# Electric effects

1. Sep 8, 2004

suppose that an ion (or electron) can equilibrate between 2 regions at different values of electrical potential V, i have to find the concentration ratio using the boltzmann distribution which i have found to be
$$c(E)=c_{0}\exp(\frac{E}{nRT})$$
where E=mgh (potential energy) and g=-9.8ms^(-2)
$$c_{0}$$=concentration at sea level
n=number of moles
R=gas constant
T=temperature
q= charge of electron

here is what i tried (after some cheating looking at the Nernst equation)
i used my expression for c(E) as follows:
$$c_{out}=c_{in}\exp(\frac{E}{nRT})$$ (*)
where $$c_{out}$$ is the outer cell concentration of ions and $$c_{in}$$ is the inner cell concentrations

since $$E=Vq, F=N_{A}q and N=nN_{A}$$ where F is faradays constant

so that $$q=\frac{Fn}{N}$$
now (*) becomes
$$\frac{c_{out}}{c_{in}}=\exp(\frac{-VF}{NRT})$$ where N is the number of molecules.

then i am asked what is the biggest concentration ratio one would imagine equilibrating between the inside and outside of a nerve cell given that a cell membrane is only about 5 nano metres thick, and from this estimate the supply voltage of a persons nervous system

any help would be greatly appreciated, thnx