A Gaseous compound of Nitrogen and Hydrogen conains 12.5% by weight of Hydrogen. The density of the compound relative to Dydrogen is 16, the molecular formula of the compound is

Options

A. `NH_(2)`
B. `NH_(3)`
C. `NH_(4)`
D. `N_(2)H_(4)`

Explanation

To find the molecular formula of the gaseous compound containing nitrogen and hydrogen, we will follow these steps:

### Step 1: Determine the mass of each element in the compound.
Given that the compound contains 12.5% by weight of hydrogen, we can find the percentage of nitrogen:
- Percentage of Nitrogen = 100% - 12.5% = 87.5%

Assuming we have 100 g of the compound:
- Mass of Hydrogen = 12.5 g
- Mass of Nitrogen = 87.5 g

### Step 2: Calculate the number of moles of each element.
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

- Molar mass of Hydrogen (H) = 1 g/mol
- Molar mass of Nitrogen (N) = 14 g/mol

Calculating the moles:
- Moles of Hydrogen = \( \frac{12.5 \, \text{g}}{1 \, \text{g/mol}} = 12.5 \, \text{moles} \)
- Moles of Nitrogen = \( \frac{87.5 \, \text{g}}{14 \, \text{g/mol}} \approx 6.25 \, \text{moles} \)

### Step 3: Find the simplest mole ratio.
Now, we will find the ratio of the moles of nitrogen to the moles of hydrogen:
- Ratio of N to H = \( \frac{6.25}{12.5} = \frac{1}{2} \)

This means for every 1 mole of nitrogen, there are 2 moles of hydrogen. Therefore, the empirical formula is:
- Empirical Formula = \( \text{NH}_2 \)

### Step 4: Calculate the molar mass of the empirical formula.
- Molar mass of \( \text{NH}_2 = 14 \, \text{g/mol (N)} + 2 \times 1 \, \text{g/mol (H)} = 16 \, \text{g/mol} \)

### Step 5: Use the density to find the molecular formula.
Given the density of the compound relative to hydrogen is 16, we can find the molecular weight of the compound using the formula:
\[ \text{Molecular weight} = 2 \times \text{vapour density} \]
- Vapour density = 16
- Molecular weight = \( 2 \times 16 = 32 \, \text{g/mol} \)

### Step 6: Determine the molecular formula.
Now, we can find the ratio of the molar mass of the compound to the molar mass of the empirical formula:
\[ \text{Ratio} = \frac{\text{Molecular weight}}{\text{Molar mass of empirical formula}} = \frac{32 \, \text{g/mol}}{16 \, \text{g/mol}} = 2 \]

Thus, the molecular formula is:
- Molecular Formula = \( \text{(NH}_2)_2 = \text{N}_2\text{H}_4 \)

### Final Answer:
The molecular formula of the compound is \( \text{N}_2\text{H}_4 \).

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