The pH Titration of a Weak Monoprotic Acid
A pH titration is an important tool in
analytical chemistry since it allows the
experimenter to better understand and the
titration process and provides important
information regarding the nature of the acid
and base reacted. Furthermore, a pH
titration provides a more accurate
end-point or “equivalence point” than can
be obtained using only an indicator. Once
the "equivalent point" is known, pH
titrations can be used to determine the pKa
of the acid, a value related to the strength
of the acid. pH titrations also allow the
experimenter to better determine the best
choice of acid-base indicator used in
conventional titrations. The adjacent
graph demonstrates a typical pH titration
and some of its important features.
Titration curve
Typical ph titration of a weak monoprotic acid vs strong base
The most important data point on the graph is the equivalence point. At the equivalence point,
the number of moles of aqueous hydrogen ion, H+(aq),which have been neutralized by exactly
the same number of moles of aqueous hydroxide ion, OH-. The equivalence point may be used
to determine the stoichiometry of the reaction and even the molar mass of the acid. The graph
has its maximum slope at the equivalence point. That is, the addition of a small volume of
titrant produces the greatest change in the pH of the solution. This concept is important since it
is the basis of the graphical analysis of the data.
Another important point on a pH titration graph is at one-half the equivalence point. At
one-half the equivalence point, exactly one-half of the acid in the solution has been neutralized
giving a solution with an equal concentration of both the acid and its conjugate base. Since the
concentration is the same, then the pH of this solution equals the pKa of the acid as predicted
by the Henderson-Hasselbach equation:
[ Base  ]
[ Acid ]
That is, since the concentration of both the acid and its conjugate base are equal, the ratio of
the log[conjugate base] to log [conjugate acid]is 1, and the log of 1 equals 0. Therefore, the pH
of the solution coincides with the pKa of the acid at one-half the equivalence point. The
purpose of this experiment is to perform a pH titration for both a strong acid, HCl(aq), and a
weak acid, acetic acid(aq),and determine the pKa of the latter.
pH  pK a  log
The determination of the Equivalence Point and pKa Graphically
A good approximation of the equivalence point of a pH titration may be determined graphically
using the following method. While not always perfect, this method allows the experimenter
to determine the equivalence point and pKa of the acid quickly.
Step 1. Draw the best straight line
through both linear regions of the graph
where buffering occurs. The best line
represents the general direction the data,
includes as many points as possible, and has
as many points above the line as below it.
Extend this line beyond the data points so
that it may be used in the next step,
determining the equivalence point. Note
the adjacent drawing.
would be 5.3.
Step 2. Draw a line through the portion of
the graph with the greatest slope.
Measure the length of this line between the
two lines drawn in Step 1, and find its
center. The center of this line is
approximately the equivalence point.
Drop a line perpendicular to the x-axis at
this point to determine the volume of
titrant added to reach the equivalence
point. Once this value is known, the
concentration of a monoprotic acid may be
determined from the relationship:
Step 1
VacidMacid=VbaseMbase
Step 2
Step 3. Once the equivalence
point has been determined, the
pKa of the acid can be obtained. At
a volume of one-half the
equivalence point volume, the pH
of the solution equals the pKa of
the acid. In the adjacent
example, the equivalence point
volume is 0.72 mL, giving a value
of 0.36ml at one-half the
equivalence point. The pH of the
solution when 0.36 ml of base has
been added to the solution is 5.3.
Consequently, the pKa of this acid
Draw the best smooth line through as many points as possible extending
the line in the general trend of the titration.
Draw the line through the vertical region of the graph. Bisect this line by
measuring the distance between the two original lines. The equivalence
point is the center point on this line.
Step 3
At the volume of one-half the equivalence point volume, the pH = pKa
Determining the Equivalence Point of a titration by Use of the First Derivative Plot
If the simple pH titration graph studied
earlier does not provide the equivalence
point with certainty, then a first
derivative plot of the data in the region
of the equivalence point may be utilized.
The equivalence point of a titration
occurs precisely at the inflection point
that separates the concave portion of
the graph from the convex portion of the
graph. The slope reaches a maximum
at this point. Bv plotting the change in
the slope
(Δ pH/Δ Volume) vs the
average volume of titrant, the
equivalence point can be readily
determined.
ΔpH/Δvolume vs. average volume
First derivative plot for determining the equivalence point of a titration.
To prepare the first derivative graph, calculate the slope(ΔpH/ ΔVolume)and average volume of
titrant within +0.15 ml of the predicted equivalence point. Note the sample calculations in the
table below.
Volume of NaOH
pH
34.68 mL
6.49
34.78 mL
35.08 mL
 pH
 Volume
Average Volume
6.53  6.49
 0.4
34.78  34.68
34.68  34.78
 34.73
2
8.40  6.53
 6.23
35.08  34.78
35.08  34.78
 34.93
2
6.53
8.40
After all of the calculations are made, the slope (the change in the pH over the change in the
volume of NaOH) is then plotted against the average volume of titrant (NaOH) for each point
calculated. The equivalence point for the titration would occur where the change in the pH
over the change in the volume is a maximum. Note the first derivative plot above.
Determine the Equivalence Point of a Titration by Use of the Second Derivative Plot
If the first derivative graph does not give a
satisfactory value for the equivalence point,
a second derivative of the graph maybe
prepared. In the second derivative graph,
the change in the slope from the first
derivative data table is plotted against the
change in the average volume. The
equivalence point occurs where the change
in the slope is zero. Observe the adjacent
second derivative plot.
Average
Volume
34.73
 pH
 Volume
( pH)
( Volume)
Δ2pH/Δ2volume vs. average volume
Change in slope from first derivative platted against change in the
average volume
0.4
6.23  0.4
 29.15
34.93  34.73
34.93
Average of the
Average
Volume of
NaOH reacted
34.93  34.73
 34.83
2
6.23
Determining the pKa of a Weak Acid Mathematically
Another method which may be used to determine the pKa of a weak acid is to calculate the pH
from a variation in the Henderson-Hasselbach equation:
 Vdp 

pK a  pH dp  log
V V 
dp 
 ep
Where V ep is the volume of the titrant
needed to arrive at the equivalence point
and Vdp represents the total volume of the
titrant added at the data point. Choose
several data points in the linear portion of
the pH titration near one-half the
equivalence point, calculate the pKa at each
point, and average these values.
Volume
pH
pKa
4.61
4.50
4.74
2.15
4.00
4.75
5.00
4.75
4.75
3.30
4.20
4.74
6.93
5.00
4.82
The data in the table above is taken from the pH titration studied earlier which has an
equivalence point at 10.0 mL. Using the first data point in the table above, the pKa calculates
to be 4.75 with an average value of 4.76.
2.15


pK a  4.00  log
  4.75
 10.00  2.15 
Materials:
2-1.0ml syringes
1.0 M sodium hydroxide
Vinegar
50-mnl beaker
ring stand and clamp
phenolphthalein in
dropper bottle
Chemistry multi sensor
connection cable
computer
pH probe
micro stir bar tip
Procedure:
1. Prepare the pH sensor and Spark System for data collection.
a. Connect the chem. multi sensor to the computer.
b. Connect the pH probe to the multi sensor.
c. Start the Spark software on the computer.
2. Put the SPARK into manual sampling mode with manually entered data:
Do one of the following to open the page-build screen.
pH sensor
Micro stir bar
a. If a SPARKlab is open, touch the New Page button.
b. If the Home screen is open, touch BUILD. Result: The page-build screen opens.
Page-build screen: 1. Measurements list. 2. Display buttons. 3. Preview section.
c. Create an empty user-entered data set:
i. In the measurements list under User-entered Number Data or under
User-entered Text Data, touch Create Data Set.
Note: You may need to scroll the list to see these options.
Result: The Define the Data Set screen opens.
ii. Touch the Measurement Name box, type a name that describes the data
or text that you plan to enter manually, and touch OK.
iii. Optionally, if you are creating a numerical data set, touch the Unit Name
box, type the units of the manually entered data, and touch OK.
iv. Touch OK to return to the page-build screen. Result: The user-entered
data set that you created now appears in the measurements list on the
page-build screen.
d. In the measurements list, touch the data set that you just created to select it.
Result: The selected data set is highlighted.
e. In the measurements list, touch pH to select it. Data from the ph probe will be
recorded alongside your user-entered data. Result: There are now two
highlighted items in the measurements list: the user-entered data set and a
sensor measurement.
f. Touch the Table button.
g. Touch OK. Result: A table prepared to display the manually entered data and
sensor
data appears.
h. In the measurements list, touch the data set that you just created to select it.
Result: The selected data set is highlighted.
i. In the measurements list, touch pH to select it. Data from the ph probe will be
recorded alongside your user-entered data. Result: There are now two
highlighted items in the measurements list: the user-entered data set and a
sensor measurement.
j. Touch the graph button.
k. Touch OK. Result: A graph prepared to display the manually entered data and
sensor
data appears.
l.
Touch the Sampling Options button.
Result: The Sampling Option screen
opens.
m. Touch Manual.
n. Touch OK to close the Sampling Options screen. Task result: The SPARK is now
ready to record manually sampled data with manually entered data.
3. If necessary, attach tip extenders to both hypodermic syringes. It is important to rinse and
prepare the syringes as directed by your instructor. Be certain that you fill both the acid
syringe and the base syringe with the correct solution. Note that both syringes are
color-coded. Record the initial syringe readings for both syringes to the nearest 0.01 ml
in your data table. Note that the graduations are upside down. Subtract the volume read
from 1 .00 ml to obtain the volume of base added to the beaker. If the volume reads 0.96
ml, that would mean that you have added 0.04 ml of base.
Thoroughly rinse the pH electrode with distilled water and secure it to a clamp on a ring
stand.
4. Add 0.60-0.70 ml of vinegar into a clean, 50 ml beaker followed by twenty milliliters of
distilled water from your wash bottle and a drop of the phenolphthalein indicator. Record
the volume of vinegar added to the beaker to the nearest 0.01 ml. Insert the pH probe into
the solution and secure it to a clamp. The glass bulb of the electrode should be totally
immersed in the solution. Thoroughly mix the mixture in the beaker by swirling or stirring
with a magnetic stirrer.
5. Begin the titration:
a. Place the beaker containing the diluted acetic acid on a magnetic stirrer and add
a stir bar.
b. Set up a ring stand and clamp to hold the pH Sensor in place. Remove the
water bottle from the end of the pH sensor, and attach the micro stir bar.
c. Position the pH sensor in the beaker so that the tip of the probe is completely
immersed.
d. Gently stir the acetic acid solution.
6. Start recording data by pressing the green Start button.
7. When the pH stabilizes, press the Keep button
8. Since you have set up the SPARK to accept manually entered data along with the pH data,
complete these sub-steps to enter you measurements for volume:
a. If the table tool palette is not already open, touch the Table Tools button.
b. If it is not already highlighted in the tool palette, touch the Select button.
Result: The Select button turns orange.
c. Touch the table cell where you would like to enter data.
Result: A yellow box appears around the cell.
d. Touch the Data Entry button.
Result: The on-screen keyboard opens.
e. Type a number or text and touch OK.
Result: The data that you entered appears in the selected table cell.
f. When the entire set has been recorded, touch the Stop
Result: The data set closes.
button.
Note: If you accidentally stop the data collection early (by touching the Stop button instead of
the Keep button), you will need to start over again from the beginning. If desired, delete the
incomplete data set before starting again.
9. Add one or two drops of base. When the pH stabilizes, press the Keep button
to save
the pH value. Read the volume of base in the syringe. Enter the volume of base added to the
beaker in the cell under volume next to the new pH value.
10. Continue to add base in one or two drop increments, recording the pH and volume of NaOH
until the pH starts to increase more rapidly. Continue the experiment by adding the NaOH
in one drop increments.
11. Continue the titration past the equivalence point until the pH curve flattens.
12. Press STOP
to stop collecting data.
13. Record the final volume of titrant used to the nearest 0.05 mL.
14. Press graph tools
and the scale-to-fit button.
15. Record the pH and volume at the equivalence point:
a. Center the steepest part of the curve on the page.
b. Touch graph tools
and then the Slope tool
.
c. Find the point with the highest slope (m) and record that pH and volume.
d. Press the slope and graph tools buttons again to remove.
16. Record the pH and volume at the half-equivalence point:
a. Touch graph tools, scale the graph to fit again
and then touch Slope tool
.
b. Find the point where slope is at a minimum and record that pH and volume.
c. Press the slope and graph tools buttons again to remove.
17. Remove the beaker, pour the solution down the drain and rinse the beaker with water.
Rinse the pH sensor with deionized water.
18. Refill your syringe and prepare a fresh solution of acid.
19. Press the new page button on the SPARK system.
20. Build a new page with a graph of pH vs. volume. Once the page appears, remove the data
from trial 1 by touching the 1 box in the top right and un-checking trial 1.
21. Repeat the procedure above to obtain a second and third trial, time permitting.
22. When finished collecting data, plug in your USB drive ( or save to your z drive) and press
Sharing.
23. Press EXPORT DATA, touch inside the filename box, rename the file, and touch OK.
touch EXPORT. When the export is complete, touch OK.
BE PATIENT WHEN EXPORTING – DON’T KEEP PRESSING BUTTONS!
Then
Questions and Calculations to address in your discussion:
1. What is the equivalence point of each of your titrations? What is the pH of each solution at
2.
3.
4.
5.
6.
7.
8.
9.
the equivalence point?
Using the concentration of the NaOH determined previously, what is the concentration of
the acetic acid solution?
Using the graphing method, determine the pKa of acetic acid.
What is the Ka of acetic acid according to the pKa determined from the graph?
Using the mathematical method, determine the pKa of acetic acid.
Calculate the pH of acetic acid for four-five volumes of NaOH near one-half of the
equivalence point as described in the introduction to this experiment. Find the average
pKa of these values.
Why are you able to use phenolphthalein as an indicator to find the equivalence point or
end point of a titration instead of a pH meter? Explain your answer using the data obtained
in this experiment.
Compare your experimentally determined pKa value with the accepted value for acetic acid
(Ka = 1.8 x 10-5 for acetic acid). Why is it better to compare pKa than Ka values?
Using the data in your exported table, create a graph for the plot of the first derivative vs.
average volume, and the second derivative vs. average volume. What is the equivalence
point and pKa of the acid based on these graphs?