Question

Using data in Appendix \(C\), calculate \(\Delta H^{\circ}, \Delta S^{\circ}\), and \(\Delta G^{\circ}\) at \(298 \mathrm{~K}\) for each of the following reactions. In each case show that \(\Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ}\). (a) \(\mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{HF}(g)\) (b) \(\mathrm{C}(\mathrm{s}\), graphite \()+2 \mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CCl}_{4}(\mathrm{~g})\) (c) \(2 \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{POCl}_{3}(\mathrm{~g})\) (d) \(2 \mathrm{CH}_{3} \mathrm{OH}(g)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\)

Short answer

For each reaction, use Appendix C to find the standard enthalpies, entropies, and Gibbs free energies of formation for the reactants and products. Calculate \(\Delta H^{\circ}\), \(\Delta S^{\circ}\), and \(\Delta G^{\circ}\) by subtracting the sum of the reactants' values from the sum of the products' values. Verify the relation \(\Delta G^{\circ} = \Delta H^{\circ} - 298 \times \Delta S^{\circ}\) for all cases.

Step-by-step solution

Find the values of enthalpies, entropies and Gibbs free energy for the reactants and products

Using Appendix C, look up the standard enthalpies, entropies, and Gibbs free energies of formation for H₂(g), F₂(g) and HF(g).

Calculate the ΔH°, ΔS°, and ΔG°

Subtract the sum of the standard enthalpies of formation of the reactants from the sum of the standard enthalpies of formation of the products to find \(\Delta H^{\circ}\). Do the same for \(\Delta S^{\circ}\) and \(\Delta G^{\circ}\).

Verify the relation ΔG° = ΔH° - TΔS°

Check if \(\Delta G^{\circ}\) is equal to \(\Delta H^{\circ}-298\times\Delta S^{\circ}\). (b) \(\mathrm{C}(\mathrm{s}\), graphite $)+2 \mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CCl}_{4}(\mathrm{~g})$

Find the values of enthalpies, entropies and Gibbs free energy for the reactants and products

Using Appendix C, look up the standard enthalpies, entropies, and Gibbs free energies of formation for C(graphite), Cl₂(g) and CCl₄(g).

Calculate the ΔH°, ΔS°, and ΔG°

Subtract the sum of the standard enthalpies of formation of the reactants from the sum of the standard enthalpies of formation of the products to find \(\Delta H^{\circ}\). Do the same for \(\Delta S^{\circ}\) and \(\Delta G^{\circ}\).

Verify the relation ΔG° = ΔH° - TΔS°

Check if \(\Delta G^{\circ}\) is equal to \(\Delta H^{\circ}-298\times\Delta S^{\circ}\). (c) $2 \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{POCl}_{3}(\mathrm{~g})$

Find the values of enthalpies, entropies and Gibbs free energy for the reactants and products

Using Appendix C, look up the standard enthalpies, entropies, and Gibbs free energies of formation for PCl₃(g), O₂(g) and POCl₃(g).

Calculate the ΔH°, ΔS°, and ΔG°

Subtract the sum of the standard enthalpies of formation of the reactants from the sum of the standard enthalpies of formation of the products to find \(\Delta H^{\circ}\). Do the same for \(\Delta S^{\circ}\) and \(\Delta G^{\circ}\).

Verify the relation ΔG° = ΔH° - TΔS°

Check if \(\Delta G^{\circ}\) is equal to \(\Delta H^{\circ}-298\times\Delta S^{\circ}\). (d) $2 \mathrm{CH}_{3} \mathrm{OH}(g)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$

Find the values of enthalpies, entropies and Gibbs free energy for the reactants and products

Using Appendix C, look up the standard enthalpies, entropies, and Gibbs free energies of formation for CH₃OH(g), H₂(g), C₂H₆(g) and H₂O(g).

Calculate the ΔH°, ΔS°, and ΔG°

Subtract the sum of the standard enthalpies of formation of the reactants from the sum of the standard enthalpies of formation of the products to find \(\Delta H^{\circ}\). Do the same for \(\Delta S^{\circ}\) and \(\Delta G^{\circ}\).

Verify the relation ΔG° = ΔH° - TΔS°

Check if \(\Delta G^{\circ}\) is equal to \(\Delta H^{\circ}-298\times\Delta S^{\circ}\).

Key concepts

Enthalpy

In thermodynamics, enthalpy is a crucial concept that represents the total heat content of a system. Denoted by the symbol \( H \), it is a measure of the energy stored within a substance due to both its internal energy and the energy needed to make space for it by displacing its environment. Calculating the change in enthalpy, \( \Delta H \), is a common step in analyzing chemical reactions, particularly those that occur at constant pressure.

When we talk about \( \Delta H^{\circ} \), we are specifically referring to the change in standard enthalpy, which means the enthalpy change under standard conditions (1 bar of pressure and usually 298 K temperature). This change can be calculated by subtracting the sum of the enthalpies of the reactants from the sum of the enthalpies of the products:

• \( \Delta H^{\circ} = \sum H^{\circ}_{\text{products}} - \sum H^{\circ}_{\text{reactants}} \)

This calculation tells us whether a reaction is exothermic (releases heat, \( \Delta H^{\circ} < 0 \)) or endothermic (absorbs heat, \( \Delta H^{\circ} > 0 \)). Knowing the enthalpy changes helps us understand the energy changes in chemical reactions and predict how a reaction may behave.

Entropy

Entropy, symbolized by \( S \), is a measure of the disorder or randomness in a system. Unlike enthalpy, which concerns energy content, entropy is concerned with the distribution of energy in a process. A higher entropy indicates a more disordered state. In chemical reactions, changes in entropy, \( \Delta S \), can influence the spontaneity of a reaction.

The key to understanding entropy is recognizing that natural processes tend to progress toward a state of maximum entropy. For any reaction at standard conditions, the standard entropy change \( \Delta S^{\circ} \) can be calculated similarly to enthalpy:

• \( \Delta S^{\circ} = \sum S^{\circ}_{\text{products}} - \sum S^{\circ}_{\text{reactants}} \)

A positive \( \Delta S^{\circ} \) means the system is becoming more disordered, while a negative \( \Delta S^{\circ} \) indicates a decrease in disorder. Entropy changes, alongside enthalpy, are vital for determining a reaction's spontaneity using the Gibbs Free Energy equation: \( \Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ} \). This equation shows how changes in entropy and enthalpy govern the feasibility of a reaction.

Thermodynamics

Thermodynamics is the branch of physical science that deals with the relations between heat and other forms of energy such as mechanical, electrical, or chemical energy. It revolves around the principles that describe how energy is transferred within a system and between systems and surroundings, especially during chemical reactions.

The core concepts of thermodynamics include the previously discussed enthalpy and entropy, as well as free energy. Together, they help chemists and engineers understand how and why reactions occur. Thermodynamics aims to predict whether a reaction is spontaneous. A spontaneous process is one that progresses on its own without any external input of energy.

• The first law of thermodynamics, or the law of energy conservation, states that energy cannot be created or destroyed, only transformed.
• The second law introduces entropy, asserting that the total entropy of a closed system will never decrease over time.
• The third focuses on the behavior of systems as temperatures approach absolute zero.

Using the Gibbs Free Energy equation is a practical application of thermodynamic principles to predict reaction spontaneity and determine the usefulness of reactions for energy production or synthesis. It provides critical insights into how thermodynamics governs chemical processes in our daily lives and industrial applications.