Question

Combustion of adipic acid yields percentage abundances of $C:49.3\% ,H:6.9\% ,$ and $O:43.8\%$ . What are the empirical and molecular formulas of adipic acid?

Answer 1

Given are the percentages of compositions of elements in the adipic acid. From these percentages and molar mass, the moles of each atom will be calculated. By dividing each component moles with the smallest mole gives the mole ratio. Empirical formulas can be written from mole ratio. Mole ratio can be calculated from empirical formulas.

Complete answer:
Given composition of atoms in adipic acid is $C:49.3\% ,H:6.9\% ,$ and $O:43.8\%$
The molar mass of carbon is $12$ amu. Thus, the number of moles of carbon will be $\dfrac{{49.3}}{{12}} = 4.1$
The molar mass of hydrogen is $1.0$ amu. Thus, the number of moles of hydrogen will be $\dfrac{{6.9}}{{1.0}} = 6.9$
The molar mass of oxygen is $16$ amu. Thus, the number of moles of oxygen will be $\dfrac{{43.8}}{{16}} = 2.74$
In the obtained moles of carbon, hydrogen and oxygen. The number of moles of oxygen were small.
Divide the moles of each atom with moles of oxygen to obtain the mole ratio.
$C:H:O = \dfrac{{4.1}}{{2.74}}:\dfrac{{6.9}}{{2.74}}:\dfrac{{2.74}}{{2.74}}$
The ratio will be $C:H:O = 1.5:2.5:1$
Thus, the empirical formula of adipic acid is ${C_3}{H_5}{O_2}$
The molecular formula is some whole number product of empirical formula which can be written as
Molecular formula $=$ empirical formula $\times$ some whole number $\left( n \right)$
The molar mass of adipic acid is $146gmo{l^{ - 1}}$
The empirical mass of adipic acid is $3\left( {12} \right) + 5\left( 1 \right) + 2\left( {16} \right) = 73$
Thus, the whole number is $\dfrac{{146}}{{73}} = 2$
Thus, the molecular formula of adipic acid is ${C_6}{H_{10}}{O_4}$ .

Note:
Empirical formula is a shortest representation of molecular formula which is obtained from the mole ratio of atoms. For some compounds both empirical formula and molecular formula are the same. In adipic acid the atoms in molecular formula are double to the atoms in empirical formula.