Question

The number of electrons in one mole of methane (CH\(_4\)) is:

• A. \( 6.023 \times 10^{23} \)
• B. \( 60.23 \times 10^{23} \)
• C. \( 0.6023 \times 10^{23} \)
• D. \( 602.3 \times 10^{23} \)
• E. \( 6023 \times 10^{23} \)

Hint:

To calculate the total number of electrons in one mole of a compound, multiply the number of electrons in one molecule by Avogadro's number, \( 6.023 \times 10^{23} \).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
To find the total number of electrons in a mole of a substance, we must determine the number of electrons in a single molecule first.
Then, we multiply that count by the total number of molecules in a mole (Avogadro's number).
Step 2: Key Formula or Approach:
The formula is: Total electrons = (Electrons per molecule) \(\times\) (Number of moles) \(\times\) (Avogadro's number, \(N_{A}\)).
Avogadro's number is approximately \(6.023 \times 10^{23} \text{ mol}^{-1}\).
Step 3: Detailed Explanation:
First, we count the electrons in one molecule of methane (CH\(_{4}\)).
A carbon atom (C) has an atomic number of 6, meaning it contains 6 electrons.
A hydrogen atom (H) has an atomic number of 1, meaning it contains 1 electron.
The total number of electrons in one CH\(_{4}\) molecule is \(6 + 4(1) = 10\) electrons.
Since one mole of methane contains \(6.023 \times 10^{23}\) molecules, we multiply this by the electron count per molecule.
\[ \text{Total electrons} = 10 \times 6.023 \times 10^{23} \] \[ \text{Total electrons} = 60.23 \times 10^{23} \] Step 4: Final Answer:
There are \(60.23 \times 10^{23}\) electrons in one mole of methane.