`5L` of an alkane requires `25L` of oxygen for its complete combustion. If all volumes are measured at constant temperature and pressure, the alkane is :

Options

A. Butane
B. Isobutane
C. Propane
D. Ethane

Answer

To determine the alkane from the given information, we can follow these steps:

### Step 1: Understand the combustion reaction of alkanes
The general combustion reaction for an alkane can be represented as:
\[ \text{C}_n\text{H}_{2n+2} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} \]

### Step 2: Write the balanced equation for the combustion of the alkane
The balanced equation for the combustion of an alkane can be written as:
\[ \text{C}_n\text{H}_{2n+2} + \frac{3n + 1}{2} \text{O}_2 \rightarrow n \text{CO}_2 + (n + 1) \text{H}_2\text{O} \]

### Step 3: Relate the volumes of alkane and oxygen
According to the problem, we have:
- Volume of alkane (V_alkane) = 5 L
- Volume of oxygen (V_oxygen) = 25 L

From the ideal gas law, we know that at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of that gas. Therefore, we can set up the following relationship:
\[ V_{\text{alkane}} \times \text{moles of O}_2 = V_{\text{oxygen}} \times \text{moles of alkane} \]

### Step 4: Substitute the known values
Given that the moles of alkane is 1 (since we are considering 1 mole of alkane for the combustion process), we can substitute the values:
\[ 5 \, \text{L} \times \left(\frac{3n + 1}{2}\right) = 25 \, \text{L} \times 1 \]

### Step 5: Solve for n
Now, we can simplify the equation:
\[ 5 \times \left(\frac{3n + 1}{2}\right) = 25 \]
\[ \frac{5(3n + 1)}{2} = 25 \]
Multiplying both sides by 2:
\[ 5(3n + 1) = 50 \]
Dividing both sides by 5:
\[ 3n + 1 = 10 \]
Now, subtract 1 from both sides:
\[ 3n = 9 \]
Finally, divide by 3:
\[ n = 3 \]

### Step 6: Determine the alkane formula
Now that we have found \( n = 3 \), we can substitute this back into the general formula for alkanes:
\[ \text{C}_n\text{H}_{2n+2} = \text{C}_3\text{H}_{2(3)+2} = \text{C}_3\text{H}_8 \]

### Step 7: Identify the alkane
The alkane with the formula \( \text{C}_3\text{H}_8 \) is propane.

### Final Answer
The alkane is **propane (C3H8)**.

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