Calculate the total number of electrons present 1.4 g of dinitrogen gas.

Explanation

To calculate the total number of electrons present in 1.4 g of dinitrogen gas (N₂), we can follow these steps:

### Step 1: Calculate the Molar Mass of Dinitrogen (N₂)
The molar mass of nitrogen (N) is approximately 14 g/mol. Since dinitrogen (N₂) consists of two nitrogen atoms, we calculate the molar mass as follows:
\[ \text{Molar mass of N₂} = 14 \, \text{g/mol} \times 2 = 28 \, \text{g/mol} \]

### Step 2: Calculate the Number of Moles of Dinitrogen
Using the formula for moles:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Substituting the values:
\[ \text{Number of moles of N₂} = \frac{1.4 \, \text{g}}{28 \, \text{g/mol}} = 0.05 \, \text{moles} \]

### Step 3: Calculate the Number of Molecules of Dinitrogen
Using Avogadro's number, which is \( 6.022 \times 10^{23} \) molecules/mol, we can find the number of molecules in 0.05 moles:
\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \]
\[ \text{Number of molecules of N₂} = 0.05 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mol} \approx 3.01 \times 10^{23} \, \text{molecules} \]

### Step 4: Calculate the Number of Electrons in Dinitrogen
Each nitrogen atom has 7 electrons, so a dinitrogen molecule (N₂) contains:
\[ \text{Electrons in 1 N₂ molecule} = 2 \times 7 = 14 \, \text{electrons} \]
Now, to find the total number of electrons in all the molecules:
\[ \text{Total number of electrons} = \text{Number of molecules} \times \text{Electrons in 1 N₂ molecule} \]
\[ \text{Total number of electrons} = 3.01 \times 10^{23} \, \text{molecules} \times 14 \, \text{electrons/molecule} \]
\[ \text{Total number of electrons} \approx 4.214 \times 10^{24} \, \text{electrons} \]

### Final Answer:
The total number of electrons present in 1.4 g of dinitrogen gas is approximately \( 4.214 \times 10^{24} \) electrons.

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