Understanding Chem. Pot.: ΔU, μ, R, N/N(all)

[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 .

 

[BigJDubs]

1. The Universal Gas Constant (R) is used because the equation for the chemical potential of a particle is derived from the equation for the molar chemical potential which uses the Universal Gas Constant. 2. The difference in potential that a particle adds to the system in relation to the concentration of that type of particle in the system is due to the fact that the potential of a particle in a mixture is lower than the potential of a particle in a pure substance. This is due to the fact that the volume of the mixture has to be taken into account when calculating the potential.