now in this example we have two compartments both have sodium chloride as it's drawn here initially sodium chloride is an is in equal amounts on either side so equal number of sodium and chloride on this side equal number of sodium and chloride on this side so both of these sides are right now electrically neutral but we can see that there is a concentration gradient from one side versus the other so I've stipulated it here that the membrane is permeable to both sodium and chloride so if that's the case we would expect to see both sodium and chloride move and they would then reach the fusional equilibrium and in this case we are left with again same numbers of sodium and chloride on either side therefore this is an electrically neutral system now imagine that if we take a similar setup but in this case we're going to have sodium and chloride just on the left side and we're also going to stipulate that the membrane is only permeable to sodium and an impermeable to chloride so using some terms we learned previously the reflection coefficient for sodium would be zero the reflection coefficient for chloride would be one so in the notice I've drawn in here we can already determine which direction the chemical gradient is the chemical driving force for these ions for sodium it's going to be moving from the left to the left and the same thing goes for chloride so even though it can't actually move because we stipulated that the membrane was impermeable to Chloride there still is a chemical gradient which would like for it to move so what's going to happen in this situation where the membrane is permeable to sodium but not to Chloride what we'll see happening is is sodium will shift across the membrane but chloride will not so realize what's happening here just as we saw in the previous slide as the positive charges move it across that's taking positive charges to the right side and leaving a relative negativity behind so in this situation we now have a separation of charge so it's developing now is we're going to develop a diffusion potential so now that this is more positive on the right side on side two compared to side one this positive charge over here is going to tend to be repelling further movement of sodium so early in the process we see that the concentration gradient or the chemical gradient for sodium those are interchangeable words is directed from the left to the right the electrical gradient that's developing is from the right to the left and initially we have an electrochemical gradient which is going to continue to tend to have sodium move from side one to side two but as sodium continues to move it's going to create a larger diffusion potential and notice what eventually happens is more and more sodium moves we finally reach a point that this electrical force this electrical gradient this diffusion potential that we've created is going to reach a point that it finally equally opposes the chemical gradient so at equilibrium notice that we still have a chemical gradient versus sodium so in this case at diffusional equilibrium when we're dealing with ions the ions are not equally concentrated on either side we have an electrical gradient that's developed this diffusion potential and notice that it stops at the point that it equals the magnitude of the chemical gradient for sodium so if we net those two out the electrochemical gradient at this point would be zero so this is what we term the equilibrium potential so in this case the magnitude of this red arrow the magnitude of the electrical potential the magnitude of the electrical gradient the magnitude of this diffusion potential notice I've used all those words interchangeably when the magnitude of that Force exactly opposes the chemical gradient for sodium then we refer to this as sodium's equilibrium potential now we can calculate a number to give us that equilibrium potential and we do so using the nernst equation and in some physiology textbooks they will refer to the equilibrium potential as the nurse potential so as I've stated previously we will not be using formulas to calculate actual numbers we're using them to understand Concepts so this is saying that the equilibrium potential for an ion is equal to Z which is the valence of that ion times 60 times the 60 millivolts time the log of the concentration of the ion outside of the cell versus the inside of the cell so really the take-home message for us here is that we can use this large equation to use the concentration gradients to determine the equilibrium potential for an ion so I've drawn here on the bottom the relative concentrations of sodium and potassium both intracellular and extracellular again these are not numbers that you have to memorize but you should be able to have a pretty good idea of the relative ranges and knowing that sodium is much more concentrated outside the cell potassium is much more concentrated inside the cell if we plug those numbers that I have here into the formula above these would be the relative numbers that we're going to end up with the equilibrium potential for sodium we're going to say is positive 60 millivolts the equilibrium potential for potassium is approximately negative 90 millivolts now those numbers aren't precise but those will be the numbers that we'll be using for their simplicity's sake this semester so the equilibrium potential is in reference to only one ion the equilibrium potential represents the electrical force or the diffusion potential that exactly counterbalances the chemical gradient or chemical Force for that specific ion okay so here again the equilibrium potential which is an electrical force the magnitude of this equilibrium potential the magnitude of this electrical force is going to be equal and opposite the magnitude of the chemical gradient of that particular ion