An organic compound on analysis gave the following data : C = 57.82%, H=3.6%, and 38.58% is oxygen. Find its empirical formula.

Answer

To find the empirical formula of the organic compound based on the given percentage composition of carbon (C), hydrogen (H), and oxygen (O), we can follow these steps:

### Step 1: Convert Percentages to Mass
Assume we have 100 grams of the compound. This means:
- Mass of Carbon (C) = 57.82 g
- Mass of Hydrogen (H) = 3.6 g
- Mass of Oxygen (O) = 38.58 g

### Step 2: Calculate Moles of Each Element
Using the molar masses:
- Molar mass of Carbon (C) = 12 g/mol
- Molar mass of Hydrogen (H) = 1 g/mol
- Molar mass of Oxygen (O) = 16 g/mol

Now, calculate the moles of each element:
- Moles of Carbon = Mass of C / Molar mass of C = 57.82 g / 12 g/mol = 4.82 mol
- Moles of Hydrogen = Mass of H / Molar mass of H = 3.6 g / 1 g/mol = 3.6 mol
- Moles of Oxygen = Mass of O / Molar mass of O = 38.58 g / 16 g/mol = 2.41 mol

### Step 3: Normalize the Moles
To find the simplest whole number ratio, divide each mole value by the smallest number of moles calculated:
- Smallest number of moles = 2.41 (for Oxygen)

Now, divide each mole value by 2.41:
- Ratio of Carbon = 4.82 / 2.41 ≈ 2.00
- Ratio of Hydrogen = 3.6 / 2.41 ≈ 1.49
- Ratio of Oxygen = 2.41 / 2.41 = 1.00

### Step 4: Convert to Whole Numbers
The ratio for Hydrogen (1.49) is close to 1.5. To convert this to whole numbers, multiply all ratios by 2:
- Carbon = 2.00 × 2 = 4
- Hydrogen = 1.49 × 2 ≈ 3
- Oxygen = 1.00 × 2 = 2

### Step 5: Write the Empirical Formula
Now we can write the empirical formula based on the whole number ratios:
- Empirical Formula = C₄H₃O₂

### Final Answer
The empirical formula of the compound is **C₄H₃O₂**.

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