Given the values of $$ \Delta H_{\mathrm{ran}}, \Delta S_{\mathrm{ran}}, \text { and } T, \text { determine } \Delta S_{\mathrm{univ}}$$ and predict whether each reaction is spontaneous. \( a.\quad \Delta H_{\mathrm{rxn}}^{\circ}=-95\mathrm{k} J ; \quad \Delta S_{\mathrm{mn}}^{\circ}=-157\mathrm{J} \quad {K} T=298 \mathrm{K} \) \( b.\quad \Delta H_{\mathrm{rxn}}^{\circ}= - 95 \mathrm{k} J ; \quad \Delta S_{\mathrm{mn}}^{\circ}=-157\mathrm{J} \quad {K} T=855\mathrm{K} \) \( c.\quad \Delta H_{\mathrm{rxn}}^{\circ}= + 95 \mathrm{k} J ; \quad \Delta S_{\mathrm{mn}}^{\circ}=-157\mathrm{J} \quad {K} T=298 \mathrm{K} \) \( c.\quad \Delta H_{\mathrm{rxn}}^{\circ}= - 95 \mathrm{k} J ; \quad \Delta S_{\mathrm{mn}}^{\circ}=+157\mathrm{J} \quad {K} T=398 \mathrm{K} \)

Entropy is a fundamental concept in thermodynamics that describes the level of disorder or randomness in a system. The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time; it can only increase or remain constant, which means that systems naturally tend to move toward a state of greater disorder.

When we consider spontaneity in chemical reactions, we are referring to whether a reaction will occur without the need for continuous outside intervention. A critical factor in determining the spontaneity of a reaction is the change in the universe's entropy, denoted as \( \Delta S_{\mathrm{univ}} \). This encompasses both the system's entropy change \( \Delta S_{\mathrm{sys}} \) and the surroundings' entropy change \( \Delta S_{\mathrm{surr}} \).

For a reaction to be spontaneous, \( \Delta S_{\mathrm{univ}} \) must be positive, signifying an overall increase in entropy. However, spontaneous reactions can occur even with a decrease in system entropy if the surroundings' entropy increases enough to offset it. As shown in the solved problem, the spontaneity of a reaction is calculated by adding the system's entropy change to the calculated surroundings' entropy change, which then determines the reaction's overall spontaneity.

Gibbs free energy (G), named after Josiah Willard Gibbs, combines enthalpy (H), temperature (T), and entropy (S) into a single value that predicts the spontaneity of a reaction under constant pressure and temperature. The change in Gibbs free energy \( \Delta G \) for a process is defined by the equation \( \Delta G = \Delta H - T\Delta S \), where \( \Delta H \) is the change in enthalpy, T is the absolute temperature in Kelvin, and \( \Delta S \) is the change in entropy.

Interpreting \( \Delta G \)

If \( \Delta G \) is negative, the reaction is spontaneous as it indicates an overall release of free energy. Conversely, a positive \( \Delta G \) implies the reaction is non-spontaneous. A \( \Delta G \) of zero indicates the system is at equilibrium, with no net change occurring over time.

Our textbook exercise shows how to calculate the universe's entropy change, but Gibbs free energy is a more commonly used parameter for spontaneity in a practical setting since it directly incorporates temperature, a variable that significantly affects the reaction conditions.

Thermodynamics is the study of heat and energy transfer, conversion, and the work done by or on a system. It plays a crucial role in chemistry, particularly when examining how energy changes affect matter during chemical reactions.

The core principles of thermodynamics are encapsulated in its four laws, which include concepts such as energy conservation, the direction of energy transfer, and the conditions for equilibrium. The exercise illustrates the application of thermodynamics principles by calculating the change in entropy for the universe (system plus surroundings) to understand the direction of a spontaneous reaction.

Practical Importance

In real-world chemistry, understanding these concepts allows scientists to predict the feasibility and conditions required for chemical reactions to occur, design processes that harness energy changes efficiently, and develop products in a controlled and predictable manner. By mastering thermodynamics, students are equipped to navigate complex reactions and contribute to innovations in energy management and material synthesis.