Problem 40 - Chemistry: Principles and Reactions

Question

Given $$ 2 \mathrm{CuO}(s) \longrightarrow 2 \mathrm{Cu}(s)+\mathrm{O}_{2}(g) \quad \Delta H^{\circ}=314.6 \mathrm{~kJ} $$ (a) Determine the heat of formation of \(\mathrm{CuO}\). (b) Calculate \(\Delta H^{\circ}\) for the formation of \(13.58 \mathrm{~g}\) of \(\mathrm{CuO}\).

Step-by-Step Solution

Answer

Answer: The heat of formation of CuO is 157.3 kJ/mol, and the enthalpy change for the formation of 13.58 g of CuO is 26.84 kJ.

Step 1: (a) Determine the heat of formation of CuO

To find the heat of formation of CuO, we need to use the given standard enthalpy change value. Given the balanced chemical equation, we see that 2 moles of CuO decompose to form 2 moles of Cu and 1 mole of O2 gas. The standard enthalpy change of this reaction is 314.6 kJ. If we divide the enthalpy change by the number of moles of CuO in the reaction, we can find the heat of formation for one mole of CuO: $$ \Delta H_{f}^{\circ}(\mathrm{CuO}) = \frac{\Delta H^{\circ}}{\text{moles of CuO decomposed}} = \frac{314.6 \mathrm{k~J}}{2 \mathrm{~moles~of~CuO}} = 157.3 \mathrm{~kJ/mol} $$ Therefore, the heat of formation of one mole of CuO is 157.3 kJ/mol.

Step 2: (b) Calculate ∆𝐻° for the formation of 13.58 g of CuO

To find the enthalpy change for the formation of 13.58 g of CuO, we first need to convert grams to moles using the molar mass of CuO. Then, we'll multiply the number of moles with the heat of formation value we calculated in part (a). 1. Calculate the number of moles of CuO: Molar mass of Cu = 63.55 g/mol Molar mass of O = 16.00 g/mol Molar mass of CuO = 63.55 + 16.00 = 79.55 g/mol $$ \text{moles of CuO} = \frac{\text{mass of CuO}}{\text{molar mass of CuO}} = \frac{13.58 \mathrm{~g}}{79.55 \mathrm{~g/mol}} = 0.1707 \mathrm{~mol} $$ 2. Calculate ΔH° for the formation of 13.58 g of CuO: $$ \Delta H = \Delta H_{f}^{\circ}(\mathrm{CuO}) \times \text{moles of CuO} = 157.3 \mathrm{~kJ/mol} \times 0.1707 \mathrm{~mol} = 26.84 \mathrm{~kJ} $$ Thus, the enthalpy change for the formation of 13.58 g of CuO is 26.84 kJ.

Key Concepts

Understanding Enthalpy Change

Enthalpy change is a crucial concept in chemistry. It refers to the heat absorbed or released during a chemical reaction at constant pressure. When we talk about the standard enthalpy change of a reaction \(\Delta H^{\circ}\), we mean the enthalpy change that occurs under standard conditions (1 atm pressure and 25°C).
Enthalpy is represented by the symbol "H," and the change in enthalpy during a reaction is represented as \(\Delta H\). This value can tell us whether a reaction is endothermic (absorbs heat) or exothermic (releases heat):

• In an endothermic reaction, \(\Delta H\) is positive, indicating heat absorption.
• In an exothermic reaction, \(\Delta H\) is negative, indicating heat release.

For example, the decomposition of \mathrm{CuO}\ has a \(\Delta H^{\circ}\) of 314.6 kJ for 2 moles of \mathrm{CuO}\, indicating that it requires 314.6 kJ of energy to decompose. This is specifically considered endothermic since heat is absorbed from the surroundings.

Calculating Molar Mass

Molar mass is another key concept in chemistry and is fundamental when converting between the mass of a substance and the amount in moles. The molar mass is the mass of one mole of a substance, which can be calculated by summing the atomic masses of all the atoms in a molecule.
For \mathrm{CuO}\, you need to consider the molar mass of copper (Cu) and oxygen (O):

• The atomic mass of Cu is 63.55 g/mol.
• The atomic mass of O is 16.00 g/mol.

By adding these values together, the molar mass of \mathrm{CuO}\ is calculated as 79.55 g/mol.
Once the molar mass is known, you can use it to convert a given mass of a substance to the number of moles, which is essential when calculating enthalpy changes in reactions. For example, for 13.58 g of \mathrm{CuO}\, the number of moles is \(\frac{13.58 \mathrm{~g}}{79.55 \mathrm{~g/mol}} = 0.1707 \mathrm{~mol}\).

Decomposing CuO: A Practical Example

The process of decomposing \mathrm{CuO}\ involves breaking down copper(II) oxide into copper and oxygen gas. This type of reaction is known as a decomposition reaction, where a single compound breaks down into two or more elements or simpler compounds.
In chemical equations, decomposition is typically represented when a single reactant yields multiple products. For \mathrm{CuO}\ decomposition, the balanced equation is:\[ 2 \mathrm{CuO} \rightarrow 2 \mathrm{Cu} + \mathrm{O}_2 \]This equation shows that 2 moles of \mathrm{CuO}\ decompose to produce 2 moles of copper and 1 mole of oxygen gas. To understand the real-world implications, consider the standard enthalpy change of 314.6 kJ. This value indicates how much energy is needed for the decomposition under standard conditions.
Understanding these concepts in the framework of \mathrm{CuO}\ decomposition helps illustrate the relationship between enthalpy changes, reaction quantities, and how chemists predict and calculate the energy involved in chemical transformations.