Question

Find out the total number of electrons present in 3.2 g methane?

• A. $6.022\times10^{23}$
• B. $1.204\times10^{24}$
• C. $3.201\times10^{23}$
• D. $4.821\times10^{22}$

Hint:

Mole concept workflow for particle counting:
Mass $\xrightarrow{\div \text{ Molar Mass}}$ Moles $\xrightarrow{\times N_A}$ Molecules $\xrightarrow{\times \text{ Particles/molecule}}$ Total Particles.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are given a physical mass of methane ($\text{CH}_4$). We must calculate the total number of individual electrons present within that exact sample.

Step 2: Detailed Explanation:
1. Determine the number of moles of methane:
The chemical formula is $\text{CH}_4$.
Molar mass of $\text{CH}_4 = (1 \times 12) + (4 \times 1) = 16 \text{ g/mol}$.
Moles of methane ($n$) = $\frac{\text{Given Mass}}{\text{Molar Mass}} = \frac{3.2 \text{ g}}{16 \text{ g/mol}} = 0.2 \text{ moles}$.
2. Determine the number of methane molecules:
Number of molecules = $n \times N_A$ (Avogadro's constant, $\approx 6.022 \times 10^{23}$).
Number of molecules = $0.2 \times 6.022 \times 10^{23}$.
3. Determine the number of electrons in a single methane molecule:
A single Carbon atom (Z=6) has 6 electrons.
A single Hydrogen atom (Z=1) has 1 electron.
Total electrons in one $\text{CH}_4$ molecule = $6 + (4 \times 1) = 10 \text{ electrons}$.
4. Calculate total electrons in the entire sample:
Total electrons = Number of molecules $\times$ Electrons per molecule
Total electrons = $(0.2 \times 6.022 \times 10^{23}) \times 10$
Total electrons = $2 \times 6.022 \times 10^{23}$
Total electrons = $12.044 \times 10^{23}$
Adjust the decimal point to match standard scientific notation:
Total electrons = $1.204 \times 10^{24}$.

Step 3: Final Answer:
The total number of electrons is $1.204\times10^{24}$, matching option (b).