when you're dealing with a voltaic cell it's important to relate the potential of the cell to the free energy of the redox reaction and here's the equation that relates free energy to the cell potential so delta g delta g is the change in free energy and we know for a spontaneous reaction delta g is negative so let me go ahead and write that down here so delta g is negative for our spontaneous redox reaction that we have in our voltaic cell and we're going to calculate the value for delta g at the end of this video e over here this it represents our cell potential or our cell voltage and this is easy to measure just hook up a voltmeter and for this cell the cell potential is positive 1.10 volts so very easy to measure the voltage associated with a voltaic cell next the n the n represents the moles of electrons that are transferred in the redox reaction in this example we're talking about two moles of electrons are transferred in our redox reaction and finally let's talk about f which represents faraday's constant and faraday's constant is the magnitude of charge that's carried by one mole of electrons so we can calculate faraday's constant let's go ahead and do that up here so one electron has a charge of 1.6 times 10 to the negative 19 coulombs so coulombs is the unit for charge so let's go ahead and write that 1.6 actually it's 1.602 times 10 to the negative 19 coulombs for every one electron so one electron has that charge if we want to find if you want to find the magnitude of charge carried by one mole of electrons we would need to multiply by avogadro's number so if we multiply by avogadro's number which we know is 6.022 times 10 to the 23rd that's how many electrons there are in one mole of electrons right so that's how many electrons in one mole of electrons if you multiply these out you're going to end up with charge per one mole of electron this is 96 472 the units would be this is coulombs per mole of electrons so coulombs per mole and if you do more careful calculation you'll get 96 485 coulombs per mole and so sometimes you'll see textbooks use this number for different calculations most of the time you can just round this to ninety six thousand five hundred so ninety six thousand five hundred coulombs per mole and that's good enough for almost all the calculations that you will do so that that explains each term of our equation here all right so this cell potential that we talked about 1.10 volts this is actually the standard cell potential which is the voltage measured when the cell operates under standard conditions which is defined as all of your solids are in pure form and that's the case for us here because we're dealing with zinc metal so that's solid in its pure form and copper metal a solid in its pure form also defined as the solutions are at one molar concentration so we have a one molar concentration solution of zinc sulfate which gives us one molar concentration of zinc two plus ions in solution and a one molar concentration of copper sulfate which gives us one molar concentration of copper two plus ions in solution and our temperature is 25 degrees so this is 25 degrees c so if those are your conditions and you hook up a volt meter this is the voltage that you will get so we can actually modify the equation that we've talked about by adding in a superscript here so we could write we could write e0 instead of just e and e zero is our standard cell potential right it just means that everything is under the conditions under standard conditions and then this would be delta g zero so that's delta g zero now the standard change in free energy so let's go ahead and solve for delta g zero right we already know it's going to be negative because this is a spontaneous redox reaction let's go ahead and plug in everything so let's get a little bit more room down here let's plug in our numbers so we're trying to solve for delta g 0 the standard change in free energy so we have a negative sign here i'll talk about what that means a little bit later so next we have n remember what n represented here so n is the moles of electrons that are transferred in our redox reaction which would be two so this would be two moles of electrons put these in parentheses here next we have faraday's constant f and so we've already seen that we can use 96 500 coulombs per mole for faraday's constant so this is 96 500 coulombs per mole next we plug in the value for our standard cell potential so e0 is 1.1 volts for this voltaic cell and when you're thinking about units so a volt is how many joules per coulomb so instead of plugging in volts here we're going to plug in joules over coulombs so our units will work out properly so this is positive 1.10 joules per coulomb all right let's do this math so let's look at our units first and let's see what cancels out here so we our moles cancels out our charge coulombs cancels out to give us joules for our answer let's go ahead and calculate how many joules so let's uh let's let's do the calculations we have 2 times 96 500 and then we're going to multiply that by 1.10 so that would give us this would give us 20 uh 212 300 joules remember this was in joules and let's go ahead and convert that to kilojoules so 212 000 joules would be 212 kilojoules remember we have a negative sign here so don't forget about this negative sign this would be negative 212 kilojoules for our value for delta g zero so the standard change in free energy for this voltaic cell is negative 212 kilojoules and we already know right that when delta g is negative that's a spontaneous reaction so this is a spontaneous redox reaction here notice that delta g0 and e0 have opposite signs right we had a positive sign for our voltage right and we ended up with a negative sign for delta g and that's why we have this negative in our equation here so a spontaneous reaction in a voltaic cell has a positive cell potential right so a positive value for the voltage but a negative change in free energy because that indicates a spontaneous reaction