Decide whether each of the following statements is true or...

Decide whether each of the following statements is true or false. If false, rewrite it to make it true. (a) The entropy of a substance increases on going from the liquid to the vapor state at any temperature. (b) An exothermic reaction will always be spontaneous. (c) Reactions with a positive $\Delta_{r} H^{\circ}$ and a positive $\Delta_{\tau} S^{\circ}$ can never be product-favored. (d) If $\Delta_{r} G^{\circ}$ for a reaction is negative, the reaction will have an equilibrium constant greater than $1 .$

Decide whether each of the following statements is true or false. If false, rewrite it to make it true. (a) The entropy of a substance increases on going from the liquid to the vapor state at any temperature.
(b) An exothermic reaction will always be spontaneous.
(c) Reactions with a positive $\Delta_{r} H^{\circ}$ and a positive $\Delta_{\tau} S^{\circ}$ can never be product-favored.
(d) If $\Delta_{r} G^{\circ}$ for a reaction is negative, the reaction will have an equilibrium constant greater than $1 .$

Key Concepts

Entropy

Entropy is a measure of the randomness or disorder of a system. It plays a critical role in phase changes, where a substance typically exhibits higher entropy in the vapor state compared to the liquid state due to increased molecular disorder. However, the magnitude of the entropy change and its direction can depend on specific conditions such as temperature and pressure.

Enthalpy

Enthalpy refers to the total heat content of a system and is a key factor in determining whether a reaction is exothermic (releases heat) or endothermic (absorbs heat). While exothermic reactions release energy, the sign of the enthalpy change alone does not determine if a reaction will be spontaneous.

Spontaneous Reaction

A spontaneous reaction is one that occurs without the need for continuous external energy input, and its tendency is governed by the change in Gibbs free energy (?G). Spontaneity is determined by both the enthalpy change and the entropy change of a system, as encapsulated by the Gibbs free energy equation.

Gibbs Free Energy

Gibbs free energy combines both enthalpy and entropy to evaluate the thermodynamic favorability of a process at a given temperature. A negative value of ?G indicates that a reaction is spontaneous under the specific conditions, while the relationship ?G = ?H - T?S shows that both energy (?H) and disorder (?S) contributions are essential considerations.

Equilibrium Constant

The equilibrium constant expresses the ratio of product concentrations to reactant concentrations when a reaction reaches equilibrium. It is intrinsically linked to the standard Gibbs free energy change through the relationship ?G° = -RT ln K, so a negative ?G° correlates with an equilibrium constant greater than one, meaning that the products are favored at equilibrium.

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