A definite amount of gaseous hydrocarbon having `("carbon atoms less than" 5)` was burnt with sufficient amount of `O_(2)`. The volume of all reactants was `600mL`. After the explosion the volume of the product `[CO_(2)(g)` and `H_(2)O (g)]` was found to be `700 mL` under the similar conditions. The molecular formula of the compound is ?

Options

A. `C_(3)H_(8)`
B. `C_(3)H_(6)`
C. `C_(3)H_(4)`
D. `C_(4)H_(10)`

Explanation

To solve the problem, we need to determine the molecular formula of the hydrocarbon (CxHy) that was burned. Here’s how we can approach the problem step by step:

### Step 1: Write the combustion reaction
The combustion of a hydrocarbon can be represented by the following equation:
\[ \text{C}_x\text{H}_y + O_2 \rightarrow x \text{CO}_2 + \frac{y}{2} \text{H}_2\text{O} \]

### Step 2: Determine the volume relationship
According to the problem, the total volume of reactants (hydrocarbon and oxygen) is 600 mL, and the total volume of products (carbon dioxide and water vapor) is 700 mL.

Using the ideal gas law, we know that the volume of gas is directly proportional to the number of moles. Therefore, we can express the volumes in terms of the coefficients from the balanced equation.

### Step 3: Set up the volume equation
The volume of the reactants can be expressed as:
\[ V_{\text{reactants}} = V_{\text{hydrocarbon}} + V_{O_2} = 600 \, \text{mL} \]

The volume of the products can be expressed as:
\[ V_{\text{products}} = V_{CO_2} + V_{H_2O} = 700 \, \text{mL} \]

From the balanced equation, we can express the volumes in terms of x and y:
- The volume of carbon dioxide produced is \( x \times 100 \, \text{mL} \) (assuming 100 mL per mole).
- The volume of water vapor produced is \( \frac{y}{2} \times 100 \, \text{mL} \).

### Step 4: Write the equations
From the combustion reaction, we can derive the following equations:
1. For the reactants:
\[ 600 = V_{\text{hydrocarbon}} + V_{O_2} \]
2. For the products:
\[ 700 = x \times 100 + \frac{y}{2} \times 100 \]

### Step 5: Substitute and simplify
Substituting the volumes into the equations:
1. The volume of the hydrocarbon can be expressed as \( \frac{1}{2}(600 - V_{O_2}) \).
2. The total volume of products can be simplified to:
\[ 700 = 100x + 50y \]
\[ 7 = x + 0.5y \]

### Step 6: Solve the equations
Now we have two equations:
1. \( 600 = V_{\text{hydrocarbon}} + V_{O_2} \)
2. \( 7 = x + 0.5y \)

From the first equation, we can express \( V_{O_2} \) in terms of \( V_{\text{hydrocarbon}} \):
\[ V_{O_2} = 600 - V_{\text{hydrocarbon}} \]

Now, we can also express the total number of moles of products in terms of x and y:
\[ 700 = 100x + 50y \]

### Step 7: Solve for x and y
From the equation \( 7 = x + 0.5y \):
Multiply through by 2:
\[ 14 = 2x + y \]

Now we have:
1. \( 2x + y = 14 \)
2. \( 100x + 50y = 700 \)

Substituting \( y = 14 - 2x \) into the second equation:
\[ 100x + 50(14 - 2x) = 700 \]
\[ 100x + 700 - 100x = 700 \]
This simplifies to:
\[ 700 = 700 \] (which is always true).

### Step 8: Find integer solutions for x and y
From \( 2x + y = 14 \), we can try integer values for \( x \) (keeping in mind that carbon atoms are less than 5):
- If \( x = 3 \), then \( y = 14 - 2(3) = 8 \).

### Step 9: Write the molecular formula
Thus, the molecular formula of the hydrocarbon is:
\[ \text{C}_3\text{H}_8 \]

### Final Answer
The molecular formula of the compound is **C3H8**.