Number of electrons lost during electrolysis of `0.14g` of `N^(-3)` is `-(N_(0)=1` Avagadro number )

Options

A. `0.03`
B. `0.03N_(0)`
C. `0.015N_(0)`
D. `(0.01)/(2N_(0))`

Explanation

To find the number of electrons lost during the electrolysis of 0.14 g of \( N^{-3} \), we can follow these steps:

### Step 1: Calculate the number of moles of nitrogen (N)
To calculate the number of moles, we use the formula:

\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]

Given:
- Mass of nitrogen = 0.14 g
- Molar mass of nitrogen (N) = 14 g/mol

Substituting the values:

\[ \text{Number of moles of N} = \frac{0.14 \, \text{g}}{14 \, \text{g/mol}} = 0.01 \, \text{moles} \]

### Step 2: Determine the number of electrons lost per mole of nitrogen
Since nitrogen in the \( N^{-3} \) state has gained 3 electrons, during electrolysis, it will lose these 3 electrons. Therefore, for every mole of \( N^{-3} \), 3 moles of electrons are lost.

### Step 3: Calculate the total moles of electrons lost
To find the total moles of electrons lost, we multiply the number of moles of nitrogen by the number of electrons lost per mole:

\[ \text{Moles of electrons lost} = 3 \times \text{Number of moles of N} \]

Substituting the value we found in Step 1:

\[ \text{Moles of electrons lost} = 3 \times 0.01 = 0.03 \, \text{moles} \]

### Step 4: Convert moles of electrons to number of electrons
Using Avogadro's number (\( N_0 = 6.022 \times 10^{23} \) electrons/mole), we can find the total number of electrons lost:

\[ \text{Number of electrons lost} = \text{Moles of electrons lost} \times N_0 \]

Substituting the value from Step 3:

\[ \text{Number of electrons lost} = 0.03 \, \text{moles} \times 6.022 \times 10^{23} \, \text{electrons/mole} \]

Calculating this gives:

\[ \text{Number of electrons lost} = 0.03 \times 6.022 \times 10^{23} \approx 1.81 \times 10^{22} \, \text{electrons} \]

### Final Answer
The number of electrons lost during the electrolysis of 0.14 g of \( N^{-3} \) is approximately \( 1.81 \times 10^{22} \) electrons.

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