Hello everyone , I'm a medical student from Bulgaria and I'm having problems understanding the following : In a thermodynamical system the change in internal energy is: ΔU=T.ΔS - p.ΔV + Ʃ μ.ΔN μ is the chemical potential that one particle of a given substance would add when being added to the system (with const. S and V) . μ = ΔU/ΔN ; Our textbook says that : μ=μ(0) + R.T.ln( N/N(all) ) where μ(0) is standard chemical potential (the chem. potential in a system with only that kind of substance) and N/N(all) - the relative concentration of the substance. Now what I do not understand is : 1. Why use the universal gas constant (R) (and not Bolzmans constant) when chemical potential is about a single particle . 2. Why is there a difference in the potential that a particle adds to the system in relation to the concentration of that type of particle in the system ?? I know that the matter is pretty narrow , so if no one has any idea , please direct me to some source , because I couldn't google the answers to the questions so far. Edit: So I read some more online and the textbook was wrong . I figured they started talking about a chemical potential of a molecule , and at some point switched without clarification to molar chemical potential . And the potential added is relative to the volume therefore lower in mixtures than in pure substances .