EXPERIMENT I
Acids, Bases, Acidity, Alkalinity, and the Carbonate System
Purpose
To study the interaction of acids and bases and to examine methods for determining
equivalence points of these reactions. To become familiar with strong acid/weak base
titrations and the concepts of alkalinity and buffer intensity. The concentration of
components of the carbonate system will be calculated from alkalinity measurements.
References
1. Weber, W. J., Jr., Stumm, W., J. Amer. Water Works Association, 55, 1963, p. 1560.
2. Standard Methods, 17th ed., American Public Health Association, 1989.
3. Methods for Chemical Analysis of Water and Wastes, Environmental Protection
Agency, 1979.
4. Butler, J. N., Ionic Equilibrium: A Mathematical Approach, Addison Wesley, 1964.
5. Sawyer, C. N., McCarty, P. L., and Parkin, G.F. Chemistry for Environmental
Engineering, 5th ed., McGraw Hill, 2003.
6. Stumm, W., Morgan, J. J., Aquatic Chemistry, 3rd ed., Wiley-Interscience, 1996.
Theory
Acids and Bases
The study of acid-base titrations involves consideration of the reactions which occur
between acids and bases. For this purpose, it is convenient to distinguish between
strong and weak acids and bases. The term "strong" usually refers to a substance
which is completely dissociated into its ions in solution while "weak" generally refers to
a substance which is partially dissociated. Of course, various degrees of "strong" and
"weak" exist. The reaction of a strong base and a strong acid involves the combination
*
of H+ and OH- to form H2O and it is governed by the ion product of water. The reaction
H+ + OH- = H2O and the pH is dictated by the concentration of excess acid or base
reactants. Thus the equivalence point of such a titration is pH = 7.0.
In the titration of a weak acid, HA, with a strong base, two sources of protons must be
considered in order to compute the pH of the system. First, there are protons
originating from the dissociation of the acid
* **
H+ is shorthand notation for the hydrated proton, H3O+.
Ka 
HA = H+ + A-
H A 


HA 
and secondly there are protons from the dissociation of water
H2O = H+ + OH-
Kw = [H+][OH-]
The second reaction can be neglected for values of pH outside the range 6 to 8. The
titration of HA with strong base, OH-, can be represented
HA + OH- = H2O + AThe pH of the system can be calculated from stoichiometric and equilibrium
relationships:
1. Initial pH. If the total concentration of HA added is CHA we can write
Ka = [H+][A-]/[HA] = [H+]2/(CHA - [H+]), since the stoichiometry shows [H+] = [A-] as
long as the contribution of H+ from H2O is negligible. Solving for [H+], we obtain
Ka (CHA [H ] )
[H+] =
If
CHA >> [H+] then
[H+] =
K aCHA
2. Prior to the equivalence point. The base reacts stoichiometrically with HA to yield A-.
Also by stoichiometry [HA] = CHA - [A-]. The sample is a buffer, a mixture of HA and A -.
Its pH is computed from the Henderson - Hasselbach equation:
pH = pKa + log
[A - ]
[HA]
3. At the equivalence point. At this point, the moles of OH- added exactly equals the
moles of the weak acid used to prepare the sample. This solution is one of the
conjugate weak base A-. It's pH is computed from its hydrolysis reaction
A- + H2O = HA + OH-
[OH-] =
K b (CA  [OH ]) 
Kb =
[HA ][ OH ] K w

[A  ]
Ka
Kw
(CA  [OH ])
Ka
which is derived in an analogous fashion to that for the weak acid. Note that the pH is
not 7 and that it is concentration dependent.
4. Past the equivalence point. The OH- added will stoichiometrically react with HA. The
pH can be computed from the OH- in excess of HA.
To determine the equivalence point of an acid-base titration, either a pH meter or an
acid-base indicator can be used. The pH meter is a null-point potentiometer that
measures the potential difference between an indicator electrode and a reference
electrode and produces a readout in pH. The two electrodes commonly used for pH
measurement are the glass electrode (indicator electrode) which develops a potential
across the glass membrane as a function of the activity of H+, and the calomel
electrode (reference electrode) which has a fixed potential independent of H + activity.
The pH meter is calibrated with buffer solutions of a known pH prior to pH
measurement. A titration curve for an acid-base titration may be obtained by plotting
measured pH vs volume of acid (or base) added.
Acid-base indicators are usually organic acids containing one or more ionizable
protons. The protonated and deprotonated forms of these molecules differ in color.
Since the acid or base form of indicators is dependent on the H + activity of the medium,
the color change of the indicator molecule can be used to "indicate" a specific H +
activity. The behavior of an indicator in solution can be represented as follows:
HIn = H+ + Inwhere HIn represents the neutral molecule and In- its anion. In acid solutions, or when
pH is less than the pKa of the indicator, the indicator is largely in the HIn forms;
similarly, for pH values greater than the pKa of this reaction, the indicator is primarily in
the In- form. Since different indicators have different pKa values, it is possible to select
an indicator which changes color near the equivalence point of a reaction of interest.
Care must be taken when adding indicators to samples for acid or base titrations since
excessive amounts can add significant error.
Alkalinity & Carbonate
The total alkalinity of a solution is operationally defined as its acid neutralizing capacity
or the amount of acid required to lower the pH to about 4.3. The alkalinity of most
natural waters is principally determined by the carbonate system. For these waters
alkalinity is defined mathematically by a charge balance involving species that are
reactive with protons, viz:
Total Alkalinity = [HCO3-] + 2[CO32-] + [OH-] - [H+] (units are mol/L H+)
Since most natural fresh waters have pH values between 6 and 9 and since the major
carbonic acid species in this range is HCO3-, the alkalinity has, under these conditions,
been equated with bicarbonate concentration. Other capacity factors have been
defined relative to natural waters in terms of quantities of strong acid and strong base
required to change the pH of a water to:
a) the pH of a CT-molar solution of CO2 (pH of CO2)
b) the pH of a CT-molar solution of HCO3- (pH of HCO3-)
c) the pH of a CT-molar solution of CO32- (pH of CO32-)
The term "CT-molar" is the total molar concentration of carbonate species in the sample
and a CT-molar solution of CO32- is prepared by adding CT moles of a carbonate salt to
1L of distilled water. The pH of CT-molar CO2 and CO32- solutions vary with CT,
whereas the pH of a CT-molar solution of HCO3- is 8.3 when CT is greater than 3 x 10-4
M. It should be noted that for most natural water, pH of CO 2 ~ 4.3 and pH of CO32- ~
10.5.
The different forms of alkalinity can be defined rigorously as follows, based on the
quantity of acid or base required to reach the defined pH values. (Note that alternative
definitions of alkalinity and acidity are based on approximations of the initial species
concentrations.)
caustic alkalinity: the amount of strong acid (moles/L) required to lower the pH of a
sample to pH of CO32carbonate alkalinity: the amount of strong acid (moles/L) required to lower the pH of a
sample to pH of HCO3- (8.3).
total alkalinity: the amount of strong acid (moles/L) required to lower the pH of a
sample to pH of CO2
Similarly, the different forms of acidity are defined as follows:
mineral acidity: the amount of strong base (moles/L) required to raise the pH of a
sample to pH of CO2
CO2 acidity: the amount of strong base (moles/L) required to raise the pH of a sample
to pH of HCO3- (8.3).
total acidity: the amount of strong base (moles/L) required to raise the pH of a sample
to pH of CO32-
Like total alkalinity, each of the acidity terms is defined precisely by a charge balance
involving species that are reactive with protons:
Total alkalinity
=
2[CO32-] + [HCO3-] + [OH-] - [H+]
Carbonate alkalinity =
[CO32-] + [OH-] - [H+] - [H2CO3*]
Caustic alkalinity
=
[OH-] - [H+] - [HCO3-] - 2[H2CO3*]
Total acidity
=
2[H2CO3*] + [HCO3-] + [H+] - [OH-]
Carbon dioxide acy =
[H2CO3*] + [H+] - [CO32-] - [OH-]
Mineral acidity
[H+] - [HCO3-] - 2[CO32-] - [OH-]
=
If the pH and the concentration of one of the carbonate species are known, the above
relationships, together with the equilibrium constants,
K1 
H HCO   10
H CO 


3
2
*
3
 6. 3
K2 
H CO   10
HCO 

2
3

3
10.2
(at 25C)
can be used to calculate all of the alkalinity and acidity terms.
The following justifiable approximations can be made for water analysis so that species
concentrations can be estimated from alkalinity titrations:
1) H+ does not exist as a major component.
2) CO32- is half titrated at the phenolphthalein endpoint (pH 8.3).
3) H2CO3* is the major species at the methyl orange endpoint (pH 4.3).
There are 3 approaches to the calculation of concentration of the species present.
Approximate method from titrimetric data alone, without pH measurement.
On this basis, and if Vp = ml of acid to reach the phenolphthalein endpoint, V mo = ml of
acid from the phenolphthalein endpoint to the methyl orange endpoint, V = sample
volume in ml, and N is the normality of the titrant, the following table can be developed:
Condition
Predominant form of alk.
Species, eq/L (note that CO32has 2 eq / mol.
Vp = Vmo
Vp = 0
Vmo = 0
Vmo > Vp
Vp > Vmo
CO32-
[CO32-] = Vp x N x V-1
HCO3-
[HCO3-] = Vmo x N x V-1
OH-
[OH-] = Vp x N x V-1
CO32- and HCO3-
[CO32-] = Vp x N x V-1
OH- and CO32-
[HCO3-] = (Vmo - Vp) x N x V-1
[CO32-] = Vmo x N x V-1
[OH-] = (Vp - Vmo) x N x V-1
Method from titrimetric data, with pH measurement
In this case the concentration of hydroxide, carbonate and bicarbonate are computed
using the expressions below. The concentration of hydroxide is computed first, directly
from the pH measurement using the formula
OH   KH 

w

Alkalinity is commonly expressed as equivalent concentration of CaCO3. That is the
amount of CaCO3 that would be required to consume the same amount of acid. The
formula weight of CaCO3 is 100 g/mol and it can consume 2 protons per mole.
Therefore, 50 g/L or 50,000 mg/L of CaCO3 is equivalent to an alkalinity of 1 mol/L and
multiplying the reults by 50,000 will convert to units of mg CaCO3/L.
The text (5) terms the hydroxide, carbonate and bicarbonate concentrations, as mg
CaCO3/L, as hydroxide alkalinity, carbonate alkalinity and bicarbonate alkalinity. This
conflicts with the general usage of these terms as defined above. The values are
determined from the hydroxide (pH measurement) and the phenolphthalein and methyl
orange alkalinities:
Hydroxide (as mg CaCO3 /L)  50,000  10pH-pK w 
and
Carbonate (as mg CaCO3/L) = 2 {phenophthalein alkalinity (as mg CaCO3/L) –
hydroxide (as mg CaCO3/L)}
Bicarbonate (as mg CaCO3/L) = {total alkalinity (as mg CaCO3/L) – [Carbonate (as mg
CaCO3/L) + Hydroxide (as mg CaCO3/L)]}
Method from equilibrium expressions
The final method is based directly on the definition of alkalinity. Writing the expression
for total alkalinity in mol/L
Total alkalinity = 2[CO32-] + [HCO3-] + [OH-] - [H+] = (2α2 + α1)CT + [OH-] - [H+]
This can be solved for CT , the concentration of inorganic caronate species as pH gives
the values of [OH-] and [H+] and α2 and α1 are functions of the equilibrium constants
and the [H+].
Procedure
1. Plot the theoretical titration curve and equivalence point for titration of
a. 50 ml of 0.01 M HCl with 0.05M NaOH
b. 50 ml of 0.0l M acetic acid with 0.05 M NaOH
(see Reference 5 and 6 for mass balance approaches to the calculation procedure).
Submit these graphs in addition to those required by the data analysis.
2. On the basis of these titration curves select an acid-base indicator that would be
appropriate for use in these titrations:
Indicator
pH of end point: acid to alk Color change:
Thymol blue
1.2 - 2.8
red - yellow
Methyl orange
3.1 - 4.4
red - orange
Methyl red
4.8 - 6.0
red - yellow
Bromthymol blue 6.0 - 7.6
yellow - blue
Phenolphthalein
colorless - red
8.0 - 9.6
3. Add 2 drops of an appropriate indicator to 50 ml 0.01 M HCl solution in a beaker and
observe the color that results. Insert the pH electrodes and observe pH. Titrate the
stirred solution with 0.05 M NaOH from a buret, taking enough readings of titrant
volume and pH that a well defined titration curve is obtained. Carry out the titration to a
point at least 2 ml beyond the point at which the indicator changes color. Observe the
values of titrant volume and pH at which the indicator changes color.
4. Repeat part 2 and 3 for the titration of 0.01 M acetic acid with 0.05 M NaOH using an
appropriate indicator.
5. With a given standardized acid, titrate 50 ml aliquots of each of the samples provided
as follows:

Measure the initial pH with pH meter.

Add 5 drops phenolphthalein indicator and titrate. Record the volume of titrant (V p)
when the phenolphthalein becomes colorless and when a pH of 8.3 is reached.

Add 5 drops methyl orange indicator and titrate. Record the volume of titrant (V mo)
when the methyl orange color change takes place and when a pH of 4.3 is reached.

If no color develops on addition of phenolphthalein, record the pH, immediately add
5 drops methyl orange indicator, and titrate as above.
6. Each student should determine the titration curve of one of the solutions. Initial pH
values should be measured very carefully, preferably with a pH meter standardized
within one pH unit of the initial solution pH. In performing the titration, add acid in
appropriate aliquots, recording the pH after addition of each aliquot to the well-mixed
solution. Titrate past the endpoint to about pH 3-3.5.
Data Analysis
1. Plot titration curves for the first two titrations performed using double abscissa scales:
a. pH vs titrant volume
b. pH vs moles base added per L solution, Ca, where
CB 
(molarity of base)( titrant vol.)
(sample vol.)
2. Graphically determine and plot the buffer intensity, β, vs pH using the plot developed
in Part 1b, where
=
C B
pH
3. Analyze the curves to determine the volume of titrant required to reach the
equivalence point. Compare this volume with the volume required to reach the
endpoint, the pH of color change for the indicator.
4. Calculate the molarity of the acid solution in the first two titrations, knowing that the
molarity of the NaOH solution was 0.05 M.
5. Present in tabular form a comparison of the reported and experimentally determined
alkalinity component concentrations for each of the five solutions, using the
approximations for computing these concentrations from the titration data.
6. Present the titration curve and label the theoretical pK's and the indicator endpoints.
Determine inflection points of the titration curve and compare these with the pK's and
indicator endpoints.
Questions
1. Assuming that an indicator 0.01 M is added to the HCl in the form of HIn, what
volume of indicator would have to added to introduce a 1% error relative to the amount
of HCl present?
2. From your observations of the pH values of color changes, estimate pK a for the
indicators to within 0.5.
3. In the titrations you have performed give an estimate of the percent error in the pH of
the equivalence point introduced by neglecting volume of the titrant added.
4. For each of the solutions titrated, why are the concentrations of OH -, CO32-, and
HCO3- somewhat different from those which were indicated on the sample
designations?
5. Using the initial pH value, the alkalinity values and the equilibrium constants,
compute precisely (use both of the other methods or approaces discussed above) the
concentration of all the species in the solution for which you performed the titration
curve. Compare with the values obtained in the Data Analysis section.
6. At what pH do the phenolphthalein and methyl orange endpoints occur for the
sample for which the titration curve was determined? If these pH values differ
significantly from the equivalence points as determined from an analysis of inflection
points of the titration curve, explain. Compare the equivalence points with the
commonly used endpoints of pH 8.3 and 4.3 and explain any difference.
7. The buffer intensity may be defined as β = (dCA/dpH) where CA is the moles/L of H+
added. With data from the titration curve, plot ß vs pH. At what pH values is the buffer
intensity greatest? What is the relationship between the minima and maxima in the
buffer intensity curve and pK1 and pK2?
Apparatus
pH meter
Glass indicator electrode
Calomel reference electrode
Magnetic stirrer
Burets
Reagents
NaOH, 0.05 M; (Approx 100 ml per student group)
HCl, 0.01 M or H2SO4, 0.005 M: (Approx 200 ml per student group)
Acetic acid, 0.01 M: (Approx 200 ml per student group)
Buffer solutions: pH 9, pH 7 and pH 4
Indicator solutions: methyl orange, methyl red, bromthymol blue, phenolphthalein,
thymol blue
Standard sulfuric acid, approx 0.02 N: To 500ml distilled water, carefully add 2.8 ml
concentrated H2SO4 and dilute to 1 L. Transfer 200 ml of this solution to a 1 L
graduated flask and make up to 1L with distilled water. Standardize against
standard sodium carbonate solution.
Sodium carbonate primary standard solution: Dry primary standard grade Na2CO3 at
140 °C. Weigh 1.060 g Na2CO3 and dissolve in 500 ml boiled and cooled distilled
water. Make up volume to 1 L with distilled water.
Phenolphthalein indicator solution.
Standard pH buffer solutions; pH 4, pH 7, pH 10.
Methyl orange indicator solution.
Samples contain the following added concentrations:
Dilute 3 ml l M NaOH to 1 L with distilled water ([OH-]  3 x 10-3 M).
Dilute 3 ml 1 M NaOH and 3 ml 1 M NaHCO3 to 1 L with distilled water ([CO32-]  3 x
10-3 M).
Dilute 3 ml 1 M NaHCO3 to 1 L with distilled water ([HCO3-]  3 x 10-3 M).
Dilute 5 ml 1 M NaOH and 3 ml 1 M NaHCO3 to 1 L with distilled water ([OH-]  2 x 10-3
M; [CO32-]  3 x 10-3 M).
Dilute 3 ml 1 M NaOH and 4 ml 1 M NaHCO3 to 1 L with distilled water ([HCO3-]  1 x
10-3 M; [CO32-]  3 x 10-3 M).
(Approx 250 ml of each sample of the above sample solutions per student group)