Chapter 4, Problem 89QP

(a)

Interpretation Introduction

Interpretation:

The percent composition of copper in ${\text{Cu}}_2\text{S}$ is to be determined.

Explanation of Solution

The percent composition of any substance is calculated by dividing the mass of substance in a sample by total mass of the sample. This ratio is multiplied by $100\text{ \%}$ .

To determine the percent composition let the sample size be $1\text{ mole}$ . Now, determine the mass of each element contained in $1\text{ mole}$ of the compound ${\text{Cu}}_2\text{S}$ as follows:

The mass of Cu from periodic table is $63.55\text{ g/mole}$ . For $2\text{ mole}$ , the mass is,

$\begin{array}{c}m=2\text{ mole}\times \text{63}\text{.55 g/mole}\\ =\text{127}\text{.1 g}\end{array}$

The mass of S from periodic table is $32.06\text{ g/mole}$ . For $1\text{ mole}$ , the mass is,

$\begin{array}{c}m=1\text{ mole}\times \text{32}\text{.06 g/mole}\\ =\text{32}\text{.06 g}\end{array}$

Therefore, the total mass for $1\text{ mole}$ of ${\text{Cu}}_2\text{S}$ is,

$\begin{array}{c}\text{total mass}=127.1\text{ g}+32.06\text{ g}\\ =159.2\text{ g}\end{array}$

Now, the percent composition of Cu is,

$\begin{array}{c}\%\text{ Cu}=\frac{127.1\cancel{\text{g}}}{159.2\cancel{\text{g}}}\times 100\text{ \%}\\ =\text{79}\text{.84 \%}\end{array}$

(b)

Interpretation Introduction

Interpretation:

The percent copper in ${\text{Cu}}_2\left({\text{CO}}_3\right){\left(\text{OH}\right)}_2$ is to analyzed.

Explanation of Solution

To determine the percent composition, let the sample size be $1\text{ mole}$ . Now, determine the mass of each element contained in $1\text{ mole}$ of the compound ${\text{Cu}}_2\left({\text{CO}}_3\right){\left(\text{OH}\right)}_2$ as follows:

The mass of Cu from periodic table is $63.55\text{ g/mole}$ . For $2\text{ mole}$ , the mass is,

$\begin{array}{c}m=2\text{ mole}\times \text{63}\text{.55 g/mole}\\ =\text{127}\text{.1 g}\end{array}$

The mass of C from periodic table is $12.01\text{ g/mole}$ . For $1\text{ mole}$ , the mass is,

$\begin{array}{c}m=1\text{ mole}\times \text{12}\text{.01 g/mole}\\ =\text{12}\text{.01 g}\end{array}$

The mass of O from periodic table is $16.00\text{ g/mole}$ . For $5\text{ mole}$ , the mass is,

$\begin{array}{c}m=5\text{ mole}\times \text{16}\text{.00 g/mole}\\ =\text{80}\text{.00 g}\end{array}$

The mass of H from periodic table is $1.008\text{ g/mole}$ . For $2\text{ mole}$ , the mass is,

$\begin{array}{c}m=2\text{ mole}\times \text{1}\text{.008 g/mole}\\ =\text{2}\text{.016 g}\end{array}$

Therefore, the total mass for $1\text{ mole}$ of ${\text{Cu}}_2\left({\text{CO}}_3\right){\left(\text{OH}\right)}_2$ is,

$\begin{array}{c}\text{total mass}=127.1\text{ g}+12.01\text{ g}+80.00\text{ g}+2.016\text{ g}\\ =221.1\text{ g}\end{array}$

Now, the percent composition of Cu is,

$\begin{array}{c}\%\text{ Cu}=\frac{\text{127}\text{.1 }\cancel{\text{g}}}{221.1\cancel{\text{g}}}\times 100\text{ \%}\\ =\text{57}\text{.49 \%}\end{array}$

(c)

Interpretation Introduction

Interpretation:

The percent copper in $\text{CuO}$ is to analyzed.

Explanation of Solution

To determine the percent composition let the sample size be $1\text{ mole}$ . Now, determine the mass of each element contained in $1\text{ mole}$ of the compound $\text{CuO}$ as follows:

The mass of Cu from periodic table is $63.55\text{ g/mole}$ . For $1\text{ mole}$ , the mass is,

$\begin{array}{c}m=1\text{ mole}\times \text{63}\text{.55 g/mole}\\ =\text{63}\text{.55 g}\end{array}$

The mass of O from periodic table is $16.00\text{ g/mole}$ . For $1\text{ mole}$ , the mass is,

$\begin{array}{c}m=1\text{ mole}\times \text{16}\text{.00 g/mole}\\ =\text{16}\text{.00 g}\end{array}$

Therefore, the total mass for $1\text{ mole}$ $\text{CuO}$ is,

$\begin{array}{c}\text{total mass}=63.55\text{ g}+16.00\text{ g}\\ =79.55\text{ g}\end{array}$

Now, the percent composition of Cu is,

$\begin{array}{c}\%\text{ Cu}=\frac{\text{63}\text{.55 }\cancel{\text{g}}}{79.55\cancel{\text{g}}}\times 100\text{ \%}\\ =\text{79}\text{.89 \%}\end{array}$

(d)

Interpretation Introduction

Interpretation:

The percent copper in ${\text{Cu}}_3{\left({\text{CO}}_3\right)}_2{\left(\text{OH}\right)}_2$ is to analyzed.

Explanation of Solution

To determine the percent composition, let the sample size be $1\text{ mole}$ . Now, determine the mass of each element contained in $1\text{ mole}$ of the compound ${\text{Cu}}_3{\left({\text{CO}}_3\right)}_2{\left(\text{OH}\right)}_2$ as follows:

The mass of Cu from periodic table is $63.55\text{ g/mole}$ . For $3\text{ mole}$ , the mass is,

$\begin{array}{c}m=3\text{ mole}\times \text{63}\text{.55 g/mole}\\ =\text{190}\text{.65 g}\end{array}$

The mass of C from periodic table is $12.01\text{ g/mole}$ . For $2\text{ mole}$ , the mass is,

$\begin{array}{c}m=2\text{ mole}\times \text{12}\text{.01 g/mole}\\ =\text{24}\text{.02 g}\end{array}$

The mass of O from periodic table is $16.00\text{ g/mole}$ . For $8\text{ mole}$ , the mass is,

$\begin{array}{c}m=8\text{ mole}\times \text{16}\text{.00 g/mole}\\ =\text{128}\text{.0 g}\end{array}$

The mass of H from periodic table is $1.008\text{ g/mole}$ . For $2\text{ mole}$ , the mass is,

$\begin{array}{c}m=2\text{ mole}\times \text{1}\text{.008 g/mole}\\ =\text{2}\text{.016 g}\end{array}$

Therefore, the total mass for $1\text{ mole}$ ${\text{Cu}}_3{\left({\text{CO}}_3\right)}_2{\left(\text{OH}\right)}_2$ is,

$\begin{array}{c}\text{total mass}=190.65\text{ g}+24.02+128.0\text{ g}+2.016\text{ g}\\ =344.7\text{ g}\end{array}$

Now, the percent composition of Cu is,

$\begin{array}{c}\%\text{ Cu}=\frac{190.7\cancel{\text{g}}}{344.7\cancel{\text{g}}}\times 100\text{ \%}\\ =\text{55}\text{.32 \%}\end{array}$

Out of all the minerals, cuprite $\left(\text{CuO}\right)$ has the highest percentage of copper, which is $79.84\text{ \%}$ .