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(adsbygoogle = window.adsbygoogle || []).push({});

[tex]c(E)=c_{0}\exp(\frac{E}{nRT})[/tex]

where E=mgh (potential energy) and g=-9.8ms^(-2)

[tex]c_{0}[/tex]=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:

[tex]c_{out}=c_{in}\exp(\frac{E}{nRT})[/tex] (*)

where [tex]c_{out}[/tex] is the outer cell concentration of ions and [tex]c_{in}[/tex] is the inner cell concentrations

since [tex]E=Vq, F=N_{A}q and N=nN_{A}[/tex] where F is faradays constant

so that [tex]q=\frac{Fn}{N} [/tex]

now (*) becomes

[tex]\frac{c_{out}}{c_{in}}=\exp(\frac{-VF}{NRT})[/tex] 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

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# Electric effects

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