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# 2015 AP Chemistry free response 1d

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- [Voiceover] Metal-air
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, (laughs) A 1.0 grm 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 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 reference it. Okay, I'll even make
it a little bit smaller just so I don't take up
too much 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 our power source right over here, this first half-reaction is what produces the hydroxide ions. The hydroxide ions migrate
their way to the left-hand side. And then they perform, 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, will, my pen has been 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 oxide, a solid version of that, plus water in the liquid state, and plus two electrons. And this is really important 'cause we wanna think about one gram of each of these metals. How many electrons would they yield? How many electrons 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. And remember, we wanna go
from the right to the left, so let me rewrite it that way. Calcium, a 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 wanna write the voltage, I would flip the sign now, 'cause I have written them
in the other direction. But they're not asking
us about the voltage. They want us to know 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 could 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 its 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, if you just took a
random sample of sodium, and you were, average their atomic masses, it would be 22.99. So that tells us that a mole of sodium is going to weigh, is going to have a mass of 22.99 grams. Or you could say, so a mole is going to, a mole is going to have
a mass of 22.99 grams. So I could write one mole, one mole of sodium is going to have a mass of 22.99 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 electrons, how many electrons 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 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, you're gonna have two. (laughs) If you have one mole of sodium, you're gonna have one mole of electrons. And so, what is this going to give us? Well, if you just multiply out. Actually, let's 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, (scoffs) why am I making an apostrophe? Moles of electrons. And it's going to be 1.0 times one, divided by 22.9, times one. So it's 1.0 divided by 22.9. 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 22.9 is equal to, so if we have two significant figures, it's approximately .044, .044 So, I'll say approximately 0.044 moles of electron. Remember, moles. All we've got is numbers. This is still a lot of electrons. A mole is 6.022 times 10 to the, you know, or 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 grams? So let's go back to the Periodic Table. And there you have
calcium right over here. The atomic weight is 40.08, or oftentimes, or now the more modern name is relative atomic mass, the weighted average of the typical, of the isotopes. 40.08. So I could write 40.08 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 that we have as a reactant over here. And so this is going to give us, this is going to be approximately, see, 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 40.08, times two. So it's going to be two divided by 40.08, which is, so, two divided by 40.08. Now we're gonna have
two significant figures right over here. 'Cause this two and those ones are kind of pure numbers, while these are from measurements. So, and this is the fewest
number of significant figures, so we have two. So two divided by that. Let's see, so it's gonna be 0.050. So 0.050 moles of electrons. So you can see, right from this calculation, that one gram of calcium 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 than, 1.0 gram of sodium. And you can see it right over here. We have done the calculation.