The following data compare the standard enthalpies and free...

The following data compare the standard enthalpies and free energies of formation of some crystalline ionic substances and aqueous solutions of the substances: $$ \begin{array}{lrr} \text { Substance } & \Delta \boldsymbol{H}_{f}^{\circ}(\mathbf{k} \mathbf{J} / \mathbf{m o l}) & \Delta \mathbf{G}_{f}^{\circ}(\mathbf{k J} / \mathbf{m o l}) \\ \hline \mathrm{AgNO}_{3}(s) & -124.4 & -33.4 \\ \mathrm{AgNO}_{3}(a q) & -101.7 & -34.2 \\ \mathrm{MgSO}_{4}(s) & -1283.7 & -1169.6 \\ \mathrm{MgSO}_{4}(a q) & -1374.8 & -1198.4 \end{array} $$ (a) Write the formation reaction for $\mathrm{AgNO}_{3}(s) .$ Based on this reaction, do you expect the entropy of the system to increase or decrease upon the formation of $\mathrm{AgNO}_{3}(s) ?$ (b) Use $\Delta H_{f}^{\circ}$ and $\Delta G_{f}^{\circ}$ of $\mathrm{AgNO}_{3}(s)$ to determine the entropy change upon formation of the substance. Is your answer consistent with your reasoning in part (a)? (c) Is dissolving $\mathrm{AgNO}_{3}$ in water an exothermic or endothermic process? What about dissolving $\mathrm{MgSO}_{4}$ in water? (d) For both $\mathrm{AgNO}_{3}$ and $\mathrm{MgSO}_{4},$ use the data to calculate the entropy change when the solid is dissolved in water. (e) Discuss the results from part (d) with reference to material presented in this chapter and in the "A Closer Look" box on page 540 .

The following data compare the standard enthalpies and free energies of formation of some crystalline ionic substances and aqueous solutions of the substances:
$$
\begin{array}{lrr}
\text { Substance } & \Delta \boldsymbol{H}_{f}^{\circ}(\mathbf{k} \mathbf{J} / \mathbf{m o l}) & \Delta \mathbf{G}_{f}^{\circ}(\mathbf{k J} / \mathbf{m o l}) \\
\hline \mathrm{AgNO}_{3}(s) & -124.4 & -33.4 \\
\mathrm{AgNO}_{3}(a q) & -101.7 & -34.2 \\
\mathrm{MgSO}_{4}(s) & -1283.7 & -1169.6 \\
\mathrm{MgSO}_{4}(a q) & -1374.8 & -1198.4
\end{array}
$$
(a) Write the formation reaction for $\mathrm{AgNO}_{3}(s) .$ Based on this reaction, do you expect the entropy of the system to increase or decrease upon the formation of $\mathrm{AgNO}_{3}(s) ?$ (b) Use $\Delta H_{f}^{\circ}$ and $\Delta G_{f}^{\circ}$ of $\mathrm{AgNO}_{3}(s)$ to determine the entropy change upon formation of the substance. Is your answer consistent with your reasoning in part (a)? (c) Is dissolving $\mathrm{AgNO}_{3}$ in water an exothermic or endothermic process? What about dissolving $\mathrm{MgSO}_{4}$ in water? (d) For both $\mathrm{AgNO}_{3}$ and $\mathrm{MgSO}_{4},$ use the data to calculate the entropy change when the solid is dissolved in water. (e) Discuss the results from part (d) with reference to material presented in this chapter and in the "A Closer Look" box on page 540 .

Key Concepts

Standard Enthalpy of Formation

This concept refers to the enthalpy change when one mole of a compound is formed from its elements in their standard states. It is a measure of the energy changes involved in bond formation and breakdown, and it serves as a reference for calculating reaction enthalpies in thermodynamics.

Standard Free Energy of Formation

This term represents the Gibbs free energy change when one mole of a compound is formed from its elements in their standard states. It not only accounts for enthalpy changes but also incorporates the effects of entropy, and it is crucial for determining the spontaneity of a reaction under constant temperature and pressure.

Entropy Change

Entropy change quantifies the change in the disorder or randomness of a system as a reaction proceeds. In thermodynamic processes, entropy increases when a reaction results in more dispersed energy or a greater number of microstates, which can be predicted by changes in physical states and molecular arrangements.

Gibbs Free Energy Equation

The Gibbs free energy equation, expressed as ?G = ?H - T?S, links the enthalpy change (?H), the entropy change (?S), and the absolute temperature (T) to determine the overall spontaneity of a process. It provides a framework to understand how heat transfer and molecular disorder jointly influence reaction feasibility.

Dissolution Process Thermodynamics

This concept involves analyzing the energy and entropy changes when a solute dissolves in a solvent. The process is governed by the interplay between the absorption or release of heat (endothermic or exothermic behavior) and the change in entropy due to the dispersion of ions or molecules in the solution, impacting the overall free energy change.

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