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AP Chem: SAP‑10 (EU), SAP‑10.A (LO), SAP‑10.A.1 (EK), SAP‑9 (EU), SAP‑9.E (LO), SAP‑9.E.1 (EK), SAP‑9.E.2 (EK), SAP‑9.E.3 (EK)

- [Instructor] Acetic acid
is an example of a weak acid and sodium hydroxide is an
example of a strong base. If we are titrating a sample of acetic acid with sodium hydroxide, acetic acid would be the analyte, the substance that we are analyzing, and sodium hydroxide would be the titrant. When acetic acid reacts
with sodium hydroxide, the products are an aqueous solution of sodium acetate and water. Next, let's look at the complete
or overall ionic equation for this reaction. Because the acetic acid is a weak acid, it does not ionize completely
in aqueous solution. Therefore, for our
complete ionic equation, we simply write a acetic acid. We don't show it as being ionized. However, sodium hydroxide is a strong base that associates 100% in aqueous solution. Therefore, we would show it as its ions, Na+ and OH-. Since sodium acetate is a
soluble salt in aqueous solution, it would consist of sodium
cations and the acetate anion. And we would also include
water in our overall or complete ionic equation. For our net ionic equation, we leave out spectator ions. Since sodium cations are on
the left and the right side, when we take those out, we're left with the net ionic equation for this weak acid-strong base titration. So acetic acid reacts
with hydroxide anions to form the acetate anion and water. Next, let's look at the titration curve for our weak acid-strong base titration, pH is on the y-axis and since
we're adding our strong base to our solution of weak acid, milliliters of base
added is on the x-axis. Let's use particulate
diagrams to help us figure out what's going on in this titration. Keep in mind that these
particulate diagrams are only meant to
represent what's going on in the solution during the titration and water molecules will
be left out for clarity. Looking at our first particulate diagram, there's only acetic acid present, only two particles of acetic acid present. Therefore, this is before
any base has been added. So on our titration curve, we're right here at zero
milliliters of base added. Next, let's add some sodium hydroxide to our initial solution of acetic acid. So for sodium hydroxide, the pink sphere represents
the sodium cation. So we think about adding
in the sodium cation and also a hydroxide anion. Remember from our net ionic equation, hydroxide anion reacts with acetic acid to form the acetate anion and water. Since water is left out of
our particulate diagrams, we don't see it here in this
second particulate diagram. However, we do see the
acetate anion that formed when the hydroxide anion reacted with the acetic acid particle. In the second particulate diagram, we also see the sodium
cation that was added and also the particle of acetic acid that was present initially. Because we started with two
particles of acetic acid and we have only one left in
the second particulate diagram, that means that half of the initial acid has been neutralized. So this second particulate
diagram is meant to represent the half equivalence
point in the titration. Next, let's add enough sodium hydroxide to neutralize the other half of acid that was initially present in solution. The acetic acid particle
reacts with the hydroxide anion to form water and the acetate anion. Since water is left out of
our particulate diagram, we don't see water in this
third particulate diagram. However, we do see the
acetate anion that was formed. We also see these sodium
cation that was added. And at the half equivalence point, we already had a sodium
cation and an acetate anion, so we can see those in our third particulate diagram as well. If we compare the third
particulate diagram to the first particulate diagram, all of the acid that was initially present has been neutralized. Therefore, the third particulate diagram represents the equivalence
point of the titration. We can estimate the equivalence
point on our titration curve by looking for the area where
we see a sharp increase in pH. So right about in here. And if we draw a little line, about halfway up that line approximately, is a good place to mark
the equivalence point. So this is a good estimate
of our equivalence point. And if we go over to where
that intersects in the y-axis, we can estimate the pH for this weak acid-strong base titration. It looks to be a little bit over eight, so between eight and nine somewhere. So the pH of the solution
at the equivalence point is greater than seven. The reason why the pH
is greater than seven is because at the equivalence point, there are acetate anions in
solution and acetate anion react with water to form
hydroxide anions and acetic acid. The pH of water at 25
degrees Celsius is seven, but because we've
increased the concentration of hydroxide anions in solution, the pH will be greater than
seven at the equivalence point. This is called anion hydrolysis and is the reason why the
pH is greater than seven at the equivalence point for a weak acid-strong base titration. Going back to our titration
curve to the equivalence point, if we drop down to the x-axis, we can see that the equivalence
point has been reached after 50 milliliters of
base have been added. So if it takes 50 milliliters of base to reach the equivalence point, it should take half that volume to reach the half equivalence point. Therefore, the half
equivalence point is reached after 25 milliliters
of base has been added. So if we go up here to
our titration curve, we can mark the location
or the approximate location of the half equivalence point. So let me draw a line here
from half equivalence point to the point on our titration curve. Let's go back to our
third particulate diagram which represents the equivalence point and let's add some more sodium
hydroxide into the solution. Because there's no more acid present to react with the sodium hydroxide in our fourth particulate diagram, we can see the sodium cation and the hydroxide anion that we added. At the equivalence point, we also had two sodium cations. So here they are on the
fourth particulate diagram and two acetate anions
which are also present. So the fourth particulate diagram represents excess base
past the equivalence point. As a quick summary of our titration curve, we started out with only weak acid so the pH was relatively low. As we add base, the pH increases slowly, and we get to the half equivalence point where half of the weak acid
that was initially present has been neutralized. Notice how the pH is changing very slowly in this region of the titration curve. As we continue to add more and more base, the pH keeps on increasing. And around the equivalence point, we see a dramatic increase in the pH. Once we go past the equivalence point, we're in the region of excess base and the pH keeps increasing as we add more and more hydroxide anions. During the titration of a
weak acid with a strong base, a buffer solution is actually formed. So let's look at more
detail at the buffer region or the buffer zone on our titration curve. The buffer region occurs around
the half equivalence point. And we can see on our titration curve, there are very small changes in pH as we add hydroxide anions in this region. That's because the weak acid
that's present in solution is neutralizing the added base and protecting against
a dramatic change in pH. We can calculate the pH at
the half equivalence point because we know at the
half equivalence point, half of the initial acid that was present has been neutralized and
turned into the conjugate base. Therefore, at the half equivalence point, the concentration of weak acid is equal to the concentration
of the conjugate base. We can use the
Henderson-Hasselbalch equation to find the pH. If the concentration of weak acid is equal to the concentration
of the conjugate base, then the ratio of their
concentrations is equal to one. And the log of one is equal to zero. Therefore, the pH is
equal to the pKa value of the weak acid at the half equivalence point. So if we wanted to find the pKa value of a weak acid from our titration curve, we would simply find the
half equivalence point and go over to the y-axis to estimate the pKa value. Because at this point,
the pH of the solution is equal to the pKa
value of the weak acid. Next, let's think about
how the titration curve can tell us about the
relative concentrations of weak acid and conjugate base. We know that the pH is
equal to the pKa value at the half equivalence point right here on our titration curve. And we know at the half equivalence point, the concentration of weak acid is equal to the concentration
of conjugate base. Therefore, if we think about a point just to the left of the
half equivalence point, so right here on our titration curve, I'll call this point P, we know that the pH at that point is less than the pKa value of the weak acid. And we know that the initial
point on our titration curve was almost all weak acid. Therefore, since point P is
in between the initial point where we have almost all acid and the half equivalence point where we have equal amounts of
weak acid and conjugate base, point P must have more weak
acid than conjugate base. Therefore, we can say when the pH is less than the pKa value. The concentration of weak acid is greater than the
concentration of conjugate base. We could have also figured this out using the Henderson-Hasselbalch equation. However, it's often simpler just to think about the
shape of the titration curve. Next, let's think about a point just to the right of the
half equivalence point. So I'm gonna call this point, point Q. At point Q, the pH of the solution is greater than the pKa
value of the weak acid. So for trying to determine
the relative concentrations of weak acid and
conjugate base at point Q, remember that point Q is in between the half equivalence point
and the equivalence point, which is right about here
on our titration curve. And at the equivalence point, there's no more weak acid present. All of the weak acid has been neutralized and only the conjugate base, A-, remains. Since point Q is in between
the half equivalence point where there are equal amounts of weak acid and conjugate base, and the equivalence point where
there's only conjugate base, at point Q, there must
be more conjugate base than weak acid. Therefore, we can say when
the pH of the solution is greater than the pKa
value of the weak acid, the concentration of weak acid is less than the concentration
of the conjugate base. Or we could say the
concentration of conjugate base is greater than the
concentration of weak acid. Finally, let's talk
about why a buffer forms on this titration curve. When we first start off, we have almost all weak acid, and therefore we do not have a buffer. However, as base is added to the solution, the weak acid is converted
into its conjugate base. And when there are significant amounts of the weak acid and its conjugate base, we have a buffer solution. So that's right about here
on our titration curve. And we can see the buffer is resisting large changes to pH in this region. However, as we continue to add base, the concentrations of weak
acid and conjugate base change. And eventually, we no longer
have a buffer solution. So the pH changes more
dramatically at this point. So the buffer region or the buffer zone is only right around the
half equivalence point on our titration curve.

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