What is a chemical potential good for? I read that the definition of the chemical potential is, that it is the partial derivative of the Free energy with respect to the number of particles, $$\mu=\frac{\partial F}{\partial N}.$$ Unfortunately, I don't get this definition, wherefore I wanted to choose an example: Let me think of a system for example a water in oil emulsion. How would one evaluate the chemical potential of this mixture? There the chemical potential would definitely depend on the question: Where do you want to insert which sort of particles?
 A: Following Wikipedia, if you have a chemical system containing $n$ constituent species, adding $dN_i$ particles of the $i$-th species, at $T$ and $p$ constant, make a change of the Gibbs free energy :
$$dG = \sum_{i=1}^n \mu_i ~dN_i$$ 
(If you prefer $T$ and $V$ constant, you will use the Helmholtz free energy $F$ instead of $G$)
So, fundamentally, the chemical potential is a (potential) energy by specy particle.
At chemical equilibrium, the free energies $F$ or $G$ have to be minimum, which means that, at equilibrium : 
$$\sum_{i=1}^n \mu_i ~dN_i = 0$$
So, chemical potential is important in all the equilibrium chemistry
Another interesting use, if you consider only one specy, is the grand-canonical situation (http://en.wikipedia.org/wiki/Grand_canonical_ensemble) where a system is in chemical (and thermal) equilibrium with a reservoir. In this case, the temperature and the chemical potential are constant, and, for a microstate, the probability to have a energy E, and a number N of particles, is given by : 
$$p(E,N) \sim e^{-\beta(E - \mu N)}$$
