F = 96500 C/mol)

Solution — Step by Step

The mass deposited is:

m = \frac{M \times I \times t}{n \times F}

where M = molar mass, I = current in amperes, t = time in seconds, n = valency (electrons exchanged), F = 96500 C/mol.

This is the most common slip in board exams — the formula demands seconds, not minutes.

t = 30 \times 60 = 1800 \text{ s}

In CuSO₄, copper exists as Cu²⁺. When it deposits at the cathode:

\text{Cu}^{2+} + 2e^- \rightarrow \text{Cu}

So n = 2 (two electrons transferred per atom).

m = \frac{63.5 \times 2 \times 1800}{2 \times 96500}

m = \frac{2,28,600}{1,93,000} = \frac{228600}{193000}

m \approx 1.185 \text{ g}

Mass of copper deposited ≈ 1.185 g

Why This Works

Faraday’s First Law tells us that mass deposited is proportional to charge passed (Q = I × t). The more charge, the more ions discharged at the electrode — makes physical sense.

The n in the denominator accounts for how many electrons each ion needs. Cu²⁺ needs 2 electrons, so the same charge deposits half as many moles compared to a monovalent ion like Ag⁺. This is essentially Faraday’s Second Law — equal charge deposits chemically equivalent amounts.

The ratio M/n is called the electrochemical equivalent weight (gram equivalent mass). For copper it’s 63.5/2 = 31.75 g/equivalent. Students appearing for JEE Main will sometimes see this quantity written as Z (the electrochemical equivalent in g/C).

Alternative Method (Using Electrochemical Equivalent)

Z = \frac{M}{n \times F} \quad \text{(in g/C)}

m = Z \times I \times t = Z \times Q

First calculate Z for copper:

Z = \frac{63.5}{2 \times 96500} = 3.29 \times 10^{-4} \text{ g/C}

Then calculate charge:

Q = I \times t = 2 \times 1800 = 3600 \text{ C}

Finally:

m = 3.29 \times 10^{-4} \times 3600 \approx 1.185 \text{ g}

Same answer. This method is faster when the question gives you Q directly instead of I and t separately.

Common Mistake

Using t = 30 minutes directly in the formula.

The formula requires time in seconds. If you plug in t = 30, you get m = 0.0197 g — a physically unreasonable answer that many students don’t question. Always convert: 30 min = 1800 s. This mistake costs 1–2 marks in board exams every year.

For NCERT-based questions, always double-check the n-factor from the ionic equation, not just the name. CuCl and CuSO₄ both contain copper — but Cu⁺ gives n = 1 while Cu²⁺ gives n = 2. Getting n wrong flips your entire answer.

Question

Solution — Step by Step

Why This Works

Alternative Method (Using Electrochemical Equivalent)

Common Mistake

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