Question

Copper(I) oxide can be oxidized to copper(II) oxide: $$\mathrm{Cu}_{2} \mathrm{O}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CuO}(s) \quad \Delta H_{\mathrm{rin}}^{0}=-146.0 \mathrm{~kJ} $$Given \(\Delta H_{i}^{\circ}\) of \(\mathrm{Cu}_{2} \mathrm{O}(s)=-168.6 \mathrm{~kJ} / \mathrm{mol},\) find \(\Delta H_{\mathrm{f}}^{\circ}\) of \(\mathrm{CuO}(s)\)

Short answer

The standard enthalpy of formation of CuO(s) is \(-157.3 \text{ kJ/mol}\).

Step-by-step solution

Write Down the Given Reaction

The reaction for the oxidation of copper(I) oxide to copper(II) oxide is given by: \(\text{Cu}_2 \text{O}(s) + \frac{1}{2} \text{O}_2(g) \rightarrow 2 \text{CuO}(s)\).

Identify Given Thermodynamic Data

We are given \(\text{ΔH}^{0}_{\text{rxn}} = -146.0 \text{ kJ}\) for the reaction and the standard enthalpy of formation of copper(I) oxide \(\text{ΔH}_{\text{f}}^{0}(\text{Cu}_2 \text{O}) = -168.6 \text{ kJ/mol}\).

Write the Expression for the Standard Enthalpy Change of the Reaction

The standard enthalpy change of the reaction can be expressed as: \(\text{ΔH}_{\text{rxn}}^{0} = \text{ΣΔH}_{\text{f}}^{0}(\text{products}) - \text{ΣΔH}_{\text{f}}^{0}(\text{reactants})\) where: - \(\text{ΔH}_{\text{f}}^{0}(\text{Cu}_2 \text{O}) = -168.6 \text{ kJ/mol}\) - \(\text{ΔH}_{\text{f}}^{0}(\text{CuO}) = x \text{ (to be found)}\)

Set Up the Enthalpy Equation

The enthalpy change for the reaction is: \(\text{ΔH}_{\text{rxn}}^{0} = 2 \times \text{ΔH}_{\text{f}}^{0}(\text{CuO}) - \text{ΔH}_{\text{f}}^{0}(\text{Cu}_2 \text{O})\) Substitute the given values: \(-146.0 \text{ kJ} = 2 \times x - (-168.6 \text{ kJ})\).

Solve for \(\text{ΔH}_{\text{f}}^{0} (\text{CuO})\)

Rearranging the equation to solve for \(x\): \(-146.0 \text{ kJ} = 2x + 168.6 \text{ kJ}\) Subtract 168.6 kJ from both sides: \(-146.0 \text{ kJ} - 168.6 \text{ kJ} = 2x\) \(2x = -314.6 \text{ kJ}\) Divide both sides by 2: \(x = \frac{-314.6 \text{ kJ}}{2}\) \(x = -157.3 \text{ kJ/mol}\)

Key concepts

Enthalpy Change

Enthalpy change, symbolized by \(\Delta H\), is an important concept in chemistry. It represents the heat absorbed or released during a chemical reaction at constant pressure. In the given problem, we are dealing with the reaction of copper(I) oxide and oxygen to form copper(II) oxide. The enthalpy change for this reaction is provided as \(\Delta H_{\text{rxn}}^0 = -146.0 \, \text{kJ}\).
Negative values indicate that the reaction releases heat (exothermic), while positive values show that the reaction absorbs heat (endothermic).
Understanding enthalpy change helps us predict energy flow in and out of chemical reactions, crucial for controlling these reactions in practical applications.

Standard Enthalpy of Formation

Standard enthalpy of formation, denoted \(\Delta H_f^0\), is the enthalpy change when one mole of a substance is formed from its elements in their standard states. This is a fundamental thermodynamic quantity used to calculate reaction enthalpies.
For instance, in the provided problem, the standard enthalpy of formation of copper(I) oxide (\(\text{Cu}_2 \, \text{O} \)) is given as \(\Delta H_f^0(\text{Cu}_2 \, \text{O}) = -168.6 \, \text{kJ/mol}\).
The goal is to find the standard enthalpy of formation for copper(II) oxide (\(\text{CuO} \)), using the given reaction enthalpy and this value. Knowing these standard enthalpies allows chemists to estimate the energy changes associated with forming various compounds.

Thermodynamic Data

Thermodynamic data, like enthalpy changes and enthalpies of formation, are essential tools in chemistry. They provide quantitative information about the energy changes during chemical processes. This data helps scientists and engineers design energy-efficient reactions, optimize industrial processes, and understand natural phenomena.
In our example, we use the given reaction enthalpy (\tex\(\text{ΔH}_{\text{rxn}}^{0}\)) and the enthalpy of formation values to solve for the unknown enthalpy (\tex\(\text{ΔH}_{\text{f}}^{0} \, (\text{CuO})\)).
Collecting and utilizing accurate thermodynamic data is crucial for predicting reaction behavior and ensuring the safe and effective implementation of chemical processes.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products and can be accompanied by energy changes, as indicated by enthalpy changes. The reaction provided in the problem is a redox reaction, involving the oxidation of copper(I) oxide to copper(II) oxide.
The balanced chemical equation: \(\text{Cu}_2 \, \text{O}(s) + \frac{1}{2} \, \text{O}_2(g) \rightarrow 2 \, \text{CuO}(s)\) shows that 1 mole of \(\text{Cu}_2 \, \text{O}\) reacts with 0.5 moles of \(\text{O}_2\) to form 2 moles of \(\text{CuO}\).
This reaction's \(\Delta H_{\text{rxn}}^{0} = -146.0 \, \text{kJ}\) tells us that the reaction releases energy, making it exothermic. Understanding the principles of chemical reactions, such as balancing equations and calculating energy changes, is key to mastering chemistry and its practical applications.