Additional Background Information and Prelab Help for the “Generating a
Titration Curve to Determine Ka for an Acid” Experiment
I. Some background and terms.
Titration: (1st Semester Description): A technique in which stoichiometry is used to calculate the amount
of a desired species (analyte) in a sample.
A soluble species that reacts with the analyte “to completion” (i.e., reaction is heavily product favored) is
dissolved to create a solution (the titrant) of known concentration. The titrant is put in a buret, and for
each analyte sample, titrant is added in small amounts until all of the analyte has been reacted. The idea
(in the 1st semester application) is to add just enough of the titrant (no “excess”) to just react with all of the
analyte. When this amount of titrant has been added, the “equivalence point” (ep) of the titration is said to
have been reached. One usually uses some kind of indicator (color change) in order to show when the
equivalence point has been reached (technically, the indicator shows the endpoint, not the true equivalence
point, but the two should be extremely close in a well-executed titration).
The volume of the titrant added to reach the equivalence point is called the equivalence point volume of
that titration (or trial), abbreviated Vep. In a standard titration, the moles of titrant are then calculated
using the molarity of the titrant along with the Vep. Then the ratio of coefficients in the balanced equation
is used to calculate the moles of the analyte species that “reacted” (i.e., stoichiometry). Since at the
equivalence point, all of the analyte is assumed to have reacted, this calculation gives the moles of
analyte originally present. (Note: there is no analyte or titrant present in the solution “at” the equivalence
point! Both have all reacted away [with one another] to make products.)
Titrant: The solution in a buret used for a titration.
Analyte: The species in the solution that is being analyzed via titration; the species in a sample that
reacts with the species in the titrant.
Equivalence Point: The point during the course of the titration at which the moles of titrant added are
just equal to the amount needed to react with all of the analyte. If the reaction stoichiometry is 1:1, the
equivalence point will be reached when the moles of titrant added is equal the initial moles of analyte
present.
Equivalence Point Volume (Vep): The volume of titrant that is (required to be) added in order to reach
the equivalence point.
Half-Equivalence Point: The point during the course of the titration at which the moles of titrant
added are half the amount needed to react with all of the analyte.
Half-Equivalence Point Volume (V½ ep): The volume of titrant that is (required to be) added in
order to reach the half equivalence point. NOTE: The half-equivalence point volume is equal to
half of the equivalence point volume. (i.e.., V½ ep = ½ x Vep), because the more volume of titrant
you add, the more moles you add (moles is proportional to mol/L).
These two are
st
not used in 1
semester type
titrations. But
see below.
Titration (II): (2nd Semester Application): A broader technique in which a titrant is added to an analyte
solution in a controlled and monitored way while also measuring a property of the solution. The
purpose of such a titration is to determine something other than (just) the amount of analyte present
in the sample. In such titrations (and in contrast to a “regular” titration), one typically adds titrant well
past the equivalence point and one plots data to generate what’s called a titration curve showing the
property measured vs. “volume of titrant added”. No indicator is generally used, as the equivalence
point can be determined from the shape of the titration curve that is plotted.
In an acid-base titration, the property measured throughout is the pH of the solution. When one starts
with a solution of a weak acid, and a strong base is the titrant, the Ka of the weak acid can be determined.
A plot of pH vs. “volume of NaOH(aq) added” (the titration curve) is made to aid in this effort.
Prelab Information and help for Titration Curve Experiment
II. Titration curve basics (help with the prelab):
Equivalence point determination: The equivalence point ends up being the point on the curve in which
the slope is greatest. In our context, it is where the change in pH per change in “volume added” is
greatest. It is not where the curve begins to get steep; it is in the middle of the steep “S” part of the
curve. See the drawing on p. 1 of the lab write-up. Technically, it is the place where the curve goes from
“curving upward (concave up)” to “curving downward (concave down)”.
Half-Equivalence point determination: Although it is true that ½ ep is associated with the point on the
curve with the smallest slope, that is not the best way to determine it! The most accurate way to get
V½ ep is to find Vep first and then take half of that value.
To find the pH at either of the above two points, just read off the value on the y-axis (pH) at the respective
“volume added” (i.e., Vep or V½ ep).
To determine the Ka of a weak acid from a titration curve: Recognize that when the titration reaction is
exactly halfway done (i.e., halfway to the equivalence point, or “at” the half equivalence point), you have
reacted away exactly half of the initial moles of HA and as such you will have an equal amount of A- in
solution. In other words, at the half-equivalence point, [HA] = [A-] (both mol amounts equal ½ moles of
HAinitial). This means that at this point only you have not only a buffer, but the “special” buffer situation (I
call this “home” for a buffer) in which [H3O+] = Ka because:
[H 3O  ]eq  K a x
[HA]
 [H3O+] = Ka (if [HA] = [A-])
[A  ]
To see this, just recognize that the equation for the reaction is:
HA + OH  A + H2O (K >> 1)
-
-
-
hopefully you can see that for every mole of HA reacted, you generate one mole of A . This means that when half of the HA
has reacted, you will have the exact same amount of A now present in the solution. For example, if you start with 0.2 moles of
HA and half (0.1 mol) reacts away, you will generate 0.1 mol of A and be left with 0.2 – 0.1 = 0.1 mol of HA remaining.
BOTTOM LINE: To find Ka from a titration curve, just identify the pH at the half equivalence point and
then calculate [H3O+] from that pH. That value of [H3O+] equals the Ka of the acid!
To determine which acid is weaker: 1) Compare Ka values (lower = weaker) OR 2) Look to see which
curve is higher at the half equivalence point. “Higher pH” means “lower [H3O+] and thus “lower Ka”.
To determine which sample has more moles of acid in it: CAREFUL: “More moles of acid” is not the
same as “lower pH”!!! Why not? (I can hear some of you asking that…) Because remember that the pH
of a weak acid solution is not just determined by [HA], it depends on Ka as well (because most of the
“acid” in a weak acid solution is not ionized!). The way to get at “moles of acid” is to assess “how much
NaOH was needed to react away all of the HA?” In other words, which took more NaOH to reach the
equivalence point?
NOTE: As part of your post-lab, you will do more than just determine the Ka for your acid. You will use
your determined Ka value, along with theory, to calculate predicted values at different points in
your titration. Then you will compare those to what was experimentally determined, to see how
well theory and experiment agree (they should be pretty close!). These kinds of calculations are
not required to be understood for the prelab and so will not be discussed here.