- [Instructor] Hydrochloric acid is an example
of a strong acid and sodium hydroxide
is an example of a strong base.
Let's say we are titrating
an unknown concentration of hydrochloric acid
with a known concentration of sodium hydroxide.
Let's say it's .20 molar.
Because we know the concentration of sodium hydroxide,
we call that the titrant.
And because we don't know
the concentration of hydrochloric acid,
we call that the analyte.
And when our strong acid, hydrochloric acid,
reacts with our strong base, sodium hydroxide,
the products are an aqueous solution
of sodium chloride and water.
As a quick review of how to write the overall
or the complete ionic equation
for a strong acid-strong base reaction,
remember that sodium hydroxide being a strong base
dissociates completely in aqueous solution
to form sodium cations and hydroxide anions.
Hydrochloric acid being a strong acid
will ionize completely in aqueous solution
to form H+ ions and chloride anions.
Sodium chloride is a soluble salt,
so an aqueous solution.
We would have sodium cations and chloride anions.
And of course, we would also have water.
When writing the net ionic equation,
we cross out these spectator ions.
So since we have sodium cations in left and on the right,
we can cross out the sodium cations
and the same with the chloride anions.
So both of those are the spectator ions.
What we're left with is our net ionic equation.
So one way to write the net ionic equation
for a strong acid-strong base reaction
is hydroxide anions plus H+ cations form water.
And our goal for the strong acids-strong based titration
is to find the concentration of hydrochloric acid
using a titration curve.
Let's say we do our titration
and we come up with this as a titration curve.
For titration curves,
you put the pH on the y-axis and the titrant on the x-axis.
So in this case,
we're adding base to our solution of hydrochloric acid.
And before we use our titration curve
to find the concentration of hydrochloric acid,
let's go through the titration curve
and look at some particulate diagrams.
And as we look at particulate diagrams,
keep in mind they're just to help us understand
what's going on in the actual solution,
so they're are just a representation.
And we're also gonna leave out water molecules
for clarity purposes.
So let's think about this point on our titration curve.
So that's zero milliliters of base added,
meaning we're starting only with hydrochloric acid.
So there are two H+ particles,
and there are two chloride anion particles.
Next, we add in some sodium hydroxide.
So the sodium cation is this purple sphere right here,
and the hydroxide anion is over here as well.
So we add in some sodium hydroxide
to our solution of hydrochloric acid
and for the hydroxide anion that's neutralized
by one of the H+ ions that's present.
So the OH- and the H+ react to form H2O.
And since we're leaving H2O out of our particulate diagrams,
we don't see it in this second particulate diagram.
What we do see in this second particulate diagram
are the chloride anions that were initially present.
So here they are.
And the other H+ ion that was initially present
and the added sodium cation.
And since there's still an H+ cation left in solution,
we haven't neutralized all of the acid
that was initially present.
So next, we add some more sodium hydroxide.
So here we're adding a sodium cation,
and we're also gonna add this hydroxide anion
to our solution.
The added hydroxide anion will be neutralized
by the H+ ion that's already present.
They will form water.
And since we're leaving water
out of the particulate diagrams,
we don't see water in this third particulate diagram.
What we do see in our third particulate diagram here
are the two chloride anions that have always been with us
in the titration.
We had one sodium cation already present,
and then we added one more sodium cation.
So this third particulate diagram represents
the equivalence point of our titration.
All of the acid that we initially had present
has been neutralized by the added base
and we're left with an aqueous solution of sodium chloride.
So there are only sodium cations
and chloride anions in solution.
At 25 degrees Celsius,
the pH of water is equal to seven.
And since neither the sodium cation
nor the chloride anion
will react with water to change the pH,
the pH at the equivalence point
of a strong acid-strong base titration is seven.
And we can find the equivalence point on our titration curve
by going over to a pH of about seven here.
And if we draw a little dash line,
wherever that dash line hits our titration curve,
represents the equivalence point.
So the first particulate diagram
was before any base was added.
So that's this point on our titration curve.
The third particulate diagram is meant to represent
the equivalence point,
so this point on our titration curve.
And our second particulate diagram
was when we haven't neutralized
all of the acid that's present.
So that's in between those two points
on the titration curve.
Also notice how steep
the graph is around the equivalence point of this titration.
Therefore, adding very small amounts
of base around the equivalence point
causes large changes in the pH of the solution.
Let's go back to our particulate diagram
at the equivalence point,
and let's add some more sodium hydroxide.
So we add one more sodium cation
and one more hydroxide anion.
This time, since there's no more acid
to neutralize the added hydroxide anion,
in our fourth particulate diagram,
here's our hydroxide anion.
And one of these sodium cations
is the one that we just added.
And we still have the chloride anions and the sodium cations
that were present at the equivalence point.
So this fourth particulate diagram represents the titration
after the equivalence point when we're adding excess base.
And we can see on our titration curve,
as we continue to add excess base, the pH keeps increasing.
Now that we've gone through the particulate diagrams
for our strong acid-strong base titration,
let's get back to our original problem
which was to find the initial concentration
of hydrochloric acid.
And we can do that by figuring out
how many milliliters of base were added
to get to the equivalence point.
So if we just drop down here on our titration curve,
we can see that after 50 milliliters of base
have been added,
the equivalence point has been reached.
Therefore, it took 50 milliliters
of our .20 molar solution of sodium hydroxide
to completely neutralize
the hydrochloric acid that was originally present.
And if we know the initial volume
of the hydrochloric acid solution,
let's say it was 100 milliliters.
We can calculate the concentration
using the MV is equal to MV equation.
So for our equation,
let's think about acid being on the left side.
So we don't know the concentration, the molarities,
we make that x.
And for the volume of the acid,
it's 100 milliliters.
So we plugged that into our equation.
On the right side,
let's think about this being the base.
So we know the molarity of the base,
it's .20 molar.
And we also know the volume of base
that was necessary to reach the equivalence point
which is 50 milliliters.
Solving for x, we find that x is equal to .10 molar.
So that was the initial concentration
of our hydrochloric acid solution.
And notice on our titration curve,
remember we started with only hydrochloric acid.
So we start with a very low pH
if we're titrating a strong acid with a strong base.
As we add more and more of the strong base,
the pH increases.
We've just looked at the titration curve
of a strong acid with a strong base.
Let's compare that titration curve to this one
which is the titration of a strong base with a strong acid.
Since we're starting with a strong base,
notice how the initial pH is very high.
And since we're adding acid notice down here on the x-axis,
it now says milliliters of acid added.
As acid is added,
we can see the pH dropping slowly.
And as we approach the equivalence point,
we see a large drop in pH with small additions of acid.
However, the pH at the equivalence point
is still equal to seven.
So if we find a pH of seven on the y-axis
and go over to our titration curve,
this point represents the equivalence point.
And we can drop down to the x-axis
and we would see it took 20 milliliters of acid
to neutralize the base that was initially present.
Finally, once we go past the equivalence point,
we can see as we add more and more acid,
the pH keeps getting lower.
So this titration curve of a strong base with a strong acid
is essentially the reverse
of the first titration curve that we saw
which was the titration of a strong acid with a strong base.