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TITRON
Automated Titration
Group R7
Pedram Afshar
Jeffrey Berman
Jess LeMay
BE 210
Spring 1998
ABSTRACT
The purpose of this project was to design and build an automated titration system capable
of constructing a titration curve and calculating pKa points for a wide range of compounds.
TITRON, the automated titration system, was constructed in the Bioengineering Laboratory
using three available components: LabVIEW 4.1, a syringe pump, and a digital pH meter. The
syringe pump and digital pH meter were independently tested to determine their functionality
and error. The syringe pump was found to be able to provide a constant flow of 45.33  0.28
L/second. The pH meter is able to report data through a serial port to LabVIEW once a second.
At this data transfer rate and the syringe pump’s flow rate, the pH of the titration solution
changed an average of 0.025 per second, producing a smooth and continuous titration curve.
During six trial titrations of amino acids, the syringe pump provided a constant flow of NaOH
while the pH meter exported the pH at 1 Hz and LabVIEW collected the data. A separate
LabVIEW virtual instrument was then used to analyze the data from the titration curve and find
the inflection points corresponding to the pKa points of Alanine and Valine. The measured pKa
points were consistently less than 3% different from accepted values. (3)
BACKGROUND
The titration is a standard laboratory procedure that can be time-intensive and very
susceptible to human error. The typical set-up includes two burets and a beaker in which the
solution is mixed. The user must carefully add acid or base from each buret in very small
increments in order to perform an accurate titration of the strong acid, strong base, or amino acid.
The procedure is tedious and involves dozens of human measurements that incur great random
error. The procedure for performing a titration is the same regardless of the compounds used.
For this reason, it would be advantageous to automate this mundane task to save time and effort
while increasing the accuracy of the experiment.
A titration curve is a plot of pH versus the amount of titrant added. Characteristics of the
substances being titrated can be determined with this titration curve. The inflection points of the
curve are either equivalence points or pKa points. The pKa points are defined as the pH at which
there are equal amounts of protonated and unprotonated functional groups (4). At a pH below
the pKa value, a group will be mainly protonated.
It is possible to reduce the human factor in the titration process through the use of
TITRON, an automated titration system capable of plotting the pH of the solution versus the
amount of titrant added and determining the pKa’s of the compound from the characteristics of
the plot. The three components of TITRON are LabVIEW, the syringe pump, and the pH meter.
The titration machines currently on the market can cost as much as $7995.00 (1). These
machines perform titrations accurately, but do not have the flexibility to be altered for different
future applications. A LabVIEW system is considerably less expensive and can be easily
customized to complete any titration application. The LabVIEW Full Development System (part
#776670-03) is listed at $1,995 and the accompanying DAQ costs on the order of $700 to
$1,200, providing significant savings over other titration systems (2). In addition to the cost
savings, LabVIEW has the flexibility to output pKa’s and equivalence points, or even perform
the titration at different rates with the use of sophistocated pump equipment. This flexibility is
found in LabVIEW’s easy to use “G” graphical programming language (5). LabVIEW can be
used to automate the repetitive procedure of a titration while providing a significant cost savings
and providing similar accuracy.
DESIGN
Design Constraints
There were many important details that needed to be taken into account when designing
the set up of this experiment. First, it is important that the syringe pump pumps the liquid at a
rate that does not vary over time. In order to make sure of this, a calibration curve of liquid
delivered versus time was created. This was accomplished by using the syringe to pump water
into a graduated cylinder for a specific amount of time and then massing water added. Since the
density of water is 1.0 gram/milliliter, this mass was equal to the volume of water collected in
milliliters. This method was chosen over recording the volume of water because it decreases the
error incurred from reading the amount collected from the graduated cylinder. By repeating this
procedure over several time spans, the longest being greater than the time needed to perform the
titration, we were able to create the calibration curve. The results of this calibration can be found
in Graph 1 under Results.
The tubing used to supply the titration beaker with base had a diameter of 1/32”, the
smallest available. A tube with as small a diameter as possible is preferred, because it allows
liquid to be added at a slow rate while minimizing the error. The small tube opening also
minimizes diffusion out of the tube while the syringe is not pumping. The length of the tube was
approximately 30 cm, which was the length necessary to reach from the syringe to the titration
beaker. The volume of the syringe was chosen based on two factors. The first was that it needed
to be large enough to contain the amount of base needed for the entire titration. Since we were
titrating at 45.33 L/sec and we wanted to collect 500 points at 1 point/sec, we needed a syringe
with a volume of at least 23 mL. The other factor was the availability of appropriate syringes in
the Bioengineering Laboratory. Since there were only 3 mL and 50 mL syringes available, the
50 mL syringe was the obvious choice.
The pH meter was connected to the computer through a serial port. LabVIEW was
instructed to gather data from this port. Since the meter was connected in this manner, there was
no discrepancy in the data taken from the pH meter. LabVIEW receives the same three decimal
floating-point numbers seen on the pH meter’s display.
The setup of the equipment was also crucial to the accuracy of the experiment. During
operation of TITRON, the pH probe is always under the surface of the liquid in the beaker. In
addition, the solution is stirred with a magnetic stirrer at the greatest rate possible without
splashing. The tubing was placed under the surface on the side of the beaker opposite the pH
probe. This was advantageous for two reasons. First, pure base or acid did not flow over the pH
meter probe resulting in an inaccurate reading. Second, there was continuous flow of base into
the titration beaker.
When determining which rate of the pump to use, we had to take into consideration the
calibration of the pH meter. Before we used the pH meter, it was necessary to calibrate it.
However, if it is run for a long period of time, the calibration can drift and it is necessary to
recalibrate the meter. By determining a rate at which the calibration could be completed without
the meter drifting significantly, we could have run the pump at a higher rate. However, high
flow rates cause rapid changes in pH, particularly near the equivalence point. During rapid pH
changes, the pH meter may not be able to respond adequately to the change in pH due to its
response time. Because of this, incorrect pH values may be recorded. In addition, high flow
rates affect the titration curve because of the data export rate of the pH meter. The meter sends
one data point per second to the PC. Therefore, the rate must be slow enough so that over the
period of rapid pH rise, the system could respond fast enough to gather an adequate amount of
points. A high point density is needed to accurately determine the equivalence point (the
inflection point in the rise of the S-shaped titration curve). It was determined that at a rate of
45.33 L/second, corresponding to 7 on the syringe pump dial, the titration time would be
approximately 8.5 minutes and the pH rise would be an average of about 0.025 per second. By
checking the calibration of the meter before and after the time it took to run the experiment at our
determined rate, it was verified that the calibration of the meter does not drift over that amount of
time. With this rate, the titration is complete before the pH meter needs to be recalibrated. Also,
the pH change between data points in the pKa and equivalence point regions is low enough for
the pH meter to create a smooth, continuous titration curve.
Data Acquisition
The Data Collection Loop synchronizes the acquisition of the pH and the volume of
titrant added. The loop cycles a user-defined number of times. The input for Number of points
to be taken is set on the front panel (Appendix A, Panel A1). Point “A” on the Data Acquisition
Diagram (Appendix A, Diagram A.1) is the node that receives a string of data from the serial
port every second. This data includes the pH outputted by the pH meter, as well as other
characters from the pH meter that are not used. In area “B”, the string is parsed to retrieve just
the pH value and convert it to a floating-point number with three decimal places. This number is
displayed on the front panel under Output: pH. This pH reading changes every second and can
be observed during the titration to confirm that the experiment is proceeding correctly. The user
can also view the Number of points taken on the front panel count up during the titration. At
area “C” the titration rate is set by the user. A knob on the front panel, Syringe pump dial
setting, corresponds to the dial on the syringe pump which controls the rate. This rate is
multiplied by the iteration number and shifted by the intercept at “D”. The result is the total
number of microliters of titrant added at each iteration of the Data Collection Loop. At “E” the
pH values and volume of titrant data are bundled into a two-variable array and plotted, creating
the titration curve. The pH values and volume of titrant arrays are also separately sent to saving
routines at “F”. At Save to file: Volume and Save to file: pH on the front panel, the user can
enter file names to which the volume data and the pH data will be saved. After completion of the
titration, these files are created for use in the Data Analysis VI.
Data Analysis
After the data collection phase of the titration, the user is left with two files containing
the pH data array and the volume array. The files are of type “text” and are simply a column of
numbers. Each file has the same number of data points. The data analysis portion of TITRON
can be used at any time after the data collection as long as the files are preserved. The data
analysis performs a user-assisted polynomial fit of the titration curve and finds inflection points
by determining the zeros of the second derivative of the polynomial fit.
At region “A” on the Data Analysis Diagram (Appendix B, Diagram B.1), the two files
are opened and their data is converted into arrays of floating point numbers. On the front panel
(Appendix B, Diagram B.1), the user defines the file names from which to retrieve the data. The
titration curve plots the pH array versus the volume array, creating the same titration curve seen
in the Data Collection VI. The user can observe the titration curve and decide in which regions
the pKa points can be found. On the front panel, the user enters the starting volume and ending
volume of the region surrounding the pKa point. Best results occur when the user selects a range
of approximately 5000 microliters. The user-defined region is used to excise the selected portion
of the titration curve. At “B” on the diagram, array operations are used in conjunction with the
user-defined range to create two new array subsets of the entire titration curve. This selected
portion is plotted in “Zoomed in” on the front panel. At “C” on the diagram, LabVIEW’s
polynomial regression function is used to create a third order polynomial approximation of the
excised region of the titration curve. This polynomial approximation is plotted on the front panel
as Original Polynomial (Appendix B, Diagram B.2). A third order polynomial was chosen
because a third order polynomial can have a maximum of one inflection point. The region
chosen by the user contains one pKa point and thus one inflection point.
The signal processing capabilities of the LabVIEW professional version are now utilized
to construct the first derivative of this polynomial at “D”. The second derivative is then
computed and scaled by a factor of 1,000,000 at “E.” The scaling is necessary for better
visualization of the second derivative plot on the front panel. The scaling does not affect the
location of the roots of the second derivative nor the pKa values calculated.
As the second derivative data is a discrete function, LabVIEW can only be used to find
where the function comes closest to zero. At “F” the absolute value of the second derivative is
taken. The minimum of the function corresponds to where the function is closest to zero. The
calculations at “G” uses the index of the root to determine the pH value of that index on the
original titration curve and outputs the pKa value.
The above procedure for data analysis can be repeated multiple times in order to find
multiple pKa and equivalence points.
RESULTS
Graph 1: Calibration of the Syringe
Graph 1: This graph shows the data collected during the calibration of the syringe pump. The purpose of this
calibration was to make sure that the pump ran at a constant rate and did not change over time.
Table1: Second pKa and Equivalence Point for Valine
pKa
Equivalence Point pH
Trial 1
9.43
5.86
Trial 2
9.50
5.81
Trial 3
9.44
5.82
Mean
9.46  0.04
5.83  0.03
Difference from accepted value (3)
1.66%
2.35%
Table 1: This table shows the LabVIEW data analysis of the amino acid valine.
Table 2: Second pKa and Equivalence Point for Alanine
Trial 1
PKa
Equivalence Point pH
9.57
5.88
Trial 2
9.51
5.81
Trial 3
9.55
5.85
Mean
9.54  0.03
5.85  0.035
Difference from accepted value (3):
1.55%
2.82%
Table 2: This table shows the LabVIEW data analysis of the amino acid alanine.
DISCUSSION/CONCLUSIONS
Systematic error in TITRON occurs in two types: errors accumulated within each
component and errors introduced between components. However, TITRON provided
consistently accurate measurements of pKa and equivalence points of valine and alanine. The
precision of the measurements varied by less than 0.5% for both amino acids. The mean
measurements of the pKa and equivalence points were on average 2.1% different from the
accepted values (3). This is significantly improved from the current laboratory techniques,
which result in a difference of anywhere from 6% to 18% different from the accepted values.
The r-square value (R2 = 1) of the syringe pump calibration curve indicates negligible
variation in the flow rate while the pump is run at least as long as the duration of the titration.
Thus, little error was introduced into the system from within the syringe pump component.
However, we cannot discount any error that may have been introduced as the tubing was moved
to the titration beaker. Since our instrumentation prevented direct communication between the
syringe pump and the LabVIEW software, we could not be certain of the exact time at which the
base began being added, although we attempted to start collecting data and adding base
simultaneously. A human error was introduced due to the fact that we calculated the amount of
base added by using the flow rate. The initial volume was set to zero at the time that LabVIEW
started taking data, and was increased incrementally by the flow rate. The imprecise volume
does not affect our calculation of pKa, however, because pKa is the pH at an inflection point in a
graph of pH against amount of base added. Inaccuracies in the amount of base added only
translate the graph in the x direction without changing the y values. However, this error does
reduce the accuracy of the amount of base added, and it adds a degree of human intervention in
an automated process. Unfortunately, this error cannot be rectified by starting with the tube in
the beaker because of the chance that the base would diffuse before the pump was turned on.
One possible method to avoid this would be to have a closed tube attached to a more
sophisticated pump that communicates with the computer. In this case, when LabVIEW was
started, the tube would open and the pump would switch on. This would greatly decrease the
error incurred by the human method discussed above.
The error in the pH meter was 0.0005, according to the specifications of the meter. No
new errors were introduced in communicating with the computer since we used a serial port
connection. However, additional errors were introduced in calibration, as the standards may have
been contaminated. To reduce this error, it is necessary to start with clean standards.
A significant source of error was the analysis technique. We originally tried using
LabVIEW’s differentiation and root-finder tools to determine the roots of the second derivative.
However, the points on the original titration curve did not create an absolutely smooth function.
Therefore, there were many small inflections and we could not differentiate the curve directly
without getting an excessive amount of second derivative roots.
In an attempt to remedy this, we chose to use LabVIEW’s built-in curve fitting,
differentiation, and data analysis techniques to find the inflection points. The analysis VI
approximated the original curve in sections with a polynomial fit, as described under Design:
Data Analysis. Inherent in this design is a certain degree of error because we are using an
approximation to the data that was collected.
We speculate that if we had titrated at a slower rate, while keeping within the necessary
constraints, we could have generated a curve smooth enough to use in the analysis without using
curve-fitting techniques. Reducing the molarity of the NaOH in the titrant will also decrease the
error in the original titration curve by decreasing the average rise in pH per second. Although
these techniques would increase the time of a titration, they would produce smoother, and thus
more accurate, titration curves.
Another source of error comes from dissolved CO2 in the titration beaker, which lowers
the pH of the solution. Covering the solution beaker with cellophane will decrease this error.
TITRON could be improved in each of its components. A more sophisticated syringe
that communicates with the computer and a pH meter with a higher response rate would greatly
decrease the already small error in the data analysis. In the future TITRON can be effectively
used to construct titration curves, find equivalence points and pKa’s, and find amount of base or
acid used to achieve them.
APPENDIX A: Data Acquisition
Panel A.1: Front Panel for Data Acquisition
Panel A.1: This panel shows the user interface for the data acquisition process.
Diagram A.1: Data Acquisition Diagram
Diagram A.1: This diagram shows the internal design of the virtual instrument used for data acquisition.
APPENDIX B: Data Analysis
Panel B.1: Data Analysis First Front Panel
Panel B.1: This panel shows the first half of the user interface for the data analysis process. (Note small
irregularities in the zoomed-in portion of the titration curve. These will be smoothed out by the polynomial fit.)
Panel B.2: Data Analysis Second Front Panel
Panel B.2: This panel shows the second half of the user interface for the data analysis process.
Diagram B.1: Data Analysis Diagram
Diagram B.1: This diagram shows the internal design of the virtual instrument used for data collection.
REFERENCES
1. http://www.analyticon.com/ttt1lit.html Analyticon’s homepage providing a description and price of
their automated titration system.
2. 1998 Price List. National Instruments, Austin, Texas. Effective December 1, 1997.
3. Bioengineering 210 Laboratory Manual, Spring 1998. Experiment 4, page 13.
4. Chang, Raymond. Chemistry, 4th edition. McGraw-Hill, Inc.: New York 1991.
5. National Instruments, LabVIEW Tutorial for Windows. Austin. National Instruments
Corporation, 1994.