Which of the following conditions regarding a chemical process ensures its spontaneity at all temperature? (a) \(\Delta H>0, \Delta G<0\) (b) \(\Delta H<0, \Delta S>0\) (c) \(\Delta H<0, \Delta S<0\) (d) \(\Delta H>0, \Delta S<0\)

Gibbs free energy, represented by the symbol \( G \), is a measure of the maximum reversible work that may be performed by a thermodynamic system at a constant temperature and pressure. It is a pivotal concept in determining the spontaneity of chemical reactions. The equation that defines Gibbs free energy is \( \Delta G = \Delta H - T\Delta S \), where \( \Delta G \) is the change in Gibbs free energy, \( \Delta H \) is the change in enthalpy, \( T \) is the absolute temperature, and \( \Delta S \) is the change in entropy.

A negative value of \( \Delta G \) indicates that a process is spontaneous, which means it can occur without the input of external energy. Conversely, a positive \( \Delta G \) suggests that the process is non-spontaneous and requires energy to proceed. Importantly, a value of zero indicates a system in equilibrium, where the forward and reverse reactions occur at equal rates.

Enthalpy change, denoted as \( \Delta H \), is the amount of heat absorbed or released by a system during a process at constant pressure. It is an extensive property and plays a crucial role in thermodynamics and chemistry, particularly in the study of heat transfer during chemical reactions.

When \( \Delta H \) is negative, the process is exothermic, meaning that heat is released into the surroundings; this is often associated with the formation of chemical bonds. On the other hand, a positive \( \Delta H \) indicates an endothermic process, in which the system absorbs heat and often involves breaking chemical bonds. The sign of \( \Delta H \) can also influence Gibbs free energy and the spontaneity of the reaction.

Entropy, symbolized as \( S \), is a measure of the disorder or randomness in a system, and \( \Delta S \) signifies the change in entropy. In a chemical reaction, it reflects the degree to which energy is distributed among the possible motions and configurations of molecules.

An increase in entropy (\( \Delta S > 0 \) ) suggests more disorder; for instance, when a solid melts into a liquid. Conversely, a decrease in entropy (\( \Delta S < 0 \) ) represents a transition to a more ordered state, such as a gas condensing into a liquid. Entropy is also closely tied to the feasibility of a chemical process. Spontaneity at all temperatures requires both a negative change in enthalpy and a positive change in entropy.

The temperature of a system, commonly measured in Kelvin (\( K \)), fundamentally influences the rate and spontaneity of chemical reactions. Temperature serves as a critical factor in the Gibbs free energy equation, acting as a multiplier to the entropy change (\( T\Delta S \) ).

At higher temperatures, entropy plays a more significant role in determining \( \Delta G \), potentially shifting a non-spontaneous reaction (positive \( \Delta G \)) to a spontaneous one (negative \( \Delta G \)) if \( \Delta S \) is positive. Conversely, at low temperatures, the value of the enthalpy change (\( \Delta H \)) is more dominant. Understanding the temperature dependence is key to controlling reaction conditions in industrial and laboratory settings to ensure the desired outcome.