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 number of moles of CH₄
To calculate the number of moles, we use the formula:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

Given:
- Mass of CH₄ = 1.6 g

First, we need to find the molar mass of CH₄:
- Atomic mass of Carbon (C) = 12 g/mol
- Atomic mass of Hydrogen (H) = 1 g/mol
- Since there are 4 hydrogen atoms in CH₄, the total mass of hydrogen = 4 × 1 = 4 g/mol

Now, calculate the molar mass of CH₄:
\[ \text{Molar mass of CH₄} = 12 + 4 = 16 \text{ g/mol} \]

Now, substituting the values into the number of moles formula:
\[ \text{Number of moles of CH₄} = \frac{1.6 \text{ g}}{16 \text{ g/mol}} = 0.1 \text{ moles} \]

### Step 2: Calculate the number of electrons in one molecule of CH₄
In one molecule of CH₄:
- Carbon has 6 electrons.
- Each of the 4 hydrogen atoms has 1 electron.

Total number of electrons in CH₄:
\[ \text{Total electrons} = 6 + (4 \times 1) = 10 \text{ electrons} \]

### Step 3: Calculate the total number of molecules in 0.1 moles of CH₄
Using Avogadro's number (6.022 × 10²³ molecules/mol):
\[ \text{Number of molecules in 0.1 moles} = 0.1 \times 6.022 \times 10^{23} = 6.022 \times 10^{22} \text{ molecules} \]

### Step 4: Calculate the total number of electrons in 1.6 g of CH₄
Now, we can find the total number of electrons:
\[ \text{Total electrons} = \text{Number of molecules} \times \text{Electrons per molecule} \]
\[ \text{Total electrons} = 6.022 \times 10^{22} \text{ molecules} \times 10 \text{ electrons/molecule} = 6.022 \times 10^{23} \text{ electrons} \]

### Conclusion
Thus, the number of electrons in 1.6 g of CH₄ is approximately \(6.022 \times 10^{23}\) electrons, which can be rounded to \(6 \times 10^{23}\) electrons.