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Figure out how to calculate an equivalent and how it relates to a mole. Rishi is a pediatric infectious disease physician and works at Khan Academy. Created by Rishi Desai.
Video transcript
I went to Wikipedia, and I decided to pick up the definition for an equivalent there. And I actually didn't find it too useful, but there are some things that I wanted to point out. So it says, "The equivalent is formally defined as the amount of a substance which will either react or supply with one mole of hydrogen ions in an acid base reaction; or do the same with one mole of electrons in a redox reaction." So all I've really figured out so far-- I was a little confused when I read this-- but I figured out what they are saying is that an equivalent is basically some amount, some number, right? So let's start there. So when someone says, hey, how many equivalents do you have? I know that they're talking about some number. So equivalent is equal to-- and this is for some ion, right? So for some ion of my choosing an equivalent equals some number. And usually that number is in terms of moles. So some number of moles that I need, so needed to balance something. I'm actually balancing some charge. So balance the charge of an oppositely charged-- so an opposite charge-- opposite monovalent. Actually, I should even add, balance the charge of-- I guess I can add without erasing-- charge of one mole-- that's actually really important-- of an oppositely charged monovalent. OK, so let's jump into an example, because I think that will clear up any confusion that you may have to this point. So let's say we're talking about, for some ion, let's say we pick potassium, OK? Here's our potassium. And I've got to balance out one mole of an oppositely charged monovalent. So this is my little line demarcating the other side. So on the other side let's say we have chloride. And chloride is oppositely charged. It's negative, right? And it's a monovalent. It's not negative 2, or negative 3. It's just negative 1, right? So we've got, let's say a mole of these, because the definition I wrote up just said that I needed a mole of an oppositely charged-- and as I'm writing this up, I'm realizing, and I hope you are, too, that there's no way in the world I can write up a mole of this stuff. There's no way, right? So let me just get the point across that, just imagine that there are a total of this many-- 6.02 times 10 to the 23rd chlorides. Because that's really the question. How many potassiums do you need to balance out the charge from all of those chlorides. And that's too big a number, too big a number to write out in any easy way, other than to say, well, maybe you need some number of moles of potassium. And that's why I wrote that right into the definition. So let's figure this out. So we know that potassium binds one to one with chloride, right? We know that's what happens. So when potassium's floating around, and it's gonna bump into chloride, it's going to go one to one. So we know that for one chloride, we're going to get one potassium. And so that means that for one mole of chlorides, we're going to get one mole of potassiums bound to them, right? And that's going to balance out the charge perfectly. So if someone says, well, how many equivalents do you have for potassium? That seems like a very simple answer. Well you say, OK, well, one equivalent would then be one mole of potassium. Or you could even rephrase it. You could say, well, in one mole of potassium-- and this is how people usually use the phrase. They say, well, 1 mole of potassium equals 1 equivalent. So I know that's the same thing flipped around, but that's how people usually state it. So now let's do a slightly more challenging example, and you'll see where this becomes a little different. So instead of potassium, let me jump into another one. Let's do calcium. Calcium-- so there's a plus 2. And same thing as before. I'm going to have to choose some oppositely charged monovalent. And I'm going to pick the same one, because this still is oppositely charged. I just needed some negatively charged monovalent, and chloride suits our purposes. And we know, just as before, we need a whole mole of them. And so if that's the case, how many calciums will bind to a chloride, and vice versa. How many chlorides will bind to a calcium? So let's imagine we have a little chloride and calcium party, and they can meet each other. Well, what's going to happen is, that you're going to have a calcium there, and a chloride there, and a chloride there, right? Because this will come here. This will come here. And they're going to basically bind and make this. They're going to make CaCl2, because the chlorides are only one negative charge-- actually, and this is two positive charges. I'm flipping around my negatives and positives. Sorry about that. There we go. Negative, negative, and plus 2. So you know that for every one calcium, you're going to get two chlorides. So let me write that out very clearly. So for every one calcium-- or actually I can write for every two chlorides you get one calcium, right? And that means that for every-- if I divide both sides by 2-- for every 1 chloride, I basically needed a 1/2 a calcium. And that's not how we think about it, usually, because it's hard to imagine 1/2 a calcium. But at least the math works out there. And so if I'm talking about one mole of chloride, then I'm left saying, well, then I have a 1/2 a mole of calcium. So far so good. And so, then, 1 equivalent, going back to our definition, equals 1/2 mole of calcium. And I said that we could flip around the equation, and we can. We could say, well, then 1 mole-- now all I did is multiplied both sides by 2-- 1 mole of calcium-- I'm not writing clearly right now, sorry-- 1 mole of calcium equals 2 equivalents. So there is how people usually phrase it. They'll say, OK, well, how many equivalents do you get for 1 mole of something? And so here you would say the answer is 2. And so I just want to point out something to you, which is that we kind of did this a long way, but here is a quick and dirty way. You could say, well, I know that calcium is divalent, and we know that potassium is monovalent, and here is kind of an interesting pattern that's emerging, right? As this Ca plus 2 emerged, we got 2 equivalents out of it. Let's test this with a third one. Let's just see what we get if we use, let's say, nitrogen. So let's do nitrogen. Nitrogen is negative 3. And I have to create my boundary, and on the other side, I need some oppositely charged monovalent. So there's a monovalent and it's opposite-- here's monovalent, check, and it's oppositely charged, check. Opposite. Opposite of the negative, right? So check, check. It meets our requirements. And I need a mole of them. So I have to draw out a mole, and you know there's no way I can do that, as I said before. And so just imagine 1 mole of these guys. And the question, again, is how much nitrogen do I need to balance all this out? And I'm gonna just underline in red the clue. So here's the clue. And let's now actually go through the steps of figuring it out kind of the longer way. So let's imagine you have a nitrogen here, negative 3, and it's going to be at this, let's say, cocktail party, and it meets some protons. And in this case, 3 of them come by. So it's going to form NH3, right? If we say 3 protons then come together with 1 nitrogen, which is what we just said, then I can divide both sides by 3, and I can see that 1 proton then comes with 1/3 of a nitrogen. So far so good. And I can then even go on to say 1 mole of protons, which is going back to our definition, would be balanced out by 1/3 of a mole of nitrogen. And if that's the case, then I can say, well, 1 equivalent equals 1/3 third of a mole of nitrogen. And I'm going to flip this around, just as we did before. I could say, then 1-- let me change that-- I could say, then 1 mole of nitrogen equals 3 equivalents. And remember, we underlined that little 3 in the beginning, and I'm going to underline it again. And now you can very clearly see the pattern that's emerging. So you can see that any time you look at the cation or anion that you're talking about, if you look at the number-- like if it's, let's say, magnesium, that's 2 plus, or calcium is 2 plus-- then you can know immediately that that probably means, if you did the work the long way like we just did, that the equivalents are going to work out to the same number. So nitrogen has 3 equivalents. Magnesium or calcium have 2 equivalents. And potassium and chloride, they all have 1 equivalent. So that's what equivalents mean in terms of the moles needed to balance out a charge on the opposite side.