A compound contains 4% hydrogen, 24% carbon and 71% chlorine. Its molar mass is 99 g. Its molecular formula is :

Question

Accepted Answer

To determine the molecular formula of the compound, we need to analyze the given percentages and the molar mass. The compound contains 4% hydrogen, 24% carbon, and 71% chlorine, with a molar mass of 99 g/mol. Let's break down the reasoning for why Option 3, $C_2H_4Cl_2$, is the correct answer.

### Explanation for Option 3: $C_2H_4Cl_2$

1. **Molar Mass Calculation:**
   - Carbon (C) has an atomic mass of approximately 12 g/mol.
   - Hydrogen (H) has an atomic mass of approximately 1 g/mol.
   - Chlorine (Cl) has an atomic mass of approximately 35.5 g/mol.

For $C_2H_4Cl_2$:
   - Carbon: 2 atoms × 12 g/mol = 24 g/mol
   - Hydrogen: 4 atoms × 1 g/mol = 4 g/mol
   - Chlorine: 2 atoms × 35.5 g/mol = 71 g/mol

Total molar mass = 24 + 4 + 71 = 99 g/mol

This matches the given molar mass of the compound, confirming that $C_2H_4Cl_2$ is the correct molecular formula.

2. **Percentage Composition:**
   - Carbon: (24 g/mol / 99 g/mol) × 100% ≈ 24%
   - Hydrogen: (4 g/mol / 99 g/mol) × 100% ≈ 4%
   - Chlorine: (71 g/mol / 99 g/mol) × 100% ≈ 71%

These percentages align perfectly with the given composition of the compound.

### Explanation for Why Other Options Are Incorrect

1. **Option 1: $CH_2Cl$**
   - Molar Mass Calculation:
     - Carbon: 1 atom × 12 g/mol = 12 g/mol
     - Hydrogen: 2 atoms × 1 g/mol = 2 g/mol
     - Chlorine: 1 atom × 35.5 g/mol = 35.5 g/mol
     - Total molar mass = 12 + 2 + 35.5 = 49.5 g/mol

The molar mass of 49.5 g/mol does not match the given molar mass of 99 g/mol.

2. **Option 2: $C_2H_2Cl_2$**
   - Molar Mass Calculation:
     - Carbon: 2 atoms × 12 g/mol = 24 g/mol
     - Hydrogen: 2 atoms × 1 g/mol = 2 g/mol
     - Chlorine: 2 atoms × 35.5 g/mol = 71 g/mol
     - Total molar mass = 24 + 2 + 71 = 97 g/mol

The molar mass of 97 g/mol is close but does not exactly match the given molar mass of 99 g/mol.

3. **Option 4: $CH_2Cl_2$**
   - Molar Mass Calculation:
     - Carbon: 1 atom × 12 g/mol = 12 g/mol
     - Hydrogen: 2 atoms × 1 g/mol = 2 g/mol
     - Chlorine: 2 atoms × 35.5 g/mol = 71 g/mol
     - Total molar mass = 12 + 2 + 71 = 85 g/mol

The molar mass of 85 g/mol does not match the given molar mass of 99 g/mol.

In conclusion, Option 3 ($C_2H_4Cl_2$) is the only choice that correctly matches both the molar mass and the percentage composition of the compound, making it the correct molecular formula.