Answer
Molecular formula for adipic acid is $C_{6}H_{10}O_{4}$ .
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:
49.3% C, 6.9 % H, and 43.8 % O. 100 g adipic acid contains: 49.3g C, 6.9 g H, and 43.8 g O. These amount converted to moles are:
49.3 g C x $\frac{1 mol (C) }{12g (C)}$= 4.11 mol C
6.9 g H x $\frac{1 mol (H) }{1g (H)}$ = 6.9 mol H
43.8 g O x $\frac{1 mol (O) }{16g (O)}$ = 2.74 mol O
Now we divide with the smallest number of moles, that is 2.74 and we get: 1.5 for C, 2.5 for H, and 1 for O, and multiplied by 2 ( to get integers we get: 3 for C, 5 for H, and 2 for O . So the empirical formula for adipic acid is $C_{3}H_{5}O_{2}$.
Mass of empirical formula : 3 x 12 + 5 x 1 + 2 x 16 = 73 amu.
2- We are given the molecular mass of 146 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 = $\frac{146}{73}$ = 2
So molecular formula should be $(C_{3}H_{5}O_{2})_2$ or molecular formula is $C_{6}H_{10}O_{4}$ .