Determine whether each of the following statements is true...

Determine whether each of the following statements is true or false. If false, modify it to make it true. (a) An exothermic reaction is spontaneous. (b) When $\Delta G^{\circ}$ is positive, the reaction cannot occur under any conditions. (c) $\Delta S^{\circ}$ is positive for a reaction in which there is an increase in the number of moles. (d) If $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are both negative, $\Delta G^{\circ}$ will be negative.

Determine whether each of the following statements is true or false. If false, modify it to make it true.
(a) An exothermic reaction is spontaneous.
(b) When $\Delta G^{\circ}$ is positive, the reaction cannot occur under any conditions.
(c) $\Delta S^{\circ}$ is positive for a reaction in which there is an increase in the number of moles.
(d) If $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are both negative, $\Delta G^{\circ}$ will be negative.

Key Concepts

Gibbs Free Energy

Gibbs free energy (?G) is a thermodynamic state function that predicts the spontaneity of a reaction. Its value, determined by the equation ?G = ?H - T?S, indicates whether a process will occur without external intervention. A negative ?G implies a spontaneous reaction under the given conditions, while a positive ?G means the process is non?spontaneous, unless altered by changing temperature or concentrations.

Reaction Enthalpy

Reaction enthalpy (?H) represents the heat absorbed or released by a reaction at constant pressure. An exothermic reaction has a negative ?H, meaning it releases heat, whereas an endothermic reaction has a positive ?H and absorbs heat. Importantly, the exothermic character of a reaction does not alone guarantee that the reaction will be spontaneous.

Reaction Entropy

Reaction entropy (?S) quantifies the change in disorder or randomness during a reaction. An increase in the number of moles of a gas or in the dispersion of energy typically results in a positive ?S, enhancing the tendency toward spontaneity. However, the overall impact on Gibbs free energy also depends on the temperature and the reaction's enthalpy change.

Spontaneous Reactions

The concept of spontaneous reactions is central to thermodynamics and is chiefly linked to the sign of Gibbs free energy. A reaction is spontaneous if it proceeds without external input of energy, corresponding to a negative ?G. However, spontaneity can be influenced by both enthalpic and entropic contributions, meaning that a reaction with favorable heat release might still be non-spontaneous if the entropy change does not support it.

Standard versus Non-standard Conditions

Standard state conditions, defined by specific pressure, concentration, and temperature values, yield the standard free energy change (?G°). However, reactions may behave differently under non-standard conditions, as actual free energy (?G) depends on the system’s temperature, pressures, and concentrations, highlighting that a reaction with an unfavorable ?G° might still proceed if the conditions are modified accordingly.

Temperature Dependence in Thermodynamics

Temperature plays a vital role in determining the spontaneity of a reaction because of its influence on the T?S term in the Gibbs free energy equation. For reactions where both ?H and ?S are negative or both are positive, varying the temperature can shift the balance between enthalpy and entropy, thus changing whether the reaction is spontaneous.

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