- [Instructor] Ammonia is an example of a weak base
and hydrochloric acid is an example of a strong acid.
And if we're doing a weak base-strong acid titration,
that means that ammonia is the analyte,
the substance we're analyzing,
and we're titrating ammonia with hydrochloric acid
and therefore hydrochloric acid is the titrant.
And when ammonia reacts with hydrochloric acid,
the product is an aqueous solution of ammonium chloride.
For our complete or overall ionic equation,
since ammonia is a weak base,
we show it as NH3 in our complete ionic equation.
However, since hydrochloric acid is a strong acid
that ionizes 100%,
we show it as breaking up into its ion,
so H+ and CL-.
Ammonium chloride is a soluble salt,
therefore we would show ammonium chloride
in aqueous solution as ammonium cations
and chloride anions.
To write the net ionic equation,
we leave out spectator ions.
And since we have chloride anions on the left side
and on the right side,
chloride anions are the spectator ions.
And leaving those out, we get the net ionic equation,
which is ammonia NH3 plus H+ goes to NH4+.
So this is one way to write to the net ionic equation
for this weak base-strong acid titration.
Next, let's look at the titration curve
for our weak base-strong acid titration.
pH is on the y-axis and milliliters of acid is on the x-axis
because we're adding our strong acid to our aqueous solution
of our weak base.
Looking at the first point on our titration curve,
the pH is relatively basic.
So this is before any strong acid has been added.
The reason why the pH is basic is because we have
an aqueous solution of our weak base, ammonia,
which reacts with water to produce ammonium cations
and hydroxide anions.
And it's these hydroxide anions that cause the pH
to be relatively high.
However, the equilibrium favors the reactants
for this reaction.
So we have mostly ammonia and very little ammonium
at this point in the titration curve.
Next, we think about adding some acid
to our aqueous solution of ammonia.
And from our net ionic equation,
when ammonia reacts with H+,
that forms the ammonium cation, NH4+.
Looking at the titration curve,
as we add more and more acid,
the pH starts to decrease.
However, in this range, there's a slow decrease in the pH.
As more acid is added,
more ammonia is turned into the ammonium cation.
Eventually, we reach a point
where all of the initial ammonia has been neutralized
by the addition of the acid.
This point is called the equivalence point.
And the way to find the equivalence point
on our titration curve
is to first look for this sharp decrease in the pH.
And then we can draw a straight line here.
And approximately halfway down that straight line
is a good estimate of the equivalence point
for this titration.
To find the pH of the solution at the equivalence point,
we simply go over to where the equivalence point is
on the y-axis.
And so for this pH,
we can see the pH at the equivalence point
is less than seven.
So let me go ahead and write that down here.
The pH is less than seven
for a weak base-strong acid titration.
The reason why the pH is less than seven
at the equivalence point
is because all the ammonia that we started with
has been completely neutralized
and turned into the ammonium cation, NH4+.
The ammonium cation is a weak acid
and reacts with water to form hydronium ions, H3O+,
and ammonia, an aqueous solution.
At 25 degrees Celsius, water has a pH of seven.
However, since the ammonium cation is a weak acid
and we're increasing the concentration of hydronium ions
in solution, that decreases the pH,
therefore the pH is less than seven
at the equivalence point.
In addition to ammonium ions,
there are also chloride anions in solution.
However, chloride anions do not react with water
and therefore do not affect the pH.
Going back to the equivalence point on our titration curve,
if we dropped down here to the x-axis,
we can see the equivalence point occurs after 50 milliliters
of acid has been added.
Therefore, if it took 50 milliliters of acid
to neutralize all of the ammonia that was initially present,
it would take half that volume or 25 milliliters of acid
to neutralize half of the ammonia.
So if we go back up here and we draw a dashed line
to our titration curve,
this point on our titration curve represents
the half equivalence point.
So this point represents the half equivalence point
on our titration curve.
And since we've neutralized half of the ammonia
that was initially present,
that means there are equal concentrations of ammonia
and the ammonium cation at this point.
Let's go back to our equivalence points
where all the ammonia that we started with
has been neutralized.
Therefore, if we add some more acid to the solution,
there's no more ammonia for it to react with.
And therefore we see the pH drop.
So this portion of the titration curve
is the region of excess acid.
Let's go back to the half equivalence point
on our titration curve.
Remember at that point,
the concentration of ammonium cation
is equal to the concentration of ammonia.
The ammonium cation and ammonia
are a conjugate acid-base pair.
And when there are significant amounts
of a weak conjugate acid-base pair,
there's a buffer solution.
Therefore, at the half equivalence point,
we have a buffer solution,
and we can calculate the pH at that point
by using the Henderson-Hasselbalch equation.
So pH is equal to the pKa of the weak acid,
plus the log of the concentration of the conjugate base,
divided by the concentration of the weak acid.
For this example, the base is ammonia, NH3,
and the conjugate acid is the ammonium cation. NH4+.
Therefore, this pKa value
in the Henderson-Hasselbalch equation
is referring to the pKa value of ammonium.
And because the concentrations of ammonium and ammonia
are equal at the half equivalence point,
the ratio of their concentrations is equal to one
and the log of one is equal to zero.
Therefore, at the half equivalence point,
the pH is equal to the pKa value of the weak acid.
So if we wanted to find the pKa value
for the ammonium cation,
we would find the half equivalence point
and we'd draw our dotted line over to
where the intersects on our y-axis
and whatever pH that is,
that's the pKa value of ammonium.
So in this case, it looks to be a little bit over nine
as a good estimate for the pKa value
of the ammonium cation.
Next, let's think about how our titration curve can tell us
about the relative concentrations
of our weak conjugate acid-base pair.
We know that at the half equivalence points
where the pH is equal to the pKa value,
the concentration of ammonium cations
is equal to the concentration of ammonia.
So let's think about a point just to the left
of our half equivalence point,
which I'm gonna call point P.
At point P, the pH is greater
than the pKa value.
And we know the initial point on our titration curve
was almost all weak base, almost all NH3.
Because point P is in between the initial point
where there was almost all NH3,
and the half equivalence point where there was equal amounts
of NH3 and NH4+,
at point P, there must be more NH3
than NH4+.
Therefore, when the pH of the solution is greater
than the pKa value,
we know the concentration of ammonia is greater than
the concentration of the ammonium cation.
Or you could say the concentration of ammonium
is less than the concentration of ammonia.
We could have also figured this out using
the Henderson-Hasselbalch equation.
However, it's often easier just to think about
the shape of the titration curve
and where the point in question is
in relation to important points.
For example, in this case,
the initial point and the half equivalence point.
Next, let's think about a point just to the right
of the half equivalence point.
And I'm gonna call this point Q.
At point Q, the pH of the solution is less than the pKa.
Point Q is in between the half equivalence point
and the equivalence point,
which is approximately here on the titration curve.
Remember at the equivalence point,
all the ammonia that we started with
has been converted into ammonium, NH4+.
And because point Q is in between the half equivalence point
where the amount of NH3 is equal to the amount of NH4+,
and the equivalence point where all the NH3
has been converted into NH4+,
all of the initial NH3.
That means that at Q, there must be more NH4+ than NH3.
Therefore, when the pH is less than the pKa value,
we can say the concentration of ammonium, NH4+,
is greater than the concentration of ammonia, NH3.
The half equivalence point, point P and point Q
are all a part of the buffer region on the titration curve.
Remember that buffers resist large changes in pH,
and that's why we see a slow decrease in pH
as acid is added at this part of the titration curve.
At the very beginning of the titration,
we had almost all ammonia and therefore we did not have
a buffer solution.
However, as acid was added and the ammonia was converted
into the ammonium cation, NH4+,
when significant amounts of both are present,
we do have a buffer solution.
And that represents the buffer region
on our titration curve, so in here.
However, as more and more acid is added,
we can see a sharp change in pH start
to occur right about here,
so we're no longer in the buffer region
as we approach the equivalence point.
So when we think about the titration curve
of a weak base-strong acid titration,
and we think about the half equivalence point
where the pH is equal to the pKa value of the weak acid,
it's important to remember that there's a buffer region
or a buffer zone around that half equivalence point.