5 ml of a gas containing only carbon and hydrogen were mixed with an excess of oxygen (30 ml) and the mixture exploded by means of an electric spark. After the explosion, the volume of the mixed gases remaining was 25 ml. On adding a concentrated solution of potassium hydroxide, the volume further diminished to 15 ml of the residual gas being pure oxygen. All volumes have been reduced to N.T.P. Calculate the molecular formula of the hydrocarbon gas.

Options

A. `C_(2)H_(6)`
B. `C_(3)H_(6)`
C. `C_(2)H_(4)`
D. None of these

Explanation

To find the molecular formula of the hydrocarbon gas (CxHy), we will follow a systematic approach based on the information given in the question.

### Step-by-Step Solution:

1. **Identify the Initial Conditions:**
- Volume of hydrocarbon gas (CxHy) = 5 ml
- Volume of oxygen (O2) = 30 ml
- After explosion, the remaining volume of gases = 25 ml

2. **Determine the Volume of Unused Oxygen:**
- Volume of unused oxygen after the explosion = 15 ml (given)
- Therefore, volume of oxygen that reacted = Total O2 - Unused O2 = 30 ml - 15 ml = 15 ml

3. **Write the Balanced Combustion Reaction:**
- The balanced equation for the combustion of a hydrocarbon can be written as:
\[ C_xH_y + O_2 \rightarrow CO_2 + H_2O \]
- From the balanced equation, we can deduce:
- For every 1 mole of hydrocarbon, it produces \(x\) moles of CO2 and \(\frac{y}{2}\) moles of H2O.
- The total moles of O2 required = \( \frac{x + \frac{y}{4}}{1} \)

4. **Calculate the Volume of CO2 Produced:**
- The total volume of gases after the explosion is 25 ml, which consists of CO2 and the remaining O2.
- Since we have 15 ml of unused O2, the volume of CO2 produced = Total volume after explosion - Remaining O2 = 25 ml - 15 ml = 10 ml.

5. **Relate CO2 Volume to Hydrocarbon Volume:**
- Given that 5 ml of hydrocarbon produces \(5x\) ml of CO2, and we found that 10 ml of CO2 was produced:
\[ 5x = 10 \implies x = 2 \]

6. **Determine the Volume of O2 Required:**
- The volume of O2 consumed can be calculated using the limiting reagent concept:
- Volume of O2 used = \(5 \text{ ml of } C_xH_y \times \left( \frac{x + \frac{y}{4}}{1} \right)\)
- We know that the remaining volume of gases after the reaction is 15 ml (which is all O2), so:
\[ 30 \text{ ml (initial O2)} - \text{Volume of O2 used} = 15 \text{ ml} \]
- Thus, Volume of O2 used = 15 ml.

7. **Set Up the Equation for O2:**
- From the balanced equation, we can express the volume of O2 used:
\[ 5 \left(2 + \frac{y}{4}\right) = 15 \]
- Simplifying gives:
\[ 10 + \frac{5y}{4} = 15 \implies \frac{5y}{4} = 5 \implies 5y = 20 \implies y = 4 \]

8. **Determine the Molecular Formula:**
- Now we have \(x = 2\) and \(y = 4\).
- Therefore, the molecular formula of the hydrocarbon gas is \(C_2H_4\).

### Final Answer:
The molecular formula of the hydrocarbon gas is **C2H4**.