we've already seen the equation on the left which relates the standard change in free energy delta-g zero to the standard cell potential e zero the equation on the right is from thermodynamics and it relates the standard change in free energy Delta G zero to the equilibrium constant K so we can set these equal to each other to relate the standard cell potential to the equilibrium constant since both of these are equal to Delta G zero we can say that this is equal to this so now we have negative and fe0 is equal to negative RT natural log of the equilibrium constant K and let's solve for e zero let's solve for the standard cell potential so to do that we need to divide both sides by negative NF so we get e zero is equal to positive RT over NF natural log of our equilibrium constant next we're gonna solve for we're gonna solve for what this is equal to so if we're at 25 degrees C all right so our temperature under standard conditions for our cells that we've been talking about T is in is in Kelvin so we need to convert degrees Celsius into Kelvin and to do that you need to add 273 point one five so that gives us 298 point 1 5 Kelvin so that's what this T is it's our absolute temperature in Kelvin R is the gas constant so R is equal to H point 3 1 4 joules over mole times Kelvin here so we're going to multiply that by our absolute temperature and so our absolute temperature was 298.15 so this is 298.15 kelvin this is all over Faraday's constant right so remember F is Faraday's constant so this F right here Faraday's constant which is ninety six thousand five hundreds coulombs per mole so the charge of one mole of electrons so this gives us RT over F and so this gives us point zero two five seven what will the units be well Kelvin would cancel out here and let's see what else cancels out the moles would cancel out and that gives us joules over coulombs which of course is equal to volts all right so we can rewrite our equation so the one we had up here so we're gonna plug in for RT over F now so now we would have we would have the standard cell potential e zero is equal to well this would be point zero two five seven and that was volts over n remember n is the number of moles that are transferred in your redox reaction and this is times the natural log of K our equilibrium constant here so this is one form of the equation that relates the standard cell potential right the standard cell potential e zero to the equilibrium constant K we can we can write this in a different way all right so what we could do is we could take that point zero two five seven point zero two five seven and we could multiply that by the natural log of ten we get we get point zero five nine two and the reason why we could do this is to write our equation in Log form right up here we have natural log so up here we have a natural log but now we can write it in Log form so now we have the standard cell potential e zero is equal to well now we'd have point zero five nine two volts so we have point zero five nine two volts once again over n the number of moles of electrons transferred in our redox reaction and this time it would be times the log the log of K so not the natural log the log okay so we've taken care of that in our calculation so this is just another form another form of the same equation right relating the standard cell potential e zero to the equilibrium at constant K