Chapter 10.3, Problem 34SP

Interpretation Introduction

Interpretation: The percent composition of the compound obtained by decomposing 14.2 g of mercury(II) oxide into its elements, 13.2 g of $\text{Hg}$ 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 34SP

The mass percent composition of $\text{Hg}$ and ${\text{O}}_2$ in the compound is $93\%$ and $7\%$ respectively.

Explanation of Solution

On heating mercury(II) oxide, the obtained elements are mercury and oxygen.

The percent by mass of each element in the compound represents the 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 decomposing 14.2 g of mercury(II) oxide and its elements, 13.2 g of $\text{Hg}$ is:

  $\begin{array}{l}{\text{mass of HgO = mass of Hg + mass of O}}_2\\ {\text{mass of O}}_2\text{ = mass of HgO - mass of Hg }\\ {\text{mass of O}}_2\text{ = 14}\text{.2 g - 13}\text{.2 g}\\ {\text{mass of O}}_2\text{ = 1g}\end{array}$

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

  $\begin{array}{l}\text{\%Hg = }\frac{\text{mass of Hg}}{\text{mass of the compound}}\times 100\%\\ \text{\%Hg}=\frac{\text{13}\text{.2 g}}{\text{14}\text{.2 g}}\times 100\%\\ \text{\%Hg = }93\%\end{array}$

Now, determining the percent composition of ${\text{O}}_2$ using relation (1):

  $\begin{array}{l}{\text{\%O}}_2\text{ = }\frac{{\text{mass of O}}_2}{\text{mass of the compound}}\times 100\%\\ {\text{\%O}}_2\text{ = }\frac{\text{1 g}}{\text{14}\text{.2 g}}\times 100\%\\ {\text{\%O}}_2\text{ = }7.0\%\end{array}$

The obtained percent of the elements adds up to:

  $\text{93 \% + 7 \% = 100\%}$