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I've drawn a bunch of titration
curves here. So let's see if we can review
everything we've learned to kind of have a more holistic
understanding of interpreting these things. So the first thing to look at
is which of these are the titration of acids
versus bases? And everything I've done now
is acids, but the logic for base titration is the exact
same thing as acid. So for example, these
are acid titrations. We start with low pH's. In all of these, this
axis is pH. I should have drawn that ahead
of time before I asked you the question, but I think you
knew that already. So before we add any of the
titrator or the reagent, in this reaction, we're starting
with a low pH. So this is kind of our
starting point. So we have a low pH there. We have a low pH there. So these are both
clearly acids. Here, our starting point before
we start titrating at all, it's a high pH. So both of these are bases. Let me write that down. These are clearly both bases. Base titration, and this
is an acid titration. Now, we haven't covered bases. But it's the same exact idea. In an acid titration, you start
with an acid and you add a strong base to it to sop up
all of the acid until all of the acid is sopped up and you
hit the equivalence point. You hit the point that all
of the acid is sopped up. And now, as you add more and
more strong base, you're making it superbasic. So in this acid,
our equivalence point is over here. And in this acid,
our equivalence point is over here. This is how much solution
we had to add to sop up all of the acid. Right there. So given what we already know,
which one's a strong acid, which one's a weak acid? Well, this one, when sopped up
all of the acid, we have a completely neutral solution. So this must have been
a strong acid. There's nothing left. Everything has been converted to
water in its natural state. pH of 7. And we might have had some
neutral leftover conjugate bases there. But since it was a strong acid,
those conjugate bases don't do anything. They don't add anything
to the pH. They're not really basic. The chlorine in hydrogen
chloride, the chlorine ion, doesn't change the pH. So this is a strong acid. And this one, when we got to the
equivalence point-- when we had used up all of the acid
in a solution, and then we hit this in inflection point, where
any OH we added was significantly increasing the
pH-- when we hit that equivalence point, our
pH was already basic. And that's because we had all
of the conjugate base of the weak acid, which does make
the solution more basic. So this is a weak acid. And in both of these situations,
we were increasing the concentration of OH minus. Maybe by adding sodium hydroxide
to the solution, a strong base. Now, In these situations, we
start with a base, and we add a strong acid to it. Maybe whatever base. We're adding hydrogen chloride,
something that will sop up the OH. Here, we want to sop up the OH
and bring its concentration down, until some point that we
have sopped up all of the OH. All of the base is gone. Or most of it is gone. In this situation, we're in a
completely neutral situation. So when we sopped up
all of the base, we're completely neutral. No basic conjugate bases left. So this is a strong base. And here, the titration, we're
increasing the hydrogen solution, or the hydrogen
concentration, to sop up all the base. Same thing here. We're sopping up all
of the base. We start over here. But over here, the inflection
point happens right over here. So we've sopped up all of its
base, but some of its conjugate acid is still left
over, even after we've sopped up all of its base. So we end up with a slightly
negative pH at the equivalence point. So this is a weak base. Let me actually draw that
reaction for you. Remember, a weak base looks
something like this. Maybe its A minus is in
equilibrium-- that second equilibrium arrow is a little
too wild for my blood-- is equilibrium with AH. It grabs hydrogen ions from
the surrounding water. Everything is in an
aqueous solution. So after you add hydrochloric
acid to this-- remember, HcL disassociates completely
into hydrogen ions plus chlorine anions. If you add hydrochloric acid
to this, these things are going to just completely
sop up these things. So we keep sopping
up those things. Our concentration of OH goes
down and down and down. And as we sop up this, our
reaction goes in that direction because Le Chatelier's
Principle. More and more of this is
going to get formed into this and that. Until some point, we're out
of that, and we have a ton of this left. And so our equivalent point is
when we're out of this stuff. And when we're adding more
hydrogens, we're getting really acidic really fast. But
we have a lot of the conjugate acid there in the solution
already. So we're going to have an acidic
equivalence point. Now, let me give you an actual
problem, just to hit all the points home. Because everything I've done now
has been very hand-wavey, and no numbers. So let me draw one. Let me draw a weak acid. And you'll recognize
it because you're good at this now. But I'll deal with some
real numbers here. So let's say that's a pH of 7. We're going to titrate it. It starts off at a low pH
because it's a weak acid. And as we titrate it,
it's pH goes up. And then it hits the equivalence
point and it goes like that. The equivalence point
is right over here. And let's say our reagent
that we were adding is sodium hydroxide. And let's say it's a
0.2 molar solution. I've been using too
round numbers. I'll use 700 milliliters of
sodium hydroxide is our equivalence point. Right there. So the first question
is how much of our weak acid did we have? So what was our original concentration of our weak acid? This is just a general
placeholder for the acid. So original concentration
of our weak acid. Well, we must have added enough
moles of OH at the equivalent point to cancel out
all of the moles of the weak acid in whatever hydrogen
was out there. But the main concentration
was from the weak acid. This 700 milliliters of our
reagent must have the same number of moles as the number
of moles of weak acid we started off with. And let's say our solution at
the beginning was 3 liters. 3 liters to begin with, before
we started titrating. Obviously, as we add reagent,
we're adding some volume to the solution. But let's just say that
in the beginning, we started with 3 liters. So how many moles have
we sopped up? Well, how many moles of OH are
there in 700 milliliters of our solution? Well, we know that we have 0.2
moles per liter of OH. And then we know that
we don't have-- times 0.7 liters, right? 700 milliliters is 0.7 liters. So how many moles have we
added to the situation? Let's see. 2 times 7 is 14. And we have 2 numbers
behind the decimal. So it's 0.14. So 700 milliliters of 0.2 molar
sodium hydroxide, and we have 700 milliliters of
it, or 0.7 liters. We're going to have 0.14 moles
of, essentially, OH that we put into the solution, which
means that it canceled out completely with the same
number of moles of our original acid. So that means that the original
concentration of our acid is equal to 0.14 moles. That's how many moles we had. And we know that our original
solution before we started titrating at all, is 3 liters. Remember, the molecules
are canceling directly with each other. So that's why I wanted to figure
out how many actual atoms, or molecules,
of OH did I add. Those canceled out with the
exact same number of atoms of out weak acid. And so this is how many atoms or
molecules of our weak acid we must have started off with. And so you divide that by the
number of liters, and then you have your original molarity. So 0.14 divided by 3. 0.046. So you're initial concentration
of the mystery acid was 0.046 molar. Fair enough. Now, the other question
is, what is the pKa of our mystery acid? Well, we just go to the half
equivalence point. So we said, OK. What was the pH of
our titration curve or of our solution? We were at the half
equivalence point. So when we had only added 350
milliliters of our reagent, of our strong base, to
the solution. So you go there, and you
say OK, the pH was 5. pH is equal to 5. And we know, from the last
video, that if you take this half equivalence point, the pH
is equal to the pKa, the negative log of our equilibrium
constant. So there. We figured out the equilibrium
constant as well. It's equal to 5. So all of this titration curve
and all of this, I'm just showing you how experimentally,
you can take some mystery acid or base. You add strong acid
or base to it. You plot out this curve. And then you can pinpoint some
of the properties, the concentration of your original
acid or base. And only if you're dealing with
a weak acid or base, you can figure out it's equilibrium
constant. Obviously, if you take a strong
acid, you say, oh, my half equivalence
point is here. So therefore, this must be the
equilibrium or the pKa-- No. There is no equilibrium constant
for a strong acid. And there is no equilibrium
constant for a strong base, because they're not
in equilibrium. They disassociate completely. Anyway, hopefully you have
a good understanding of titration now.