10 " mL of " a gaseous organic compound containing C, H and O only,mixed with 100 " mL of " `O_(2)` and exploded under conditionwhich allowed the `H_(2)O` formed to condense.Volume of the gas after explosion was 90 mL. On treatment with KOH solution,further contraction of 20 mL in volume was observed. The vapour density of the compound is 23. All volume measurements were made under the same condition.
Q.The molecular formula of the compound is

Options

A. `C_(3)H_(8)O`
B. `C_(3)H_(6)O`
C. `C_(2)H_(6)O`
D. `C_(2)H_(4)O`

Explanation

To find the molecular formula of the gaseous organic compound containing carbon (C), hydrogen (H), and oxygen (O), we will follow these steps:

### Step 1: Identify the volumes given in the problem
- Volume of organic compound (V_compound) = 10 mL
- Volume of O2 = 100 mL
- Volume after explosion = 90 mL
- Volume after treatment with KOH = 70 mL (90 mL - 20 mL contraction)

### Step 2: Determine the volume of CO2 produced
The contraction of 20 mL after treatment with KOH indicates that this volume is due to the absorption of CO2. Thus, the volume of CO2 produced is:
- Volume of CO2 = 20 mL

### Step 3: Relate the volume of the organic compound to the volume of CO2 produced
From the stoichiometry of combustion, we know that:
- 10 mL of the organic compound produces 20 mL of CO2.
This implies that each molecule of the organic compound produces 2 molecules of CO2. Therefore, the organic compound must contain at least 2 carbon atoms.

### Step 4: Calculate the mass of carbon in the compound
The molar volume of a gas at standard conditions is 24 L (or 24000 mL). Thus:
- 10 mL of the organic compound corresponds to 10/24000 moles.
- 20 mL of CO2 corresponds to 20/24000 moles.

Since 1 mole of CO2 contains 1 mole of carbon, the number of moles of carbon produced is:
- Moles of C = 20/24000 = 1/1200 moles.

Since each molecule of the organic compound produces 2 moles of CO2, the moles of the organic compound is:
- Moles of organic compound = (1/1200) / 2 = 1/2400 moles.

### Step 5: Calculate the vapor density and molecular mass
The vapor density (VD) is given as 23. The molecular mass (M) can be calculated using the formula:
- M = 2 × VD = 2 × 23 = 46 g/mol.

### Step 6: Determine the mass of carbon in the compound
Since we have established that there are 2 carbon atoms in the compound:
- Mass of carbon = 2 × 12 = 24 g/mol.

### Step 7: Calculate the remaining mass for hydrogen and oxygen
The remaining mass for hydrogen and oxygen is:
- Remaining mass = Molecular mass - Mass of carbon = 46 - 24 = 22 g/mol.

### Step 8: Determine the number of hydrogen and oxygen atoms
Assuming there is 1 oxygen atom (mass = 16 g/mol), we can calculate the mass of hydrogen:
- Mass of hydrogen = Remaining mass - Mass of oxygen = 22 - 16 = 6 g/mol.
Since the mass of one hydrogen atom is 1 g/mol, the number of hydrogen atoms is:
- Number of hydrogen atoms = 6.

### Step 9: Write the molecular formula
Thus, the molecular formula of the compound is:
- C2H6O.

### Final Answer:
The molecular formula of the compound is **C2H6O**.

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