A moth repellent has the composition `49% C, 2.7%H and 48.3% Cl`. Its molecular weight is 147 gm. Determine its molecular formula

Answer

To determine the molecular formula of the moth repellent with the given composition, we will follow these steps:

### Step 1: Determine the Moles of Each Element
We start with the percentage composition of each element:
- Carbon (C): 49%
- Hydrogen (H): 2.7%
- Chlorine (Cl): 48.3%

Next, we convert these percentages to moles using their atomic masses:
- Atomic mass of Carbon (C) = 12 g/mol
- Atomic mass of Hydrogen (H) = 1 g/mol
- Atomic mass of Chlorine (Cl) = 35.5 g/mol

The formula to calculate moles is:
\[ \text{Moles} = \frac{\text{Percentage}}{\text{Atomic Mass}} \]

Calculating the moles for each element:
- Moles of Carbon = \( \frac{49}{12} \approx 4.08 \)
- Moles of Hydrogen = \( \frac{2.7}{1} = 2.7 \)
- Moles of Chlorine = \( \frac{48.3}{35.5} \approx 1.36 \)

### Step 2: Find the Simplest Molar Ratio
Next, we find the simplest molar ratio by dividing the number of moles of each element by the smallest number of moles calculated:
- Smallest number of moles = 1.36 (for Cl)

Calculating the ratios:
- Carbon: \( \frac{4.08}{1.36} \approx 3 \)
- Hydrogen: \( \frac{2.7}{1.36} \approx 1.98 \) (approximately 2)
- Chlorine: \( \frac{1.36}{1.36} = 1 \)

Thus, the simplest molar ratio is approximately:
- C: 3
- H: 2
- Cl: 1

### Step 3: Write the Empirical Formula
From the simplest molar ratio, we can write the empirical formula:
\[ \text{Empirical Formula} = C_3H_2Cl_1 \]

### Step 4: Calculate the Empirical Formula Mass
Next, we calculate the mass of the empirical formula:
\[ \text{Empirical Formula Mass} = (3 \times 12) + (2 \times 1) + (1 \times 35.5) = 36 + 2 + 35.5 = 73.5 \text{ g/mol} \]

### Step 5: Determine the Value of N
We know the molecular weight of the compound is given as 147 g/mol. We can find the value of \( N \) using the formula:
\[ N = \frac{\text{Molecular Mass}}{\text{Empirical Mass}} = \frac{147}{73.5} \approx 2 \]

### Step 6: Calculate the Molecular Formula
Finally, we can find the molecular formula by multiplying the subscripts in the empirical formula by \( N \):
\[ \text{Molecular Formula} = (C_3H_2Cl_1) \times 2 = C_6H_4Cl_2 \]

### Final Answer
The molecular formula of the moth repellent is:
\[ \text{Molecular Formula} = C_6H_4Cl_2 \]

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