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you can use the Nernst equation to calculate cell potentials here we need to calculate the cell potential for a zinc copper cell where the concentration of zinc two plus ions and the concentration of copper two plus ions in solution is one molar and we're at 25 degrees C so we're talking about standard conditions here just to remind you of the of the reduction half-reaction and the oxidation half-reaction copper two-plus ions are reduced they gain electrons to form solid copper and solid zinc is oxidized so zinc loses two electrons to form zinc two-plus ions those two electrons right the electrons lost by zinc are the same electrons gained by copper two-plus so they cancel out when you write your overall reaction so down here we have our overall redox reaction and the standard cell potential is equal to positive one point one zero volts so you just add the standard reduction potential and the standard oxidation potential so all this we've covered in earlier videos and now we're going to see how to calculate the cell potential using the Nernst equation so let's go and write down the Nernst equation which is the cell potential is equal to the standard cell potential e zero minus point zero five nine two volts over n times the log of Q so this is the form of the Nernst equation this is one of the forms that we can use when our temperature is 25 degrees C so let's think about what these things mean in the Nernst equation so the standard cell potential e zero right we've already found that that's 1.10 volts so this one point one zero would get plugged in to here in the Nernst equation n is the number of moles that are transferred number of moles of electrons that are transferred in our redox reaction and that's to write two moles of electrons are transferred so n is equal to two Q is the reaction quotient so Q is the reaction quotient and Q has the same form as K but you're using non equilibrium concentration so think about writing an equilibrium expression so to to write Q think about an equal expression where you have your concentration of products over the concentration of your reactants and you leave out pure solids so we're going to leave out leave out solid copper and we have concentration of zinc two-plus so concentration of our product over the concentration of our reactants we're going to leave out the solid zinc so we have the concentration of copper two-plus alright we know what those concentrations are they were given to us in the problem the concentration of zinc two plus is one molar concentration of copper two plus is one molar so we have one over one so the reaction quotient for this example is equal to one so let's go ahead and plug in everything alright so we have the cell potential e is equal to the standard cell potential that was 1.10 volts all right - point zero five nine two over N where n is number of moles of electrons that's equal to two times the log of the reaction quotient well log of one right our reaction quotient for this example is equal to one log of one is equal to zero so we have the cell potential is equal to one point one zero right minus zero so the cell potential is equal to one point one zero volts so we know the cell potential is equal to the standard cell potential right which is equal to one point one zero volts positive 1.10 volts so this is this makes sense right because easy ro right the standard cell potential let me go ahead and highlight that up here the standard cell potential e zero is the voltage under standard conditions and that's what we have here we have standard conditions our concentrations our concentrations are one molar alright we're at 25 degrees C we're dealing with we're dealing with pure zinc and pure copper so this makes sense right the Nernst equation should give us that the cell potential is equal to the standard cell potential let's find the cell potential again for our zinc copper cell but this time the concentration of zinc two plus ions is 10 molar and we'll keep the concentration of copper two plus ions name one molar so if we're trying to find the cell potential we can use our Nernst equation all right so the cell potential e is equal to the standard cell potential e zero minus point zero five nine two volts over n times the log of Q where Q is the reaction quotient let's plug in everything we know we know the standard cell potential is positive one point one zero volts so we have one point one zero volts we're trying to find the cell potential e so E is equal to one point one zero minus point zero five nine two over N so n is number of moles of electrons that are transferred so that was two electrons so n is equal to two so we plug that in here times the log of Q and from the previous example remember Q the reaction quotient is the concentration of zinc two-plus right concentration of zinc two-plus over the concentration of copper two plus so concentration of products over reactants are ignoring your pure solids so for this example for this example the concentration of zinc two plus ions in solution is 10 molar all right so that's 10 molar over copper two plus is one molar so 10 over one so Q is equal to 10 for this example so now let's find the cell potential so the cell potential is e so E is equal to one point one zero minus you can actually do all this in your head so point zero five nine two let's say that's let's say that's point zero six zero so this is point zero six zero divided by two which is point zero three zero so we have point zero three zero log of 10 is just equal to one so this is point zero three zero times one so one point one zero minus point zero three zero is equal to one point zero seven so the cell potential is equal to one point zero seven volts I like to think about this as the instantaneous cell potentials so when your concentrations are 10 molar for zinc two-plus and one molar for copper two plus one point zero seven volts is your instantaneous cell potential what happens to the cell potential as the reaction progresses well let's think about that let's go back up here to our overall reaction alright what happens as we make more and more of our products well the concentration of zinc two plus ions should increase and we're losing or losing our reactants here so the concentration of copper two plus should decrease so what happens to Q right if we're increasing the concentration of zinc two plus and decreasing the concentration of copper two plus Q should increase and what does that do to the cell potential right so in the Nernst equation if we're increasing Q what does that do to e well let's go ahead and let's let's just plug in a number let's just say that Q is equal to 100 so let's say that your Q is equal to 100 let's plug that into the Nernst equation let's see what happens to the cell potential so E is equal to e zero which we'll go ahead and plug in one point one zero there so one point one zero minus point zero five nine two over two times log of 100 so now we're saying that Q is equal to 100 so we have more we have more of our products as the reaction progresses so what is the cell potential e is equal to one point one zero log of 100 is equal to two so log of 100 is equal to two that cancels out this two here so we have one minus point zero five nine to one minus point zero five nine two I'll just say that's equal to point zero six zero and just just to make things easier so one point one zero minus point zero six zero is equal to one point zero four so the cell potential is equal to one point zero four volts so notice what happened to the cell potential alright so we increased change colors here we increased Q we went from Q is equal to 10 to Q is equal to 100 what happened to the cell potential the cell potential 1 front went from 1.0 7 volts to 1.0 4 volts so as the reaction progresses right Q increases and this the instantaneous cell potential e decreases so Q increases and E decreases so what happens what happens at equilibrium what is the cell potential at equilibrium so what is the cell potential at equilibrium if you remember if you remember the equation that relates Delta G to the cell potential so we talked about this one Delta G is equal to negative n F e and from thermodynamics right at equilibrium Delta G is equal to zero so if Delta G is equal to zero at equilibrium what is the cell potential at equilibrium e must be equal to zero so the cell potential is equal to zero at equilibrium so let's let's think about that so if the cell potential is equal to zero equilibrium let's write down our Nernst equation so the Nernst equation is e is equal to e zero minus point zero five nine two over n times the log of Q well at equilibrium at equilibrium is equal to zero so we plug that in so we have zero is equal to the standard cell potential e zero minus point zero five nine two over N times the log of Q but at equilibrium remember Q is equal to K so we can plug in K here so now we have the log of K and notice that this is the equation we talked about in earlier video the standard cell potential e zero is equal to point zero five nine two over n times the log of K so just an interesting way to think about the Nernst equation so the Nernst equation is is very useful for calculating cell potentials right you when you have different concentrations

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