- [Voiceover] We're gonna talk about the relationship
between pH and pK_a
and buffers.
And specifically, we're going to be talking mostly
about this in terms of the Henderson-Hasselbalch equation.
But before we go to the Henderson-Hasselbalch equation,
which I am gonna assume you've seen before,
and if not we have some other videos introducing it
and also deriving it, let's do a quick review
of what exactly is a buffer.
So a buffer is something that contains
an aqueous solution.
It's something that contains both a weak acid,
which generically we write as HA,
and it also contains in equilibrium
the conjugate base of our acid, so A minus.
This is, as written,
it's the acid dissociation on reaction for HA
and since it's an equilibrium
we can write an expression called K_a,
which is just the equilibrium constant for this equation.
And it just has a special name, 'cause it happens to be
for the dissociation of an acid.
K_a is just equal to
H_three O plus times A minus
all over the concentration of HA,
and we don't include water because it's a pure liquid,
so we assume that the concentration is always one.
Based on this expression for K_a, we can, and do,
in the separate video, derive the
Henderson-Hasselbalch equation.
So the Henderson-Hasselbalch equation
just says that the pH is equal to
the pK_a plus the log
of A minus over HA,
where HA is our weak acid
and A minus is its conjugate base.
And as you can see up here,
an acid and its conjugate base
are just related by the fact that the acid has an extra H.
We can rearrange the Henderson-Hasselbalch equation
to get a lot of different kinds of information.
One kind of problem you see a lot
is for some buffer,
you know, they might ask you,
oh, what's the pH?
And then that means you probably know the pK_a
and you know the concentrations of A minus and HA.
The other thing that you can use the
Henderson-Hasselbalch equation to tell you
is the relationship
between A minus and HA
which is something you might wanna know.
A lot of times, you just wanna know,
you know, what's in your solution,
depending on what you wanna do to your solution,
if you wanna add things to it,
maybe you wanna add some acid, you wanna add some base.
You wanna know what's going on.
The Henderson-Hasselbalch equation
gives you a really quick and easy way of doing that.
So what we're gonna do, is we're gonna
rearrange this equation to solve for this ratio
that we might be interested in.
So we're gonna subtract
pK_a from both sides
and that gives us a log
of A minus over HA.
And I don't know about you, but I actually find,
well, (laughs) I find logs not super-intuitive sometimes.
So I'm actually going to get rid of the log
by raising both sides to the 10th power.
So that gives us
10 to the pH minus pK_a
is equal to
A minus over HA.
So what does this tell us?
It may not look like it tells us a whole lot more,
but actually, it tells us a lot.
It tells us about the relative relationship and size
between A minus and HA concentration.
And it's saying that these two things are related
to the relative size of pH and pK_a.
So if we look at this, we can derive a couple relationships.
We're saying that pH versus pK_a,
this relationship, can tell us
about A minus
over HA, which is a ratio,
but that in turn we can relate to
just the relative size of HA versus A.
So let's go ahead and look at all the possible scenarios
for these three things.
We're going to start with the simplest possible scenario,
which is that pH is equal to pK_a.
When pH is equal to pK_a, we're raising
10 to the zeroth power.
So anything to the zeroth power is equal to one.
Which tells us that this ratio is equal to one.
And if A minus concentration
over HA concentration is equal to one,
that means that they have the same concentration.
I forgot a minus sign there.
This is a really helpful thing to remember.
Any time you have a buffer
and the pH of your solution
is equal to the pK_a of your buffer,
you immediately know that the concentration
of your acid and its conjugate base are the same.
And this comes up a lot not just when you're talking
about buffers by themselves, but also when
you're doing titrations.
And the point in your titration
where the HA is equal to A minus
is called the half-equivalence point.
Half-equivalence point.
And if you haven't learnt about buffers, that's okay.
Oh, sorry, if you haven't learn about titrations yet,
that's fully fine.
Just ignore what I just said (laughs),
but if you have, the moral is just that,
this is a really, really important relationship
that is really helpful to remember.
And I said really a lot there.
So there are two other possibilities
for pH and pK_a.
We can have a pH that's greater than pK_a
for your buffer, and you can have a pH
that is less than you pK_a for your buffer.
So if your pH is bigger than your pK_a,
then this term up here,
10 to the pH minus pK_a, is going to be positive.
And when you raise 10 to a positive number,
when you raise 10 to a positive number,
you get a ratio that is
greater than one.
So if our ratio A minus over HA
is greater than one, that tells us that
A minus, the numerator, is actually greater than
the denominator, HA.
So if you know the pH
and you know it's bigger than the pK_a of your buffer,
buffer's acid, to be more specific,
then you immediately know that you have
more conjugate base around than your acid.
The last scenario, pH is less than pK_a,
well in that case, we're raising 10
to a negative number, because
we're subtracting a bigger number from a smaller number.
And that means that our ratio,
A minus over HA, is actually less than one.
So that tells us that our denominator, HA,
is actually bigger than our numerator.
So just to wrap up, we can look at
the Henderson-Hasselbalch equation
and we can just look at the relationship
between pK_a and pH,
and depending on whether they're equal to each other
or one is bigger than the other,
we can immediately know what the relationship is
between our acid and its conjugate base in our solution.
It's very easy to derive.
We did it in just a few minutes,
so it's okay if you don't remember this all the time.
I usually just remember that pH equals pK_a
means you have the same concentration,
and then, if I forget, I will derive the other relation.