1
Determination of Ka and Identification of an Unknown
Weak Acid
Purpose: To determine the molar mass and acid
dissociation constant Ka for an unknown weak
acid and thereby identify the acid
Introduction
A Bronsted-Lowry acid is a substance which will donate a proton (H+ ion) in aqueous
solution to another substance. Similarly, a Bronsted-Lowry base is a substance which is capable
of accepting a proton from another substance in aqueous solution. A Bronsted-Lowry acid base
reaction then involves the transfer of a proton from a Bronsted-Lowry acid to a Bronsted-Lowry
base. For example, in the reaction
H2SO3
+ HCO3-

HSO3- + H2CO3
(eq. 1)
H2SO3 behaves as the acid, donating a proton to HCO3- to yield carbonic acid, H2CO3, and
producing the bisulfite ion, HSO3-, as a result of loss of the proton from H2SO3.
H2SO3
+ HCO3-

HSO3- + H2CO3
H+
Monoprotic acids have only one ionizable, or transferable, hydrogen ion (proton).
Examples include acids like hydrochloric acid (HCl), nitric acid (HNO3), and acetic acid
(HC2H3O2). Diprotic acids have two ionizable hydrogen ions per molecule of acid, and include
such acids as sulfuric acid (H2SO4) and oxalic acid (H2C2O4). Some salts are considered acids if
they contain H atoms; compounds like sodium hydrogen sulfate, NaHSO4, are produced from
diprotic acids (like H2SO4) and are thus considered to be half-neutralized. The compound
NaHSO4 is therefore treated as a monoprotic acid since it has a proton that it can potentially give
up to another substance in an acid-base reaction.
Acids are further classified as being either strong acids or weak acids. A strong acid is
one which dissociates completely into its constituent ions in aqueous solution. A weak acid, on
the other hand, is one which only partially ionizes into ions in aqueous solution. The distinction
between strong and weak acids is a very important one to make, and it is very straightforward as
there are only seven strong acids, and their names and formulas should be committed to memory.
Any acids that you encounter that are not one of the strong acids must therefore be considered a
weak acid. The formulas and names, respectively, of the seven strong acids are
2
HCl
HBr
HI
hydrochloric acid
hydrobromic acid
hydroiodic acid
HNO3
HClO4
H2SO4
nitric acid
perchloric acid
sulfuric acid
So weak acids only partially dissociate, or ionize, in water to produce H+ ions and an
anion that is characteristic of the acid. Representing a generic weak acid with the formula HA,
we can write an equation for the dissociation of the weak acid in one of two ways;
or as
HA + H2O  H3O+ + A-
(eq. 2)
HA  H+ + A-
(eq. 3)
Since the second equation above is simpler, this is the way these equations will be written.
Since the equation for the dissociation of a weak acid represents an equilibrium process,
it can be represented with an equilibrium constant Ka, sometimes called the acid dissociation
constant. For acid HA, this can be written as either
Ka =
or as
[H 3O + ][A - ]
[HA]
[H + ][A - ]
Ka =
[HA]
(eq. 4)
(eq. 5)
depending on whether equation 2 or 3 is used to represent the equilibrium reaction.
Because values of Ka are often quite small, chemists sometimes compare acids and their
relative strengths by comparing their pKa values.
pKa = -log Ka
(eq. 6)
A relatively strong acid will have a larger value of Ka, and will thus have a smaller value of pKa.
Conversely, a very weak acid will have a very small Ka and thus a very large value of pKa. For
example, if two acids are compared in terms of their Ka values and pKa’s;
Ka
pKa
acetic acid, HC2H3O2
1.8 x 10-5
4.74
hydrocyanic acid, HCN
6.2 x 10-10
9.21
it becomes more obvious that the stronger acid of the two, acetic acid, has the larger Ka but the
smaller pKa.
In this experiment you will perform an acid-base titration to experimentally determine the
value of the molar mass and Ka for an unknown monoprotic acid, and from that information you
will determine the identity of the unknown acid.
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Titration Curves
A titration is an experimental procedure in which a standardized solution (one whose
concentration is very precisely known), called the titrant, is carefully added to a solution whose
concentration is imprecisely known. In an acid-base reaction like the one you will carry out in
today’s lab, one piece of useful information obtained from the titration is the exact volume of
titrant (base) required to exactly neutralize the acid. The point at which the acid and base have
exactly neutralized one another is called the equivalence point. The pH at the equivalence point
is not necessarily equal to 7, but at that point the number of moles of H+ will equal the number of
moles of OH- added. The equation for the neutralization reaction is
HA(aq) + NaOH(aq)  NaA(aq) + H2O(l)
(eq. 7)
In a previous chemistry course, you probably carried out a titration in which you used an
acid-base indicator, such as phenolphthalein, to give a color change (colorless to pink) signaling
the point at which the acid and base had just neutralized one another. In this experiment, instead
of using an indicator color change to mark what is called the endpoint of the titration, you will
use a pH meter to continuously follow the progress of the neutralization reaction and determine
the equivalence point. As you will see shortly, this will provide even more information than
could be obtained from using only a visual indication of the endpoint.
You will measure the pH of the titration mixture after successive portions of base have
been added during the titration, and will then construct a titration curve by plotting pH (on the
y-axis) versus volume NaOH (on the x-axis). A typical titration curve is shown in Figure 1
below. Notice that as base is added, the pH rises very slowly at first, then begins to rise more
sharply approaching the equivalence point.
Figure 1
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The equivalence point is the point at which the pH rises very rapidly. Since this point is
sometimes difficult to determine precisely from a titration curve (depending on how sharply the
pH rises), we will use a mathematical “trick” to get a very precise value of the equivalence point.
You may remember from a previous math course that the derivative of a curve is just the slope of
the curve at a given point. On your titration curve, the slope reaches a maximum at the
equivalence point, so if we make a first derivative plot of the derivative of pH versus volume
NaOH, the result makes determination of the equivalence point very easy (see Figure 2). This
graph is essentially a plot of the slope of Graph 1 at a given point versus volume of NaOH.
Figure 2
In this case the equivalence point is clearly the top of the peak (maximum slope), which in this
example occurs at 32.00 mL base. The equivalence point can then be use to determine the molar
mass of the acid.
In this experiment, the volume of base needed to get halfway to the equivalence point,
logically called the half-equivalence point, is just as important as the equivalence point. In the
above example (Figure 2) this would be 32.00 mL ÷ 2 = 16.00 mL base. Remember that
Ka =
[H + ][A - ]
[HA]
(eq. 8)
But at the half-equivalence point, exactly half the acid has been converted into its conjugate
base, A-, so at that point, [HA] = [A-].
Ka =
Thus Ka = [H+] and
[H + ][A - ]
[HA]
pH = pKa
(eq. 9)
So by first obtaining the equivalence point, and from that the pH halfway to the equivalence
point, you can easily determine pKa for your unknown weak acid directly from the titration
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curve. This, along with the molar mass of the unknown acid, which can be calculated from the
mass of acid used and the moles of base needed to get to the equivalence point, allows you to
identify the unknown acid from a list of possible unknowns.
Procedure
1.
Obtain a vial with a solid unknown weak acid. The vial will be marked with an unknown
number and the approximate amount of acid you will need to use for each titration trial
such that a reasonable volume of base (i.e. less than a buret full) will be needed for
complete neutralization of the acid sample.
2.
Record the acid unknown number on Data Sheet 1. Then weigh a sample of the acid
using the analytical balance. The mass should be close to that shown on the vial, but must
be known to four decimal places.
3.
Transfer the acid sample to a clean 250 mL beaker. Add about 50 mL deionized water to
dissolve the sample. Don’t worry if the acid doesn’t completely dissolve yet, because as
you begin to titrate and the acid reacts with base, the reaction in equation 7 will be driven
to the right and the acid will dissolve.
4.
Carefully add a small Teflon-coated magnetic stir bar to the beaker, and position the
beaker on the center of a magnetic stirring plate.
SAFETY NOTE!!
Handle solutions of sodium hydroxide (NaOH) with care. Avoid contact with
your skin. If you do spill some on yourself, wash immediately with cold water.
Notify your instructor.
5.
After rinsing a buret thoroughly, first with deionized water, then with several small (~3-5
mL) portions of the standardized NaOH solution (don’t forget to rinse some liquid
through the buret tip, too), finally go ahead and fill the buret with the base solution to just
above the 0.00 mL line. Drain liquid out until the volume reads exactly 0.00 mL. This is
not a normal procedure in titrations, but in this experiment it makes subsequent
calculations much easier if you start at exactly 0.00 mL. Make sure there are no air
bubbles in the buret tip before starting the titration. Make sure all your buret readings are
recorded to the nearest 0.01 mL; that is, to two digits to the right of the decimal point.
6.
Position the buret such that the tip is over the beaker containing the unknown acid
solution and near the side of the beaker, as shown in Figure 3.
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Figure 3
7.
Your instructor will show you correct procedures for operating the pH meter. In addition,
there is a printed sheet of instructions next to each pH meter. Be especially careful not to
bump the tip very hard as the glass bulb on the tip may break. After calibrating the pH
meter to both pH 4.0 and 7.0 buffers, immerse the pH electrode into your acid solution
such that the bulb is covered in liquid. If the bulb is not covered with liquid at this point,
add just enough deionized water to cover the bulb of the electrode. You are now ready to
begin titrating.
8.
Begin by adding 1.0 mL of NaOH solution from the buret. (You don’t have to use exactly
1.00 mL of base, but it should be close to 1.00 mL.) Once the pH meter reading is stable,
record the pH and buret reading on Data Sheet 1. Then add another 1.0 mL of base and
record the pH and buret reading. Initially, the pH will not go up by more than one or two
hundredths (0.01-0.02) of a pH unit after addition of each 1.0 mL of base. Continue in
this fashion, using 1.0 mL aliquots of base until the pH rises by more than about 0.3-0.4
pH units. At that point you MUST decrease the size of the portions of NaOH that are
being added. If not, you risk having insufficient data through the equivalence point, in
which case you will have to start all over again and anger your instructor immensely! If
in doubt, ask your instructor for guidance in adjusting the portions of base when the pH
begins to rise more significantly.
9.
As you continue to titrate, the size of the portions of base added will have to decrease
such that, ideally, as you approach the equivalence point you will be adding fractions of
drops of NaOH through the most rapid pH rise region. To add a fraction of a drop of
titrant (base), turn the buret stopcock just until about a half of a drop forms on the buret
tip, then close the stopcock immediately before the drop falls off. Tip off the buret, i.e.
gently touch the tip of the buret with the half drop, to the inside of the beaker and rinse
down with a small stream of deionized water from a squeeze bottle. Then record the buret
reading and pH as before.
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10.
Continue titrating in this fashion until the pH stops rising as fast, and increase the
portions of base added again to about 0.3-0.5 mL. Once the pH stops rising as fast as it
did through the equivalence point, only a few more data points are needed to complete
the titration curve.
11.
Before cleaning up your apparatus, show your data to your instructor to confirm that the
results are satisfactory. Rinse your buret thoroughly (including the tip) with lots of water
and store it in the buret stand upside down with the stopcock open. All waste from this
experiment can be poured down the drain along with lots of water.
Calculations
1.
Using Microsoft Excel or the Graphical Analysis software in the Science Learning
Center, make a graph of pH on the y-axis versus volume of NaOH, in mL, on the xaxis. Print this graph and its data table, as separate printouts, and include both with your
lab report. Label this graph as Graph 1.
2.
Make a second graph that consists of the derivative of pH, and plot those values on the yaxis to obtain your first derivative plot. Print this graph and its data table as well, as
separate printouts, and label this graph as Graph 2. The equivalence point in the titration
is the maximum on this graph.
3.
Clearly indicate on Graph 1 how you determined the volume of NaOH required to get to
the half-equivalence point. The pH at this point should equal pKa for your unknown
acid. Label pKa on the pH axis of Graph 1.
4.
Use the volume of base at the equivalence point and the molarity of the NaOH solution to
calculate the number of moles of base required to reach the equivalence point.
moles NaOH = molarity NaOH x liters NaOH
(eq. 10)
Record the number of moles of base used on Data Sheet 2.
5.
For titration of a monoprotic acid with a base, the 1:1 stoichiometry suggests that
moles acid = moles base
(eq. 11)
Record the number of moles of acid used on Data Sheet 2.
6.
Since you now know the mass of acid used and the moles of acid needed to neutralize the
base, calculation of the molar mass of the unknown acid is as simple as dividing mass
of acid, in grams, by the number of moles of acid.
g acid
(eq. 12)
= molar mass of acid (in g/mole)
moles acid
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Record the molar mass of your unknown acid on Data Sheet 2.
7.
Now that you know both the molar mass of your unknown acid and its pKa, compare
these values to those in Table 1 to determine the identity of your unknown acid. Record
the name of your unknown acid on Data Sheet 2.
Table 1
acid name
molar mass,
g/mole
Ka
pKa
trans-crotonic
86.09
2.04 x 10-5
4.69
cis-crotonic
86.09
3.89 x 10-5
4.41
sodium hydrogen
tartrate
190.09
4.27 x 10-5
4.37
mandelic
152.15
3.89 x 10-4
3.41
204.23
3.89 x 10-6
5.41
104.06
6.17 x 10-8
7.21
potassium hydrogen
phthalate
sodium hydrogen
sulfite
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Determination of Ka and Identification of an Unknown Weak Acid
Data Sheet 1
Name______________________
Lab Partner________________________
First Determination
Unknown number_______________
Mass of acid used_______________ g
Molarity of NaOH _______________ M
buret reading,
mL
0.00
pH
buret reading,
mL
pH
buret reading,
mL
pH
10
Second Determination (if needed)
Mass of acid used_______________ g
buret reading,
mL
0.00
pH
buret reading,
mL
pH
buret reading,
mL
pH
11
Determination of Ka and Identification of an Unknown Weak Acid
Data Sheet 2
det. 1
det. 2
mass of acid used, g
____________
____________
volume of base at equivalence point, mL
(obtained from Graph 2)
____________
____________
molarity of base, M
____________
____________
moles of base to reach equivalence point
____________
____________
moles of acid neutralized
____________
____________
molar mass of unknown acid, g/mole
____________
____________
half-equivalence point, mL base
____________
____________
pKa of unknown acid
____________
____________
Ka of unknown acid
____________
____________
name of unknown acid
______________________________
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Determination of Ka and Identification of an Unknown Weak Acid
Post-lab Question
1.
Suppose that a student performing this experiment mistakenly calibrated the pH meter
using pH 8 buffer instead of pH 7 buffer. As a result of this error, all of the student’s
pH readings were too low.
a) Would this error have affected the calculated molar mass of the unknown acid?
Briefly explain.
b) Would this error have affected the experimentally determined pKa of the unknown
acid? Briefly explain.
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Determination of Ka and Identification of an Unknown Weak
Acid
Pre-laboratory Assignment
1.
Explain the difference between the terms endpoint and equivalence point.
2.
Explain how to determine pKa for an unknown acid from a titration curve like the one
you will prepare in this experiment.
3.
Calculate pKa for an acid whose Ka is 5.92 x 10-6.
4.
Calculate Ka for an acid whose pKa is 5.96.
5.
A student does a monoprotic weak acid-strong base titration using 0.4774 g. of an
unknown acid, and finds that 26.98 mL of 0.1157 M NaOH are required to reach the
equivalence point.
a)
How many moles of base were needed to reach the equivalence point?
b)
How many moles of acid were neutralized?
c)
Calculate the molar mass of the unknown acid.