# Deriving the entropy as a function of concentration

In a physical chemistry class, the professor derived entropy $$S$$ as a function of concentration starting from $$S=k\ln(W)$$. Somehow he made a mistake and ended up with the wrong sign. This remains unsolved until the end of the class.

So I would like to figure out the correct solution before the next class. The final answer is

$$S=-k\ln(\text{conc.}) + S^\circ,$$

where $$S^\circ$$ is the entropy of the substance in standard state. I know that concentration is inversely proportional to the multiplicity should be used somewhere, but I cannot complete the whole derivation.

So far I have got that

$$S = -k\ln(\text{conc.}) + k\ln(N),$$

where $$N$$ is the number of particles. But why is the $$k\ln(N)$$ part $$S^\circ$$?