Chapter 10, Problem 71A

Interpretation Introduction

Interpretation: The percent composition of the compound formed by combining 2.70 g of aluminum with oxygen to form 5.10 g of aluminum oxide should be calculated.

Concept Introduction: The percent composition represents the relative amount of the elements in a compound. It is represented as the percent by mass of each element in the compound.

Answer to Problem 71A

The mass percent composition of $\text{Al}$ and $\text{O}$ in the compound is $52.9\%$ and $47.1\%$ respectively.

Explanation of Solution

The percent by mass of each element in the compound represents percent composition as:

  $\text{percent by mass of an element = }\frac{\text{mass of an element}}{\text{mass of the compound}}\times 100\%$   ...... (1)

The mass of the oxygen formed by combining 2.70 g of aluminum with oxygen to form 5.10 g of aluminum oxide is:

  $\begin{array}{l}{\text{mass of Al}}_2{\text{O}}_{\text{3}}{\text{ = mass of Al + mass of O}}_2\\ {\text{mass of O}}_2{\text{ = mass of Al}}_2{\text{O}}_{\text{3}}\text{ - mass of Al}\\ {\text{mass of O}}_2\text{ = 5}\text{.10 g - 2}\text{.70 g}\\ {\text{mass of O}}_2\text{ = 2}\text{.4 g}\end{array}$

Now determining the percent composition of $\text{Al}$ using relation (1):

  $\begin{array}{l}\text{\%Al = }\frac{\text{mass of Al}}{\text{mass of the compound}}\times 100\%\\ \text{\%Al}=\frac{\text{2}\text{.7 g}}{\text{5}\text{.1 g}}\times 100\%\\ \text{\%Al = }52.9\%\end{array}$

Now determining the percent composition of $\text{O}$ using relation (1):

  $\begin{array}{l}\text{\%O = }\frac{\text{mass of O}}{\text{mass of the compound}}\times 100\%\\ \text{\%O = }\frac{\text{2}\text{.4 g}}{\text{5}\text{.1 g}}\times 100\%\\ \text{\%O = }47.1\%\end{array}$

The obtained percent of the elements add up to:

  $\text{52}\text{.9 \% + 47}\text{.1 \% = 100\%}$