A gaseous alkane was exploded with oxygen. The volume of `O_(2)` for complete combustion to `CO_(2)` formed was in the ratio of `7:4`. The molecular formula of alkane is:

Explanation

To determine the molecular formula of the gaseous alkane, we will follow these steps:

### Step 1: Write the balanced combustion reaction for the alkane
The general formula for an alkane is \( C_nH_{2n+2} \). When an alkane combusts in oxygen, it produces carbon dioxide and water. The balanced equation for the combustion of an alkane can be written as:

\[ C_nH_{2n+2} + \left(n + \frac{1}{2}\right) O_2 \rightarrow n CO_2 + (n + 1) H_2O \]

### Step 2: Identify the volumes of reactants and products
From the balanced equation, the volume of \( O_2 \) required for complete combustion is \( n + \frac{1}{2} \) moles, and the volume of \( CO_2 \) produced is \( n \) moles.

### Step 3: Set up the ratio given in the problem
According to the problem, the ratio of the volume of \( O_2 \) used to the volume of \( CO_2 \) produced is given as \( 7:4 \). This can be expressed mathematically as:

\[ \frac{n + \frac{1}{2}}{n} = \frac{7}{4} \]

### Step 4: Cross-multiply to solve for \( n \)
Cross-multiplying gives:

\[ 4\left(n + \frac{1}{2}\right) = 7n \]

Expanding this, we have:

\[ 4n + 2 = 7n \]

### Step 5: Rearrange the equation to isolate \( n \)
Rearranging the equation gives:

\[ 2 = 7n - 4n \]
\[ 2 = 3n \]

### Step 6: Solve for \( n \)
Dividing both sides by 3, we find:

\[ n = \frac{2}{3} \]

### Step 7: Determine the molecular formula
Since \( n \) must be a whole number (as it represents the number of carbon atoms in the alkane), we need to find a suitable integer. The simplest integer ratio that maintains the original ratio of \( 7:4 \) is \( n = 2 \).

Using \( n = 2 \):

\[ \text{Molecular formula} = C_2H_{2(2)+2} = C_2H_6 \]

### Conclusion
The molecular formula of the alkane is \( C_2H_6 \), which is ethane.

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