What will be the molecular formula of a compound with vapour density 15 and empirical formula `CH_2O`?

Options

A. `C_2H_4O_2`
B. `C_6H_12O_12`
C. `CH_2O`
D. `C_6H_6O`

Explanation

To determine the molecular formula of a compound with a given vapor density and empirical formula, we can follow these steps:

### Step 1: Understand Vapor Density
Vapor density (VD) is defined as the density of a gas compared to the density of hydrogen. It can also be expressed in terms of molar mass (M) of the compound:
\[ \text{Vapor Density} = \frac{\text{Molar Mass}}{2} \]

### Step 2: Calculate Molar Mass from Vapor Density
Given that the vapor density of the compound is 15, we can calculate the molar mass (M) as follows:
\[ M = \text{Vapor Density} \times 2 \]
\[ M = 15 \times 2 = 30 \, \text{g/mol} \]

### Step 3: Find the Mass of the Empirical Formula
The empirical formula given is \( CH_2O \). To find the mass of the empirical formula, we calculate the molar mass of \( CH_2O \):
- Carbon (C): 12 g/mol
- Hydrogen (H): 1 g/mol (2 H atoms contribute 2 g/mol)
- Oxygen (O): 16 g/mol

Calculating the total:
\[ \text{Mass of } CH_2O = 12 + 2 + 16 = 30 \, \text{g/mol} \]

### Step 4: Determine the Value of n
To find the molecular formula, we need to determine the value of \( n \), which is the ratio of the molar mass of the compound to the mass of the empirical formula:
\[ n = \frac{\text{Molar Mass}}{\text{Mass of Empirical Formula}} \]
\[ n = \frac{30}{30} = 1 \]

### Step 5: Write the Molecular Formula
Since \( n = 1 \), the molecular formula is the same as the empirical formula. Thus, the molecular formula is:
\[ \text{Molecular Formula} = (CH_2O) \times 1 = CH_2O \]

### Conclusion
The molecular formula of the compound is \( CH_2O \), which is known as formaldehyde.

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