Calculate the number of moles and number of gram molecules contained in 56 g of `N_2`.

Answer

To solve the question of calculating the number of moles and the number of gram molecules contained in 56 g of \(N_2\), we can follow these steps:

### Step 1: Calculate the Molecular Mass of \(N_2\)
The molecular mass of nitrogen gas (\(N_2\)) can be calculated as follows:
- Each nitrogen atom has an atomic mass of approximately 14 g/mol.
- Since \(N_2\) consists of two nitrogen atoms, the molecular mass is:
\[ \text{Molecular mass of } N_2 = 2 \times 14 \, \text{g/mol} = 28 \, \text{g/mol} \]

### Step 2: Calculate the Number of Moles
The number of moles can be calculated using the formula:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molecular mass}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{56 \, \text{g}}{28 \, \text{g/mol}} = 2 \, \text{moles} \]

### Step 3: Calculate the Number of Gram Molecules
The number of gram molecules is equivalent to the number of moles, since 1 mole of any substance is defined as 1 gram molecule. Therefore:
\[ \text{Number of gram molecules} = 2 \, \text{gram molecules} \]

### Step 4: Calculate the Number of Molecules
To find the number of molecules, we can use Avogadro's number, which is \(6.022 \times 10^{23}\) molecules/mol. The number of molecules can be calculated as:
\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \]
Substituting the values:
\[ \text{Number of molecules} = 2 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mol} = 12.044 \times 10^{23} \, \text{molecules} \]

### Final Results
- Number of moles of \(N_2\) in 56 g: **2 moles**
- Number of gram molecules of \(N_2\) in 56 g: **2 gram molecules**
- Number of molecules in 56 g of \(N_2\): **\(12.044 \times 10^{23}\) molecules**