Chapter 6.3, Problem 4RQ

Interpretation Introduction

Interpretation : The mass of copper and the product formed by their reaction is given. The empirical formula of the compound is to be determined.

Concept Introduction : The formula that determines the proportion of the elements that is present in a compound is defined as empirical formula. It does not state the actual number of atoms that is present in the compound.

The number of moles is calculated as shown below.

  $\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$

Answer to Problem 4RQ

The empirical formula of given compound is ${\text{CuO}}_2$ .

Explanation of Solution

Given information : The mass of copper is $1.50\text{g}$ , the mass of product is $2.14\text{g}$ .

The general formula for given compound is ${\text{Cu}}_{\text{a}}{\text{O}}_{\text{b}}$ . The mass of oxygen present in the compound is given as shown below.

  $\begin{array}{c}\text{Mass of oxygen}=2.14\text{g}-1.50\text{g}\\ =0.64\text{g}\end{array}$

The molar mass of copper is $63.546\text{g/mol}$ and the molar mass of oxygen is $16.0\text{g/mol}$ .

Substitute given mass and molar mass of copper in above formula to calculate its moles.

  $\begin{array}{c}\text{Number of moles}=\frac{\text{1}\text{.50}\text{g}}{\text{63}\text{.546}\frac{\text{g}}{\text{mol}}}\\ =0.0236\text{mol}\end{array}$

Substitute given mass and molar mass of oxygen in above formula to calculate its moles.

  $\begin{array}{c}\text{Number of moles}=\frac{\text{0}\text{.64}\text{g}}{16.0\frac{\text{g}}{\text{mol}}}\\ =0.04\text{mol}\end{array}$

Divide the number of moles of copper and oxygen with the smallest of number as shown below.

  $\begin{array}{c}\text{a}=\frac{\text{Moles of copper}}{\text{Smallest number of moles calculated}}\\ =\frac{0.0236}{0.0236}\\ =1\end{array}$

  $\begin{array}{c}\text{b}=\frac{\text{Moles of oxygen}}{\text{Smallest number of moles calculated}}\\ =\frac{0.04}{0.0236}\\ =2\end{array}$

The formula thus comes out to be ${\text{CuO}}_2$ .

Conclusion

The empirical formula of given compound is ${\text{CuO}}_2$ .