The total number of electrons in 4.2 g of `N^(3-)` ion is (`N_(A)` is the Avogadro's number)

Options

A. `2.1 N_(A)`
B. `4.2 N_(A)`
C. `3 N_(A)`
D. `3.2 N_(A)`

Answer

To find the total number of electrons in 4.2 g of the N³⁻ ion, we can follow these steps:

### Step 1: Calculate the number of moles of N³⁻ ion.
The number of moles can be calculated using the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Given:
- Mass of N³⁻ ion = 4.2 g
- Molar mass of nitrogen (N) = 14 g/mol

Since the N³⁻ ion is derived from nitrogen, its molar mass remains 14 g/mol.

\[ \text{Number of moles of N³⁻} = \frac{4.2 \text{ g}}{14 \text{ g/mol}} = 0.3 \text{ moles} \]

### Step 2: Determine the number of electrons in one N³⁻ ion.
A neutral nitrogen atom has 7 electrons. Since the N³⁻ ion has gained 3 additional electrons (due to the 3 negative charges), the total number of electrons in one N³⁻ ion is:
\[ \text{Electrons in N³⁻} = 7 + 3 = 10 \text{ electrons} \]

### Step 3: Calculate the total number of electrons in 0.3 moles of N³⁻ ions.
Using Avogadro's number (Nₐ = \(6.022 \times 10^{23}\) mol⁻¹), we can find the total number of electrons in 0.3 moles of N³⁻ ions:
\[ \text{Total electrons} = \text{Number of moles} \times \text{Electrons per ion} \times Nₐ \]
Substituting the values:
\[ \text{Total electrons} = 0.3 \text{ moles} \times 10 \text{ electrons/ion} \times 6.022 \times 10^{23} \text{ mol}^{-1} \]
\[ \text{Total electrons} = 0.3 \times 10 \times 6.022 \times 10^{23} = 1.8066 \times 10^{24} \text{ electrons} \]

### Final Answer:
The total number of electrons in 4.2 g of N³⁻ ion is approximately \(1.81 \times 10^{24}\) electrons.

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