Problem 24 - General Chemistry: Principles and Modern Applications

Question

Use data from Appendix D to determine values of \(\Delta G^{\circ}\) for the following reactions at \(25^{\circ} \mathrm{C}\) (a) \(\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{g})\) (b) \(2 \mathrm{SO}_{3}(\mathrm{g}) \longrightarrow 2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})\) (c) \(\mathrm{Fe}_{3} \mathrm{O}_{4}(\mathrm{s})+4 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 3 \mathrm{Fe}(\mathrm{s})+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (d) \(2 \mathrm{Al}(\mathrm{s})+6 \mathrm{H}^{+}(\mathrm{aq}) \longrightarrow 2 \mathrm{Al}^{3+}(\mathrm{aq})+3 \mathrm{H}_{2}(\mathrm{g})\)

Step-by-Step Solution

Answer

The solution involves converting temperature from Celsius to Kelvin, utilizing Appendix D to derive \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) values and substituting them in the given formula to calculate \(\Delta G^{\circ}\). As we don't have Appendix D's data to get exact figures; the answer may vary.

Step 1: Convert temperature to Kelvin

Given the temperature is \(25^{\circ}\) Celsius, we need to convert it to Kelvin for the calculations: T = \(25 + 273.15 = 298.15 K\)

Step 2: Determine \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) for each reaction

For each reaction, we need to determine the standard enthalpy change (\(\Delta H^{\circ}\)) and the standard entropy change (\(\Delta S^{\circ}\)) using the tables in Appendix D. Remember that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) for a reaction can be found by subtracting the sum of the \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) values of the reactants from those of the products.

Step 3: Calculate \(\Delta G^{\circ}\) for each reaction

Use the determined values of \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) to calculate \(\Delta G^{\circ}\) by substituting them into the formula \(\Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ}\). Once the calculations are performed correctly for all four reactions, values of \(\Delta G^{\circ}\) for each reaction are obtained.

Key Concepts

Standard Enthalpy Change

The standard enthalpy change, \(\Delta H^{\circ}\), is a key concept in thermodynamics that tells us about the heat absorbed or released during a chemical reaction under standard conditions. **Standard Conditions** mean that the reaction takes place at 1 atm pressure and 25°C (298 K). Heat exchange is crucial because it impacts the overall energy balance of a reaction.
When a chemical reaction occurs, bonds are broken and new bonds are formed. Breaking bonds requires energy, while forming bonds releases energy.

• **Exothermic Reactions:** These reactions release heat to the surroundings, and typically have a negative \(\Delta H^{\circ}\). This is because the energy released in forming new bonds is greater than the energy needed to break the old bonds.
• **Endothermic Reactions:** In contrast, these reactions absorb heat from the surroundings and usually show a positive \(\Delta H^{\circ}\). Here, more energy is needed to break the bonds than is released when new bonds are formed.

This change in enthalpy can be determined using data from tables of standard enthalpy values for different substances, such as those found in Appendix D of your textbook. To find the standard enthalpy change of a reaction, you subtract the total enthalpy of the reactants from the total enthalpy of the products.

Standard Entropy Change

Entropy, symbolized by \(S\), is a measure of disorder or randomness in a system. The standard entropy change, \(\Delta S^{\circ}\), reflects the change in entropy from reactants to products under standard conditions. It provides insight into the degree of disorder involved in a chemical reaction.
A high \(\Delta S^{\circ}\) typically means the products are more disordered than the reactants, possibly due to a higher number of gas molecules formed from liquids or solids.

• **Positive \(\Delta S^{\circ}\):** Indicates an increase in disorder. For example, when solid reactants form gaseous products.
• **Negative \(\Delta S^{\circ}\):** Points to a decrease in disorder, common when gas molecules form solids or liquids.

Just like with enthalpy, you can obtain \(\Delta S^{\circ}\) values from standard entropy tables. To find the standard entropy change for a reaction, calculate the total entropy of the products and subtract the total entropy of the reactants. This will tell you how much the disorder of the system changes during the reaction.

Chemical Reactions

Chemical reactions are the processes by which substances interact to form new products. They are fundamental in both natural and engineered processes, like digestion in our bodies or the production of energy in power plants. Here's how they typically unfold:
Reactions often involve a transformation in matter, energy, and the rearranging of atoms.

• **Reactants**: These are the starting substances in a reaction. They undergo changes as bonds are broken.
• **Products**: These are the substances formed as a result of the reaction. New bonds are made here.

Understanding the enthalpy and entropy changes for a reaction helps predict its spontaneity and progress under standard conditions. Calculating the Gibbs Free Energy (\(\Delta G^{\circ}=\Delta H^{\circ} - T\Delta S^{\circ}\)) allows us to determine whether a reaction can occur on its own without input energy, making these concepts invaluable in the study of chemistry and the design of chemical processes.