In the context of gases, what does the equation G(p_f) = G(p_i) + nRT ln(p_f/p_i) signify?

The equation ( G(p_f) = G(p_i) + nRT \ln(p_f/p_i) ) describes the change in Gibbs free energy (( G )) of an ideal gas when its pressure changes from an initial pressure (( p_i )) to a final pressure (( p_f )). In this context, ( n ) represents the number of moles of the gas, ( R ) is the ideal gas constant, and ( T ) is the absolute temperature.

This equation is derived from the thermodynamic relationship involving the Gibbs free energy and is particularly relevant for processes occurring isothermally (constant temperature) within an ideal gas. It indicates how the Gibbs energy varies with pressure for an ideal gas, highlighting the logarithmic relationship between the pressures.

When the pressure of an ideal gas increases or decreases, the Gibbs free energy changes accordingly, reflecting the system's willingness to do work or the potential for chemical reactions. Therefore, this equation is fundamentally important in physical chemistry for understanding how thermodynamic potentials like Gibbs free energy depend on pressure changes in gaseous systems.

Other choices, such as the total internal energy change, the work done during gas expansion, or the heat absorbed during a reaction, do