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when you're dealing with a voltaic cell it's important to relate to potential 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 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 I overhear 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 able to excel next the N the end 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 let's go ahead write that 1.6 actually is one point six zero two 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 a Boccaccio's number so if we multiplied by Avogadro number which we know is six point zero two two times ten to the 23rd that's how many electrons there are in one mole of electrons all right so some of the electrons in one mole of electrons if you multiply these out you're going to end up with charge per one mole of electrons let's get out the calculator and it's fine Faraday's constant so we have one point six zero two times ten to the negative 19 and we're going to multiply that by Avogadro's number six point zero two two times ten to the 23rd and we get 96 thousand four hundred and seventy-two so this is 96 thousand four hundred and seventy-two the units would be this is coulombs per mole of electrons so coulombs per mole and if you do a more careful calculation you'll get 96 thousand four hundred and eighty-five 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 96 thousand five hundred so 96,500 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 one point one zero 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 a solid in its pure form and copper metal a solid in its pure form also defined as the solutions are at one molar concentrations we have a one molar concentration solution of zinc sulfate which gives us one more 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 voltmeter 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 0 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 g0 so that's Delta g0 now the standard change in free energy so let's go ahead and solve for Delta g0 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 bit more room down here let's plug in our numbers so we're trying to solve for Delta g0 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 2 so this would be 2 moles of electrons and 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 easy Rho is 1 point 1 0 volts for this will take Excel and we'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 one point one zero 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 are moles cancels out our charge coulombs cancels out to give us Joule for our answer let's go ahead and calculate how many joules so let's uh let's do the calculations we have two times ninety six thousand five hundred and then we're going to multiply that by one point one zero so that would give us this would give us twenty two hundred twelve thousand three hundred joules so remember this was in joules and let's go ahead and convert that to kilojoules so two hundred twelve thousand joules would be 212 kilojoules and number 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 G zero and E zero 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

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