Answer
Molecular formula for sorbic acid is $(C_{3}H_{4}O)_2$ or $C_{6}H_{8}O_{2}$.
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:
64.3% C, 7.2 % H, and 28.5 % O. 100 g sorbic acid contains: 64.3g C, 7.2 g H, and 28.5 g O. These amount converted to moles are:
64.3 g C x $\frac{1 mol (C) }{12 g (C)}$= 5.4 mol C
7.2 g H x $\frac{1 mol (H) }{1.01g (H)}$ = 7.2 mol H
28.5 g O x $\frac{1 mol (O) }{16.0 g (O)}$ = 1.78 mol O
Now we divide with the smallest number of moles, that is 1.78 and we get: 3.0 for C, 4 for H, and 1 for O .
So the empirical formula for sorbic acid is $C_{3}H_{4}O$.
Mass of empirical formula : 3 x 12 + 4 x 1 + 1 x 16 = 56 amu.
2- We are given the molecular mass of 112 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 = $\frac{112 amu}{56 amu)}$ = 2
So molecular formula for sorbic acid is $(C_{3}H_{4}O)_2$ or $C_{6}H_{8}O_{2}$.
