Using values of Δf H^∘ and S^∘, calculate the standard molar...

Using values of $\Delta_{f} H^{\circ}$ and $S^{\circ},$ calculate the standard molar free energy of formation, $\Delta_{f} G^{\circ},$ for each of the following compounds: (a) $\mathrm{CS}_{2}(\mathrm{g})$ (b) $\mathrm{NaOH}(\mathrm{s})$ (c) $\mathrm{ICl}(\mathrm{g})$ Compare your calculated values of $\Delta_{f} G^{\circ}$ with those listed in Appendix L. Which of these formation reactions are predicted to be product-favored at equilibrium at $25^{\circ} \mathrm{C} ?$

Using values of $\Delta_{f} H^{\circ}$ and $S^{\circ},$ calculate the standard molar free energy of formation, $\Delta_{f} G^{\circ},$ for each of the following compounds:
(a) $\mathrm{CS}_{2}(\mathrm{g})$
(b) $\mathrm{NaOH}(\mathrm{s})$
(c) $\mathrm{ICl}(\mathrm{g})$
Compare your calculated values of $\Delta_{f} G^{\circ}$ with those listed in Appendix L. Which of these formation reactions are predicted to be product-favored at equilibrium at $25^{\circ} \mathrm{C} ?$

Key Concepts

Reaction Equilibrium and Product-Favored Condition

The sign of the calculated ?_f G° indicates whether a formation reaction is thermodynamically favored at equilibrium. A negative ?_f G° means the reaction is product-favored, signifying that the formation of the compound is spontaneous under standard conditions such as 25°C. Comparing calculated ?_f G° values to tabulated data is a common method for assessing the reliability of thermodynamic predictions.

Standard Enthalpy and Standard Entropy

Standard enthalpy (?_f H°) and standard entropy (S°) values provide the necessary thermodynamic data required to apply the ?G = ?H ? T?S equation. ?_f H° reflects the heat absorbed or released during formation, while S° measures the degree of disorder. Together, they determine the free energy change for a reaction under standard conditions.

Gibbs Free Energy

Gibbs Free Energy (?G) is a thermodynamic quantity that indicates the maximum amount of work that a system can perform at constant temperature and pressure. It combines enthalpy (heat content) and entropy (degree of disorder) to predict whether a process will occur spontaneously. A negative ?G indicates a process that is thermodynamically favored under the given conditions.

?G = ?H ? T?S Relationship

This fundamental equation links the enthalpy change (?H) and entropy change (?S) of a reaction with temperature (T) to calculate the Gibbs free energy change (?G). It is essential for understanding how energy and disorder affect reaction spontaneity. The equation shows that even if a reaction is endothermic (positive ?H), it can still be spontaneous if the T?S term is large enough.

Standard Molar Free Energy of Formation

The standard molar free energy of formation (?_f G°) is the change in Gibbs free energy when one mole of a compound is formed from its constituent elements in their standard states. It is a key reference quantity used to predict reaction spontaneity and to compare the stability of different compounds under standard conditions.

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