Chemical potential is closely related to potential energy as a concept. However, it differs from physical potential energ in that it concerns the potential for one substrance to be converted into another. In physics we can speak of the potential energy of water at the top of a waterfall. The water at the top has a higher potential energy than the water at the bottom. Thus, the water will flow down the cliff spontanesouly until it reaches the bottom. In chemistry we can speak of the chemical potential of two (or more) substances that have the potential to reach chemical equilibrium. Just as water flows down a waterfall to decrease its potential the chemical substances change their composition so as to decrease their poential. One difference in the chemical system is that the two substances (or more) substances involved in a chemical reactoin have different potentials. Typically one decrease and the other increases until they become equal. In chemistry a difference in chemical potential means that the system is not at equilibrium and once all of the chemical potentials of the species in a reaction are equal the system reaches equilibrium.
The standard state of the free energy is the same as that of the enthalpy. It is not a new concept, but the free energy applications give us a motivation for the choice of the standard state. We find that the standard state of 1 bar of pressure or 1 molar of concentration is useful since this prmits us to define the quantities in the reaction quotient (and therefore also the equilibrium constant) in terms of a ratio. Every substance in the reaction quotient expression is a ratio of the species and its standard state of 1 bar of pressure or 1 molar of conccentration. Thus, each quantity is unitless. This resolves a potential problem if we examine an equilibrium constant (or reqction quotient). Without these ratios that make the substances unitless.
