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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 in 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, at equilibrium, will have passed over to the left side as it would in Case A, right?

Could someone please clarify?

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  • $\begingroup$ This is an interesting question that is rarely discussed in chemistry. Acids (such as sulfuric acid, nitric acid, phosphoric acid etc) typically come as H+ cations and specified anion (SO4-2 NO3-1 etc) and thus do carry almost no charge when mixed in solution, this is true for salts as well (NaCl, KCl, etc). When a charge does build up in a solution such as in electrolysis the reaction is reversed or stopped. Perhaps study capacitor electrolytes but static shock from liquids is an oddity $\endgroup$
    – ChemEng
    Aug 4, 2021 at 12:17
  • $\begingroup$ Take for example adding sodium to water. The sodium becomes Na+ and the H+'s have to fuck off out of solution to maintain electroneutrality. In fact the reactivity of a salt being oxidizing and/or reducing depends on the electronegativities of the anion and cation. Strongly electropositive and electronegative ions will not react unless the replacement is even more electropositive or electronegative (dependent on concentration and temperature). Once again maintaining electroneutrality in solution $\endgroup$
    – ChemEng
    Aug 5, 2021 at 10:00

1 Answer 1

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I would say that the required assumption is that neither half-cell has a net charge (i.e. both are electrically neutral). This assumption is kind of implicit:

  1. the Nernst equation applies to electrochemical cells,
  2. electrochemical cells are generally viewed as containing stable solutions which would persist indefinitely if the cell were not connected to a circuit, and
  3. "stable solutions" must be neutral because solutions with significant charge imbalances would be torn apart by electrostatic forces.

Basically, we could argue that the missing constraint is not so much an assumption as a proper definition of the system that the equation applies to.

In your example, you've provided the concentrations of the cations, but without further information one would usually assume that there are unspecified balancing anions.

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