Chapter U5.109, Problem 7E

Interpretation Introduction

Interpretation: The amount of energy required to extract 10 g of copper from copper (II) oxide needs to be determined.

Concept Introduction: The change in enthalpy by formation of a compound in 1 mole from its constituent elements in their standard state is said to be standard heat of formation. The ${\text{ΔH}}_{\text{f}}^{\text{o}}$ for a chemical reaction can be calculated using formula:

  ${\text{ΔH}}_{\text{f}}^{\text{o}}{\text{ = ΣnH}}_{\text{f}}^{\text{o}}{\text{(products) - ΣmH}}_{\text{f}}^{\text{o}}\text{(reactants)}$

Where m and n are stoichiometric numbers.

Answer to Problem 7E

The amount of energy required to extract 10 g of copper from copper (II) oxide is $\text{25 kJ}$ .

Explanation of Solution

The balanced chemical reaction for the extraction of copper from copper (II) oxide is:

  $\text{2CuO(s) }\to {\text{ 2Cu(s) + O}}_{\text{2}}\text{(g)}$

The value of heat of formation of all the species involved in the reaction is:

  $\begin{array}{l}\text{CuO(s)}=\text{ -157 kJ/mol}\\ \text{Cu(s) = 0 kJ/mol}\\ {\text{O}}_{\text{2}}\text{(g) = 0 kJ/mol}\end{array}$

The ${\text{ΔH}}_{\text{f}}^{\text{o}}$ for a chemical reaction is calculated as:

  ${\text{ΔH}}_{\text{f}}^{\text{o}}\text{ = }\left[2\Delta {\text{H}}_{\text{f}}^{\text{o}}\text{(Cu) + }\Delta {\text{H}}_{\text{f}}^{\text{o}}{\text{(O}}_{\text{2}}\text{)}\right]\text{ - 2}\Delta {\text{H}}_{\text{f}}^{\text{o}}\text{(CuO)}$

Substituting the values:

  $\begin{array}{l}{\text{ΔH}}_{\text{f}}^{\text{o}}\text{ = }\left[\text{4(0 kJ/mol) + (0 kJ/mol)}\right]\text{ - 2}\Delta {\text{H}}_{\text{f}}^{\text{o}}\text{(- 157 kJ/mol)}\\ {\text{ΔH}}_{\text{f}}^{\text{o}}\text{ = +314 kJ/mol}\end{array}$

Thus, the heat of reaction for the extraction of 2 moles of copper from 2 moles of copper (II) oxide is $\text{+314 kJ}$ .

Now, calculating the moles of copper present in 10 g using formula:

  $\text{number of moles = }\frac{\text{ mass of substance}}{\text{Molar mass}}$

The molar mass of copper is $\text{63}\text{.546 g/mol}$ .

So, the number of moles in 10 g of copper is:

  $\begin{array}{l}\text{number of moles = }\frac{\text{10 g}}{\text{63}\text{.546 g/mol}}\\ \text{number of moles = }0.157\text{ mol}\end{array}$

Since, the amount of energy required to extract 2 moles of copper is $\text{+314 kJ/mol}$ so, the amount of energy required to extract 0.157 mol of copper is:

  $\text{0}\text{.157 mol}\times \frac{\text{+314 kJ}}{2\text{ mol}}=\text{ 24}\text{.649 kJ }\simeq \text{ 25 kJ}$

Hence, the amount of energy required to extract 10 g of copper from copper (II) oxide is $\text{25 kJ}$ .

Conclusion

  $\text{25 kJ}$ is the amount of energy required to extract 10 g of copper from copper (II) oxide.