The total number of electrons in 1.6 g of `CH_(4)` to that in 1.8 g of `H_(2)O`

Options

A. Double
B. Same
C. Triple
D. One fourth

Answer

To solve the problem of finding the total number of electrons in 1.6 g of CH₄ (methane) compared to 1.8 g of H₂O (water), we will follow these steps:

### Step 1: Calculate the number of moles of CH₄
- Molar mass of CH₄:
- Carbon (C) = 12 g/mol
- Hydrogen (H) = 1 g/mol × 4 = 4 g/mol
- Total molar mass of CH₄ = 12 + 4 = 16 g/mol

Using the formula for moles:
\[ \text{Number of moles of CH₄} = \frac{\text{mass}}{\text{molar mass}} = \frac{1.6 \text{ g}}{16 \text{ g/mol}} = 0.1 \text{ moles} \]

### Step 2: Calculate the total number of electrons in CH₄
- Each molecule of CH₄ contains:
- 1 Carbon atom (6 electrons)
- 4 Hydrogen atoms (1 electron each, total 4 electrons)

Total electrons in one molecule of CH₄:
\[ 6 + 4 = 10 \text{ electrons} \]

Total electrons in 0.1 moles of CH₄:
\[ \text{Total electrons} = 0.1 \text{ moles} \times 10 \text{ electrons/molecule} \times N_A \]
Where \(N_A\) (Avogadro's number) = \(6.022 \times 10^{23}\):
\[ \text{Total electrons in CH₄} = 0.1 \times 10 \times 6.022 \times 10^{23} = 6.022 \times 10^{24} \text{ electrons} \]

### Step 3: Calculate the number of moles of H₂O
- Molar mass of H₂O:
- Hydrogen (H) = 1 g/mol × 2 = 2 g/mol
- Oxygen (O) = 16 g/mol
- Total molar mass of H₂O = 2 + 16 = 18 g/mol

Using the formula for moles:
\[ \text{Number of moles of H₂O} = \frac{\text{mass}}{\text{molar mass}} = \frac{1.8 \text{ g}}{18 \text{ g/mol}} = 0.1 \text{ moles} \]

### Step 4: Calculate the total number of electrons in H₂O
- Each molecule of H₂O contains:
- 2 Hydrogen atoms (1 electron each, total 2 electrons)
- 1 Oxygen atom (6 electrons)

Total electrons in one molecule of H₂O:
\[ 2 + 6 = 8 \text{ electrons} \]

Total electrons in 0.1 moles of H₂O:
\[ \text{Total electrons} = 0.1 \text{ moles} \times 8 \text{ electrons/molecule} \times N_A \]
\[ \text{Total electrons in H₂O} = 0.1 \times 8 \times 6.022 \times 10^{23} = 4.818 \times 10^{24} \text{ electrons} \]

### Step 5: Compare the total number of electrons
- Total electrons in CH₄ = \(6.022 \times 10^{24}\)
- Total electrons in H₂O = \(4.818 \times 10^{24}\)

### Conclusion
The total number of electrons in 1.6 g of CH₄ is greater than that in 1.8 g of H₂O.

### Final Result
The total number of electrons in CH₄ is approximately 1.25 times that in H₂O.