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# What is an equivalent?

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.