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: Determine the molecular weight of dinitrogen (N₂)
Dinitrogen consists of two nitrogen atoms. The atomic weight of nitrogen (N) is approximately 14 g/mol. Therefore, the molecular weight of dinitrogen (N₂) is calculated as follows:
\[ \text{Molecular weight of N₂} = 2 \times 14 \, \text{g/mol} = 28 \, \text{g/mol} \]

### Step 2: Calculate the number of moles of dinitrogen in 1.4 g
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{Given weight}}{\text{Molecular weight}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{1.4 \, \text{g}}{28 \, \text{g/mol}} = 0.05 \, \text{moles} \]

### Step 3: Calculate the number of molecules in 0.05 moles of dinitrogen
Using Avogadro's number (approximately \(6.022 \times 10^{23}\) molecules/mol), we can find the number of molecules:
\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \]
Substituting the values:
\[ \text{Number of molecules} = 0.05 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mol} \approx 3.011 \times 10^{22} \, \text{molecules} \]

### Step 4: Calculate the total number of electrons in dinitrogen
Each nitrogen atom has 7 electrons. Since there are 2 nitrogen atoms in a dinitrogen molecule (N₂), each molecule of dinitrogen has:
\[ \text{Electrons per molecule} = 2 \times 7 = 14 \, \text{electrons} \]
Now, we can find the total number of electrons in 3.011 x \(10^{22}\) molecules:
\[ \text{Total number of electrons} = \text{Number of molecules} \times \text{Electrons per molecule} \]
Substituting the values:
\[ \text{Total number of electrons} = 3.011 \times 10^{22} \, \text{molecules} \times 14 \, \text{electrons/molecule} \approx 4.2154 \times 10^{23} \, \text{electrons} \]

### Final Answer
The total number of electrons present in 1.4 g of dinitrogen gas is approximately \(4.2154 \times 10^{23}\) electrons.

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