Change in the internal energy with/without different kinds of particles in the mix

petko10

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 .