Find moles of electrons present in 64 g of ` CH_4`

Options

A. 64
B. 40
C. 24
D. 16

Answer

To find the moles of electrons present in 64 g of CH₄ (methane), we can follow these steps:

### Step 1: Calculate the molar mass of CH₄
The molar mass of CH₄ can be calculated by adding the atomic masses of carbon (C) and hydrogen (H):
- 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 calculation is:
\[ \text{Molar mass of CH₄} = 12 \, \text{g/mol (C)} + 4 \times 1 \, \text{g/mol (H)} = 12 + 4 = 16 \, \text{g/mol} \]

### Step 2: Calculate the number of moles of CH₄ in 64 g
Using the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
we can find the number of moles of CH₄:
\[ \text{Number of moles of CH₄} = \frac{64 \, \text{g}}{16 \, \text{g/mol}} = 4 \, \text{moles} \]

### Step 3: Determine the number of electrons in CH₄
In CH₄, each carbon atom shares electrons with four hydrogen atoms. The total number of electrons contributed by each atom is:
- Carbon (C) contributes 4 valence electrons.
- Each Hydrogen (H) contributes 1 valence electron.

Thus, the total number of electrons in one molecule of CH₄ is:
\[ \text{Electrons in CH₄} = 4 \, \text{(from C)} + 4 \times 1 \, \text{(from H)} = 4 + 4 = 8 \, \text{electrons} \]

### Step 4: Calculate the total number of electrons in 4 moles of CH₄
To find the total number of electrons in 4 moles of CH₄, we can use Avogadro's number (approximately \(6.022 \times 10^{23}\) molecules/mol):
\[ \text{Total number of molecules in 4 moles} = 4 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mol} = 2.4088 \times 10^{24} \, \text{molecules} \]

Now, we multiply the number of molecules by the number of electrons per molecule:
\[ \text{Total electrons} = 2.4088 \times 10^{24} \, \text{molecules} \times 8 \, \text{electrons/molecule} = 1.92704 \times 10^{25} \, \text{electrons} \]

### Final Answer
The total number of moles of electrons present in 64 g of CH₄ can be calculated by dividing the total number of electrons by Avogadro's number:
\[ \text{Moles of electrons} = \frac{1.92704 \times 10^{25} \, \text{electrons}}{6.022 \times 10^{23} \, \text{electrons/mol}} \approx 32 \, \text{moles of electrons} \]