Let's have 1 molar of-- let me pick a strong acid.
Let's say it's hydrochloric acid.
HCl.
And we know, of course, that since it's a strong acid it
disassociates completely.
So HCl in an aqueous solution-- or a solution of
water-- disassociates completely into hydrogen ions
in an aqueous solution, which is really hydronium.
I've said that multiple times.
Plus your chlorine anion in an aqueous solution.
So if you actually have a molar of this, as soon as you
put it in the water, you really have 1 molar of this.
So your hydrogen concentration is really 1 molar.
And of course we know, what's the pH of that?
Well, the pH is just the minus log base 10 of your hydrogen
concentration, which is 1.
Which is the minus log of 0.
So minus 0, which is equal to 0.
So your pH is going to be equal to 0.
And let's say for use in the later part of this, let's say
I have a liter of this.
Right.
This just tells me how many moles per liter, and now I
just told you that I have 1 liter.
So you know that you have 1 mole.
Let me make a little chart here.
I'll make a little box here.
And let's make this access right here.
This is going to be my pH.
And right when I take that first measurement-- let's say
this is 0 here, this is 7, and this is 14 up here.
When I take that first measurement, my solution of
hydrogen chloride, or hydrochloric acid, has a pH 0.
Now, what I'm going to do is I'm going to titrate this
aqueous solution of acid.
And titrate just means drop something else into it in
controlled increments to see what happens.
And what I'm doing here is going to be
an acid-base titration.
I have an acid here, and what I'm actually going to titrate
it with, or the reagent that I'm going to add to it--
The reagent is essentially a reactant that, when you view
it this way, that you're adding to the solution.
So it's the titrant.
So in this case, my solution already has
hydrochloric acid in it.
The pH is already 0.
But what I'm going to do is I'm going to
add a strong base.
Let's say sodium hydroxide.
That's my favorite strong base.
And let's say I have a solution that I have prepared
ahead of time.
Let's say it's a 1 molar solution.
But I'm not going to add all of it at the same time.
I'm going to add it in increments of
a tenth of a liter.
So this is 1 liter that I've added.
And then this would be 2 liters.
And so this would be 500 milliliters.
500 mL.
This is 1 liter.
This is 1.5 liters.
This 2 liters.
And so on this axis, I'm going to slowly add more and more of
this hydroxide.
So what's going to happen?
As I slowly add hydroxide, it's going to increase the pH.
Why is it going to increase the pH?
Because this OH.
Remember, hydroxide is a strong base.
So the NaOH disassociates completely
in an aqueous solution.
To OH minus plus sodium cation.
Right?
Now if I'm adding this to this stuff here, what do you
think's going to happen?
Well this stuff right here, these OHs are just going to
sop up your hydrogens.
So for the most part-- obviously, everything is
probabalistic.
And whenever we're dealing with chemistry, there's always
some molecules that won't completely react, and there
will always be some concentration of anything.
And that's why you actually can never get to a 0
concentration of hydrogen, no matter how much base you add.
Because there will always be some hydrogen molecules that
are just hiding just perfectly, or they're in
perfect equilibrium so they don't react.
But most of them will react.
But as I add more H, these are going to disappear.
So my hydrogen concentration is going to go down.
The pH is a negative log of that, so your pH will go up.
Your pH will go up slowly-- well, it will look slowly,
because it's a log chart, so maybe it's doing
something like this.
Your pH concentration is going to look something like-- as
you add more and more.
But you might say, oh that's such a slow movement.
Why isn't it occurring faster.
But you have to think about something.
This right here, if this is a pH of 1, this means-- so, at a
pH of 0, this means your hydrogen
concentration is 1 molar.
At a pH of 1, this means your hydrogen concentration is at
10 to the minus 1.
Which is 0.1 molar.
So even though on a log chart it looks like you've made a
very small movement, you've actually gone
by a factor of 10.
In terms of your reduction of your hydrogen concentration.
You started off with 1 molar of your hydrogen.
By the time you've added roughly 900 milliliters of
your solution, you probably would have gotten
rid of most of it.
And obviously the denomenator's changing,
because I'm actually adding volume here.
Right?
Because I'm actually adding some volume here.
So you would have to add them.
But you get the I general idea.
That these actual molecules of hydroxide are going to react
with these things.
They're going to essentially turn into water and disappear
into the solution.
So these are going to disappear with those
disappearing, for the most part.
Which leads in an overall reduction concentration of
your hydrogen ions, which will lead to an
increase in your pH.
Until some point where you have pretty much sopped up as
many of these things as you can.
There will always be a few of them, but you've sopped up as
many of them as you can.
And so any incremental hydroxide you add will
actually go to build the hydroxide concentration.
Where the hydroxide concentration is going to be
greater than your hydrogen concentration.
But even better than that, there's going to be some point
where you've added just enough of this that you have an equal
amount of this and this.
You have an equal amount of hydroxide and hydrogen.
Right?
What happens, first of all, when there's an equal amount
of hydroxide and hydrogen?
Well, then you're neutral.
Right?
If your hydroxide concentration is equal to your
hydrogen concentration, you're neutral.
This is just like water.
You're at a pH of 7.
So there's some point where your hydroxide concentration
is equal to your hydrogen concentration, and your pH is
going to be 7.
And then above that, you're just adding
more and more hydroxide.
The hydroxide concentration is overwhelming your hydrogen
concentration.
And so you're going to get really, really basic.
And since this is a strong base, you're eventually going
to get to a pH of 14.
Because you're essentially going to have-- well, you're
not going to have 1 molar.
Let me erase that point.
You're going to have half a molar of OHs
at the end of this.
So your graph is going to look something like this.
Now, I mean, you're still going to have hydrogen
concentration, but it's going to go really small.
It's going to get really, really small.
Now.
What's interesting about what just happened here?
At this point right here, your OH is equal to your hydrogen.
And the way I think about it is the great majority of your
moles of hydrogen were sopped up at that point.
So in order to stop up 1 mole of hydrogen, you essentially,
for the most part-- and there's always things that
don't get completely sopped up-- but you'll essentially
have to add 1 mole of OH to sop up
your 1 mole of hydrogen.
Remember, this is 1 molar and you had 1 liter of it.
So you had 1 mole of hydrogen to sop up.
So you need 1 mole of OH to sop up, and how do you get 1
mole of OH?
Well, we said the concentration of the solution
was 1 molar.
So once you put a liter in there-- because that's 1 mole
per liter-- once you put a liter in there, you would have
put 1 mole of hydroxide cations in there
to sop up the hydrogen.
So this is the equivalence point.
Where have essentially, you have an equal amount and very
low concentrations of both hydroxide and hydrogen.
You've essentially sopped up all of the hydrogen, but you
also have sopped up all of the hydroxide that
you've added so far.
After this point, any hydroxide you add will
essentially contribute to increasing the pH even more.
Or it'll kind of overwhelm your hydrogen concentration.
Now what's interesting about this?
In this example, I told you, oh, I have hydrochloric acid
and I gave you its concentration ahead of time.
But let's say I didn't tell you that.
Let's say it was some mystery substance, and you just
measured the mystery substance's pH.
At this point, you said OK, it's pH is 0.
And you titrated it with this sodium hydroxide.
And you said, well, gee, when I added 1 mole-- because you
figured out at a liter of the solution-- of hydroxide ions.
At that point, I've essentially eliminated all of
the hydrogen ions that were in my original solution.
So I must have had 1 mole of whatever acid
this was over here.
So this would have told you that my initial concentration
was 1 mole of H plus.
And since we know it's easy to see how much volume you have,
you see I have a liter.
So you say my original concentration of
this acid is 1 molar.
And you could also know that what you're dealing with is a
strong acid.
And I encourage you to watch the next to do I do the same
thing with a weak acid.
But because it's a strong acid and a strong base reacting
with each other, when you have the same number moles of both,
you get exactly to a pH of 7.
They completely neutralize each other, and you have a
completely neutral solution.
If you had a strong base with a weak acid, the strong base--
once you have the same amount as the weak acid, it would've
neutralized it.
But you would have also had some of the
conjugate weak base left.
So you would have actually ended up with a basic pH.
And I'm going to do that in the next video.
But if you see that the equivalence point occurs at a
pH of 7, you'd know that you were titrating-- what you were
dealing with was a strong acid.
Because it was completely neutralized, not more than
neutralized, by the strong base.
And if you want to eye-ball where is equivalence point,
you look for the steepest point in the graph.
Because that's the point where you're going from having a
majority of hydrogen versus hydroxide, to having a
majority of hydroxide versus hydrogen.
So it creates this inflection in the graph, and you just
would have to look at this chart.
And say, I added a liter of this solution.
The concentration of this solution is 1 mole per liter.
It's 1 molar.
It has a molarity of 1.
So I must have added 1 mole of hydroxide
to get to this point.
So I must have neutralized 1 mole hydrogen.
So there must have been 1 mole of hydrogen to begin with.
And since I had 1 liter of solution, I had 1 mole
hydrogen and 1 liter of solution.
So my original molarity was 1.
Anyway, I don't want to confuse you too much.
In the next video, I'm going to try to do the same thing,
but I'm going to do it with a weak acid.