Problem One

The experimental system shown in the figure $($bottom of page$)$ has two aqueous

solutions in contact through a membrane, which is permeable to both $N{a}^{+}$and $K^{+}.$

The solution to the left of the membrane contains $10mMKCl$ and $1$mMNaCl

$($Solution $1).$ The solution to the right of the membrane contains $1mMKCl$ and

$10$mMNaCl $($Solution $2).$ In addition, electronics are attached to the experimental

system, so that the observer can apply a potential difference across the membrane.

a$.$ Box $2\mathrm{.}5$ shows that the flux due to passive diffusion of molecules across a

membrane can be described by:

$J_x=K(C_1-C_2)$

where $J_x$ is the flux through the membrane $(mo\frac{l}{s}-c{m}^2),K$ is a permeability

constant $,$ equal to the diffusion coefficient divided by the membrane

thickness, $\frac{D}{}x),$ and $C_1$ and $C_2$ are concentrations in the fluids on the two

sides $(mo\frac{l}{L}.$ If the cross$-$sectional area of the membrane is $1c{m}^2,$ the volume

of each solution is $1mL,$ and $K$ is equal to ${10}^{-5}c\frac{m}{s},$ show that will it take more

than $)$ for the concentration of $K^{+}$to drop by $1\%.$

b$.$ What is the Nernst potential for $K^{+}$and $N{a}^{+}$across the membrane?

c$.$ What is the net direction of $K^{+}$and $N{a}^{+}$flux under the following conditions: no

applied voltage; $-58mV$ applied to Solution $1($relative to Solution $2)$; $-28mV$

applied; $58mV$ applied; $68mV$ applied?

d$.$ In this experimental system, if you wanted to confirm that your predictions in

part c were true, is the time period over which you measure the fluxes

important? Describe why or why not.