Imagine an ion which has a charge of 1 going from a concentr

Imagine an ion, which has a charge of +1, going from a concentration c1 on one side of the plasma membrane to a concentration c2 on the opposite side of the membrane: c1 <--> c2. Imagine also that at equilibrium an uneven distribution of the ion across the membrane (due in part to relatively large, net negatively charged and impermeable proteins on one side of the membrane) leads to a resting membrane potential of –107 mV (inside the cell negative relative to outside the cell). Such an equilibrium is called a Donnan Equilibrium. What is the maximum ratio of c2/c1 that would exist? Use 23.1 kcal/V\\cdot mol for Faraday\'s constant and 37 °C for the temperature (which you of course have to convert to the Kelvin scale by adding 273). Report your answer to the nearest ones.

Solution

Ionic balance is C1 <--------> C2

Potential of this concentration cell is given as,

Ecell = -(RT / F) ln([C2]/[C1]) ------------ (1)

Given : Appropriate changes in unit done.

Ecell = -107 mV

= -107 x 10^-3 V.

R = 1.986 x 10^-3 kcal.mole^-1.K^-1.

F = 23.1 kcal.V^-1.mole^-1.

T = 37 ^oC

= 37 + 273

= 310 K

Using these values in eq.(1) we get,

-107 x 10^-3 = -(1.986 x 10^-3 x 310 / 23.1) ln ([C2]/[C1])

107 = (1.986 x 310 / 23.1) ln ([C2]/[C1])

107 = 26.652 ln ([C2]/[C1])

ln ([C2]/[C1]) = 107 / 26.652

ln ([C2]/[C1]) = 4.015

[C2]/[C1] = e^4.015.

[C2]/[C1] = 55.42

The maximum [C2]/[C1] ratio that would exist is 55.42.