How much calcium will be obtained when 4 Faradays of electricity is passed through molten \(CaCl_2\)?

80 g

The correct answer is option 3. 80 g.

To determine how much calcium will be obtained when 4 Faradays of electricity is passed through molten calcium chloride (\(CaCl_2\)), we can use the concept of electrolysis and Faraday’s laws of electrolysis.

During the electrolysis of molten \(CaCl_2\), calcium ions (\(Ca^{2+}\)) are reduced to calcium metal:

\(Ca^{2+} + 2e^- \rightarrow Ca\)

This reaction shows that 2 moles of electrons (\(2 \, \text{Faradays}\)) are required to reduce 1 mole of calcium (\(Ca\)).

The molar mass of calcium is 40 g/mol.

According to Faraday’s law, the amount of substance deposited or liberated at an electrode is directly proportional to the amount of electricity (Faradays) passed through the electrolyte.

From the reaction, we know that 2 Faradays of electricity deposit 1 mole of calcium, which has a mass of 40 g.

Given:

We are passing 4 Faradays of electricity, and we know that 2 Faradays deposit 40 g of calcium.

If 2 Faradays deposit 40 g of calcium, then 4 Faradays will deposit:

\(\text{Mass of calcium} = \frac{4 \, \text{Faradays}}{2 \, \text{Faradays}} \times 40 \, \text{g} = 80 \, \text{g}\)

The amount of calcium obtained when 4 Faradays of electricity is passed through molten \(CaCl_2\) is 80 g.