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metal ear cells need to be lightweight for many applications in order to transfer more electrons with a smaller mass sodium and calcium are investigated as potential anodes a 1.0 gram anode of anode of which of the and a 1.0 gram anode of which of these metals would transfer more electrons assuming that the anode is totally consumed during the lifetime of a cell justify your answer with calculations so let's go to the top where they showed the reactions where they showed the reactions involving sodium and calcium and actually let me just copy and paste this so it's easier for me to reference near the bottom where we're actually doing the question so let me just copy this and then let's paste it down here that I can I can reference it okay and I'll even make it a little bit smaller just so I don't take up too much real estate and so the reactions that we care about are actually going to go in the reverse direction of these half reactions remember when we looked at when we looked at our power source right over here this first half reaction is what produces the hydroxide ions the hydroxide ions migrate the way their way to the left hand side and then they perform then they then they are involved in oxidizing in oxidizing whatever metal you have here if this was zinc the hydroxide combines with the zinc they're going to oxidize the zinc and those extra electrons that are released in that reaction those are the ones that are going to travel across the wire and provide the current but the hydroxide it could react with sodium if this metal is sodium it could react with calcium if this metal is calcium so the reactions we care about are going from this side the right side to the left side and so let me just rewrite that again and actually just the act of rewriting it will help well my pen is me having trouble is having trouble actually scrolling down but just the act of rewriting it will help with digesting what's going on so the sodium reaction for every two molecules of sodium it's solid it's actually forming our anode plus two molecules of hydroxide dissolved in the water aqueous solution we are going to yield sodium sodium oxide solid version of that plus water in the liquid state and plus two electrons and this is really important because we want to think about one gram of each of these metals how many electrons would they yield how many electrons are they going to is are they going to be able to transfer through potentially through that wire so that's the first relationship up there and then actually let me just leave the sodium there and then let me do the calcium over here remember we want to go from the right to the left so let me rewrite it that way calcium the solid state plus two hydroxides dissolved in water is going to yield calcium oxide solid plus liquid water liquid plus two electrons so once again I just rewrote each of these in the opposite direction and if I were to write the voltage I would flip the sign now because I have written them in the other in the other direction but they're not asking us about the voltage they want us to know one a one gram anode of which of these metals would transfer more electrons so if we think about sodium the case with sodium we have 1.0 grams 1.0 grams of sodium well let's think about how many moles of sodium that is well that's going to be well let's see we're going to have we can look we can look up sodium on our periodic table of elements and this is actually the one that they give you when you take the AP test and you see sodium right over here we could read it's atomic weight sometimes now called relative atomic mass and that's the weighted average of the atomic masses of the isotopes that you would typically find of sodium on earth take a random sample sodium and you were average their atomic masses it would be twenty two point nine nine so that tells us that a mole of sodium is going to weigh it's going to have a mass of twenty-two point nine nine grams or you could say so a mole is going to a mole is going to have a mass of twenty-two point nine nine grams so I could write one mole one mole of sodium is going to have a mass of twenty-two point nine nine grams and of course this is still talking about sodium and so I made sure that I have it in terms of moles per gram because when you do our dimensional analysis grams divided by grams or grams of sodium divided by grams of sodium they're gonna cancel out and I'm gonna be left with moles of sodium so this part of the expression this is gonna give me how many moles of sodium we are dealing with if I have one gram of sodium but we need to think about how many how many electrons how many electrons are we going to be able to are we going to be able to transfer and that's where we actually have to look at this reaction so for every two for every two moles of sodium we are going to transfer two moles of electrons or another way you can think about it is for every mole that here you have a two to two relationship or you could say for every mole of sodium we are going to transfer one mole of electrons and so let's do that we're gonna transfer one mole one mole of let me write it this way one mole of electrons per moles per mole of sodium if you have two moles of sodium you're going to get two moles of electrons if you have one mole of sodium I'm gonna have to if say for one mole of sodium I'm gonna have one mole of electrons and so what is this going to give us well if you just multiply out actually we look at the units first grams of sodium cancel out with grams of sodium moles of sodium cancel out with moles of sodium and so you're left with just moles of electrons moles of by my vagin ' moles of electrons it's going to be 1.0 though times one divided by twenty two point nine times one so it's 1.0 divided by twenty two point nine and let's see i'm gonna have two significant digits right over here two significant figures so let me get the calculator out and it is let's see so it's just one i could just say one divided by twenty two point nine is equal to so if we have two significant figures it's approximately 0.04 four point zero four four so i'll say approximately zero point zero four four moles of electrons remember moles Avogadro's numbers this is still a lot of electrons the mole is 6.022 times 10 to the you know roughly that times 10 to the 23rd so it's a very very large number of electrons that we are going to potentially transfer over here if we have one gram of sodium now let's do the same thing with the calcium so if we have calcium it's going to be the same exercise here we have one gram of calcium times one mole of calcium has what mass one mole of calcium has a mass of how many of how many grams so let's go back to the periodic table and there you have calcium right over here the atomic weight is forty point zero eight or often times are now the more modern name is relative atomic mass the weighted average of the typical of the isotopes forty point zero eight so I can write 40 point zero eight right over here and then in our reaction for every mole of calcium how many moles of electrons are we going to generate well we have in this reaction one for every one calcium we have two electrons so for every mole of calcium we're gonna have two moles of electrons so we could say times two moles of electrons for every mole of calcium in our that we have as a a reactant over here and so this is going to give us this is going to be approximately C our units grams of calcium cancels with grams of calcium moles of calcium cancel with moles of calcium and so we're gonna have one times one divided by forty point zero eight times two so it's going to be two divided by 40 point zero eight which is so two divided by forty point zero eight and we're gonna have two significant figures right over here because this two and those ones are kind of pure numbers while these are from measurements so this is the fewest number of significant figures so we have two so two divided by that let's see so it's going to be zero point zero five zero so zero point zero five zero moles of electrons so you can see right from right from this calculation that the one gram of calcium has the Kin Kin can transfer more electrons than one gram of sodium if sodium was the anode so we see very clearly that calcium so one gram of calcium can transfer more electrons can transfer more electrons more electrons then 1.0 gram of sodium you can see it right over here we have done we have done the calculation
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