# Assumptions for Nernst Equation

While I am familiar with some of the conditions for the Nernst Equation, for example:

1) "The membrane is only permeable to one ion even if there are several other ions in the system"

there is an assumption/condition that I have yet to see mentioned (and I am pretty sure that it is an essential one that must be included). That assumption is as follows:

The two solutions separated by the selectively permeable membrane must initially have the same total charge...i.e. there is no initial potential difference between the 2 sides of the membrane

I believe this must be true because of the following 3 cases:

for all 3 cases, only potassium is permeable, and there is a "Left Side" and a "Right Side" on either side of the selectively permeable membrane.

A) Left Side: 25 mM K+, 125 mM Na+ |&| Right Side: 125 mM K+, 25 mM Na+

B) Left Side: 25 mM K+, 10000000000 mM Na+ |&| Right Side: 125 mM K+, 25 mM Na+

C) Left Side: 25 mM K+, 0.00000000001 mM Na+ |&| Right Side: 125 mM K+, 25 mM Na+

Without using my proposed assumption, in all 3 cases, the Nernst equation for potassium would be the same:

(RT)/(ZF) * ln (25/125)

However, I fail to see how case B & C could have the same Nernst potential for potassium as case A when the electrical forces on the left side of the membrane are completely different! Let's use case B as an example. Clearly, the potassium concentration differences exist between the two sides (25 mM vs 125 mM), BUT there is an enormous electrical repulsive force imposed by the sodium (1000000000 mM Na+) so there is no way that the same amount of potassium will pass over to the left side as it would in Case A, right?