Chapter 10, Problem 109A

Interpretation Introduction

Interpretation: The empirical formula of THG needs to be calculated. Also, the molecular formula needs to be calculated.

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 percentage composition of THG is 80.8% of carbon, 8.97% of hydrogen, and 10.3% of oxygen. Also, the molar mass of THG is 312 g/mol.

Taking 100 g of the compound, thus, the mass of carbon, hydrogen, and oxygen is 80.0 g, 8.97 g, and 10.3 g respectively. The molar mass of carbon, hydrogen, and oxygen is 12 g/mol, 1 g/mol, and 16 g/mol respectively.

The number of moles of C, H, and O can be calculated as follows:

  $n=\frac{m}{M}$

Here, m is mass and M is molar mass.

Thus,

  $\begin{array}{c}{n}_{\text{C}}=\frac{80.0\text{ g}}{12\text{ g/mol}}\\ =6.67\text{ mol}\\ n_{\text{H}}=\frac{8.97\text{ g}}{1\text{ g/mol}}\\ =8.97\text{ mol}\\ n_{\text{O}}=\frac{10.3\text{ g}}{16\text{ g/mol}}\\ =0.644\text{ mol}\end{array}$

The simplest ratio of the number of C, H, and O atoms is:

  $\begin{array}{c}{n}_{\text{C}}:n_{\text{H}}:n_{\text{O}}=6.67:8.97:0.644\\ =10.5:14:1\\ =\frac{21}{2}:14:1\\ =21:28:2\end{array}$

Thus, empirical formula will be ${\text{C}}_{21}{\text{H}}_{28}{\text{O}}_2$ . Now, empirical mass can be calculated as follows:

  $\begin{array}{c}M=21\left(12\text{ g/mol}\right)+28\left(1\text{ g/mol}\right)+2\left(16\text{ g/mol}\right)\\ =\left(252+28+32\right)\text{ g/mol}\\ =312\text{ g/mol}\end{array}$

Since, molar mass of compound is 312 g/mol thus, molecular formula of compound will be ${\text{C}}_{20}{\text{H}}_{28}{\text{O}}_2$