Measurement of Acid Neutralization Capacity in Acid Lakes
Remediation
Objectives
The focus of this experiment was to develop a sodium bicarbonate dosage schedule maintaining the
pH of Adirondack lakes between 6.5 and 8.2. The development of a practical, successful schedule
would allow Arm & Hammer and the Environmental Protection Agency (EPA) to join forces in
maintaining healthy pH levels in the Adirondack lakes despite new legislation resulting in more
acidic rain.
In order to develop a sodium bicarbonate dosage schedule, a model of an acidified-lake response to
remediation was developed that simulated an Adirondack lake subject to acid rain and dosed with
sodium bicarbonate to neutralize the acid. Based on this simulation, as well as ideal models of pH
response to acid and carbonate species inputs, a model of acid lake remediation response was
developed. This model will help determine an optimal schedule for adding sodium bicarbonate. Arm
& Hammer and the EPA can then implement this schedule, protecting the Adirondack lakes from
acid rain, which can greatly reduce the biodiversity in these precious lakes.
Procedures
In order to evaluate the feasibility of using sodium bicarbonate to maintain a healthy pH within the
Adirondack lakes, a model was developed. This model consisted of a 4 L “lake” and an influent of
“acid rain.” Using a peristaltic pump, an acidic solution of known pH was pumped steadily into the
lake. The lake was set up so that its volume remained constant, meaning that the inflow of acid was
equal to the outflow of lake water. A magnetic stir bar was placed in the lake to create a completely
mixed flow reactor, avoiding variance of pH due to concentration gradients across the volume of the
lake due to incomplete mixing of the sodium bicarbonate.
A measured quantity of sodium bicarbonate was added to and mixed with the lake, establishing an
initial acid neutralizing capacity (ANC). A solution’s acid neutralizing capacity is the extent of its
ability to react with strong acids. In addition to sodium bicarbonate, a small amount of bromocresol
green indicator solution was added to the lake in order to provide a visual representation of its pH
and a qualitative observation of the completeness of the mixing. The pH of the lake was measured
using a pH probe.
The design parameter of primary interest was ANC, since it is conservative while pH is not. However,
pH may be used to calculate the solution’s ANC, and, as a result, pH measurements were taken
continuously throughout the experiment. In order to measure ANC, Gran plot analysis was used. An
initial sample of the lake was taken for this method of ANC determination; thereafter, samples were
taken every 5 minutes for 20 minutes. At the end of the 20-minute run time, the actual flow of the
peristaltic pump was measured with a graduated cylinder and a stopwatch, and the actual volume of
the lake was measured with a mass balance. See Table 1 for a complete list of these experiment
parameters.
Table 1: Relevent experiment parametrs
NaHCO3 (g)
0.63
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[NaHCO3]
Flowrate (mL/min)
Mass with lake (g)
Mass without lake (g)
Vol of lake (L)
θ (min)
0.0019
296.296
4552.6
605
3.9476
13.32
Gran plot analysis involves titrating each sample past its equivalence point, the point at which the
titrant volume added equals the equivalent volume V e . V e is defined as
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where V s is the volume of the sample, N s is the normality of the sample (i.e., ANC), and N t is the
normality of the titrant. A Gran plot determines V e , from which ANC can be calculated.
The titrant used in this experiment was 0.05 N HCl. During titration, the sample was continuously
stirred with a magnetic stir bar to ensure complete mixing. The initial pH of each sample was taken;
Gran analysis was not performed on samples of pH < 4.5 because in these cases the hydrogen ion
concentration is the dominant term in determining ANC. Thus, ANC could be simply calculated from
the pH.
As each titration began, relatively large titration increments were used. The pH of the solution after
each titration was recorded after it stabilized. The titration increment was decreased as the pH of the
solution decreased. More specifically, for a sample of approximately 50 mL, the titration increment
was decreased to 0.1 mL in order to determine the volume of equivalency as accurately as possible.
Each sample was titrated beyond its point of equivalence, and the measured pH data was used by the
software to create a Gran plot for each titration. This plot was then used to calculate the equivalent
volume of titrant, from which the ANC was calculated.
As Figure 1 demonstrates, the Gran function F1 , which is defined as F1 
V s V t
H   , varies only
Vs
slightly for low volumes of titrant. However, when the equivalence volume is reached, the pH of the
solution spikes dramatically due to an increase in the number of free hydrogen ions. When F is
graphed as a function of titrant volume added, the region of hydrogen ion concentration increase is
linear. By finding the x-intercept of a linear regression through this linear region, one is able to find
the equivalent volume of titrant.
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4.00E-04
3.50E-04
First Gran Function (M)
3.00E-04
2.50E-04
2.00E-04
y = 0.0005x - 0.0024
1.50E-04
R2 = 0.999
1.00E-04
5.00E-05
0.00E+00
-5.00E-05
0
1
2
3
4
5
6
Volume of Titrant (mL)
Figure 1: Gran plot for sodium carbonate
Results and Discussion
In order to create a schedule for sodium bicarbonate dosage, a model of the Adirondack lake system
was developed with a simulation. The simulation involved two inputs: an initial dose of sodium
bicarbonate, and a continuous input of acid of a known pH. The simulation was kept at a constant
volume and stirred to ensure complete mixing. To accurately model the Adirondack lake system,
where the simulation lies between two ideal extremes, volatile and non-volatile systems, must be
determined.
One ideal extreme is a non-volatile system, also known as a closed or conservative system. In a closed
system, aqueous carbon dioxide is not allowed to exchange and equilibrate with atmospheric carbon
dioxide. In this case, ANC can be found as a function of pH and C T (described below).
The other theoretical model is of the volatile system, also known as an open system. In an open
system, aqueous carbon dioxide is allowed to exchange and equilibrate with atmospheric carbon
dioxide. In this case, ANC is a function of pH and the partial pressure of carbon dioxide in the
atmosphere.
In both models, ANC is a conserved quantity. ANC, in this application, is formally defined by
ANC  HCO3   2CO32   OH    H  
Page 3 of 10
Thus, it is a function of the concentration of components in the carbonate pH buffering system and
pH. The carbonate system consists of aqueous carbon dioxide, carbonic acid, bicarbonate, and
carbonate. When acid rain falls on a lake, bicarbonate and carbonate react with the acid to form
aqueous carbon dioxide and carbonic acid. The carbonate system can be represented by C T , the sum
of the molar concentrations of each component of the system, and  0 ,  1 ,  2 , the proportions of C T
which are aqueous carbon dioxide and carbonic acid, bicarbonate, and carbonate, respectively. ANC
is thus a function of C T . C T , in turn, is a function of pH and the partial pressure of atmospheric
carbon dioxide in an open system.
Once the correct model has been determined, one may calculate when more sodium bicarbonate
must be added to the lake and how much is necessary in order to maintain the proper lake pH. The
optimal dosage schedule would minimize dose and frequency while maintaining a lake pH between
6.5 and 8.2. Thus, the desired effect of each dose is to raise the initial pH to its highest acceptable
level, 8.2, and the next dose would occur when the pH is at its lowest acceptable level, 6.5. Since
ANC is the design parameter (due to its conservative nature, in contrast to pH), the desired initial and
final ANC levels must be determined from these desired pHs. Since the relationship between ANC
and pH is dependent on the extent to which atmospheric carbon dioxide affects C T , that extent must
be characterized.
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In this laboratory investigation, collected pH data allowed for the calculation of Ct, as is displayed in
Figure 2. This figure clearly shows that the lake system is best modeled as a closed system
(“Conservative CT I”) rather than as an open system (“Equilibrium CT I”). Despite being open to the
atmosphere, the small, simulated lake was not in equilibrium with the atmosphere. However, this
result may not hold for actual lakes, because they may have longer hydraulic residence times,
allowing them to equilibrate further with the atmosphere. As a result, the assumption of nonvolatility should be verified with an actual lake by measuring pH, calculating C T , and comparing
measured C T with theoretical values of C T under volatile and non-volatile conditions. This
verification would be one step in assessment and monitoring after the dosage schedule has been
implemented. Some additional factors which should be taken into consideration include wind
strength, phytoplankton growth, water temperature, and inflow of water from various other sources1.
Conservative CT I
Measured CT I
Equilibrium CT I
2.5E-03
2.0E-03
CT (M)
1.5E-03
1.0E-03
5.0E-04
0.0E+00
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
t/θ
Figure 2: Comparison of actual CT with theoretical CTs
Note that for the simulated lake, measured C T was actually higher than expected C T in a
conservative system. Similarly, measured ANC was higher than expected ANC for a conservative
system, as can be seen in Figure 3. Consequently, caution must be used in determining dosage, so as to
prevent an initial pH that is too high. Thus, a conservative estimate of the dose required will be made
using the assumption of a conservative system. However, the deviation of measured C T and ANC
from the theoretical expectation of the conservative model may be due in part to pH probe error. The
1
PGSF Research Programme: “Marine Chemistry of Carbon Dioxide”. Accessed at
http://neon.otago.ac.nz/chemistry/research/mfc/progs/co2progs.htm on 21 September 2006.
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pH probe may have been poorly calibrated and may have been failing due to age and wear. In fact,
one pH probe is particular had to be discarded because it was not working properly; others may have
been subject to the same problems, if not to the same severity.
Conservative ANC
Measured ANC
2.5E-03
2.0E-03
ANC (eq/L)
1.5E-03
1.0E-03
5.0E-04
0.0E+00
-5.0E-04
-1.0E-03
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
t/θ
Figure 3: Comparison of actual ANC with theoretical ANC
It was seen in this lab that the lowest acceptable pH, 6.5, was seen at an ANC of approximately
1.08 meq/L. Unfortunately, the highest acceptable pH, 8.2, was not seen at all in this lab, and
performing another simulation that reaches this pH is recommended. After finding these initial and
final ANC values, respectively, the period between doses can be calculated by solving for t in the
following equation:

ANC out  ANC in 1  e

t

t

  ANC 0 e 

where θ is the hydraulic residence time. Notice that ANC in will have to be estimated from the
acidity of typical rainfall in the area.
Note also that there may be some pre-existing ANC (either negative or positive) in the lake that must
be taken into account when calculating the dose necessary to achieve the desired initial ANC. This
pre-existing ANC may be a result of the extent of acidification (which decreases ANC), presence of
soluble, calcareous minerals (which increase ANC), and significant amounts of organic matter (which
increases ANC).
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One way in which ANC of the carbonate system exhibits itself is through the buffering capacity of
sodium bicarbonate. Observe in Figure 4 that the slope of the curve denoting pH is lower when the
pH value is near the pKa2 value of sodium bicarbonate. This difference is a result of sodium
bicarbonate’s ability to act as a buffer, neutralizing free H+ ions. For buffers in general, at pH values
near the buffer’s pKa value(s) the addition of more H+ ions has a significantly smaller effect on the
solution’s pH than it does at pH values further away from the pKa. This phenomenon is most clearly
illustrated in Figure 5, which shows data collected from a sample titration of sodium carbonate with
0.05 N HCl.
9
8
7
pH
6
5
4
3
2
1
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
t/θ
Figure 4: Change in pH over time expressed in units of hydraulic residence
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12
CO3-2 + H+ ↔ HCO310
8
pH
HCO3- + H+ ↔ H2CO3
6
Ve = 4.4957 mL
4
2
0
0
1
2
3
4
5
6
Titrant Volume (mL)
Figure 5: Titration curve of sodium carbonate
The rate of change in pH near the periods when pH ~ pKa (pKa1 = 10.3, pKa2 = 6.3) is very slow in
comparison to the rate of change at other pH values. This difference shows that sodium bicarbonate
is neutralizing the acid being added to the system.
The addition of sodium bicarbonate to the Adirondack lakes may be complicated by several factors.
Although sodium bicarbonate is relatively soluble (7.8g/100g water), its dissolution results in a
solution with a higher density than that of plain lake water. As a result, regions where the sodium
bicarbonate has dissolved are denser than regions that have not come into contact with the solute.
These regions of higher density may sink to the bottom of the lake. Since the lake is not a completely
mixed system, and complete lake turnover takes a relatively long time, the sodium bicarbonate
solution may remain on the bottom of the lake. As a result, it will not be effective in neutralizing
acid rain entering the lake from the surface.
In order to ensure that all of the sodium bicarbonate dissolves in the lake, the solute should be spread
over as large a surface area as possible. Releasing the solute as a pulse input would result in areas of
differing concentration, leading to uneven acid neutralization. To aid dissolution, the sodium
bicarbonate should be ground as finely as possible. Several methods of transporting the sodium
bicarbonate into the lake exist as viable options. One possible method is through the use of a crop
duster. The sodium bicarbonate would be “dusted” along the surface of the lake. Since it is relatively
soluble, not much stirring would be necessary for it to dissolve.
One possible problem with the use of sodium bicarbonate as a remediation agent is its potential to
harm organisms in the lake and on its surrounding shores. Since crop dusting is not completely
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accurate in where it deposits its material, it is likely that a relatively large amount of sodium
bicarbonate may end up on the shores of the lake where it could be consumed by organisms.
However, the oral rat LD50 of sodium bicarbonate is 4220 mg/kg, and no toxic effects in organisms
have been discovered thus far. This potential problem should be investigated more thoroughly to
ensure that the lake’s ecosystem is not disrupted by the attempted remediation.
In this simulation, there was a continuous inflow of acid at a constant pH. Outside of laboratory
conditions, rain clouds can come from all different directions, and the pollution in the area of their
formation is variable. As a result, the pH of the rain water is not constant, and neither is the inflow
of rainwater into the lake. These observations may lead to a decrease in the amount of sodium
bicarbonate necessary for lake remediation.
Monitoring of lake conditions after the addition of the sodium bicarbonate will be essential to a
successful remediation. Any problems with the remediation process should be identified and
ameliorated as quickly as possible to ensure that the project is successful. This will require a
relatively large amount of data collection. The most important value that monitors should be
concerned with is the lake’s ANC. However, this may not be measured directly. Instead, pH values
should be taken from lake samples in order to calculate the ANC. Since the lake is not completely
mixed, these samples should be taken from a variety points spread across the lake’s surface as well as
at varying depths. This will ensure that sodium bicarbonate is not pooling at the bottom of the lake
while the top is left with an extremely low ANC. Analysis of the ANC at varying points across the
lake’s volume will allow for identification of areas that require more mixing. Additionally, pH
measurements will give observers an idea of whether or not the remediation effort has been
successful. Other measurements that should be taken periodically include temperature
measurements. This information would allow for correct density calculations, as well as a better idea
as to whether or not the rate of carbon dioxide exchange between the lake and the atmosphere is
significant enough to consider in the remediation process. Finally, observers should record the
amount of biodiversity within the lake. As the remediation process continues, biodiversity should
rise to its pre-acid rain levels. A decrease in the amount of biodiversity within the lake would alert
observers to problems with the remediation program.
Conclusions
The remediation of Adirondack lakes is a complicated issue, and the feasibility of using sodium
bicarbonate as a potential neutralization agent is dependent on the observations of carefully planned
simulations. In the simulation performed during this laboratory investigation, it was revealed that
sodium bicarbonate is an effective means of neutralizing acid in a lake system, and that the lake
system is best modeled as a conservative system. However, several problems with this method of
remediation must be solved before it can be implemented. More advanced modeling must be
performed in order to better simulate actual lake conditions such as incomplete mixing, and varying
levels carbon dioxide exchange between the lake and the atmosphere, temperature differences, and
aquatic life.
Although sodium bicarbonate is effective as a neutralizing agent, the amount necessary for
remediation is still unclear since several factors were ignored during this investigation. Determinants
such as the presence of dissolved carbonates in the lake before remediation begins, the initial acidity
of the lake as a result of years of acid rainfall, the variance of rain water pH with respect to its cloud’s
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origin of formation, and the contributions of tributaries should be more thoroughly investigated
before any action is taken. Once more data has been collected and more simulations have been
analyzed, a “test run” of remediation should be performed on one of the smallest and most stable
lakes available. Ideally, this lake should be relatively isolated so that any large mistakes involving the
remediation do not have adverse effects on conditions in the surrounding ecosystem.
Suggestions
Future simulations might include several realities that this simulation did not. These include a
variable input of acid, rather than a constant and continuous input; setting a more realistic initial
ANC than that of distilled water; and increasing the length of the simulation by increasing hydraulic
residence time, and checking for effects of atmospheric carbon dioxide.
In the future, the data acquisition software for the Gran plot analysis may be improved by providing
more thorough documentation. Determining when to click which button was ambiguous, until
extensive testing of the software’s workings in a few trials was conducted.
Sorry about the lack of documentation. You can find information on the pH software at
http://ceeserver.cee.cornell.edu/mw24/Software/ph%20meter.htm. I have now added a help button
link to the pH meter software.
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