A membrane$-$bound compartment contains a macromolecule $x$ with a net charge of $-3.$ The

membrane is not permeable to $x_{,},$ but is permeable to $N{a}^{+},K^{+}$and $C{l}^{-}.$ The known concentrations

of ionic species are: $[x^{3-}{]}_{in}=50mM,[N{a}^{+}{]}_{in}=20mM,[N{a}^{+}{]}_{\text{o}\text{u}\text{t}}=80mM,$ and $[C{l}^{-}{]}_{\text{o}\text{u}\text{t}}=100mM.$

Calculate $[K^{+}{]}_{\text{i}\text{n}\text{t}}[K^{+}{]}_{\text{o}\text{u}\text{t}}$ and $[C{l}^{-}{]}_{in}$ and determine the potential across the membrane. Assume that

$N{a}^{+},K^{+},C{l}^{-}$and $x^{3-}$ are the only charged species present. $(15$pt$)$