Question

A peroxide in the absence of n. (Br = 80).

A moth repellent has the composition 49% C, 2.7% H and 48.3% Cl. Its molecular weight gm. Determine its molecular formula.

Answer 1

The molecular formula of the moth repellent is $C_6H_4Cl_2$.

Answer 2

The question contains two parts, 46 and 47. Question 46 is incomplete and cannot be answered. We will solve question 47.

Solution for Question 47:

To determine the molecular formula, we follow these steps:

1. Calculate the moles of each element: Assume 100 g of the moth repellent.

   • Mass of Carbon (C) = 49 g Moles of C = $\frac{49 \text{ g}}{12 \text{ g/mol}} = 4.083 \text{ mol}$

   • Mass of Hydrogen (H) = 2.7 g Moles of H = $\frac{2.7 \text{ g}}{1 \text{ g/mol}} = 2.7 \text{ mol}$

   • Mass of Chlorine (Cl) = 48.3 g Moles of Cl = $\frac{48.3 \text{ g}}{35.5 \text{ g/mol}} = 1.361 \text{ mol}$

2. Determine the simplest whole-number ratio (Empirical Formula): Divide the number of moles of each element by the smallest number of moles (1.361 mol for Cl):

   • Ratio of C = $\frac{4.083}{1.361} \approx 3$

   • Ratio of H = $\frac{2.7}{1.361} \approx 2$

   • Ratio of Cl = $\frac{1.361}{1.361} = 1$

   The empirical formula is $C_3H_2Cl$.

3. Calculate the Empirical Formula Weight (EFW): EFW = (3 × Atomic mass of C) + (2 × Atomic mass of H) + (1 × Atomic mass of Cl)
   EFW = (3 × 12) + (2 × 1) + (1 × 35.5) = 36 + 2 + 35.5 = 73.5 g/mol

4. Determine the Molecular Formula: The question states "Its molecular weight gm." which is incomplete. For a complete problem, the molecular weight (MW) must be provided. Assuming a common molecular weight for a moth repellent that is a multiple of the empirical formula weight, such as 147 g/mol (which corresponds to p-dichlorobenzene, a common moth repellent):

   • Calculate the integer 'n' by which the empirical formula must be multiplied:
     $n = \frac{\text{Molecular Weight}}{\text{Empirical Formula Weight}}$
     $n = \frac{147 \text{ g/mol}}{73.5 \text{ g/mol}} = 2$

   • Multiply the empirical formula by 'n' to get the molecular formula:
     Molecular Formula = $n \times (C_3H_2Cl) = 2 \times (C_3H_2Cl) = C_6H_4Cl_2$

The molecular formula of the moth repellent is $C_6H_4Cl_2$.

Explanation of the solution:

1. Convert given percentages to mass (assuming 100g sample) and then to moles for each element.
2. Find the simplest whole-number ratio of moles to determine the empirical formula ($C_3H_2Cl$).
3. Calculate the empirical formula weight (73.5 g/mol).
4. Assume the molecular weight is 147 g/mol (as the question was incomplete).
5. Divide the molecular weight by the empirical formula weight to find the integer 'n' (n=2).
6. Multiply the empirical formula by 'n' to obtain the molecular formula ($C_6H_4Cl_2$).