Question

What is the number of moles of electrons passed when current of 5 ampere is passed through a solution of $\text{FeCl}_3$ for 20 minutes?

• A. $6.25 \times 10^{-2}$
• B. $1.56 \times 10^{-2}$
• C. $3.12 \times 10^{-2}$
• D. $4.25 \times 10^{-2}$

Hint:

Do not let the chemical formula $\text{FeCl}_3$ trick you into overcomplicating things with valency factors or equivalence ratios!
When a question asks for the "moles of electrons passed," it is purely tracking the total electric charge flowing through the wire: $\text{Moles of } e^{-} = \frac{I \times t}{96500}$.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The problem asks for the total quantity of electrons, expressed specifically in moles, that flow through an electrolytic circuit when a current of 5 A is sustained for a duration of 20 minutes.

Step 2: Key Formula or Approach:
First, calculate the total electrical charge ($Q$) in Coulombs passed through the solution using Faraday's relationship:
$$Q = I \times t$$
Where $I$ is the current in Amperes and $t$ is the elapsed time converted strictly into standard seconds.
By physical definition, the charge carried by exactly one mole of electrons is equal to 1 Faraday ($1\ \text{F} \approx 96500\ \text{C}$). Therefore, the number of moles of electrons is:
$$\text{Moles of electrons} = \frac{Q}{96500}$$
The identity of the solute ($\text{FeCl}_3$) is extra information here because the question asks for the total electrons passed through the circuit, not the mass of metal deposited.

Step 3: Detailed Explanation:
Let's list our variables and execute the calculation:
Current ($I$) = $5\ \text{A}$
Time ($t$) = $20\ \text{minutes} = 20 \times 60\ \text{seconds} = 1200\ \text{s}$
Calculate total charge $Q$:
$$Q = 5\ \text{A} \times 1200\ \text{s} = 6000\ \text{C}$$
Now, convert this charge into moles of electrons by dividing by the Faraday constant:
$$\text{Moles of electrons} = \frac{6000\ \text{C}}{96500\ \text{C/mol}} \approx 0.062176\ \text{mol}$$
Expressing this in proper scientific notation gives:
$$\text{Moles of electrons} \approx 6.22 \times 10^{-2}\ \text{mol}$$
This closely rounds to the value $6.25 \times 10^{-2}$ provided in option (A).

Step 4: Final Answer:
The total number of moles of electrons passed through the solution is $6.25 \times 10^{-2}$, matching option (A).