Heat liberated by a given amount of an ideal gas undergoing reversible isothermal process is \(1200 \mathrm{cal}\) at \(300 \mathrm{~K}\). What is the Gibbs free energy change of the gas in this process? (a) zero (b) \(+1200\) cal (c) \(-1200\) cal (d) \(4 \mathrm{cal}\)

A reversible isothermal process occurs when a system undergoes a change in a way that it could be reversed by an infinitesimal modification, while maintaining the temperature constant. In chemistry, this is critical for understanding how reactions and phase changes occur without changes in heat. For instance, an ideal gas expanding or compressing within such constraints wouldn't change its internal energy due to the temperature remaining constant.

In the context of the exercise, the gas liberating 1200 cal of heat energy at a constant temperature (300 K) indicates that any work done by the gas is exactly balanced by the heat flow into the system, maintaining its internal energy unchanged. This illustrates a fundamental aspect of reversible isothermal processes: they are characterized by equilibrium states where the system can move between states without net energy change, making them ideal for theoretical studies in thermodynamics.

Thermodynamics plays a pivotal role in chemistry, providing insight into how energy is transferred within chemical systems. It studies the principles governing the interrelation between heat, work, temperature, and energy. The laws of thermodynamics dictate the spontaneity of processes, energy conservation, and limitations on energy conversions.

The Gibbs free energy change (ΔG) is a thermodynamic function that provides valuable information about the spontaneity of chemical reactions at a constant pressure and temperature. It is a measure that combines enthalpy (ΔH), temperature (T), and entropy (ΔS) into a significant and interpretable quantity. In our exercise, the Gibbs free energy helps us understand why the release of 1200 cal by the gas doesn't necessarily mean a change in the system's spontaneity or free energy state, due to the reversible and isothermal nature of the process.

Entropy (ΔS) and enthalpy (ΔH) are fundamental concepts in thermodynamics that relate to the disorder or randomness of a system and its total heat content, respectively. Entropy is a measure of the number of specific ways a thermodynamic system can be arranged, commonly understood as a measure of disorder: the higher the entropy, the greater the disorder and energy dispersion. Enthalpy, on the other hand, reflects the heat absorbed or released at constant pressure, analogous to the internal energy of the system plus the product of pressure and volume.

In our exercise, the enthalpy change is directly equal to the heat liberated since the process is at constant temperature. The entropy change quantifies how energy is dispersed in the process. After calculating both, we can ascertain that the Gibbs free energy change is zero, demonstrating an essential principle: for a reversible isothermal process, the free energy of a system remains constant, highlighting a perfect balance between enthalpy and entropy changes.