A compound contains 4.07% hydrogen, 24.27% carbon and 71.65% chlorine. Its molar mass is 99 g, then its molecular formula is :

Question

Accepted Answer

To determine the molecular formula of the compound, we need to use the given percentage composition and the molar mass of the compound. Let's break down the process step by step:

1. **Determine the Empirical Formula:**

- **Percentage to Mass:** Assume we have 100 grams of the compound. This means we have:
     - 4.07 grams of hydrogen
     - 24.27 grams of carbon
     - 71.65 grams of chlorine

- **Convert Mass to Moles:**
     - Moles of hydrogen = 4.07 g / 1.01 g/mol = 4.03 mol
     - Moles of carbon = 24.27 g / 12.01 g/mol = 2.02 mol
     - Moles of chlorine = 71.65 g / 35.45 g/mol = 2.02 mol

- **Determine the Simplest Ratio:**
     - The simplest whole number ratio of moles is approximately 2:2:2, which simplifies to 1:1:1.

- **Empirical Formula:** The empirical formula based on the simplest ratio is CHCl.

2. **Determine the Molecular Formula:**

- **Calculate the Empirical Formula Mass:**
     - Empirical formula mass of CHCl = 12.01 (C) + 1.01 (H) + 35.45 (Cl) = 48.47 g/mol

- **Determine the Molecular Formula:**
     - The molar mass of the compound is given as 99 g/mol.
     - Divide the molar mass by the empirical formula mass: 99 g/mol / 48.47 g/mol ≈ 2.04

- **Multiply the Empirical Formula by this Factor:**
     - Since the factor is approximately 2, the molecular formula is (CHCl)₂, which is C₂H₂Cl₂.

3. **Justification for Option 2:**

- The molecular formula C₂H₄Cl₂ corresponds to the empirical formula multiplied by 2, which matches the calculated factor.
   - The molar mass of C₂H₄Cl₂ is 98.96 g/mol, which is very close to the given molar mass of 99 g/mol, confirming the correctness of this option.

4. **Explanation of Incorrect Options:**

- **Option 1: $CH_{2}Cl$**
     - This formula does not match the calculated molecular formula, as it does not account for the correct molar mass of 99 g/mol.

- **Option 3: $C_{2}HCl_{2}$**
     - This formula does not match the calculated molecular formula, as it does not provide the correct ratio of hydrogen to carbon and chlorine.

- **Option 4: $C_{2}H_{2}Cl_{2}$**
     - Although this formula seems similar, it does not match the correct ratio of hydrogen to carbon and chlorine as determined by the empirical formula calculation.

In conclusion, Option 2 ($C_{2}H_{4}Cl_{2}$) is the correct molecular formula for the compound based on the given percentage composition and molar mass.