Number of lone pairs of electrons in 9 gms. Of water are [N= Avogadro Number]

Options

A. 2N
B. N/2
C. N
D. N/4

Answer

To determine the number of lone pairs of electrons in 9 grams of water (H₂O), we can follow these steps:

### Step 1: Calculate the molecular weight of water (H₂O)
- The molecular weight of water is calculated as follows:
- Hydrogen (H) has an atomic mass of approximately 1 g/mol, and there are 2 hydrogen atoms in water: \(2 \times 1 = 2\) g/mol.
- Oxygen (O) has an atomic mass of approximately 16 g/mol.
- Therefore, the molecular weight of water is:
\[ \text{Molecular weight of H₂O} = 2 + 16 = 18 \text{ g/mol} \]

### Step 2: Determine the number of moles in 9 grams of water
- To find the number of moles of water in 9 grams, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
- Substituting the values:
\[ \text{Number of moles of H₂O} = \frac{9 \text{ g}}{18 \text{ g/mol}} = 0.5 \text{ moles} \]

### Step 3: Calculate the number of molecules in 0.5 moles of water
- Using Avogadro's number (\(N_A\)), which is approximately \(6.022 \times 10^{23}\) molecules/mol, we can find the number of molecules in 0.5 moles:
\[ \text{Number of molecules} = 0.5 \text{ moles} \times N_A = \frac{N_A}{2} \]

### Step 4: Determine the number of lone pairs in one molecule of water
- In one molecule of water (H₂O), the oxygen atom has 2 lone pairs of electrons. Therefore:
\[ \text{Lone pairs in 1 molecule of H₂O} = 2 \]

### Step 5: Calculate the total number of lone pairs in 0.5 moles of water
- Since there are \(\frac{N_A}{2}\) molecules of water, the total number of lone pairs can be calculated as:
\[ \text{Total lone pairs} = \left(\frac{N_A}{2}\right) \times 2 = N_A \]

### Conclusion
- Therefore, the number of lone pairs of electrons in 9 grams of water is \(N_A\).