Question

What is the number of electrons passed through an electrolyte solution when 1 ampere current is passed for 16.1 minutes?

• A. $5.022 \times 10^{24}$
• B. $3.011 \times 10^{22}$
• C. $6.022 \times 10^{21}$
• D. $2.022 \times 10^{23}$

Hint:

Always ensure time is converted to seconds when working with Amperes to get Coulombs. $1\text{ Ampere} = 1\text{ Coulomb per second}$.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We need to calculate the exact number of electrons that flow through a circuit given the current in amperes and the time in minutes.

Step 2: Key Formula or Approach:
First, calculate the total electrical charge ($Q$) in Coulombs using the formula: $Q = I \times t$, where $I$ is current in Amperes and $t$ is time in seconds.
Next, determine the number of moles of electrons using Faraday's constant ($1\text{ F} = 96500\text{ C/mol}$): $\text{Moles of } e^- = \frac{Q}{96500}$.
Finally, multiply by Avogadro's number ($N_A = 6.022 \times 10^{23}$) to find the total number of electrons.

Step 3: Detailed Explanation:
Convert time to seconds:
$t = 16.1\text{ min} = 16.1 \times 60\text{ s} = 966\text{ s}$.
Calculate total charge:
$Q = 1\text{ A} \times 966\text{ s} = 966\text{ C}$.
Calculate moles of electrons passed:
$\text{Moles of } e^- = \frac{966\text{ C}}{96500\text{ C/mol}} \approx 0.01\text{ moles}$.
Calculate total number of electrons:
$\text{Number of } e^- = 0.01\text{ mol} \times 6.022 \times 10^{23}\text{ electrons/mol}$.
$\text{Number of } e^- = 6.022 \times 10^{21}$.

Step 4: Final Answer:
The number of electrons is $6.022 \times 10^{21}$, which corresponds to option (C).