Chapter 10, Problem 93A

Interpretation Introduction

Interpretation: The molecular formula of lactic acid needs to be determined.

Concept Introduction: For any compound, the empirical formula shows the simplest ratio of atoms of different elements present in the compound. On the other hand, the molecular formula shows the actual number of atoms of elements present in the compound.

Explanation of Solution

The percent composition of lactic acid is 40.0% C, 6.67% H, and 53.3% O. Molar mass of lactic acid is 90.0 g/mol.

Taking 100 g of the compound, the mass of C, H, and O is 40.0 g, 6.67 g, and 53.3 g respectively. Since, the molar mass of C, H, and O is 12 g/mol, 1 g/mol, and 16 g/mol respectively.

The number of moles can be calculated as follows:

  $n=\frac{m}{M}$

Substitute the values,

  $\begin{array}{c}{n}_{\text{C}}=\frac{40.0\text{ g}}{12\text{ g/mol}}\\ =3.33\text{ mol}\end{array}$

And,

  $\begin{array}{c}{n}_{\text{H}}=\frac{\text{6}\text{.67 g}}{1\text{ g/mol}}\\ =6.67\text{ mol}\end{array}$

Also,

  $\begin{array}{c}{n}_{\text{O}}=\frac{53.3\text{ g}}{16\text{ g/mol}}\\ =3.33\text{ mol}\end{array}$

Calculate the simplest ratio of the number of moles:

  $\begin{array}{c}{n}_{\text{C}}:n_{\text{H}}:n_{\text{O}}=3.33:6.67:3.33\\ =1:2:1\end{array}$

The empirical formula of the compound will be ${\text{CH}}_2\text{O}$ . Calculate the empirical mass of the compound as follows:

  $\begin{array}{c}M=1\left(12\text{ g/mol}\right)+2\left(1\text{ g/mol}\right)+16\text{ g/mol}\\ \text{=}\left(\text{12+2+16}\right)\text{ g/mol}\\ =30\text{ g/mol}\end{array}$

Thus, the empirical mass of the compound is $30\text{ g/mol}$ . Since the molar mass of the compound is given 90 g/mol thus, the molecular formula can be calculated as follows:

  $\begin{array}{c}x\left({\text{CH}}_2\text{O}\right)\\ x=\frac{90\text{ g/mol}}{30\text{ g/mol}}\\ =3\end{array}$

Thus, the molecular formula of the compound is ${\text{C}}_3{\text{H}}_6{\text{O}}_3$ .