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+[1] 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
HA = H+ + A-
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 + A-
The 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
[H+] =
If CHA > [H+] then [H+] =
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
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- Kb =
[OH-] =
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+ + In-
where 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 CO2 ~ 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 CO32-
carbonate 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,
(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, Vmo = 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 CO32- has 2 eq / mol.Vp = Vmo / CO32- / [CO32-] = Vp x N x V-1
Vp = 0 / HCO3- / [HCO3-] = Vmo x N x V-1
Vmo = 0 / OH- / [OH-] = Vp x N x V-1
Vmo > Vp / CO32- and HCO3- / [CO32-] = Vp x N x V-1
[HCO3-] = (Vmo - Vp) x N x V-1
Vp > Vmo / OH- and CO32- / [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
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:
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 / 8.0 - 9.6 / colorless - red
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 (Vp) 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 (Vmo) 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.