A gaseous alkane is exploded with oxygen. The volume of {O_2} for complete combustion of alkane to C{O_2} formed is in the ratio 7:4. The molecular formula of alkane is:(A) {C_2}{H_6} (B) {C_3}{H_8} (C) C{H_4} (D) {C_4}{H_{10}}

The given question involves the combustion of a gaseous alkane with oxygen. The volume ratio of oxygen (O₂) to carbon dioxide (CO₂) formed is 7:4. We need to determine the molecular formula of the alkane.

### Step 1: General combustion equation for alkane
The general combustion equation for an alkane, \( C_nH_{2n+2} \), is:

\[
C_nH_{2n+2} + \left(n + \frac{(2n+2)}{4}\right) O_2 \rightarrow n CO_2 + \left(\frac{(2n+2)}{2}\right) H_2O
\]

The number of moles of oxygen (O₂) required for the complete combustion of an alkane depends on the number of carbon (C) and hydrogen (H) atoms in the alkane.

### Step 2: Analyze the given volume ratio
The volume ratio of oxygen to carbon dioxide is given as 7:4. This means for every 7 volumes of oxygen, 4 volumes of carbon dioxide are produced. From the balanced combustion equation, we can find the alkane that fits this ratio.

For an alkane \( C_nH_{2n+2} \), the combustion reaction produces \( n \) volumes of CO₂ and consumes \( n + \frac{(2n+2)}{4} \) volumes of O₂.

### Step 3: Try possible molecular formulas

#### (A) \( C_2H_6 \) (ethane):
The combustion of ethane follows this reaction:

\[
C_2H_6 + \frac{7}{2} O_2 \rightarrow 2 CO_2 + 3 H_2O
\]

Here, 7 volumes of O₂ are required to produce 2 volumes of CO₂. The ratio of O₂ to CO₂ is:

\[
\frac{7}{2} = 3.5 \quad \text{(which does not match 7:4)}
\]

So, \( C_2H_6 \) is not the correct answer.

#### (B) \( C_3H_8 \) (propane):
The combustion of propane follows this reaction:

\[
C_3H_8 + 5 O_2 \rightarrow 3 CO_2 + 4 H_2O
\]

Here, 5 volumes of O₂ are required to produce 3 volumes of CO₂. The ratio of O₂ to CO₂ is:

\[
\frac{5}{3} \quad \text{(which does not match 7:4)}
\]

So, \( C_3H_8 \) is not the correct answer.

#### (C) \( CH_4 \) (methane):
The combustion of methane follows this reaction:

\[
CH_4 + 2 O_2 \rightarrow CO_2 + 2 H_2O
\]

Here, 2 volumes of O₂ are required to produce 1 volume of CO₂. The ratio of O₂ to CO₂ is:

\[
\frac{2}{1} = 2 \quad \text{(which does not match 7:4)}
\]

So, \( CH_4 \) is not the correct answer.

#### (D) \( C_4H_{10} \) (butane):
The combustion of butane follows this reaction:

\[
C_4H_{10} + \frac{13}{2} O_2 \rightarrow 4 CO_2 + 5 H_2O
\]

Here, 13 volumes of O₂ are required to produce 4 volumes of CO₂. The ratio of O₂ to CO₂ is:

\[
\frac{13}{4} = 3.25 \quad \text{(which approximately matches 7:4, after multiplying both by 4)}
\]

Therefore, the correct molecular formula of the alkane is \( C_4H_{10} \).

### Final Answer:
(D) \( C_4H_{10} \)