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 comparing the total number of electrons in 1.6 g of CH₄ (methane) to that in 1.8 g of H₂O (water), we will follow these steps:

### Step 1: Calculate the molar mass of CH₄
- The molar mass of CH₄ is 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 in CH₄.

\[ \text{Molar mass of CH₄} = 12 \, \text{g/mol (C)} + 4 \times 1 \, \text{g/mol (H)} = 16 \, \text{g/mol} \]

### Step 2: Calculate the number of moles of CH₄ in 1.6 g
- Using the molar mass, we can find the number of moles in 1.6 g of CH₄:

\[ \text{Number of moles of CH₄} = \frac{1.6 \, \text{g}}{16 \, \text{g/mol}} = 0.1 \, \text{mol} \]

### Step 3: Calculate the number of molecules of CH₄
- The number of molecules can be calculated using Avogadro's number (6.022 × 10²³ molecules/mol):

\[ \text{Number of molecules of CH₄} = 0.1 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} = 6.022 \times 10^{22} \, \text{molecules} \]

### Step 4: Calculate the total number of electrons in CH₄
- Each molecule of CH₄ contains:
- 1 Carbon atom (6 electrons) + 4 Hydrogen atoms (4 electrons) = 10 electrons

\[ \text{Total electrons in CH₄} = 10 \, \text{electrons/molecule} \times 6.022 \times 10^{22} \, \text{molecules} = 6.022 \times 10^{23} \, \text{electrons} \]

### Step 5: Calculate the molar mass of H₂O
- The molar mass of H₂O is calculated as follows:
- Oxygen (O) has an atomic mass of 16 g/mol.
- Hydrogen (H) has an atomic mass of 1 g/mol, and there are 2 hydrogen atoms in H₂O.

\[ \text{Molar mass of H₂O} = 2 \times 1 \, \text{g/mol (H)} + 16 \, \text{g/mol (O)} = 18 \, \text{g/mol} \]

### Step 6: Calculate the number of moles of H₂O in 1.8 g
- Using the molar mass, we can find the number of moles in 1.8 g of H₂O:

\[ \text{Number of moles of H₂O} = \frac{1.8 \, \text{g}}{18 \, \text{g/mol}} = 0.1 \, \text{mol} \]

### Step 7: Calculate the number of molecules of H₂O
- The number of molecules can be calculated using Avogadro's number:

\[ \text{Number of molecules of H₂O} = 0.1 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} = 6.022 \times 10^{22} \, \text{molecules} \]

### Step 8: Calculate the total number of electrons in H₂O
- Each molecule of H₂O contains:
- 2 Hydrogen atoms (2 electrons) + 1 Oxygen atom (8 electrons) = 10 electrons

\[ \text{Total electrons in H₂O} = 10 \, \text{electrons/molecule} \times 6.022 \times 10^{22} \, \text{molecules} = 6.022 \times 10^{23} \, \text{electrons} \]

### Conclusion
- The total number of electrons in 1.6 g of CH₄ is equal to the total number of electrons in 1.8 g of H₂O:

\[ \text{Electrons in CH₄} = \text{Electrons in H₂O} = 6.022 \times 10^{23} \]

Thus, the answer is that the total number of electrons in both cases is the same.

### Final Answer
- The answer is **Option B: Same**.

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