The number of electrons in 1.6 g of `CH_(4)` is approximately

Options

A. `25 xx 10^(24)`
B. `1.5 xx 10^(24)`
C. `6 xx 10^(23)`
D. `3.0 xx 10^(24)`

Answer

To find the number of electrons in 1.6 g of CH₄ (methane), we can follow these steps:

### Step 1: Calculate the moles of CH₄
To find the number of moles, we use the formula:

\[ \text{Moles of CH}_4 = \frac{\text{mass of CH}_4}{\text{molar mass of CH}_4} \]

The molar mass of CH₄ can be calculated as follows:
- Carbon (C) has an atomic mass of 12 g/mol.
- Hydrogen (H) has an atomic mass of 1 g/mol, and there are 4 hydrogen atoms.

Thus, the molar mass of CH₄ is:

\[ \text{Molar mass of CH}_4 = 12 + (4 \times 1) = 16 \text{ g/mol} \]

Now we can calculate the moles:

\[ \text{Moles of CH}_4 = \frac{1.6 \text{ g}}{16 \text{ g/mol}} = 0.1 \text{ mol} \]

### Step 2: Calculate the number of molecules of CH₄
To find the number of molecules, we use Avogadro's number (\(N_A\)), which is approximately \(6.022 \times 10^{23}\) molecules/mol.

\[ \text{Number of molecules} = \text{moles} \times N_A = 0.1 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} \]

Calculating this gives:

\[ \text{Number of molecules} = 0.1 \times 6.022 \times 10^{23} \approx 6.022 \times 10^{22} \text{ molecules} \]

### Step 3: Calculate the number of electrons in CH₄
Next, we need to find the total number of electrons in one molecule of CH₄.

- One carbon atom contributes 6 electrons.
- Each of the 4 hydrogen atoms contributes 1 electron.

Thus, the total number of electrons in one molecule of CH₄ is:

\[ \text{Total electrons in one molecule of CH}_4 = 6 + (4 \times 1) = 10 \text{ electrons} \]

### Step 4: Calculate the total number of electrons in 1.6 g of CH₄
Now, we multiply the total number of molecules by the number of electrons per molecule:

\[ \text{Total electrons} = \text{Number of molecules} \times \text{Electrons per molecule} \]

\[ \text{Total electrons} = 6.022 \times 10^{22} \text{ molecules} \times 10 \text{ electrons/molecule} \]

Calculating this gives:

\[ \text{Total electrons} \approx 6.022 \times 10^{23} \text{ electrons} \]

### Conclusion
The number of electrons in 1.6 g of CH₄ is approximately \(6.022 \times 10^{23}\) electrons.