If `N_(A)` is Avogadro's number then number of valence electrons in 4.2 g of nitride ions `(N^(3-))`

Options

A. (a)`2.4 N_(A)`
B. (b)`4.2 N_(A)`
C. (c )`1.6 N_(A)`
D. (d)`3.2 N_(A)`

Explanation

To find the number of valence electrons in 4.2 g of nitride ions (N³⁻), we can follow these steps:

### Step 1: Determine the molar mass of nitride ions (N³⁻)
The atomic mass of nitrogen (N) is approximately 14 g/mol. Since the nitride ion is derived from nitrogen, its molar mass is also 14 g/mol.

### Step 2: Calculate the number of moles of nitride ions in 4.2 g
To find the number of moles of nitride ions in 4.2 g, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{4.2 \, \text{g}}{14 \, \text{g/mol}} = 0.3 \, \text{mol} \]

### Step 3: Determine the number of valence electrons in one nitride ion
The nitride ion (N³⁻) has gained three additional electrons compared to a neutral nitrogen atom. A neutral nitrogen atom has 5 valence electrons (since it is in group 15 of the periodic table). Therefore, the nitride ion has:
\[ 5 \, \text{(from N)} + 3 \, \text{(extra electrons)} = 8 \, \text{valence electrons} \]

### Step 4: Calculate the total number of valence electrons in 0.3 moles of nitride ions
Since each nitride ion has 8 valence electrons, the total number of valence electrons in 0.3 moles of nitride ions can be calculated as follows:
\[ \text{Total valence electrons} = \text{Number of moles} \times \text{Avogadro's number} \times \text{valence electrons per ion} \]
Substituting the values:
\[ \text{Total valence electrons} = 0.3 \, \text{mol} \times N_A \times 8 \]
Where \(N_A\) is Avogadro's number (approximately \(6.022 \times 10^{23}\) mol⁻¹).

### Step 5: Simplify the expression
Now we can simplify the expression:
\[ \text{Total valence electrons} = 0.3 \times 8 \times N_A = 2.4 \times N_A \]

### Conclusion
Thus, the total number of valence electrons in 4.2 g of nitride ions (N³⁻) is \(2.4 \times N_A\).

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