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our goal is to predict whether or not lead to Plus can oxidize solid aluminum or solid copper under standard state conditions and also to calculate the standard cell potential z0 for each reaction at 25 degrees C so we have a standard reduction potential table a very shortened version of it where we have our half reactions written as reduction half-reactions on the left and the standard reduction potentials for those half reactions on the right measured in volts our question wants to know whether lead to + can oxidize these solid metals so therefore lead to + is functioning as an oxidizing agent so it itself must be being reduced but it is functioning as an oxidizing agent in general an oxidizing agent can oxidize any reducing agent that lies below it on our standard reduction potential table so here is lead to + alright so we have our stronger oxidizing agents going up on the left side and an oxidizing agent can oxidize any reducing agent blow it on our table so if I find aluminum here aluminum is below lead 2 plus so we would predict that lead to + can oxidize aluminum so our prediction is yes for aluminum so we can actually draw a diagonal line from lead 2 plus 2 aluminum and we predict we predict this will work this reaction will work so sometimes you'll see this called the diagonal rule next let's predict whether lead to + can oxidize solid copper an oxidizing agent can't oxidize a reducing agent that appears above it on our standard reduction potential table so if I I draw a line from lead two plus to solid copper right we're going up here so this reducing agent copper is above lead two + and so this should not work so our prediction is no this will not work so no led to + cannot oxidize copper under standard state conditions let's go ahead and calculate the standard cell potential for each of these reactions to just confirm our predictions so we'll start with lead two plus oxidizing solid aluminum so if lead two plus is oxidizing we're going to write the lead two plus this half reaction here we're going to leave it how it is as a reduction half reaction so our reduction half-reaction is lead two plus plus two electrons going to solid lead and so the standard reduction potential for this half-reaction is negative 0.1 three volts so this is negative point one three volts next we're going to write the oxidation half-reaction for aluminum alright so here is aluminum so we could write an oxidation half-reaction so we need to reverse we need to reverse this reduction half-reaction so we write solid aluminum alright is going to aluminum three plus to do that it needs to lose three electrons so loss of electrons is oxidation so we have we need to find the standard oxidation potential for this half-reaction now we've done this several times when you reverse when you reverse a reduction half-reaction to turn it into an oxidation half-reaction which is what we've done down here you just change the sign on there standard reduction potential so the standard reduction potential is negative one point six six volts all we have to do is change the sign so it's positive one point six six volts so the standard oxidation potential is positive one point six six if we wanted to write the overall reaction we need to balance everything so we need to get our number of electrons equal so we could do that by multiplying our first half reaction here by three because that gives us six electrons so three times two gives us six electrons the number of electrons needs to be the same so we need to multiply our second half reaction by two because two times three also gives us six electrons so let's do that let's do that let's do that calculation here so we have three PB two plus so for reduction we would have three PB two plus plus three times two electrons gives us six electrons and this would give us three PB 3 solid PB so 3p be solids so we're multiplying our half reaction but remember we do not multiply our standard reduction potential by three because voltage is an intensive property so we leave our standard reduction potential as negative point one three volts all right let's do our next half reaction so our oxidation half reactions we would have two aluminum's so two aluminum and then two this is going to give us two al three plus and six electrons two times three gives us six electrons and once again we do not multiply our oxidation potential by two because voltage is an intensive property so our standard oxidation potential remains positive one point six six volts to get our overall reaction we just add together our two half reactions right so let's add these together so we're going to add these together to get our over all alright so the electrons would cancel out so six electrons so let's write our reactants which are right here so we would have three PB two plus plus two al so plus two al giving us so for our products we would have three PB so three PB plus two al three plus so we have two al three plus so is this reaction spontaneous all right so is our overall reaction spontaneous we could figure that out by calculating the standard cell potential right which is what our problem asks us to do so what is the standard cell potential we know we just have to add up our standard reduction potential and our standard oxidation potential so just like we add our half reactions we add our potentials together we're going to add our standard reduction potential for that half reaction and we're going to add our standard oxidation potential for that half reaction to get the standard cell potential for the cell so that's negative 0.1 3 all right so it's negative 0.1 three plus one point six six so plus positive one point six six so that's equal to positive one point five three so the standard cell potential is positive one point five three volts remember when you're when your cell potential is positive that means a spontaneous reaction so this is this is a spontaneous this is a spontaneous reaction which is what we predicted right we predicted that led to plus could oxidize aluminum all right so let's go back up here to our problem again so remember our problem asked us can lead to plus two plus oxidize aluminum and we predicted yes right by using the the diagonal rule here by drawing this arrow down here and then we just calculated the standard cell potential and we saw that it confirmed and confirmed our prediction all right next let's do let's do copper so we said that lead to plus will not be able to oxidize copper let's go ahead and do it's fine let's find the standard cell potential to confirm our prediction so we're going to keep this half-reaction right so we're going to keep this half-reaction for lead and then for copper we need to reverse this half reaction as it's written right so we need to write we need to write the reverse of this reaction and when you're writing the reverse remember you need to change the sign all right this is a this is positive 0.34 for the reduction of Cu 2 plus so for the oxidation of copper right it's negative point three for the standard oxidation potential so let's go back down here where we have some more room and let's let's figure out the standard cell potential so we're going to write our reduction half-reaction first which was lead two plus plus two electrons right to give us to give a solid lead here so the standard reduction potential for this half-reaction is negative 0.1 three volts and the oxidation half-reaction this was to oxidize solid copper all right so copper turns into copper two plus and we need to lose two electrons right we're oxidizing here so we're losing electrons and the and the standard oxidation potential for this half-reaction we just talked about it above its negative point three four all right negative 0.34 because we're writing this as an oxidation half-reaction so to find our overall reaction we just add up our half reactions here right we already have the number of electrons the same so those electrons will cancel out and we have our reactants so let's write those in here so we have lead two plus plus solid copper and our products so our products would be lead and Cu 2 plus so this would be so be lead and Cu 2 plus all right let's calculate the standard cell potential we know to find the standard cell potential all we have to do is add all you have to do is add the standard reduction potential and the standard oxidation potential so what is negative point 1 3 plus negative point 3 4 that's equal to negative point 4 7 volts so the standard cell potential right 4 for this reaction that we've just written out here for this overall reaction is negative and since the standard cell potential is negative we know this is not a spontaneous reaction all right so let me write that in red here so this is not this is not a spontaneous reaction so standard cell potential is negative so if you found if you if you calculated the standard change in free energy since the standard cell potential is negative you get a positive value for the standard change in free energy so this is not a spontaneous reaction so we've seen let's go back up to here let's go back up to the beginning alright so we made our predictions using our standard reduction potential all right we just confirmed that lead to plus will not oxidize solid copper this is not a spontaneous reaction so aluminum aluminum is more easily oxidized than copper all right you could you could figure that out just by thinking about this example or you could actually look at the standard reduction potentials right you can see that aluminum down here right has a more negative value for the standard reduction potential and therefore and therefore it's more easily oxidized alright so aluminum is more easily oxidized than copper we say aluminum is more active than copper so let me write that down aluminum is more active it's more active than copper so if you remember the activity series right you can explain the Activity series in general chemistry by looking at standard reduction potentials so this is a just another way to think about something you probably already know