PASSAGE-II : Empirical formula is the simplest formula of the compound which gives the atomic ratio of various elements present in one molecule of the compound. However, the molecular formula of the compound gives the number of atoms of various elements present in one molecule of the compound. Molacular formula = (Empirical formula) `xxn`
implies `n=("Molecular mass")/("Empirical formula mass")`
A compound may have same empirical and molecular formula. Both these formulae are calculated using percentage composition of constituent elements.
10 g of hydrofluoric acid gas occupies 5.6 litre of volume at STP. If the empirical formula of the gas is HF, then its molecular formula in the gaseous state will be

Options

A. HF
B. `H_(2)F_(2)`
C. `H_(3)F_(3)`
D. `H_(4)F_(4)`

Explanation

To determine the molecular formula of hydrofluoric acid (HF) based on the information provided, we will follow these steps:

### Step 1: Understand the Given Information
We know that:
- Mass of hydrofluoric acid (HF) = 10 g
- Volume at STP = 5.6 L

### Step 2: Calculate the Number of Moles of HF
At Standard Temperature and Pressure (STP), 1 mole of any gas occupies 22.4 L. To find the number of moles of HF in 5.6 L, we can use the formula:

\[ \text{Number of moles} = \frac{\text{Volume}}{22.4 \, \text{L/mol}} \]

Substituting the values:

\[ \text{Number of moles} = \frac{5.6 \, \text{L}}{22.4 \, \text{L/mol}} = 0.25 \, \text{mol} \]

### Step 3: Calculate the Molar Mass of HF
Now, we can calculate the molar mass of HF using the mass and the number of moles we just calculated:

\[ \text{Molar Mass} = \frac{\text{Mass}}{\text{Number of moles}} = \frac{10 \, \text{g}}{0.25 \, \text{mol}} = 40 \, \text{g/mol} \]

### Step 4: Determine the Empirical Formula Mass
The empirical formula of hydrofluoric acid is HF. The molar mass of HF can be calculated as follows:
- Molar mass of H = 1 g/mol
- Molar mass of F = 19 g/mol

Thus, the empirical formula mass of HF is:

\[ \text{Empirical formula mass} = 1 + 19 = 20 \, \text{g/mol} \]

### Step 5: Calculate the Value of n
Using the formula for the molecular formula:

\[ n = \frac{\text{Molecular mass}}{\text{Empirical formula mass}} = \frac{40 \, \text{g/mol}}{20 \, \text{g/mol}} = 2 \]

### Step 6: Write the Molecular Formula
The molecular formula can be determined by multiplying the empirical formula by n:

\[ \text{Molecular formula} = (\text{Empirical formula}) \times n = HF \times 2 = H_2F_2 \]

### Conclusion
The molecular formula of hydrofluoric acid in the gaseous state is **H₂F₂**.

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