An organic compound contains C = 40%, H = 6.66%. If the V.D. of the compound is 15, find its molecular formula.

Explanation

To find the molecular formula of the organic compound given the percentages of carbon and hydrogen, and the vapor density, we can follow these steps:

### Step 1: Calculate the Molecular Weight
The molecular weight can be calculated using the vapor density (VD). The formula relating vapor density to molecular weight (MW) is:

\[ \text{Molecular Weight} = 2 \times \text{Vapor Density} \]

Given that the vapor density is 15:

\[ \text{Molecular Weight} = 2 \times 15 = 30 \, \text{g/mol} \]

### Step 2: Determine the Percent Composition of Elements
We are given:
- Carbon (C) = 40%
- Hydrogen (H) = 6.66%

To find the percentage of oxygen (O), we subtract the sum of the percentages of carbon and hydrogen from 100%:

\[ \text{Percentage of Oxygen} = 100\% - (40\% + 6.66\%) = 100\% - 46.66\% = 53.34\% \]

### Step 3: Convert Percentages to Moles
Next, we convert the percentages to moles by dividing by the atomic masses of the elements:
- Atomic mass of C = 12 g/mol
- Atomic mass of H = 1 g/mol
- Atomic mass of O = 16 g/mol

Calculating the moles of each element:

\[ \text{Moles of C} = \frac{40}{12} \approx 3.33 \]
\[ \text{Moles of H} = \frac{6.66}{1} \approx 6.66 \]
\[ \text{Moles of O} = \frac{53.34}{16} \approx 3.33 \]

### Step 4: Find the Simplest Whole Number Ratio
Now, we divide the number of moles of each element by the smallest number of moles calculated:

\[ \text{Ratio of C} = \frac{3.33}{3.33} = 1 \]
\[ \text{Ratio of H} = \frac{6.66}{3.33} = 2 \]
\[ \text{Ratio of O} = \frac{3.33}{3.33} = 1 \]

This gives us the simplest whole number ratio of C:H:O as 1:2:1.

### Step 5: Write the Empirical Formula
From the ratios, we can write the empirical formula:

\[ \text{Empirical Formula} = \text{CH}_2\text{O} \]

### Step 6: Calculate the Mass of the Empirical Formula
To find the mass of the empirical formula:

\[ \text{Mass of CH}_2\text{O} = 12 \, (\text{C}) + 2 \times 1 \, (\text{H}) + 16 \, (\text{O}) = 12 + 2 + 16 = 30 \, \text{g/mol} \]

### Step 7: Calculate the Value of n
Now, we can find the value of n using the formula:

\[ n = \frac{\text{Molecular Weight}}{\text{Mass of Empirical Formula}} = \frac{30}{30} = 1 \]

### Step 8: Determine the Molecular Formula
Finally, the molecular formula can be determined by multiplying the empirical formula by n:

\[ \text{Molecular Formula} = n \times \text{Empirical Formula} = 1 \times \text{CH}_2\text{O} = \text{CH}_2\text{O} \]

### Final Answer
The molecular formula of the organic compound is:

\[ \text{CH}_2\text{O} \]

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