If 16 g of `H_(2)` and 56 g of `N_(2)` are present in a 2 liter vessel at STP then the total number of molecules in the vessel will be

Options

A. ` 6.022 xx 10^(23)`
B. `6.022 xx 10^(24)`
C. ` 6.022 xx 10^(25) `
D. `6.022 xx 10^(22)`

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the number of moles of \( H_2 \)
To find the number of moles of hydrogen gas (\( H_2 \)), we use the formula:

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

Given:
- Mass of \( H_2 = 16 \, \text{g} \)
- Molar mass of \( H_2 = 2 \, \text{g/mol} \)

Now, substituting the values:

\[ \text{Number of moles of } H_2 = \frac{16 \, \text{g}}{2 \, \text{g/mol}} = 8 \, \text{moles} \]

### Step 2: Calculate the number of moles of \( N_2 \)
Next, we calculate the number of moles of nitrogen gas (\( N_2 \)) using the same formula:

Given:
- Mass of \( N_2 = 56 \, \text{g} \)
- Molar mass of \( N_2 = 28 \, \text{g/mol} \)

Now, substituting the values:

\[ \text{Number of moles of } N_2 = \frac{56 \, \text{g}}{28 \, \text{g/mol}} = 2 \, \text{moles} \]

### Step 3: Calculate the total number of moles in the mixture
Now, we can find the total number of moles in the vessel by adding the moles of \( H_2 \) and \( N_2 \):

\[ \text{Total moles} = \text{Moles of } H_2 + \text{Moles of } N_2 = 8 + 2 = 10 \, \text{moles} \]

### Step 4: Calculate the total number of molecules
Now, we use Avogadro's number to find the total number of molecules. Avogadro's number is:

\[ N_A = 6.022 \times 10^{23} \, \text{molecules/mol} \]

To find the total number of molecules in 10 moles:

\[ \text{Total molecules} = \text{Total moles} \times N_A = 10 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mol} \]

Calculating this gives:

\[ \text{Total molecules} = 6.022 \times 10^{24} \, \text{molecules} \]

### Final Answer
The total number of molecules in the vessel is \( 6.022 \times 10^{24} \, \text{molecules} \).

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