Chapter 10, Problem 100A

(a)

Interpretation Introduction

Interpretation: Interpret the given graph to determine the empirical formula for phenylalanine.

Concept Introduction: For any compound, the empirical formula shows the simplest ratio of atoms of different elements present in the compound.

Explanation of Solution

According to the graph, the percentage composition of phenylalanine is given as follows:

The percent by mass of elements C, H, O, and N is 68%, 8%, 19%, and 9% respectively. Considering 100 g of phenylalanine the mass of C, H, O, and N is 68 g, 8 g, 19 g, and 9g respectively.

Calculate the number of moles of C, H, O, and N as follows:

  $\begin{array}{l}{n}_C:n_{\text{H}}:n_{\text{O}}:n_{\text{N}}=\frac{68\text{ g}}{12\text{ g/mol}}:\frac{8\text{ g}}{1\text{ g/mol}}:\frac{19\text{ g}}{16\text{ g/mol}}:\frac{9\text{ g}}{14\text{ g/mol}}\\ =5.67:8:1.2:0.64\\ =\frac{5.67}{0.64}:\frac{8}{0.64}:\frac{1.2}{0.64}:\frac{0.64}{0.64}\\ =9:11:2:1\end{array}$

The empirical formula of phenylalanine will be ${\text{C}}_{\text{9}}{\text{H}}_{\text{11}}{\text{NO}}_{\text{2}}$ .

(b)

Interpretation Introduction

Interpretation: The molecular formula phenylalanine 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

Now, to calculate the molecular formula, first, calculate the empirical mass as follows:

  $\begin{array}{c}\text{M}=9\left(12\text{ g/mol}\right)\text{+11}\left(1\text{ g/mol}\right)+\left(14\text{ g/mol}\right)\text{+2}\left(16\text{ g/mol}\right)\\ =108+11+13+32\\ =164\text{ g/mol}\end{array}$

Since the given molar mass is 164 g/mol, thus, the empirical mass is the same as the molar mass.

Therefore, the molecular formula of the compound will be ${\text{C}}_{\text{9}}{\text{H}}_{\text{11}}{\text{NO}}_{\text{2}}$