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Hi guys, so in part D of the lab you're also going to calculate Ka which you also did in
the previous part,
however in this case you're going to determine Ka for an unknown acid, so that's
the difference. Earlier you are using
acetic acid, now you're going to use an unknown acid
and you're going to use in this case the buffer method to do the Ka.
Now what is the buffer method?
First off, this video is going to describe what a buffer is and how to calculate its
pH using an equation that
we'll derive here.
So in this case if buffer is already covered in lecture,
then you can skip this video.However if buffer has not been covered lecture
then you should watch the entire video
which will discuss a particular equation called the Henderson-Hasselbalch equation
which we would use to calculate the pH of buffers.
So let's start with the definition of a buffer.
A buffer is a solution which happens to be a mixture of
one of the following
A weak acid and its conjugate base, for example
HA and A-
together
or a weak base and its conjugate acid which is something like
B
with BH+.
So you can think that
an example of a buffer with acid
and its conjugate base
could be HF and F-,
which will form a buffer.
Something like B and BH+ could be
ammonia
with ammonium, that would be a buffer as well.
As it turns out if you make a mixture like this: a weak acid with its conjugate base or
a weak base with its conjugate acid,
if you use the appropriate concentration
the solution that results from this mixture
can resist
large changes in pH, when you add strong acid or strong base to it.
For example,
we would actually do this in lecture or we've done this (example) in lecture,
but if you add 5 mL of 0.1M HCl,
a strong acid
to 50 mL of water,
you can do calculations and you'll see that the pH
will change from 7 to 2.04.
So in other words, you have a change
of about
a 5 pH units, which is a hundred thousand
difference in proton concentration.
If you were to add the same amount of HCl, 5 mL of
0.1 M
to a buffer,
you can see that the pH will actually change very little, from 9.26 to 9.17,
in this case we're adding it to
say an ammonia buffer, the type that is shown right here.
And like I said, this calculation will be done in lecture as well
so you can actually verify it.
So buffers are actually very important in physiological systems, organisms and
what not,
and the importance of course is that buffers can help you maintain a relatively
constant pH,
despite all the different kinds of chemical reactions that are going on (in the environment).
So for example
our human blood
is a mixture
of solution, but
the ph of the human blood stays relatively constant at pH 7.4,
and this is because it's a buffered system of various
bicarbonates,
carbonate
and
carbonic acid
system.
All these three maintained
the pH of the human blood to be around seven point four.
Here's the figure that shows the range of pH that is normal with human blood.
So usually you're kind of expecting the normal range to be around
7.4.
If you even go down about 0.4 pH units to 7.0,
your enter this region called
acidic blood which result in a condition called acidosis and that is
dangerous because now a lot of the things
that are supposed to work, proteins for example, that are supposed to work at
pH 7.4,
can no longer work
at this
pH 7.0.
environment. So as a result you might have
certain pain or illness that is going to make you feel very
uncomfortable. Now if this keeps dropping
then eventually
you're going to die as a result of it.
Same thing if the pH goes up by about
0.4 units to 7.8, then you have this condition called alkalosis which is
the opposite, which means that your pH is now becoming too basic,
for the proteins that are needed
to work in the blood.
And again if you go too high, then
you're going to die.
And you can see that the range of pH that is tolerable is really very small, from
7.3 to 7.5.
So it turns out that you can calculate the pH of buffers using an equation called
the Henderson Hasselbalch equation.
This equation can be derived
using your usual equilibrium
for acid,
for a weak acid, so we're gonna do that,
deriving the Henderson Hasselbalch equation for a weak acid and we're going to start with an ICE table for a weak acid
which is of course given right here.
We have HA going to H+ and A-,
the difference between this versus
the usual weak acid
equilibrium
is that
in the case of a buffer you have a
considerable
amount of the conjugate base present with the weak acid as well. So in this case, we have
1M of HA and
also we have 1M of A- present initially and the source of this A-
comes usually from some kind of a salt
that is soluble
that contains the conjugate base, so for example NaA
is the sodium salt for this particular acid. So you can imagine
a mixture of HF with NaF,
in this case HF would just be the weak acid,
NaF will dissociate to form Na+ and F-,
the F- will then be
in equilibrium with the HF and let's say both of them are 1M.
So that's the difference between this (buffer) and just a weak acid, because
in just a weak acid
this number is zero, right.
So then you do your usual equilibrium, this is -x, +x and +x
because we have 0M H+ at the beginning,
so it has to be plus on the right side,
and then you get
1-x, x and 1-x.
Now it turns out that
as you know, because this is a weak acid,
the Ka value
is going to be less than one, usually it's quite a bit less than one,
for something like HF, the Ka is actually,
0.0001,
and generally when we make these kind of calculations,
Ka =
(x) (1-x)
over (1-x). Usually we just assume
this is about equal to 1,
and this is about equal to 1. The reason we could do this is because the
Ka value is small.
So as a result what you get in the end is
(x) (1)
over 1.
But if we look back here, what is 1?
1M, is just the initial concentration of HA,
it's also the initial concentration
of A-.
So in other words, I can just write this as follows. Ka,
is equal to H+ concentration at equilibrium
times
one, which is just
A- concentration initial because
we're making that assumption
and then we also have HA
initial
so that's the way you can
simplify the buffer equation because generally speaking you can
make the assumption
that concentration of A- at equilibrium
is approximately equal to A- concentration
initially
and same thing with the HA. HA at equilibrium
is approximately equal to HA
initially.
Once you write it in this way then you can solve this
as a pH.
In order to solve for pH, we need to isolate H+, but before I do that
let me just rewrite this equation
take negative log of both sides. So this is what I'll do
I'll have Ka
equal to H+
and then
A-
I'm going to write it this way, a little differently
It's the same ratio as before, same equation, I just write it where
I isolate these two factors together
or put them together I should say
Let me tell take the negative log of both sides of this equation, so I'll have the -log (Ka)
is equal to
-log of this entire factor. Now remember that because these two things are being
multiplied with each other, it's the same as saying,
- log (H+)
plus
the - log of
A-
over
HA.
And again these are for initial concentration right, so you want to keep that
in mind,
as we are deriving this
and now we want to isolate -log (H+), because of course
that's our
pH,
This of course is our
pKa,
So we have pH = pKa and we want to take this whole thing and move it over to
this side of the equation which means that because it was negative earlier it now becomes
positive
log
of A-
concentration initially over
HA concentration
initially.
This
equation at the bottom is what is called the Henderson
Hasselbalch
equation
and it is used to calculate
pH of buffers.
And again what
constitutes a buffer
is a solution that contains
approximately
equal
concentration of
an acid with its conjugate base or a base with its conjugate acid.
okay that's something to keep in mind.
This equation only works
if you have a buffer. It doesn't work for a weak acid or a weak base,
it only works if you have a buffer.
And a buffer means you have
about equal concentration of HA and A- at the beginning.
What we will do in the next video is show how we can use this equation to help
us figure out the
Ka of an unknown acid.