The empirical formula of a compound is `CH_2O` and its vapour density is 30. The molecular formula of the compound is:

Options

A. `C_3H_6O_3`
B. `C_2H_4O_2`
C. `CH_2O`
D. `C_2H_4O`

Explanation

To find the molecular formula of the compound with an empirical formula of CH₂O and a vapor density of 30, we can follow these steps:

### Step 1: Calculate the Molecular Weight
The molecular weight can be calculated using the formula:
\[ \text{Molecular Weight} = 2 \times \text{Vapor Density} \]
Given that the vapor density is 30:
\[ \text{Molecular Weight} = 2 \times 30 = 60 \]

### Step 2: Calculate the Empirical Weight
Next, we need to calculate the empirical weight of the compound based on its empirical formula CH₂O. The empirical weight is calculated as follows:
- Carbon (C): 1 × 12 = 12
- Hydrogen (H): 2 × 1 = 2
- Oxygen (O): 1 × 16 = 16

Adding these together:
\[ \text{Empirical Weight} = 12 + 2 + 16 = 30 \]

### Step 3: Determine the Value of n
Now, we can find the value of n, which is the ratio of the molecular weight to the empirical weight:
\[ n = \frac{\text{Molecular Weight}}{\text{Empirical Weight}} \]
Substituting the values we calculated:
\[ n = \frac{60}{30} = 2 \]

### Step 4: Calculate the Molecular Formula
The molecular formula can be determined by multiplying the empirical formula by n:
\[ \text{Molecular Formula} = n \times \text{Empirical Formula} \]
Substituting the values:
\[ \text{Molecular Formula} = 2 \times \text{CH}_2\text{O} \]
This results in:
- Carbon: 2 × 1 = 2
- Hydrogen: 2 × 2 = 4
- Oxygen: 2 × 1 = 2

Thus, the molecular formula is:
\[ \text{C}_2\text{H}_4\text{O}_2 \]

### Final Answer
The molecular formula of the compound is **C₂H₄O₂**.

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