Problem 46 - Chemistry: Principles and Reactions

Question

Use the appropriate table to calculate \(\Delta H^{\circ}\) for (a) the reaction between copper(II) oxide and carbon monoxide to give copper metal and carbon dioxide. (b) the decomposition of one mole of methyl alcohol (CH \(_{3} \mathrm{OH}\) ) to methane and oxygen gases.

Step-by-Step Solution

Answer

Question: Calculate the standard enthalpy change (ΔH°) for the following reactions: (a) CuO (s) + CO (g) -> Cu (s) + CO2 (g) (b) 2 CH3OH (l) -> CH4 (g) + O2 (g) + H2O (l) Answer: (a) ΔH° = -125.7 kJ/mol (b) ΔH° = 116.8 kJ/mol

Step 1: Write the balanced chemical equation

The balanced chemical equation for this reaction is: CuO (s) + CO (g) -> Cu (s) + CO2 (g)

Step 2: Find the standard enthalpies of formation

According to a table of standard enthalpies of formation, we have: ΔHf°(CuO) = -157.3 kJ/mol ΔHf°(CO) = -110.5 kJ/mol ΔHf°(Cu) = 0 kJ/mol (Standard enthalpy of formation for elements in their standard states is always zero) ΔHf°(CO2) = -393.5 kJ/mol

Step 3: Calculate ΔH° for the reaction

Use the equation mentioned in the analysis: ΔH° = Σ ΔHf°(products) - Σ ΔHf°(reactants) ΔH° = [ΔHf°(Cu) + ΔHf°(CO2)] - [ΔHf°(CuO) + ΔHf°(CO)] ΔH° = [(0) + (-393.5)] - [(-157.3) + (-110.5)] ΔH° = -393.5 - (-267.8) ΔH° = -125.7 kJ/mol So, the standard enthalpy change for this reaction is ΔH° = -125.7 kJ/mol. (b) Decomposition of one mole of methyl alcohol to methane and oxygen gases:

Step 1: Write the balanced chemical equation

The balanced chemical equation for this reaction is: 2 CH3OH (l) -> CH4 (g) + O2 (g) + H2O (l)

Step 2: Find the standard enthalpies of formation

According to a table of standard enthalpies of formation, we have: ΔHf°(CH3OH) = -238.7 kJ/mol ΔHf°(CH4) = -74.8 kJ/mol ΔHf°(O2) = 0 kJ/mol (Standard enthalpy of formation for elements in their standard states is always zero) ΔHf°(H2O) = -285.8 kJ/mol

Step 3: Calculate ΔH° for the reaction

Use the equation mentioned in the analysis: ΔH° = Σ ΔHf°(products) - Σ ΔHf°(reactants) ΔH° = [ΔHf°(CH4) + ΔHf°(O2) + ΔHf°(H2O)] - [2 × ΔHf°(CH3OH)] ΔH° = [(-74.8) + (0) + (-285.8)] - [2 × (-238.7)] ΔH° = -360.6 - (-477.4) ΔH° = 116.8 kJ/mol So, the standard enthalpy change for this reaction is ΔH° = 116.8 kJ/mol.

Key Concepts

Chemical Reactions

Chemical reactions are processes in which substances, known as reactants, transform into new substances called products. This occurs when chemical bonds in reactants break and new bonds form in products. Reactions can either release energy (exothermic) or absorb energy (endothermic).
Learning about chemical reactions is essential:

• They explain everyday phenomena, like cooking or combustion.
• Understanding reactions helps in fields like medicine, engineering, and environmental science.

By studying chemical reactions, we gain insights into how materials change and interact with each other. This knowledge is used to develop new materials, understand natural processes, and create energy solutions.

Enthalpies of Formation

Enthalpies of formation are pivotal in understanding energy changes during chemical reactions. It refers to the change in enthalpy when one mole of a compound forms from its elements in their standard states. These values are crucial when calculating reaction enthalpy changes because they provide a standardized way to measure energy changes.
Why is it important to know about enthalpies of formation?

• It allows for the prediction of reaction feasibility.
• It aids in the calculation of energy changes using Hess's Law.

For example, knowing the enthalpies of formation of copper(II) oxide and carbon monoxide helps calculate the enthalpy change when these substances react, giving insights into whether the reaction is endothermic or exothermic.

Balanced Chemical Equation

A balanced chemical equation accurately represents a chemical reaction by ensuring the number of each type of atom is the same on both sides of the equation. This reflects the conservation of mass—a fundamental principle in chemistry.
Balancing equations is essential because:

• It ensures the correct stoichiometric relationships between reactants and products.
• It helps in calculating the amounts of reactants required and products formed.

To balance a reaction, adjust coefficients to get an equal number of each atom on both sides. This step is crucial before using the equation for any further calculations, such as determining changes in enthalpy. For example, balancing the reaction of copper(II) oxide with carbon monoxide ensures accurate enthalpy calculations.