`44g` of a sample C,H & O on complete combustion given `88g CO_2 and 36g` of `H_2 O.` The molecular formula of the compound may be :

Options

A. `C_(4)H_(9)`
B. `C_(2)H_(6)O`
C. `C_(2)H_(4)O`
D. `C_(3)H_(6)O`

Answer

To determine the molecular formula of the compound containing carbon (C), hydrogen (H), and oxygen (O) based on the complete combustion data provided, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of the compound = 44 g
- Mass of CO₂ produced = 88 g
- Mass of H₂O produced = 36 g

2. **Calculate Moles of CO₂ and H₂O:**
- Molar mass of CO₂ = 12 (C) + 16*2 (O) = 44 g/mol
- Moles of CO₂ = Mass / Molar mass = 88 g / 44 g/mol = 2 moles

- Molar mass of H₂O = 2 (H) + 16 (O) = 18 g/mol
- Moles of H₂O = Mass / Molar mass = 36 g / 18 g/mol = 2 moles

3. **Determine Moles of Carbon and Hydrogen:**
- Each mole of CO₂ contains 1 mole of carbon, so from 2 moles of CO₂, we have:
- Moles of C = 2 moles

- Each mole of H₂O contains 2 moles of hydrogen, so from 2 moles of H₂O, we have:
- Moles of H = 2 * 2 = 4 moles

4. **Calculate the Mass of Carbon and Hydrogen:**
- Mass of Carbon = Moles of C × Molar mass of C = 2 moles × 12 g/mol = 24 g
- Mass of Hydrogen = Moles of H × Molar mass of H = 4 moles × 1 g/mol = 4 g

5. **Calculate the Mass of Oxygen:**
- Total mass of the compound = Mass of C + Mass of H + Mass of O
- 44 g = 24 g + 4 g + Mass of O
- Mass of O = 44 g - (24 g + 4 g) = 44 g - 28 g = 16 g

6. **Determine Moles of Oxygen:**
- Molar mass of O = 16 g/mol
- Moles of O = Mass / Molar mass = 16 g / 16 g/mol = 1 mole

7. **Determine the Empirical Formula:**
- Moles of C = 2, Moles of H = 4, Moles of O = 1
- The ratio of C:H:O = 2:4:1
- Simplifying this gives us the empirical formula: C₂H₄O

8. **Determine the Molecular Formula:**
- The empirical formula mass = (2 × 12) + (4 × 1) + (1 × 16) = 24 + 4 + 16 = 44 g/mol
- Since the molar mass of the compound is also 44 g/mol, the molecular formula is the same as the empirical formula: C₂H₄O.

### Final Answer:
The molecular formula of the compound is **C₂H₄O**.