Answer
Molecular formula is $(C_{3}H_{2}Cl)_2$ or $C_{6}H_{4}Cl_{2}$.
Work Step by Step
Strategy: 1- Find the empirical formula mass.
2- by dividing molecular mass with empirical formula mass, we can find the number that empirical formula mass must be multiplied to find the molecular formula.
To find the empirical formula mass:
49.1% C, 2.7% H, and 48.2% Cl. 100 g moth repellent contains: 49.1 g C, 2.7 g H, and 48.2 g Cl. These amount converted to moles are:
49.1 g C x $\frac{1 mol (C) }{12g (C)}$= 4.09 mol C
2.7 g H x $\frac{1 mol (H) }{1.01g (H)}$ = 2.67 mol H
48.2 g Cl x $\frac{1 mol (Cl) }{35.5g (Cl)}$ = 1.36 mol Cl
Now we divide with the smallest number of moles, that is 1.36 and we get: 3.0 for C, 1.9 for H, and 1 for Cl or 3.0 for C, 2 for H, and 1 for Cl
So the empirical formula for moth repellent is $C_{3}H_{2}Cl$.
Mass of empirical formula : 3 x 12 + 2 x 1 + 1 x 35.5 = 73.5 amu.
2- We are given the molecular mass of 147 amu, so we can find the number empirical formula mass must be multiplied to find the molecular mass:
n = $\frac{Molecular mass}{empirical (formula-mass)}$
n = $\frac{147}{73.5}$ = 2
So molecular formula should be $(C_{3}H_{2}Cl)_2$ or $C_{6}H_{4}Cl_{2}$