If a sulution of an ivnic macrumulecule is equilibrated with a salt solution from which it is separated by a membrane through which the salt ions but not the macromolecule can pass, a membrane potential is generated across the membrane. This so-called Donnan equilibrium arises because the impermeability of the membrane to some ions but not others prevents the equalization of the ionic concentrations on the two sides of the membrane. To demonstrate this effect, assume that the $\mathrm{Cl}^{-}$ salt of a monocationic protein, $P^{+},$ is dissolved in water to the extent that $\left[\mathrm{Cl}^{-}\right]=0.1 M$ and is separated by a membrane impermeable to the protein but not $\mathrm{NaCl}$ from an equal volume of $0.1 \mathrm{M} \mathrm{NaCl}$ solution. Assuming no volume change in either compartment, what are the concentrations of the various ionic species on either side of the membrane after the system has equilibrated? What is the membrane potential across the membrane? (Hint: Mass is conserved and the solution on each side of the membrane must be electrically neutral. At
\[
\text { equilibrium, } \Delta G_{\mathrm{Na}^{*}}+\Delta G_{\mathrm{C}^{\prime}}=0
\]