# How do the assumptions of the Nernst equation impact its accuracy?

I was just wondering what impact the assumption that the equilibrium membrane potential for an ion is dependent on just the ion itself (if it is the only thing that is permeable). For instance, if I had a membrane that was only permeable to K+ but I had a lot of another cation on the same side as the K+ (which was impermeable), then according to the Nernst equation, I would still get the same equilibrium potential, Ek. However, I am confused as to how the fact that there might be a lot of positive charge on the same side as these K+ has no impact on the distribution of K+;is there a reason as to why it is not accounted for/ has no impact on the membrane potential or the electrochemical gradient of the potassium ions? (I realise that in reality there is no such large positive charge on the same side as K+, I am just asking this from a theoretical perspective).

• It is rather issue of having a more complex system than the Nernst equation describes. Additionally, a lot of other ions would affect $a_{\ce{K+}}$ even at the same $\ce{[K+]}$ Oct 20, 2021 at 9:33
• @Poutnik So the presence of charged but impermeable ions does have an effect on the equilibriums potential of potassium? How would I quantify this/ what sort of model would I use in order to take these factors into account and is there a name for this effect? Thank you for your help :) Oct 20, 2021 at 9:41
• N.E. is written for ion activities which depend on ionic power which depends on summary ion concentrations and charges. // But there can be other influences due complexity of system, as cross-ion sensitivities. $$E=f(a_{\ce{K+}})=f([\ce{K+}],[ion2],[ion3],...,[ionN])$$ Oct 20, 2021 at 10:34
• @Poutnik What is the name of the function that would take account of these? And are the ions that impact the equilibrium potential of K+ a major deviation from the results predicted by nernst/Goldman equations alone, and what physical reasoning is there behind these effects. Sorry for all these questions, but if you have any sort of books or text recommendations that I could read to find out it would be much appreciated :) Oct 20, 2021 at 14:59
• See membrane potential, Nernst equation, activity, activity coefficitent, Debye–Hückel equation. General site resources. Great education source is chem.libretexts.org. Oct 20, 2021 at 15:05