Problem 90 - Chemistry: An Atoms-Focused Approach

Question

Copper forms two oxides, \(\mathrm{Cu}_{2} \mathrm{O}\) and \(\mathrm{CuO}\). a. Name these oxides. b. Predict over what temperature range this reaction is spontaneous using the following thermodynamic data:$$\mathrm{Cu}_{2} \mathrm{O}(s) \rightarrow \mathrm{CuO}(s)+\mathrm{Cu}(s)$$ $$\begin{aligned}&]\\\&\begin{array}{lcc} & \Delta H_{f}^{\circ}(\mathrm{kJ} / \mathrm{mol}) & S^{\circ}[J /(\mathrm{mol} \cdot \mathrm{K})] \\\C u_{2} \mathrm{O}(s) & -170.7 & 92.4 \\\\\hline \mathrm{CuO}(s) & -156.1 & 42.6 \\\\\hline\end{array}\end{aligned}$$.c. Why is the standard molar entropy of \(\mathrm{Cu}_{2} \mathrm{O}(s)\) larger than that of \(\mathrm{CuO}(s) ?\)

Step-by-Step Solution

Answer

Question: Name the two oxides of copper, determine the temperature range in which the reaction between them is spontaneous using thermodynamic data, and explain why the standard molar entropy of \(\mathrm{Cu}_{2} \mathrm{O}\) is larger than that of \(\mathrm{CuO}\). Answer: The two oxides of copper are Copper(I) oxide (\(\mathrm{Cu}_{2} \mathrm{O}\)) and Copper(II) oxide (\(\mathrm{CuO}\)). The reaction between them is spontaneous at any temperature below 879 K. The standard molar entropy of \(\mathrm{Cu}_{2} \mathrm{O}\) is larger than that of \(\mathrm{CuO}\) due to the difference in molecular complexity and crystal structures. Copper(I) oxide has a more complex structure compared to Copper(II) oxide, which leads to a higher molar entropy.

Step 1: Naming the oxides

a. To name these oxides, we will use the IUPAC naming system. Copper forms more than one oxide, so we need to use the Roman numeral (or "Stock" system) to indicate the oxidation state of copper. The two oxides are: 1. \(\mathrm{Cu}_{2} \mathrm{O}\): Copper has an oxidation state of +1 in this oxide. Therefore, it is named "Copper(I) oxide" or "Cuprous oxide." 2. \(\mathrm{CuO}\): Copper has an oxidation state of +2 in this oxide. Hence, it is named "Copper(II) oxide" or "Cupric oxide."

Step 2: Predicting the temperature range for the spontaneous reaction

b. To determine the temperature range where the reaction is spontaneous, we will use the Gibbs free energy change (\(\Delta G\)) equation:$$\Delta G = \Delta H - T\Delta S$$The reaction is spontaneous when \(\Delta G < 0\). First, let's calculate \(\Delta H_{rxn}\) and \(\Delta S_{rxn}\) for the reaction:$$\begin{aligned} &\mathrm{Cu}_{2} \mathrm{O}(s) \rightarrow \mathrm{CuO}(s) + \mathrm{Cu}(s)\\ \Delta H_{rxn} &= \Delta H_f^\circ(\mathrm{CuO})+\Delta H_f^\circ(\mathrm{Cu}) - \Delta{H}_f^\circ(\mathrm{Cu}_2\mathrm O)\\ &=-156.1 - (-170.7)\\ &=14.6 \mathrm{kJ/mol}\\ \Delta S_{rxn} &= S^\circ(\mathrm{CuO}) + S^\circ(\mathrm{Cu}) - S^\circ(\mathrm{Cu}_2\mathrm O)\\ &= 42.6 + 33.2-92.4\\ &= -16.6 \mathrm{J/mol\cdot K} \end{aligned}$$Now, we'll substitute these values into the Gibbs free energy equation and set \(\Delta G\) to zero, then solve for T:$$\begin{aligned} \Delta G &= \Delta H - T\Delta S\\ 0 &= 14.6 \mathrm{kJ/mol} - T(-16.6 \mathrm{J/mol\cdot K})\\ T &= \frac{14.6\, \mathrm{kJ/mol}}{16.6\, \mathrm{J/mol\cdot K}}\\ T &= 879\, \mathrm K \end{aligned}$$Therefore, the reaction is spontaneous at any temperature below 879 K.

Step 3: Comparing the molar entropy of \(\mathrm{Cu}_{2} \mathrm{O}(s)\) and \(\mathrm{CuO}(s)\)

c. The standard molar entropy of \(\mathrm{Cu}_{2} \mathrm{O}(s)\) is larger than that of \(\mathrm{CuO}(s)\) possibly due to the difference in molecular complexity and crystal structures. \(\mathrm{Cu}_{2} \mathrm{O}\) has a more complex structure compared to \(\mathrm{CuO}\). A compound with a more complex molecular structure tends to have higher molar entropy because it can have more ways of distributing its energy as microstates.

Key Concepts

Oxidation States

In chemistry, oxidation states, also known as oxidation numbers, help us understand electron distribution in chemical compounds. When it comes to copper oxides like \(\text{Cu}_2\text{O}\) and \(\text{CuO}\), the oxidation states are crucial for naming these compounds
using the systematic IUPAC naming system. Copper can exhibit more than one oxidation state:

• For \(\text{Cu}_2\text{O}\), each copper atom has an oxidation state of +1. The compound is hence called Copper(I) oxide, or Cuprous oxide.
• For \(\text{CuO}\), copper's oxidation state is +2, leading to the name Copper(II) oxide, or Cupric oxide.

Oxidation states direct us in recognizing how many electrons are lost or gained in reactions. By understanding this, you can predict compound behavior in chemical reactions and during compound formation.

Gibbs Free Energy

Gibbs Free Energy, or \(\Delta G\), is a term that describes the energy available for a reaction to occur. It helps predict
whether a chemical reaction is spontaneous under constant temperature and pressure. The equation is defined as:

• \(\Delta G = \Delta H - T \Delta S\)

Here, \(\Delta H\) is the enthalpy change, \(T\) is the temperature in Kelvin, and \(\Delta S\) is the change in entropy. For a reaction to be spontaneous, \(\Delta G\) must be negative. In the example with copper oxides, we calculate:

• \(\Delta H_{rxn}\) for the transition between \(\text{Cu}_2\text{O}\) and \(\text{CuO}\).
• \(\Delta S_{rxn}\) which indicates disorder change in the reaction.

By setting \(\Delta G = 0\) and solving for \(T\), we find the temperature below which the reaction becomes spontaneous. This approach illuminates how certain reactions are favored depending on conditions.

Molar Entropy

Molar entropy \(S^\circ\) is a measure of the disorder or randomness at the molecular level of a substance. It reflects the number of ways energy can be arranged in a system. For copper oxides, the difference in molar entropy between \(\text{Cu}_2\text{O}\) and \(\text{CuO}\) can be beneficial for understanding material qualities:

• \(\text{Cu}_2\text{O}\) has a higher molar entropy than \(\text{CuO}\), meaning it has more configurational possibilities due to its complex crystal structure.
• Higher molar entropy is associated with more energy states, leading to greater randomness.
• The intricacy of the compound's molecular and structural makeup increases entropy.

Understanding these differences helps predict reaction behaviors and the nature of a material at the microscopic level.

Thermodynamics

Thermodynamics involves the study of energy and its transformations. It forms the backboneof understanding how reactions occur and whether or not they are feasible under specific conditions. In the context of copper oxides,

• We assess the changes in enthalpy \(\Delta H\) which reflects heat absorption or release.
• Entropy \(\Delta S\) changes, which indicate the disorder and randomness energy in a system.
• Gibbs Free Energy links \(\Delta H\), \(\Delta S\), and Temperature to predict reaction spontaneity.

The primary laws of thermodynamics guide us,

• The First Law, focusing on energy conservation.
• The Second Law, introduces the concept of entropy as a measure of irreversibility.

Through thermodynamics,we discern that reactions like \(\text{Cu}_2\text{O} \rightarrow \text{CuO} + \text{Cu}\) might require a balance of conditions to be spontaneous.

IUPAC Naming System

The IUPAC naming system is a standardized method for naming chemical compounds,
ensuring that chemists across the globe can understand exactly what compound is referred to. This clarity is vital, not just for communication, but also for conveying information about the structure and reactivity of compounds. In the context of copper oxides:

• Copper(I) oxide represents \(\text{Cu}_2\text{O}\), indicating copper's +1 oxidation state, often dubbed "cuprous."
• Copper(II) oxide is \(\text{CuO}\), designating copper's +2 oxidation state, sometimes called "cupric."

The system relies on the oxidation state of the metal, shown in Roman numerals, to distinguish between the varied oxidation states metals can possess. This prevents confusion that might arise from using common names,especially in cases where a metal can form multiple different compounds with the same element.