A hydrocarbon contain `80%` C . The vapour density of compound in 30 . Molecular formula of compound is :-

Options

A. `CH_(3)`
B. `C_(2)H_(6)`
C. `C_(4)H_(12)`
D. All of these

Answer

To determine the molecular formula of the hydrocarbon given that it contains 80% carbon and has a vapor density of 30, we can follow these steps:

### Step 1: Calculate the Molecular Weight from Vapor Density
The vapor density (VD) of a compound is related to its molecular weight (MW) by 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: Set Up the Molecular Formula
Let the molecular formula of the hydrocarbon be \( C_xH_y \). The molecular weight can be expressed in terms of \( x \) and \( y \):
\[ \text{Molecular Weight} = 12x + 1y \]
Setting this equal to the molecular weight we calculated:
\[ 12x + y = 60 \quad \text{(Equation 1)} \]

### Step 3: Use the Percentage Composition
We know that the hydrocarbon contains 80% carbon by mass. This means that the mass of carbon in the compound can be expressed as:
\[ \frac{12x}{60} = 0.8 \]
This implies:
\[ 12x = 0.8 \times 60 \]
Calculating the right side:
\[ 12x = 48 \]
Now, solve for \( x \):
\[ x = \frac{48}{12} = 4 \]

### Step 4: Substitute \( x \) Back into Equation 1
Now that we have \( x = 4 \), we can substitute this value back into Equation 1 to find \( y \):
\[ 12(4) + y = 60 \]
This simplifies to:
\[ 48 + y = 60 \]
Solving for \( y \):
\[ y = 60 - 48 = 12 \]

### Step 5: Write the Molecular Formula
Now that we have both \( x \) and \( y \), we can write the molecular formula:
\[ \text{Molecular Formula} = C_4H_{12} \]

### Final Answer
The molecular formula of the compound is \( C_4H_{12} \).

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