Chapter 10, Problem 163A

Express the composition of each compound as the mass percent of its elements (percent composition).

a. sucrose $\left({\text{C}}_{12}{\text{H}}_{22}{\text{O}}_{11}\right)$ c. magnetite $\left({\text{Fe}}_{\text{3}}{\text{O}}_{\text{4}}\right)$

b. aluminum sulfate $\left({\text{Al}}_{\text{2}}{\left({\text{SO}}_{\text{4}}\right)}_{\text{3}}\right)$

Interpretation Introduction

Interpretation:

The percent composition of the elements present in sucrose should be predicted.

Concept introduction:

The way of representation of concentration of an element in a compound or a component of a mixture is known as mass percentage. It can be expressed as follows:

$\text{Mass}\text{percent}\text{of}\text{component}=\frac{\text{Mass}\text{of}\text{component}}{\text{Total}\text{mass}\text{of}\text{the}\text{component}}\text{×100\%}$

Answer to Problem 163A

The mass percent of carbon, hydrogen, and oxygen in sucrose is 42.10%, 6.5%, and 51.4% respectively.

Explanation of Solution

The molar mass of sucrose is 342.3 g/mol. Sucrose is composed of 12 carbon, 22 hydrogen, and 11 oxygen atoms. Thus, the mass percent of each element is represented as follows:

$\begin{array}{c}\text{Mass}\text{percent}\text{of}\text{carbon}=\frac{\text{Mass}\text{of}\text{carbon}}{\text{Molar}\text{mass}\text{of}\text{sucrose}}\times 100\%\\ =\frac{12\times 12.0107}{342.3}\times 100\%\\ =42.10\%\\ \text{Mass}\text{percent}\text{of}\text{hydrogen}=\frac{\text{Mass}\text{of}\text{hydrogen}}{\text{Molar}\text{mass}\text{of}\text{sucrose}}\times 100\%\\ =\frac{22\times 1.008}{342.3}\times 100\%\\ =6.5\%\\ \text{Mass}\text{percent}\text{of}\text{oxygen}=\frac{\text{Mass}\text{of}\text{oxygen}}{\text{Molar}\text{mass}\text{of}\text{sucrose}}\times 100\%\\ =\frac{11\times 15.999}{342.3}\times 100\%\\ =51.4\%\end{array}$

Thus, the mass percent of carbon, hydrogen, and oxygen in sucrose is 42.10, 6.5, and 51.4% respectively.

Interpretation Introduction

Interpretation:

The percent composition of the elements present in aluminum sulfate should be predicted.

Concept introduction:

The way of representation of concentration of an element in a compound or a component of a mixture is known as mass percentage. It can be expressed as follows:

$\text{Mass}\text{percent}\text{of}\text{component}=\frac{\text{Mass}\text{of}\text{component}}{\text{Total}\text{mass}\text{of}\text{the}\text{component}}\text{×100\%}$

Answer to Problem 163A

The mass percent of aluminum, sulfur and oxygen in aluminum sulfate is 15.8%, 28.11%, and 56.11% respectively.

Explanation of Solution

The molar mass of sucrose is 342.15 g/mol. Aluminum sulfate is composed of 2 aluminum, 3 sulfur, and 12 oxygen atoms. Thus, the mass percent of each element is represented as follows:

$\begin{array}{c}\text{Mass}\text{percent}\text{of}\text{aluminum}=\frac{\text{Mass}\text{of}\text{aluminum}}{\text{Molar}\text{mass}\text{of}\text{aluminum sulfate}}\times 100\%\\ =\frac{2\times 26.981539}{342.15}\times 100\%\\ =15.8\%\\ \text{Mass}\text{percent}\text{of}\text{sulfur}=\frac{\text{Mass}\text{of}\text{sulfur}}{\text{Molar}\text{mass}\text{of}\text{aluminum sulfate}}\times 100\%\\ =\frac{3\times 32.065}{342.15}\times 100\%\\ =28.11\%\\ \text{Mass}\text{percent}\text{of}\text{oxygen}=\frac{\text{Mass}\text{of}\text{oxygen}}{\text{Molar}\text{mass}\text{of}\text{aluminum sulfate}}\times 100\%\\ =\frac{12\times 15.999}{342.15}\times 100\%\\ =56.11\%\end{array}$

Thus, the mass percent of aluminum, sulfur and oxygen in aluminium sulfate is 15.8, 28.11, and 56.11% respectively.

Interpretation Introduction

Interpretation:

The percent composition of the elements present in magnetite should be predicted.

Concept introduction:

The way of representation of concentration of an element in a compound or a component of a mixture is known as mass percentage. It can be expressed as follows:

$\text{Mass}\text{percent}\text{of}\text{component}=\frac{\text{Mass}\text{of}\text{component}}{\text{Total}\text{mass}\text{of}\text{the}\text{component}}\text{×100\%}$

Answer to Problem 163A

The mass percent of iron, and oxygen in magnetite is 72.4%, and 27.6% respectively.

Explanation of Solution

The molar mass of sucrose is 231.533 g/mol. Magnetite is composed of 2 iron atoms and 3 oxygen atoms. Thus, the mass percent of each element is represented as follows:

$\begin{array}{c}\text{Mass}\text{percent}\text{of}\text{Fe}=\frac{\text{Mass}\text{of}\text{Fe}}{\text{Molar}\text{mass}\text{of}{\text{Fe}}_3{\text{O}}_4}\times 100\%\\ =\frac{3\times 55.845}{231.533}\times 100\%\\ =72.4\%\\ \text{Mass}\text{percent}\text{of}\text{oxygen}=\frac{\text{Mass}\text{of}\text{oxygen}}{\text{Molar}\text{mass}\text{of}{\text{Fe}}_3{\text{O}}_4}\times 100\%\\ =\frac{4\times 15.999}{231.533}\times 100\%\\ =27.6\%\end{array}$

Thus, the mass percent of iron, and oxygen in magnetite is 72.4, and 27.4% respectively.