A gaseous hydrocarbon has 85% carbon and vapour density of 28. The possible formula of the hydrocarbon will be

Options

A. `C_(3)H_(6)`
B. `C_(2)H_(4)`
C. `C_(2)H_(2)`
D. `C_(4)H_8`

Explanation

To solve the problem of identifying the possible formula of a gaseous hydrocarbon with 85% carbon and a vapor density of 28, we can follow these steps:

### Step 1: Calculate the Molecular Mass
The vapor density (VD) is related to the molecular mass (M) of the gas by the formula:
\[ \text{Vapor Density} = \frac{\text{Molecular Mass}}{2} \]
From this, we can derive the molecular mass:
\[ \text{Molecular Mass} = 2 \times \text{Vapor Density} = 2 \times 28 = 56 \text{ g/mol} \]

### Step 2: Determine the Mass Percentages
We know that the hydrocarbon is 85% carbon. To find the percentage of hydrogen:
\[ \text{Percentage of Hydrogen} = 100\% - 85\% = 15\% \]

### Step 3: Calculate the Mass of Carbon and Hydrogen in 100 g of Hydrocarbon
Assuming we have 100 g of the hydrocarbon:
- Mass of Carbon = 85 g
- Mass of Hydrogen = 15 g

### Step 4: Convert Mass to Moles
Next, we convert the mass of carbon and hydrogen to moles using their atomic masses:
- Moles of Carbon (C):
\[ \text{Moles of C} = \frac{85 \text{ g}}{12 \text{ g/mol}} \approx 7.08 \text{ moles} \]
- Moles of Hydrogen (H):
\[ \text{Moles of H} = \frac{15 \text{ g}}{1 \text{ g/mol}} = 15 \text{ moles} \]

### Step 5: Find the Simplest Mole Ratio
To find the simplest ratio, we divide by the smallest number of moles:
- For Carbon:
\[ \text{Ratio of C} = \frac{7.08}{7.08} = 1 \]
- For Hydrogen:
\[ \text{Ratio of H} = \frac{15}{7.08} \approx 2.12 \approx 2 \]
Thus, the simplest whole number ratio of C to H is approximately 1:2.

### Step 6: Write the Empirical Formula
The empirical formula based on the ratio is:
\[ \text{C}_1\text{H}_2 \quad \text{or} \quad \text{CH}_2 \]

### Step 7: Determine the Molecular Formula
To find the molecular formula, we need to check if the empirical formula's molar mass matches the calculated molecular mass of 56 g/mol. The molar mass of CH2 is:
\[ \text{Molar Mass of CH}_2 = 12 + (2 \times 1) = 14 \text{ g/mol} \]
Now, we find how many times the empirical formula fits into the molecular mass:
\[ \frac{56 \text{ g/mol}}{14 \text{ g/mol}} = 4 \]
Thus, the molecular formula is:
\[ \text{C}_4\text{H}_8 \]

### Final Answer
The possible formula of the hydrocarbon is **C4H8**.

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