# Question about chemical potential

1. Dec 14, 2012

### Einj

It is probably a silly question, but here it is. Suppose we have a gas composed by two different kinds of particles. There will be two different kinds of chemical potential? One for each specie?

2. Dec 14, 2012

### Jano L.

Chemical potential is not some substance that can "be there in the container". It is rather an abstract mathematical quantity that gives the change of energy of the container when one particle is added, while the entropy, volume and numbers of other particles are kept at the same value.

As the change of energy depends on the kind of particle one is adding, there is different chemical potential to each different kind of particle.

3. Dec 14, 2012

### Andy Resnick

Yes- a good example is an electrolytic solution, such as found within biological systems. The cytosol of your cells has high potassium, low sodium, and *very* low calcium concentrations, while the outside (extracelluar space) has high sodium, low potassium and low calcium concentrations. Thus, there are different driving forces on the ions corresponding to the different concentration gradients across the cell membrane. For sodium and calcium, the electrochemical potential difference is always strongly negative- sodium and calcium ions experience a strong driving force into the cell. Potassium's electrochemical difference is close to zero or slightly positive, so potassium ions experience a weak driving force out of the cells.

The Nernst equation shows that in equilibrium, the chemical potential difference across a membrane is equivalent to a voltage. In my lab, we measure this voltage as an electrophysiological readout of cellular function.

4. Dec 14, 2012

### Einj

Perfect! Thank you very much!

5. Dec 15, 2012

### DrDu

Just wanted to add that in case of ideal gasses the chemical potential of each species is $\mu_i=\mu_0+RT \ln p_i/p_0$, i.e. the chemical potential is proportional to the logarithm of partial pressure of each species.