The \(\Delta G^{\circ}\) values for the hydrolysis of creatine phosphate (creatine-P) and glucose-6-phosphate \((\mathrm{G}-6-\mathrm{P})\) are (i) Creatine-P \(+\mathrm{H}_{2} \mathrm{O} \rightarrow\) Creatine \(+\mathrm{P}\) \(\Delta G^{\mathrm{o}}=-29.2 \mathrm{~kJ}\) (ii) \(\mathrm{G}-6-\mathrm{P}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{G}+\mathrm{P} ; \Delta G^{\mathrm{o}}=-12.4 \mathrm{~kJ}\) \(\Delta G^{0}\) for the reaction: \(\mathrm{G}-6-\mathrm{P}+\) Creatine \(\rightarrow \mathrm{G}+\) Creatine- \(\mathrm{P}\), is (a) \(+16.8 \mathrm{~kJ}\) (b) \(-16.8 \mathrm{~kJ}\) (c) \(-41.6 \mathrm{~kJ}\) (d) \(+41.6 \mathrm{~kJ}\)

Understanding the interplay between enthalpy and entropy is fundamental to grasping the concept of Gibbs Free Energy in physical chemistry. Enthalpy (\(H\)) is a measure of heat content in a system and reflects the bond energies of the compounds involved in a reaction. In essence, it represents the total potential energy of a system, which can be released or absorbed during a reaction.

On the flip side, entropy (\(S\)) is a measure of disorder or randomness in a system. The second law of thermodynamics states that entropy in an isolated system always increases over time. In chemical reactions, creating more disorder (higher entropy) is a naturally favoured process.

These two properties relate to Gibbs Free Energy (\(G\)) through the equation \[\Delta G = \Delta H - T\Delta S\] where \(\Delta G\) is the change in Gibbs Free Energy, \(\Delta H\) is the change in enthalpy, \(T\) is the temperature in Kelvin, and \(\Delta S\) is the change in entropy. For a reaction to be spontaneous at a certain temperature, \(\Delta G\) must be negative. In the discussed exercise, the breaking and forming of chemical bonds, represented by enthalpy, and changes in the systems' disorder, as indicated by entropy, are both essential to tackling problems involving Gibbs Free Energy.

The concept of chemical equilibrium arises when a chemical reaction reaches a state where the concentrations of reactants and products remain constant over time because the forward and reverse reactions occur at equal rates. At this point, the Gibbs Free Energy change of the process (\(\Delta G\)) is zero, indicating no net change in the system's composition.

As a reaction approaches equilibrium, the changes in Gibbs Free Energy guide the reaction's direction. A negative \(\Delta G\) indicates that the reaction will proceed in the forward direction, converting reactants into products until equilibrium is reached. Conversely, a positive \(\Delta G\) suggests the reaction will proceed in the reverse direction. In the exercise provided, understanding how to use \(\Delta G\) values to predict the direction of a reaction is crucial in determining the possibility of chemical processes reaching equilibrium.

The study of bioenergetics and metabolism explores how living organisms transform energy to sustain life. Metabolism includes all chemical reactions that occur within an organism to maintain life, categorized into two types: catabolism (breaking down molecules to obtain energy) and anabolism (using energy to construct components of cells, such as proteins and nucleic acids).

The Gibbs Free Energy equation is pivotal in bioenergetics as it predicts whether a metabolic reaction can occur spontaneously. If \(\Delta G\) is negative, the metabolic reaction is considered exergonic, releasing energy and typically associated with catabolic pathways. Conversely, an endergonic reaction has a positive \(\Delta G\), requiring energy input and is commonly linked to anabolic pathways.

In the provided exercise, the hydrolysis reactions of creatine phosphate and glucose-6-phosphate represent typical catabolic reactions that release energy, which could be used to power other cellular processes, including the synthesis of molecules like creatine phosphate which, in the example, is an anabolic reaction indicated by the positive \(\Delta G\) value.