For a reaction taking place at constant \(p\) and \(\mathrm{T}\), why can we say that the \(\Delta \mathrm{G}^{0}\) remains constant, but we cannot say the same for \(\Delta G\) ?

Gibbs free energy change (\(\Delta G\)) is a thermodynamic property, which is used to determine the spontaneity of a chemical reaction at a constant temperature and pressure. The equation for Gibbs free energy change is: \(\Delta G = \Delta H - \mathrm{T} \Delta S\) Where, \(\Delta G\) = Gibbs free energy change \(\Delta H\) = Enthalpy change of the reaction \(\mathrm{T}\) = Absolute temperature (in Kelvin) \(\Delta S\) = Entropy change of the reaction It is essential to note that \(\Delta G\) depends on the changes in enthalpy and entropy of the reaction, as well as the temperature.

Standard Gibbs free energy change (\(\Delta \mathrm{G}^{0}\)) is the change in Gibbs free energy at standard conditions, namely 1 bar pressure and a specific temperature (\(\mathrm{T}\)). For the calculation, all the components in the reaction are considered to be in their standard states. The relation between \(\Delta G\) and \(\Delta \mathrm{G}^{0}\) can be expressed by the following equation: \(\Delta G = \Delta \mathrm{G}^{0} + RT \ln Q\) Where, \(\Delta G\) = Gibbs free energy change \(\Delta \mathrm{G}^{0}\) = Standard Gibbs free energy change \(R\) = Universal gas constant \(\mathrm{T}\) = Absolute temperature (in Kelvin) \(Q\) = Reaction quotient

The standard Gibbs free energy change is calculated at standard conditions of pressure and temperature, where all reactants and products are in their standard states. Thus, at a constant pressure (\(p\)) and temperature (\(\mathrm{T}\)), \(\Delta \mathrm{G}^{0}\) remains constant because it only depends on the properties of the reactants and products in their standard states.

On the contrary, the actual Gibbs free energy change (\(\Delta G\)) depends on the concentration of reactants and products, which varies throughout the course of the reaction. As the reaction proceeds, the concentration of reactants decreases, while the concentration of products increases. From the equation \( \Delta G = \Delta \mathrm{G}^{0} + RT \ln Q \), we can see that the value of \(\Delta G\) will change, given that the reaction quotient (\(Q\)) is affected by the changing concentrations of the reactants and products. Therefore, even at a constant pressure (\(p\)) and temperature (\(\mathrm{T}\)), \(\Delta G\) does not remain constant. In conclusion, during a reaction at constant pressure and temperature, standard Gibbs free energy change (\(\Delta \mathrm{G}^{0}\)) remains constant because it depends only on the standard state properties of reactants and products. However, the actual Gibbs free energy change (\(\Delta G\)) does not remain constant, as it is influenced by the changing concentrations of reactants and products in the system.