CHAPTER XVI VOLUMETRIC METHODS

A. Fundamentals of Volumetric Analysis

Volumetric or titrimetric analyses are quantitative analytical techniques which employ a titration in comparing an unknown with a standard. In a titration, a volume of a standardized solution containing a known concentration of reactant "A" is added incrementally to a sample containing an unknown concentration of reactant "B". The titration proceeds until reactant "B" is just consumed (stoichiometric completion). This is known as the equivalence point. At this point the number of equivalents of "A" added to the unknown equals the number of equivalents of "B" originally present in the unknown. Volumetric methods have the potential for a precision of up to 0.1%.

For volumetric methods to be useful, the reaction must reach 99%+ completion in a short period of time. In almost all cases, a buret is used to meter out the titrant. When a titrant reacts directly with an analyte (or with a reaction the product of the analyte and some intermediate compound), the procedure is termed a direct titration. The alternative technique is called a back titration. Here, an intermediate reactant is added in excess of that required to exhaust the analyte, then the exact degree of excess is determined by subsequent titration of the unreacted intermediate with the titrant. Regardless of the type of titration, an indicator is always used to detect the equivalence point. Most common are the internal indicators, compounds added to the reacting solutions that undergo an abrupt change in a physical property (usually absorbance or color) at or near the equivalence point. Sometimes the analyte or titrant will serve this function (auto indicating). External indicators, electrochemical devices such as pH meters, may also be used. Ideally, titrations should be stopped precisely at the equivalence point. However, the ever-present random and systematic error, often results in a titration endpoint, the point at which a titration is stopped, that is not quite the same as the equivalence point. Fortunately, the systematic error, or bias may be estimated by conducting a blank titration. In many cases the titrant is not available in a stable form of well-defined composition. If this is true, the titrant must be standardized (usually by volumetric analysis) against a compound that is available in a stable, highly pure form (i.e., a primary standard). The basic requirements or components of a volumetric method are:

1. A standard solution (i.e., titrant) of known concentration which reacts with the analyte with a known and repeatable stoichiometry (i.e., acid/base, precipitation, redox, complexation)

2. A device to measure the mass or volume of sample (e.g., pipet, graduated cylinder, volumetric flask, analytical balance)

3. A device to measure the volume of the titrant added (i.e., buret)

4. If the titrant-analyte reaction is not sufficiently specific, a pretreatment to remove interferents

5. A means by which the endpoint can be determined. This may be an internal indicator (e.g., phenolphthalein) or an external indicator (e.g., pH meter).

Table 16.1

Volumetric Methods for Environmental Analysis

Analyte	Titrant	Indicator	Pretreatment	Method
Acid/Base
Alkalinity	HCl	methyl orange	none
Acidity	NaOH	phenolphthalein	none
N(-III)	H2SO4	methyl red	digest/distill (N NH4OH)	Macro-Kjeldahl & Acidimetric
Volatile Acids	NaOH	phenolphthalein	distillation	Distillation
Precipitation
Chloride	Ag	potassium chromate
Chloride	Hg	diphenylcarbazone		Mercuric Nitrate
Complexation or Chelation
Ca	EDTA	Eriochrome Blue Black R
Hardness	EDTA	Eriochrome Black T
CN	Ag	p-dimethylamino benzalrhodanine
Oxidation/Reduction
Dissolved O2	Na2S2O3	starch	Mn(+II), I(-I)	Winkler
Ca	MnO4	auto	oxalate	Permanganate Titr
Chlorine/ClO2	Na2S2O3	starch	I(-I)	Iodometric
SO3^-2	Na2S2O3	starch	I(-I)	Iodometric
Chlorine/ClO2	FeSO4	DPD		DPD Ferrous Titr.
COD	Fe(NH4)2(SO4)2	ferroin	K2Cr2O7

Volumetric methods may be based on acid/base reactions. precipitation reactions, complexation reactions and redox reactions. Table 16.1 presents a summary of the volumetric methods commonly used for environmental analysis. The acid/base methods generally use a strong acid or base as a titrant with methyl orange/red (acid titration) or phenolphthalein (base titration) as the indicator. For all but acidity and alkalinity determinations, the analyte must be separated from the major cations and anions prior to titration. Precipitative volumetric analysis relies on the formation of solid phase with a very low solubility product constant. In environmental analysis, it may be used for chloride determination. Specific indicators are used to detect excess silver or mercury. Complexometric titrations often employ ethylenediaminetetraacetic acid or EDTA [HOOCCH₂)₂NHCH₂CH₂NH(CH₂COOH)₂]. This is a hexadentate ligand which binds very strongly to many metals. For calcium and total hardness determination, a couple of specific dyes are used to determine the presence of excess cation. Many oxidation/reduction based volumetric methods employ the iodometric method. This involves the oxidation of iodide to iodine and subsequent titration with sodium thiosulfate using starch as an indicator. Many of these employ a series of redox reactions. The permanganate method for calcium is somewhat unique in that the calcium is precipitated as the oxalate, and it is the solid-phase oxalate group which participates in the redox reaction, not the calcium.

B. Acid/Base Titrations

1. ALKALINITY & ACIDITY

a. Environmental Significance

Alkalinity is a measure of a water's ability to neutralize strong acids. It reflects the water's buffer capacity or resistance to a drop in pH upon addition of acid. Conversely, acidity is a measure of a water's ability to neutralize strong bases.

Alkalinity is important in assessing the need for additional buffering or pH control with pH-sensitive operations. For example, the alkalinity of a water must be known in order to calculate lime and soda ash doses for precipitative softening. Species responsible for either alkalinity or acidity can affect rates of corrosion, the speciation of metals and organic compounds, the rates of certain types of reactions, and numerous biological processes. Alkalinity and acidity might also correlate with other properties of a water such as hardness and TDS.

b. Species Responsible for Alkalinity and Acidity in Waters

Alkalinity and acidity can be interpreted in terms of concentrations of specific constituents only when the chemical composition of the water is known. Species that impart alkalinity to a water are bases. Species that impart acidity to a water are acids. In unpolluted fresh waters, hydroxide, carbonate and bicarbonate are the most important bases. Therefore, total alkalinity is often interpreted as the sum of the number of equivalents of these bases (minus the hydrogen ion concentration). Thus, alkalinity can be expressed in terms of eq/L or meq/L, but not moles/L or mmoles/L.

Alk_tot = [HCO₃^-] + 2[CO₃^-2] + [OH^-] - [H⁺] (16.1)

In rare cases other bases may also be important such as the silicates, ammonia, phosphates, borates and organic bases. For example, extremely soft waters (< 10 mg/l as CaCO₃) contain so little bicarbonate that ammonia and silicate concentrations become important. Aside from H and OH^-, the nonmetals found in fresh waters in order of importance are the carbonates, sulfate, chloride, silicate, organic anions, nitrate, fluoride, boron, bromide, ammonia and phosphate. Of these, sulfate, chloride, nitrate, fluoride and bromide are insufficiently basic to contribute alkalinity regardless of their concentration. Similarly, most of the major cations such as calcium, sodium, magnesium, potassium and strontium do not hydrolyze to a sufficient extent within the pH range of interest to account for much alkalinity. The remaining species of interest are listed in Table 16.2. Based on the average concentrations shown here, the practice of interpreting fresh water alkalinity in terms of the carbonate system is justified.

It is important to point out here that although carbonates contribute to alkalinity, the addition of carbon dioxide to a water will not alter its alkalinity. This is true, because carbon dioxide consumes one hydroxide molecule for each bicarbonate molecule formed.

CO₂(aq) + OH^- = HCO₃^- (16.2)

The addition or loss of carbon dioxide might, however, result in a change in pH.

In contrast to fresh waters, seawater has such high concentrations of other bases that the following chemical interpretation is commonly used (Alk & Acy are always in units of equivalents/liter):

Alk_tot = [HCO₃^-] + 2[CO₃^-2] + [B(OH)₄] + [HPO₄^-2] + [H₃SiO₄] + [MgOH^-] + [OH^-] - [H⁺] (16.3)

Important acids that contribute to acidity are the hydrogen ion, bicarbonate and dissolved carbon dioxide. Organic acids may also contribute acidity in highly colored waters.

Acy_tot = 2[H₂CO₃] + [HCO₃^-] + [H⁺] - [OH^-] (16.4)

Table 16.2

Chemical Species Which May Contribute to the Alkalinity of Fresh Waters

Species	pKa	Average Conc. (M)	Equilibria
Carbonates	10.3/6.4	1x10^-3	CO3^-2 + 2H^+= HCO3^- + H^+= H2CO3
Silicates	9.8	2x10^-4	H3SiO4 + H^+= H4SiO4
Organics	3 to 10	1x10^-4	R-COO^-+ H^+ = R-COOH
Borates	9.2	1x10^-6	B(OH)4^- + H^+= B(OH)3 + H2O
Ammonia	9.2	2x10^-6	NH4OH + H^+= NH4^++ H2O
Iron	6.0/4.6	2x10^-6	Fe(OH)4^- + 3H^+= Fe(OH)2^+ + H^+ = Fe(OH)^+2
Aluminum	8.0/5.7	2x10^-6	Al(OH)4^- + 2H^+= Al(OH)3 + H^+ = Al(OH)2^+
	4.3/5.0		Al(OH)2^+ + 2H^+= Al(OH)^+2+ H^+= Al^+3
Phosphates	7.2	7x10^-7	HPO4^-2+ H^+= H2PO4^-
Hydroxide	14.0	2x10^-7	OH^-+ H^+= H2O
Copper	9.8/7.3	1x10^-7	Cu(OH)3^- + 3H^+= Cu(OH)^++ H^+= Cu^++ H2O
Nickel	6.9	2x10^-8	Ni(OH)2 + H^+=NiOH^+
Cadmium	7.6	1x10^-8	Cd(OH)^++ H^+= Cd^+2+ H2O
Lead	6.2	1x10^-8	Pb(OH)^++ H^+= Pb^+2+ H2O
Sulfides	7.0	variable	HS^-+ H^+= H2S
Zinc	6.1/9.0	variable	Zn(OH)2+ 2H^+= Zn(OH)^++ H3O^+=Zn^+2+ 2H2O

c. Notes on the determination of alkalinity & acidity

i. Principles All waters undergo some drop in pH with the addition of strong acids, and some rise in pH with the addition of strong bases. The greater the alkalinity or acidity, the smaller the shifts in pH, however, they never completely disappear. Thus, alkalinity and acidity cannot be determined by the addition of an acid or base until a pH change occurs, because the first drop will always result in some change. Instead, samples are commonly titrated to a pre-determined pH. By convention, the pH is usually about 4.5 for the alkalinity titration and 8.3 for acidity. However, these are not purely arbitrary choices. Titration to pH 8.3 corresponds to the point where the quantity of base added equals the sum of the strong acid, carbon dioxide and bicarbonate originally present. Because this pH represents the approximate point of color change for the indicator, phenolphthalein, the amount of titrant required to reach this pH is often referred to as the phenolphthalein acidity. Similarly, titration to pH 4.5 corresponds to the point where the quantity of acid added equals the amount of strong base, carbonate and bicarbonate originally present. Since this pH represents the approximate point of color change for the indicator, methyl orange, the amount of titrant required to reach this pH is often referred to as the methyl orange alkalinity.

Methyl orange is an azo dye that changes color from yellow to red as the pH is lowered below about 4.5. It is also known as p-dimethylaminoazobenzene-p'-sulfanilic acid.

Phenolphthalein is a polyphenolic compound which loses both a water molecule and a hydrogen ion at high pH. As the deprotonation occurs the color changes from colorless to bright red.

ii. Choice of Titration Flasks It is good practice to have as little space between the sample and the buret (and pH electrode) as practical. With conventional-sized electrodes, the 200 mL tall form Berzelius beaker is a good choice. For miniature combination electrodes and for the colorimetric method, an erlenmeyer flask (125 mL or 250 mL) is recommended. In general a magnetic stirrer is recommended for proper mixing and electrode response, however the speed should be kept low to minimize exchange with the atmosphere. A rubber stopper with holes for the electrode(s) and buret may be used to further reduce atmospheric contact. For the colorimetric method, manual agitation of the erlenmeyer flask via a swirling wrist motion may be used.

iii. Sampling Procedures

1. Handle carefully to avoid loss of carbon dioxide

2. Analyze promptly after opening to avoid loss of volatiles (carbon dioxide, ammonia, hydrogen sulfide)

3. Collect samples in polyethylene or glass bottles and keep cool to avoid changing gas solubilities.

iv. Colorimetric vs Potentiometric Methods

In the vast majority of cases both the colorimetric and potentiometric methods are acceptable. However, there are certain circumstances where one might be preferred over another. For example, some highly colored or turbid samples may mask the color of indicators, and render it impossible to use the colorimetric method. If free residual chlorine is present, it will have to be removed by addition of 1 drop of 0.1M sodium thiosulfate solution prior to using the colorimetric method. This is necessary to avoid bleaching of the indicators. With some very dilute waters, this type of sample pretreatment may effect the results and the potentiometric method is recommended. For greatest accuracy, the potentiometric method is recommended. Under ideal conditions this method allows one to graphically determine a sample's equivalence point. Otherwise, one must rely on some predetermined endpoint which has been found to correspond to the equivalence point in many samples of the same alkalinity. Unfortunately, the potentiometric-graphical method is more time-consuming, and it requires a great deal more analyst experience.

The potentiometric method also suffers from some disadvantages. For example, it may not be a convenient method for rapid on-site analysis. Potentiometric determination relies on the proper operation of a sensitive instrument (i.e., the pH meter). Harsh conditions in the field or the lack of electrical power may preclude its use. Even in the laboratory the potentiometric method may be subject to certain types of interferences. With some waters, surfactants and precipitates which coat the pH electrode will impede its response. These substances must not be removed as they may contribute to acidity or alkalinity. Instead, the electrode should be cleaned frequently, or the colorimetric method should be employed.

d. Analytical Procedures

1.Alkalinity

a. HCl standardization

1. Add 15 ml of the primary standard sodium carbonate solution to the titration vessel with about 60 ml of CO₂-free water and 5 drops of methyl orange or bromcresol green-methyl red indicator solution. Alternatively, potentiometric pH determination may be used (~pH 4.3).

2. Fill buret with HCl stock using a 250 ml beaker as a transfer vessel and note starting point (you should keep the solution in the transfer beaker covered with a watch glass during titrations). Titrate, while stirring, until a pH of about 5 is reached or until the first signs of a color change appear.

3. Remove electrodes, cover the sample with a watch glass and boil slowly for 3-5 minutes. Allow solution to return to room temperature and resume titration to endpoint.

4. Repeat this procedure (steps a-c) until 2 titrations give results that agree within 2%. Rinse the buret and 250-ml beaker thoroughly with distilled water.

5. Calculate the normality of the titrant, N_t, from the concentration of the primary standard sodium carbonate solution, N_ps, the volume of the sodium carbonate solution used, V_ps, and the volume of hydrochloric acid titrant used, V_t. It should be close to 0.02N.

N_t = N_psV_ps/V_t

b. Sample Titration (Alkalinity)

1. Choose a sample volume that is expected to contain less than 50 mg of alkalinity as CaCO₃. For most waters, 100 ml is a convenient volume.

2. Add 2 drops of either methyl orange or bromcresol green-methyl red indicator solution or insert electrodes and titrate with the HCl titrant to the endpoint. The first potentiometric endpoint is pH 8.3 and from this the phenolphthalein alkalinity (Alk_ph) is calculated. The second endpoint (Alk_tot) depends somewhat on the alkalinity range. Experience has shown the following pHs may be used to establish an endpoint in lieu of a potentiometric determination of the inflection point:

Alkalinity	Potentiometric	Colorimetric
(mg/L)	(pH)	(from greenish blue to)
30	4.9	light blue & lavender
150	4.6	light pink
500	4.3	red

Caution: Excessive agitation or prolonged titrations may lead to loss of volatiles (e.g., carbon dioxide) or significant uptake of atmospheric carbon dioxide. Avoid heating the sample above room temperature by a magnetic stirrer.

2. Acidity

a. NaOH Standardization

1. Add 15 ml of the primary standard KHP solution to the titration vessel with about 60 ml of CO₂-free water and 5 drops of phenolphthalein indicator solution. Alternatively, potentiometric pH determination may be used (~pH 8.7).

2. Fill burette with NaOH stock using 250 ml beaker and note starting point. As before, you must keep the solution covered with a watch glass during titrations. Titrate, while stirring, until the endpoint is reached.

3. Repeat this procedure (steps a-b) until 2 titrations give results that agree within 2%. Rinse the buret and 250-ml beaker thoroughly with distilled water.

4. Calculate the normality of the titrant, N_t, from the concentration of the primary standard KHP solution, N_ps, the volume of the KHP solution used, V_ps, and the volume of sodium hydroxide titrant used, V_t. It should be close to 0.02N.

N_t = N_psV_ps/V_t

b. Sample Titration (Acidity)

1. Choose a sample volume that is expected to contain less than 50 mg of acidity as CaCO₃. For most waters, 100 ml is a convenient volume.

2. Add 2 drops of phenolphthalein indicator solution or insert electrodes and titrate with the NaOH titrant to the endpoint. The potentiometric endpoint is pH 8.3. For some highly acidic waters (e.g., acid mine drainage) the volume of titrant required to reach pH 3.7 should also be recorded for determination of mineral acidity.

e. Reagents

1. Alkalinity

a. Primary Standard Sodium Carbonate Solution.

1. Dry at least 10 g of anhydrous sodium carbonate at 250 degrees C for at least 4 hours and allowed to cool in a desiccator charged

with "Drierite".

2. Tare a piece of weighing paper.

3. Open the desiccator and place about 2.5 g sodium carbonate on the paper, close the desiccator and quickly re-weigh paper + primary standard to the nearest milligram. Subtract combined weight from the tare weight and record.

4. Gently pour the sodium carbonate into a 1-liter volumetric flask. Fill to the mark with distilled water. You may wish to use a distilled water wash bottle for the final few ml.

5. Calculate the normality of the primary standard, N_ps, from the mass in grams of the primary standard sodium carbonate added, m_ps, and the gram equivalent weight of the sodium carbonate (GEW_ps= 52.99). It should be close to 0.05 N.

N_ps = m_ps/GEW_ps

b. Hydrochloric Acid Stock Solution (about 0.1N)

1. Add 9 mls of reagent-grade HCl (11.6 M) to a 1-liter volumetric flask and fill to the mark with distilled water.

c. Hydrochloric Acid Titrant (about 0.05N) - dilute stock appropriately

d. Mixed Bromcresol Green-Methyl Red Indicator Solution.

1. Dissolve 20 mg methyl red sodium salt and 100 mg bromcresol green sodium salt in 100 ml distilled water

2. Acidity

a. Primary Standard Potassium Hydrogen Phthalate Solution.

1. Dry at least 15 g of potassium hydrogen phthalate (KHP) at 120 degrees C for at least 2 hours and allowed to cool in a desiccator charged with "Drierite".

2. Tare a piece of weighing paper.

3. Open the desiccator and place about 10 g Potassium Acid Phthalate (KHP) on the paper, close the desiccator and quickly re-weigh paper + primary standard to the nearest milligram. Subtract combined weight from the tare weight and record.

4. Gently pour the KHP into a 1-liter volumetric flask. Fill to the mark with distilled water. You may wish to use a distilled water wash bottle for the final few ml.

5. Calculate the normality of the primary standard, N_ps, from the mass in grams of the primary standard KHP added, m_ps, and the equivalent weight of the KHP (GEW_ps= 204.10). It should be close to 0.05 N.

N_ps = m_ps/GEW_ps

b. Sodium Hydroxide Stock Solution (about 0.1N)

1. Add 5.8 mls of a commercial 50% NaOH solution (19.1 M) to a 1-liter volumetric flask and fill to the mark with distilled water.

c. Sodium Hydroxide Titrant (about 0.05N) - dilute stock appropritately

3. General

a. Carbon dioxide-free water: Use freshly distilled water or distilled water that has been freshly boiled for 15 min and cooled to room temperature. Conductivity should be less than 2umhos/cm.

f. Data Analysis

i. Calculation of Alkalinity If a water contains only hydroxide, bicarbonate and carbonate as significant bases, then the amount of acid (represented here by H⁺ or a proton) required to reach the Phenolphthalein endpoint is equal to the amount of hydroxide originally present plus the amount of carbonate originally present:

H⁺ + OH^- « H₂O (16.5)

H⁺ + CO₃^-2 « HCO₃^- (16.6)

This is true, because at the pH where phenolphthalein changes color (8.3) most of the alkalinity will be in the form of bicarbonate. Also, any remaining under-protonated forms (i.e., hydroxide or carbonate) would be exactly balanced by an equivalent amount of over-protonated forms (i.e., carbon dioxide).

To reach the final, methyl orange or methyl red, endpoint one must add an additional amount of acid equivalent to the amount of bicarbonate present at the phenolphthalein endpoint:

H + HCO₃^- « H₂CO₃ « CO₂ + H₂O (16.7)

This will be equal to the amount of bicarbonate initially present in the sample plus the amount of carbonate originally present since carbonate was entirely converted to bicarbonate in the first stage.

Theoretically Alk_OH can be calculated directly from the starting pH (pH_i) by the following:

Alk_OH = 50,000(10^pHi-14) (16.8)

However, in practice, small errors in initial pH result in large errors in Alk_OH. Thus it is best to use the following scheme:

If Alk_ph > 0.5* Alk_mo

Alk_OH = 2*Alk_ph - Alk_mo (16.9a)

Alk_CO3 = 2(Alk_mo - Alk_ph) (16.9b)

Alk_HCO3 = 0 (16.9c)

If Alk_{ph _<} 0.5* Alk_mo

Alk_OH = 0 (16.10a)

Alk_CO3 = 2*Alk_ph (16.10b)

Alk_HCO3 = Alk_mo - 2*Alk_ph (16.10c)

Where:

Alk_ph = 50,000V_phN_t/V_s (16.11a)

Alk_mo = 50,000V_moN_t/V_s (16.11b)

The factor of 50,000 is used because alkalinities are commonly expressed in terms of milligrams per liter of equivalent calcium carbonate. Calcium carbonate has a formula weight of 100g/mole. Since it has two equivalents per mole we must divide this by two to get 50 g/equivalent or 50,000 mg/equivalent.

Presuming that all of the alkalinity is due to carbonate species and hydroxide, one can use the values determined in equations 16.9 or 16.10 to calculate molar carbonate and bicarbonate concentrations.

[HCO₃^-] = Alk_HCO3/50,000 (16.12a)

[CO₃^-2] = Alk_CO3/100,000 (16.12b)

g. Chemical Interpretation of Potentiometric Titration Curves

i. General Features The significance of the preceeding calculations is best illustrated with a complete titration curve. Figure 16.1 shows a titration of an extremely alkaline water where the pH was measured continuously as a function of titrant added. Curve B corresponds to a water containing 1.5mM hydroxide plus 1.0mM carbonate. Curve A shows what one would obtain with a similar water containing only the 1.5mM hydroxide. The titrant is 0.100M HCl and the sample volume is 1000 mL

The carbonate water curve (B) is composed of three plateaus and two points of inflection, and the hydroxide solution (A) gives two plateaus and one point of inflection. A point of inflection is one where the second derivative of the curve equals zero. In other words it occurs where the slope is a maximum and the curve goes from concave to convex. We will now describe the significance of each of these features.

First, consider curve A. The upper plateau represents the neutralization of hydroxide by the strong acid (equation #16.5). At the point of inflection all of the initially present hydroxide has been consumed and H⁺ begins to accumulate in solution. As a result, the inflection point is often termed the equivalence point. This means that at this stage in the titration, an amount of acid has been added that is equivalent to the starting concentration of base. Since we're plotting pH versus added acid the curve beyond the equivalence point is not linear.

Figure 16.1

Acid Titration Curve for a Water Containing

Hydroxide and Carbonate Alkalinity

Near neutrality (pH 7) only very small amounts of acid (~10^-6 M) are required to lower the pH by one unit, however, at pH 3 one must add 10,000 times as much to drop one pH unit (i.e., to reach pH 2). Therefore, this semi-log plot gives us a sloping curve beyond the equivalence point even though little or no reaction is occurring.

For curve B, the first plateau corresponds to both the neutralization of hydroxide and the protonation of carbonate (equations #16.5 and #16.6). Here the point of inflection or equivalence point occurs at pH of about 8.4 rather than 7 for the hydroxide solution. At this point in the titration the amount of acid added equals the molar amount of carbonate and hydroxide originally present. With the exhaustion of the original carbonate (most hydroxide would have been neutralized well before this point), H⁺ begins to accumulate in solution until it reaches a certain level where it becomes favorable to combine with bicarbonate to give carbonic acid and carbon dioxide. This then gives rise to the second plateau and a second equivalence point. Equations 16.9a-16.9c should be used with sample B, because the volume to reach the first endpoint is greater than half the volume to reach the second.

Figure 16.2

Acid Titration Curve for a Water Containing

Carbonate and Bicarbonate Alkalinity

Figure 16.2 shows a titration curve of a less alkaline water. This one contains significant amounts of carbonate alkalinity, but little or no hydroxide alkalinity. Let's assume the starting solution contains "Y" moles of carbonate and "Z" moles of bicarbonate. At the first equivalence point all of the initial carbonate has been protonated to give bicarbonate. Thus, the volume to reach this point (V_ph) is equal to "Y" times the sample volume divided by the titrant normality. This volume is clearly less than half of the final titrant volume (V_mo), and thus equations 10a-10c must be used. Across the second plateau, bicarbonate is converted to carbonic acid and aqueous carbon dioxide. Since at the start of the plateau we had "Y+Z" bicarbonate, this addition titrant volume (V_mo-V_ph) will be equal to "Y+Z" times V_s/N_t. The original amount of carbonate, "Y", is obtained simply from the first titration (see equation 16.10b), and the original amount of bicarbonate, "Z" is obtained from the final titrant volume minus two times the volume to reach the first equivalence point (equation 16.10c).

Figure 16.3

Acid Titration Curve for a Water Containing

Only Bicarbonate Alkalinity

Figure 16.3 shows titration curves from three waters containing varying amounts of bicarbonate alkalinity. In each case the upper plateau and first equivalence point is completely gone. The lower plateau (bicarbonate to carbonic acid) and final equivalence point remain. As a result, V_ph=0, and equations 16.10a-16.10c should be used with these samples. Note that as the bicarbonate concentrations increase from curve D to curve F, the final equivalence points decrease.

ii. General Mathematical Solution The titration curve of a water dominated by the carbonate system will be defined by three equilibrium expressions:

(16.13)

(16.14)

(16.15)

In addition we need to consider a couple of mass balance equations. First, the total concentration of carbonate species, C_T, is assumed to be unchanged during the titration. Rather they are just converted from one form into another. Note that in contrast to alkalinity, C_T must always be expressed on terms of moles/L or mmoles/L, and not eq/L or meq/L.

(16.16)

A mass balance must also be written for electrical charge. The starting solution is neutral and it must remain electrically neutral throughout the titration. Equation #16.17 indicates that the sum the the positive charges must equal the sum of the negative charges. Initially the water contains carbonate and an equivalent concentration of counter ions such as calcium or sodium. The charge (i.e., equivalent concentration) of these counter ions, C_B, remains constant throughout the titration since only HCl is being added. Similarly, the hydrochloric acid has negative counter ions (chloride) whose concentration, C_A, increases as more acid is added. These charges must also be included in equation #16.17,

(16.17)

where C_A is approximately equal to the ratio of acid titrant added, V_t, to sample volume, V_s, times the titrant concentration:

(16.18)

Equation 16.16 can be rewritten:

(16.19)

This can then be combined with the carbonic acid-bicarbonate equilibrium expression (equation 16.13) to get:

(16.20)

The bicarbonate-carbonate equilibrium expression (equation 16.14) can be rearranged to get:

(16.21)

and then inserted into equation 16.20:

(16.22)

This may be rearranged to get an expression for bicarbonate concentration exclusively in terms of hydrogen ion and base cation concentration:

(16.23)

And now combining equations 16.23 and 16.21 we get an analogous expression for carbonate concentration exclusively in terms of hydrogen ion and base cation concentration:

(16.24)

Note that the right-hand side of equations 16.23 and 16.24 are commonly represented as ₁C_T and ₂C_T respectively (e.g., see Stumm & Morgan, 1981). The hydroxide concentration may also be expressed in terms of the hydrogen ion concentration by rearranging equation 16.15:

(16.25)

Finally these last three equations may be combined with the charge balance (equation 16.17) to get the full equation describing the carbonate titration curve:

(16.26)

This is a very cumbersome equation that must be solved by trial and error or by some numerical technique. There are, however, some simplifying assumptions that one can make to facilitate its solution.

iii. Titration Midpoint By definition, at the midpoint of the first plateau:

(@MP) (16.27)

and according to equation 16.14 this must take place at the following pH.

[H⁺] = K₂ = 4.7x10^-11 (@MP) (16.28)

or

pH = pK₂ = 10.33 (@MP) (16.29)

At this point carbonic acid (or carbon dioxide) concentration is insignificant. Therefore half of the total carbonate, C_T, is bicarbonate and half is carbonate. This means that the last two terms in the final modified charge balance (equation 16.26) become C_T/2 and C_T.

(@MP) (16.30)

This can be rearranged to get the quantity of acid required to reach this midpoint:

(@MP) (16.31)

Combining equation 16.28 and 16.13 with this we calculate:

(@MP) (16.32)

iv. Equivalence Point Perhaps the most significant feature on the alkalinity titration curve is the equivalence point. This is defined as the point where the number of equivalents of acid added just equals the number of equivalents of alkalinity originally present, or:

C_A = C_B (@EP) (16.33)

For greatest accuracy in the determination of total alkalinity, this should be the endpoint of the titration. Under ideal conditions the equivalence point may be located on a titration curve as the point of inflection. In practice it is difficult to place the point of inflection with any accuracy. As a result, most alkalinity titrations are carried out to a pre-determined endpoint pH which depends on the initial alkalinity. At the equivalence point, it follows from the charge balance (equation 16.17) and equation 16.33 that:

(@EP) (16.34)

Because we know that the equivalence point will be well below neutrality, the carbonate and hydroxide concentrations should be insignificant compared to the bicarbonate and hydrogen ion concentrations. Thus, equation 16.34 reduces to:

(@EP) (16.35)

And substituting from equation 16.23 we get an expression in terms of C_B and the equilibrium constants only.

(@EP) (16.36)

Once again we can simplify based on the anticipated low pH. Since we expect the equivalence point to be well below the pK₁, the first term, [H ]/K₁, should be much greater than the other two terms in that set of brackets. Thus we can eliminate the others and rearrange.

[H⁺] = C_TK₁/[H⁺] (@EP) (16.37)

and solving for the hydrogen ion concentration:

[H⁺] = (C_TK₁)^0.5 (@EP) (16.38)

If we assume that natural waters are dominated by bicarbonate, the number of moles of total carbonate (i.e., C_T) will be approximately equal to the number of equivalents of alkalinity. So if we express alkalinity in mg/l as CaCO₃ this becomes:

C_T = Alk_tot/50,000 (16.39)

Finally combining this with equation 16.38 and taking the negative logarithm of both sides we get the following expression for the pH at the final equivalence point in an alkalinity titration:

(@EP) (16.40)

Note that equation 16.40 predicts equivalence points very close to the pHs where they have been observed experimentally (i.e., compare with table in section on analytical procedures).

h. Calculation of Acidity

The mineral acidity, also known as the methyl orange acidity, is equivalent to the amount of base (i.e., the titrant) required to bring the pH up to 4.5 (methyl orange endpoint). It is so named, because mineral acids such as HCl, when present at significant concentrations, are almost completely neutralized before the pH reaches 4.5. The carbon dioxide acidity is the additional base required to raise the pH from 4.5 or the initial pH, whichever is higher, to pH 8.3 (phenolphthalein endpoint). Likewise carbon dioxide does not begin to become neutralized until pH 4.5 is passed, and its neutralization reaches completion (equivalence point) at pH 8.3. Finally, the total acidity, or phenolphthalein acidity, is the sum of the mineral acidity and the carbon dioxide acidity.

(16.41)

(16.42)

(16.43)

As before, the factor of 50,000 is used because acidities as well as alkalinities are commonly expressed in terms of milligrams per liter of equivalent calcium carbonate.

i. Correlations With Other Water Quality Parameters

i. Total Dissolved Solids Since alkalinity is dominated by the major anion, bicarbonate, it is possible to relate alkalinity to the total concentration of dissolved solids. If we assume that fresh waters are composed exclusively of calcium and bicarbonate, for every mole of calcium bicarbonate (Ca(HCO₃)₂) we will have two equivalents of alkalinity. Since one mole of calcium bicarbonate should weigh 162 grams and one equivalent of alkalinity is equal to 50 g as CaCO₃, the mass ratio should be 100/162 or 0.62.

Alk_tot = 0.62(TDS) (16.44)

Such relationships are inherently site specific and they must be verified with each new water.

ii. Conductivity Alternatively, alkalinity might be expected to correlate with conductivity. Since the equivalent ionic conductances at infinite dilution are 59.5 mho-cm²/equivalent for calcium and 44.5 mho-cm²/equivalent for bicarbonate, the total solution equivalent conductance at infinite dilution, G_o, is 104 mho-cm²/equivalent (at 25^oC). While this value will decrease some with increasing concentration, it may be considered constant for solutions up to 200 mg/l alkalinity (as CaCO₃) without introducing too much error. The equivalent conductance, , is related to the conductivity according to:

Conductivity = C(1000) (16.45)

when conductivity is in umho/cm. Here "C" represents the equivalent concentration of the salt. For a pure solution of calcium and bicarbonate this would just be equal to the alkalinity (in mg/L as CaCO₃) divided by 50,000. Also as previously stated we will assume that the equivalent conductance, G, is equal to the limiting equivalent conductance at infinite dilution G_o. Thus equation 16.45 can be rearranged to get:

Alk_tot = 0.50(Conductivity) (16.46)

In practice this relationship is not useful below 50 mg/l alkalinity as the presence of other non-alkalinity anions contributes significantly to the overall conductivity. Thus, with soft waters equation 16.46 overestimates the alkalinity.

j. Special Considerations for Samples of Low Ionic Strength

It is important to avoid streaming potential effects in dilute solutions. Therefore, such samples should be allowed to stand quiescently for several minutes before measuring (McQuaker et al., 1983).

RESEARCH TOPIC

2. DETERMINATION OF ORGANIC FUNCTIONAL GROUPS

The determination of organic functional groups is useful for research on natural organic matter (NOM), its behavior in engineered systems (e.g., drinking water treatment) and its behavior in natural systems. Unfortunately, all titrimetric methods for total functional group content and for speciation of these groups in NOM (especially humic materials) are inherently operational (Perdue, 1985).

a. Direct Method for Total Carboxyl and Phenolic Content

Carboxyl and phenolic groups can be determined by direct potentiometric titration. For best results, the samples should be free from acidic inorganic species and hydrogen saturated. The sample is titrated with NaOH to a carboxyl end point of pH 8. The titration can be continued to pH 10 where roughly half of the phenolic groups are deprotonated. One may then estimate the phenolic content by doubling the amount of base required to change the pH from 8 to 10. Thurman (1985) points out that since ortho substituted carboxyl groups render the phenolic-OH groups very weakly acidic (pKa of about 13), these may be missed by such a titration.

Problems inherent in direct titrations of natural organic matter may limit their usefulness. A slow pH drift (downwards in alkaline titrations) and hysteresis often accompanies these measurements. The reasons for this are not clear, but alkaline hydrolysis (of organic matter, Me-org complexes, and metals), conformational changes, alkaline oxidation, biodegradation may be responsible (Perdue, 1985). In order to minimize oxidation and biodegradation, these titrations should be carried out under nitrogen. Another problem arises from the difficulty in accurately measuring high pH values. This is in part due to the high concentration of alkali metal ions which interfere with potentiometric pH measurements.

b. Barium hydroxide method for total acidity.

A popular method for the determination of total acidity in terrestrial humic materials utilizes barium hydroxide. The addition of an excess of Ba(OH)_{2 to a sample containing organic matter brings the pH up to about 13 where nearly all acidic protons are removed. The high concentration of barium coupled with the high complexation constants of barium-organic salts, leads to nearly complete binding by barium of the charged functional groups. In the process, the complexed organic matter is rendered less soluble and must be physically removed by filtration. Then, the protons originally liberated from the organic matter upon addition of the hydroxide may be determined by back titration of the residual hydroxide in the filtrate. Unfortunately, this method has some serious weaknesses for analysis of aquatic organic matter. First, for efficient separation, it is critical that the barium-complexed organic matter rapidly precipitate. However, the greater hydrophilic nature and lower molecular weight of aquatic organic matter as compared to terrestrial matter makes precipitation of this material less complete. Second, any functional groups that are not protonated at the start (i.e., anionic or complexed by metals) are not likely to be measured by this technique. Lowering the starting pH would minimize the problems of incomplete titration, however, this would introduce additional uncertainties from the difficulty of accurately measuring high concentrations of hydrogen ions.}

C. Complexation Titrations

Complexation or complexometric titrations are based on the formation of a complex. Commonly, a metal is the analyte to which some ligand is added. This ligand must be chosen so that complexation is quick, has a well defined stoichiometry, and goes very nearly to completion. The most frequently used ligand is ethylenediaminetetraacetic acid or EDTA [HOOCCH₂)₂NHCH₂CH₂NH(CH₂COOH)₂]. This is a hexadentate ligand which binds very strongly to many metals giving a 1:1 stoichiometry. It has been applied to the determination of many metals (for example see: Flaschka, 1959; Schwarzenbach & Flaschka, 1969). Table 16.3 shows some stability constants for EDTA complexes based on formation only with the fully deprotonated species, Y^-4.

M⁺ⁿ + Y^-4 = MY^n-4 (16.47)

and:

K = [MY^n-4]/[M⁺ⁿ][Y^-4] (16.48)

Table 16.3

EDTA Stability Constants

(from Martell & Smith, 1974)

Metal	Log K	Metal	Log K
K (+I)	0.8	Pb (+II)	18.04
Na (+I)	1.66	Sn (+II)	18.3
Li (+I)	2.79	Ni (+II)	18.62
Ba (+II)	7.86	Cu (+II)	18.80
Mg (+II)	8.79	Hg (+II)	21.7
Ca (+II)	10.69	Al (+III)	16.3
Cr (+II)	13.6	Cr (+III)	23.4
Mn (+II)	13.87	Mn (+III)	25.3
Fe (+II)	14.32	Fe (+III)	25.1

Note that these constants are quite large indicating that complexation goes very nearly to completion. The strong binding of metals by EDTA is due in part to its ability to completely surround the metal, often forming a six-coordinate species. In general, the more coordinating sites a ligand has, the stronger the metal binding. Also, the high the charge on the metal, the stronger the binding is with EDTA.

Since its only the Y^-4 species of EDTA that is considered to form strong complexes, one must take into account the speciation of this ligand. EDTA has the following dissociation constants:

Carboxylic groups

pK₁ = 0.0 pK₂ = 1.5 pK₃ = 2.0 pK₄ = 2.66

Amine groups

pK₅ = 6.16 pK₆ = 10.24

Therefore, at neutral pH all four of the carboxyl groups are deprotonated, and one of the amine groups is partially deprotonated (HY^-3 form). The fraction of the total EDTA that is in the Y^-4 form at any pH is given by the ₆ (loss of 6 protons from the fully-protonated H₆Y⁺² form).

₆ = 1/{[H ]⁶/K₁K₂K₃K₄K₅K₆ + [H⁺]⁵/K₂K₃K₄K₅K₆ + [H⁺]⁴/K₃K₄K₅K₆

+ [H⁺]³/K₄K₅K₆ + [H⁺]²/K₅K₆ + [H⁺]/K₆ + 1} (16.49)

Substitution of the appropriate acidity constants into equation 16.49 gives an estimate of fraction of EDTA that is in the appropriate form for complexation (Table 16.4)

The endpoint of complexometric titrations may be detected by either an ion-selective electrode sensitive to the metal being analyzed, or a metal ion indicator. This latter method employs a chelating ligand which changes color in going from the complexed to the uncomplexed form. For a metal ion indicator to be effective, it must bind the metal less strongly than EDTA does at the given pH. Also, it must not be affected by other metal ions in the sample.

Table 16.4

₆ Values for EDTA as a function of pH

pH	6	pH	6
1	1.9x10^-18	2	3.3x10^-14
3	2.6x10^-11	4	3.9x10^-9
5	3.7x10^-7	6	2.3x10^-5
7	5.0x10^-4	8	5.6x10^-3
9	0.054	10	0.36
11	0.85	12	0.98

For calcium and total hardness determinations, a couple of specific dyes, Eriochrome black T (Figure 16.4) and Eriochrome blue black R, are used as metal ion indicators. These dyes do not bind magnesium and calcium as strongly as EDTA. However, Eriochrome black T will bind Cu(+II), Ni(+II), Co(+II), Cr(+III), Fe(+III) and Al(+III) more strongly than EDTA. It is said to be blocked by these metals, and cannot be used for their direct determination with EDTA as a titrant.

Figure 16.4. Eriochrome black T

1. TOTAL HARDNESS

A. Definition and Environmental Significance

Hardness is a term used for the total concentration of divalent cations in water. These may include Ca(+II), Mg(+II), Sr(+II), Ba(+II), Fe(+II) and Mn(+II), although the last four are usually negligible. It is a parameter of concern in drinking waters, and sometimes industrial process waters and agricultural waters. Hardness is considered a nuisance, because divalent cations will bind (complex) with the carboxyl groups in soap and cause its precipitation. In this way is inhibits its action (sudsing), and is often said to "consume" soap. In addition, hardness species may cause severe hydraulic problems in pipes by precipitating as metal carbonates. This is especially true when the water is heated such as in home water-heaters, and boilers. On the other hand, hardness has been associated with lower incidences of cardiovascular disease. This last point is controversial, however.

Hardness is derived from limestone and related minerals. Highest concentrations in US surface waters are found in the mid-west and south-west. Hardness has historically been expressed as a mass concentration of equivalent calcium carbonate. This is done, because calcium is the dominant hardness species and carbonate-bicarbonate is the most prevalent counter ion. Therefore, the conversion factor is just the molecular weight of CaCO₃.

1 mole/L of Hardness = 100 g/L of hardness as CaCO₃ (16.50)

1 equivalent/L of Hardness = 50 g/L of hardness as CaCO₃ (16.51)

Hardness may be categorized by the constituent anions (i.e., calcium-hardness, magnesium-hardness) or by the counter ions (i.e., carbonate and non-carbonate hardness). The carbonate hardness is the maximum amount of hardness that could possibly be precipitated as carbonates. Such a precipitation might occur if the sample were to be heated, evaporated or if the pH was raised. Carbonate hardness is equal to the alkalinity (in mg/L as CaCO₃) when the alkalinity is less than the total hardness. The remaining hardness is referred to as non-carbonate. When the reverse is true (i.e., hardness < alkalinity), the carbonate hardness is equal to the total hardness, and non-carbonate hardness is zero.

Total hardness = Ca-hardness + Mg-hardness (16.52)

Total hardness = Carbonate hardness + non-carbonate hardness (16.53)

Hardness is commonly removed in drinking water treatment plants by alkaline precipitative softening. In order to calculate chemical requirements for precipitative softening, it is necessary to know both the total hardness, and the calcium hardness (i.e., calcium concentration). Point of use treatment systems generally use cation exchange to remove hardness.

B. Principle

Eriochrome black T is added to the sample at high pH (about 10). The high pH causes the metal ion indicator to partially deprotonate, giving a form that is effective as a chelating agent (pKs are 6.3 and 11.6). A deep red complex then forms with calcium and magnesium present in the sample. Also at this pH the color change experienced by the indicator is most easily seen (e.g., at lower pH the uncomplexed, protonated Eriochrome black T is also somewhat reddish). Furthermore, the EDTA is most effective at high pH (recall Table 16.4). On the other hand, calcium and magnesium as well as many other metals, will hydrolyze and precipitate at high pH. This is undesirable as it would take them out of solution and prevent their determination. To avoid this problem an auxiliary complexing agent is added. These are ligands that bind strongly enough with the analyte to out-compete hydroxide binding, and thereby prevent its precipitation, but not so strongly as to interfere with binding by the EDTA or metal ion indicator. In the case of total hardness, triethanolamine and ammonia are used, but other types of titrations might also use citrate or tartrate. Whether or not the auxiliary complexing agent reacts with metal ions other than the analyte is not important.

In all but the softest of waters, calcium and magnesium will be present in large excess as compared to the metal ion indicator. When EDTA is titrated, it ties up this excess magnesium and calcium. Once the excess hardness is exhausted, the EDTA begins stripping the Eriochrome black T of its calcium and magnesium. The indicator then loses its intense red color (to blue color) and the titration is at its endpoint. The presence of magnesium improves the sharpness of the endpoint. To ensure that some magnesium will be present, a small amount of Mg-EDTA is added along with the buffer. Because both analyte and titrant are added in a 1:1 ratio, this does not effect the final determination. The moles of EDTA added as titrant are equal to the moles of calcium and magnesium originally present. This type of procedure is referred to as a direct complexometric titration.

In a back complexometric titration, EDTA is added in excess and a metal other than the analyte metal is used as the titrant. For this type of titration it is important that the titrant metal bind less strongly to EDTA than does the analyte. A back titration is useful under conditions where the metal cannot be kept in solution in the absence of EDTA, where the analyte blocks the indicator, or where complexation kinetics with EDTA are slow.

When high concentrations of interfering metal are present, certain inhibitors must be added prior to titration. These are ligands that will strongly bind the interfering metal, such as cyanide, sulfide, and hydroxylamine. A large interlaboratory study found a relative standard deviation of 2.9% and a relative bias of 0.8% for a synthetic sample containing 610 mg/L total hardness as CaCO₃.

C. Procedures

1. Place exactly 50 ml of the sample into a 125 ml erlenmeyer flask.

2. Add 1-2 ml of the buffer solution

3. Add 5-6 drops of the EBT indicator.

4. Titrate with the EDTA solution until all reddish coloration disappears. Maintain constant stirring during this operation. For best results the titration should be completed within 5 minutes.

D. Reagents

1. Buffer Solution - Dissolve 16.9 g ammonium chloride in 143 ml conc ammonium hydroxide. <caution: avoid inhalation of fumes!> Add 1.25 g Mg-EDTA and dilute to 250 ml with distilled water.

2. Hardness Indicator Solution (approx. 0.011M) - Dissolve 0.5 g of Eriochrome Black T (1-(1-hydroxy-2-naphthylazo)-5-nitro-2-naphthol-4-sulfonic acid) in 100 g triethanolamine (2,2',2''-nitrilotriethanol).

3. EDTA Titrant Solution (approx. 0.01M) - dissolve 3.723 g Na-EDTA (sodium ethylenediaminetetraacetate dihydrate) in 1000 ml distilled water. Determine titer by standardizing agaist the standard calcium solution (follow steps 1-4).

4. Standard Calcium Solution (5.00 mM) - Weigh 0.5005 g anhydrous calcium carbonate (primary standard grade) and place in a 500-ml erlenmeyer flask. Carefully add small amounts of 6 M HCl (approx 50% of conc.) until CaCO₃ just dissolves. Add 200 ml distilled water and boil for a few minutes to expel dissolved CO₂. Cool, add a few drops of methyl red indicator and adjust to the "intermediate" orange color by adding 3N NH₄OH or 6M HCl as needed. Transfer quantitatively to a 1-liter volumetric flask and dilute to the "mark" with distilled water.

2. CALCIUM

A. Principle

Calcium can be determined by atomic absorption spectrophotometry, by a redox titrimetric method and by a complexometric method. The complexometric procedure outlined here is quite similar the the total hardness method. Several modifications must be made however, to make the analysis specific for this one hardness species. First, a metal ion indicator that complexes with calcium, but not magnesium (Eriochrome blue black R) is used. Second magnesium is partially removed by using a higher pH (about 12) which results in precipitation as Mg(OH)₂. Note that auxiliary complexing agents are not used in this procedure. Calcium hydroxide does not precipitate at this elevated pH. In addition, EDTA binds preferentially with Ca by virtue of its larger stability constant. An extensive interlaboratory study found a standard deviation of 9.2%, and a relative bias of 1.9% for a synthetic water containing 108 mg/L calcium and 82 mg/L magnesium.

B. Procedures

1. Place exactly 50 ml of the sample into a 125-ml erlenmeyer flask.

2. Add 3 ml of NaOH solution. If the pH is still below 12, add more base.

3. Add 1 scoop of Eriochrome Blue Black R indicator (0.1-0.2 g)

4. Titrate with the EDTA solution until the color changes completely from red to royal blue. Maintain continuous stirring throughout.

C. Reagents

1. EDTA Titrant Solution (approx. 0.01M) - (same as with hardness determination) dissolve 3.723 g Na-EDTA (sodium ethylenediaminetetraacetate dihydrate) in 1000 ml distilled water. Determine titer by standardizing against the standard calcium solution (follow steps 1-4).

2. Sodium Hydroxide Solution (1N) - Dilute 40 g NaOH to 1 liter with distilled water.

3. Eriochrome Blue Black R indicator - Grind together in a mortar 200 mg powdered dye [sodium-1-(2-hydroxyl-1-naphthylazo)-2-naphthol-4-sulfonic acid] and 100 g solid NaCl to about 40-50 mesh. Store in a tightly stoppered bottle.

4. Standard Calcium Solution (5.00 mM) - Weigh 0.5005 g anhydrous calcium carbonate (primary standard grade) and place in a 500-ml erlenmeyer flask. Carefully add small amounts of 6 M HCl (approx 50% of conc.) until CaCO₃ just dissolves. Add 200 ml distilled water and boil for a few minutes to expel dissolved CO₂. Cool, add a few drops of methyl red indicator and adjust to the "intermediate" orange color by adding 3N NH₄OH or 6M HCl as needed. Transfer quantitatively to a 1-liter volumetric flask and dilute to the "mark" with distilled water.

D. Redox Titrations

Redox titrations are based on oxidation-reduction reactions between the analyte and the titrant or some intermediate redox carrier. Common oxidants used in redox titrations include dichromate (Cr₂O₇^-2), iodate (IO_3-), iodine (I₂), and permanganate (MnO_4-). Common reducing agents are arsenite (AsO₃^-3), ferrocyanide (Fe(CN)₆^-4), ferrous (Fe⁺²), sulfite (SO₃^-2) and thiosulfate (S₂O₃^-2). Although many of the oxidizing agents are relatively stable, the reducing agents are often susceptible to oxidation by atmospheric oxygen, and therefore their titer must be checked regularly against a standard.

Many redox titrations utilize iodine. When a reducing analyte is added to I₂ to form I^-, the process is called Iodimetry. Instead, when an ozidizing analyte converts I^- to I₂, it is Iodometry. In the presence of iodide (I^-), iodine (I₂) will form a triiodide complex (I_3-) which greatly enhances its solubility in water. For the determination of triiodide, sodium thiosulfate is almost always used as the titrant. Although triiodide can be self-indicating, starch is generally used as an end point indicator. It forms an intense blue color with triiodide which can increase the sensitivity of endpoint detection by a factor of ten. It is important not to add starch until just before the endpoint. This allows one to see a more more gradual color change in the early part of the titration, and it avoids problems with excessively strong triiodide binding by the starch and over shoot.

Thiosulfate reacts with triiodide rapidly under neutral or acidic conditions to give iodide and titrathionate. Commercial thiosulfate is not of sufficient purity to be a primary standard. Instead, it must be titrated against a standard triiodide solution prepared by reaction of iodide with some primary standard oxidant (e.g., KIO₃). Thiosulfate is also readily oxidized by atmospheric oxygen at neutral to acidic conditions. It must be stored in a slightly alkaline buffered solution; often carbonate is used for this purpose.

1. RESIDUAL CHLORINE (DPD Titrimetric Method)

A. Principle

Either chlorine or triiodide react with N,N-Diethyl-p-phenylene diamine (DPD) to form a relativly stable free radical species with an intense red color. This is then back titrated to the original colorless form with ferrous iron. The detection limit is about 18 ug/L. Oxidized manganese species will interfere. The DPD methods are the most widely used of the chlorine residual procedures (Gordon et al., 1988).

Free residual chlorine is measured first via direct reaction with DPD. Monochloramine will react slowly with DPD through a direct pathway at a rate of about 5% per minute depending on concentration. For this reason mercuric chloride is added (HgCl₂). It apparently inhibits the reaction between monochloramine and DPD. Although the reaction mechanisms isn't known, it is presumed to act by formation of an unreactive complex with monochloramine.

Combined residuals are measured after addition of iodide. Monochloramine will react quickly with trace quantities of iodide to form triiodide which then reacts with the DPD. For dichloramine, the reaction is much slower, and relatively large amounts of iodide are needed for the reaction to go to completion. Both hydrogen peroxide and persulfate will also oxidize iodide, and can therefore interfere with the combined residual chloring determination.

The DPD reagent is also subject to base catalyzed oxidation by atmospheric oxygen. For this reason it is kept in an acidified state, and replaced every month. Since the reaction with chlorine and triiodide is best when carrier out at neutral pH, a neutral buffer is used and the DPD must be stored separately from the buffer and added at the last minute.

Figure 16.5

DPD Titrimetric Determination of Chlorine

B. Procedure

1. Place 5 ml of both the buffer reagent and the DPD indicator solution in the titration flask and mix.

2. Add 100 ml sample and mix.

3. Free Residual Chlorine (FRC): Titrate rapidly with standard ferrous ammonium sulfate (FAS) titrant until the red color disappears (Reading A).

4. Monochloramine (MCA): Add one very small crystal of Potassium Iodide (KI) to solution from step 3 and mix. Continue titration until the red color again disappears (Reading B).

5. Dichloramine (DCA): Add several crystals of KI (about 1 g) to the solution titrated in step 4 and mix to dissolve. Allow to stand for 2 minutes and then continue titration until the red color is again discharged (Reading C). For very high dichloramine concentrations, allow an additional 2 minutes standing time if color driftback indicates incomplete reaction. When dichloramine concentrations are not expected to be high, use half the specified amount of potassium iodide.

6. CALCULATIONS

The various forms of chlorine residual are best calculated according to the following scheme. Note that for a 100 ml sample, 4.00 ml standard FAS titrant = 1.00 mg/l residual chlorine.

Species	Formula
HOCl + OCl	A/4
NH2Cl	(B-A)/4
NHCl2	(C-B)/4

C. REAGENTS

1. Phospate buffer solution: Dissolve 24 g anhydrous Na₂HPO₄, and 46 g anhydrous KH₂PO₄ in distilled water. Combine this solution with 100 ml distilled water in which 800 mg Na₂EDTA have been dissolved. Dilute to 1 liter with distilled water and add 20 mg HgC1₂ to inhibit biological growth and to control iodide interferences in the FRC titration.

2. DPD Solution: Dissolve 1 g N,N-diethyl-p-phenylenediamine oxalate in distilled water containing approximately 2 ml conc. H₂SO₄ and 200 mg Na₂EDTA dihydrate. Make up to 1 liter, store in a brown glass-stoppered bottle.

3. Standard ferrous ammonium sulfate (FAS) titrant: Dissolve 1.106 g Fe(NH₄)₂(SO₄)₂ . 6H₂0 in distilled water containing 1/4 ml of conc. H₂SO₄ and make up to 4 liters with distilled water.

4. Potassium Iodine Crystals

2. OZONE (iodometric method)

Gas-phase concentrations of ozone are most easily measured iodometrically. A portion of the gas stream is directed to a gas bubbler filled with 2% KI solution for an exact period of time. Ozone reacts stoichiometrically to form an equivalent amount of iodine.

O₃ + 2KI + H₂O ---------> I₂ + O₂ + 2OH^- + 2K⁺ (16.55)

The iodine formed is then titrated with sodium thiosulfate using starch as an indicator to accentuate the endpoint (APHA et al., 1985).

3. DISSOLVED OXYGEN

A. Significance to Environmental Engineering

Dissolved Oxygen (D.O.) is an important water quality parameter for natural aquatic systems. A minimum concentration is required for the survival of higher aquatic life. In particular, the larval stages of certain cold-water fishes are quite sensitive. Significant discharges of organic wastes may depress the D.O. concentrations in receiving waters. This occurs due to the rapid, microbially-mediated oxidation of these wastes upon discharge. For this reason each state has established ambient dissolved oxygen standards that must not be violated. These standards effectively limit the organic waste loading and spatial distribution of these loads to natural waters.

Another use of D.O. is the assessment of oxidation state in groundwaters and sediments. As samples are collected deeper into the subsurface or into aquatic sediments, the D.O. often drops. Eventually the level is low enough so that anaerobic process predominate.

Dissolved oxygen is also a very important parameter in biological treatment processes. In a gross sense, D.O. concentrations indicate when aerobic and anaerobic organisms will predominate. However, more commonly, dissolved oxygen determinations are used to assess the adequacy of oxygen transfer systems to aerobic suspended culture operations such as activated sludge. It may also be used to indicate the suitability for the growth of such sensitive organisms such as the nitrifying bacteria.

Finally, dissolved oxygen is used in the assessment of the strength of a wastewater through either the Biochemical Oxygen Demand (BOD) or respirometric studies. Briefly, the BOD test employs a bacterial seed to catalyze the oxidation of 300 mL of full-strength or diluted wastewater. The strength of the un-diluted wastewater is then determined from the dilution factor and the difference between the initial D.O. and the final D.O.

Oxygen is a rather insoluble gas, and as a result its is often the limiting constituent in the purification of wastes and natural waters. Its solubility ranges from 14.6 mg/l at 0^oC to about 7 mg/l at 35^oC. In addition to temperature, its solubility varies with barometric pressure and salinity. The saturation concentration of oxygen in distilled water may be calculated from the following empirical expression:

(16.56)

where:

P_vw = water vapor partial pressure (atm)

= 11.8571 - (3840.70/T_k) + (216,961/T_k²)

P = total atmospheric (barometric) pressure (atm), which may be read directly or calculated from a remote reading at the same time from:

= P_o - (0.02667)H/760

H = Difference in elevation from the location of interest (at P) to the reference location (at P_o) in feet.

P_o = Simultaneous barometric pressure at a nearby reference location

= pressure/temperature interactive term

= 0.000975 - (1.426x10^-5T) + (6.436x10^-8T²)

T = Temperature in degrees centigrade

C_s1 = Saturation concentration of oxygen in distilled water at 1 atmosphere total pressure.

ln(C_s1) = -139.34411 + (1.575701x10⁵/T_k) - (6.642308x10⁷/T_k²) + (1.243800x10¹⁰/T_k³) - (8.621949x10¹¹/T_k⁴). (16.57)

T_k = Temperature in degrees Kelvin (T_k = T + 273.15)

Under most circumstances (elevation less than 1000 ft, average weather) the pressure may be assumed to be 1 atm, and C_s can be approximated by C_s1 using only the above equation. One might also turn to any one of a number of tabulations of C_s1 (as a function of temperature) such as is found on pg 413 of the 16th edition of Standard Methods for the Examination of Water and Wastewater.

Dissolved oxygen may be measured by two common methods, the Winkler titrimetric method and the Membrane Electrode method. The Winkler method, like all classical methods of analysis, measures dissolved oxygen concentration. The electrode method measures dissolved oxygen activity. The two are related by the activity coefficient, _O2:

(16.58)

where the square brackets ([....]) indicate concentration (Moles/liter) and the curved brackets ({....}) indicated activity. For most unpolluted or moderately polluted waters, the activity coefficient will be very close to 1.0, and concentration will equal activity. However, for some waters containing high concentration of salinity, oxygen activities will be greater than concentrations. Activity better describes the "availability" of oxygen, and is therefore, more important in determining oxygenation kinetics. Concentration better represents the "buffering capacity" against anoxic conditions, and it is more important in stoichiometric calculations. Nevertheless, with most engineering application, the two are essentially equivalent. Other concerns and relative advantages of the two methods are as follows:

Winkler

1. Does not require expensive or sophisticated equipment.

2. It is little hindered by surfactants and surface-coating species

3. Mixing intensity is of little concern

Figure 16.6

Chemical Scheme for the Winkler D.O. Analysis

Electrode

1. Final determinations can be readily made in the field

2. In situ D.O. measurements are easily made, because the electrodes are generally immersible

3. It can be used for continuous monitoring

4. It is non-destructive. Thus, the sample may be returned or used for additional analyses.

5. It may be used with highly-colored waters

B. Principles

Manganese is rapidly oxidized by dissolved oxygen at high pH. It then oxidizes iodide to iodine at low pH, and the resulting iodine is titrated with sodium thiosulfate. Starch is used to obtain a sharper endpoint.

Final acidification is employed to reach a pH below 5 where the proper stoichiometry for the iodine/thiosulfate reaction is obtained, however, the pH must not drop too low so that the decomposition of thiosulfate becomes important. Under acidic conditions, the iodine will react with any residual iodide to form triodide anion (I₃). It is actually this species which reacts with thiosulfate giving tetrathionate and three iodide anions.

The alkali azide iodide reagent also contains sodium azide, NaN₃. This is a recent modification designed to eliminate interferences due to nitrite. The azide will react with nitrite to give nitrogen gas and nitrous oxide, neither of which cause interferences.

NaN₃ + H⁺ -------------> HN₃ + Na⁺ (16.59)

HN₃ + NO₂^- + H⁺ ---------> N₂ + N₂O + H₂O (16.60)

Otherwise nitrite would oxidize iodide to iodine thereby raising the apparent dissolved oxygen concentration.

2NO₂^- + 2I^- + 4H⁺ -------------> I₂ + N₂O₂ + 2H₂O (16.61)

Note that the product, a nitric oxide species, can then scavenge any oxygen introduced during titration and reform nitrite to start the cycle over again.

N₂O₂ + 1/2O₂ + H₂O -----------------> 2NO₂^- + 2H⁺ (16.62)

Other substances which may interfere include reducing agents such as sulfite, thiosulfate, ferrous iron, and aldehydes.

Because thiosulfate often contains an ill-defined number of waters of hydration, it is difficult to prepare an exact concentration by weight alone. Thus, it is necessary to standardize this solution against a primary standard such as potassium dichromate or potassium biniodate. Biniodate is preferred, because the reaction with dichromate is slow and the color of trivalent chromium may interfere with the endpoint. In either case, a known amount of the primary standard is added to an excess of iodide.

2IO₃^- + 10I^- + 12H⁺ --------> 6I₂ + 6H₂O (16.63)

Cr₂O₇^-2 + 6I^- + 14H⁺ --------> 2Cr⁺³ + 3I₂ + 7H₂O (16.64)

The resulting equivalent concentration of iodine is titrated with the thiosulfate solution. Thiosulfate solutions should be preserved with a small amount of sodium hydroxide. This serves to discourage the growth of sulfur bacteria which oxidize thiosulfate to sulfate. Also the high pH will retard downward pH drift (from absorption of atmospheric carbon dioxide) and thereby minimize the disproportionation of thiosulfate to sulfate and elemental sulfur.

Duplicate analyses using the Winkler method (with azide modification) should agree within a standard deviation of 20 ug/l for distilled water and 60 ug/l for wastewater. Samples containing high concentrations of interfering substances may show greater variabilities. Negative systematic errors can occur due to the loss of iodine prior to (or during) titration through volatilization or reaction with organic matter. Positive systematic error may result from a small amount of air oxidation of iodide also during titration.

C. Sampling

It is important to limit contact of the sample with air. Where possible use a Kemerer or Van Dorn-type sampler. Specialized D.O. samplers are also available that passively flush the sample bottle with 1 or 2 volumes of sample before taking the final sample. A typical field sampling procedure using a Van Dorn sampler would be:

1. Prepare Van Dorn sampler by pulling back the plungers and setting their lines in the triggering mechanism.

2. Lower sampler to the desired height and release messenger.

3. Raise sampler, insert rubber tube deep into a BOD bottle, release clamp and open vent. Allow the BOD bottle to overflow by two full volumes.

4. Remove rubber tube, cap the BOD bottle and close the tube clamp.

5. Repeat until the desired number of samples have been taken.

It is common practice to "fix" (add all three reagents) in the field for later titration. However, this may tend to give negative bias due to loss of iodine. An alternative is to add 0.7ml sulfuric acid, 0.02g sodium azide to each sample, keep cold and away from light for complete analysis up to 6 hours later. In this case it would be necessary to add additional 2 ml of the manganous sulfate reagent, 3 ml of the alkali-iodide-azide reagent and 2 ml of the sulfuric acid.

D. Procedures

1. To a 300 ml BOD bottle filled with sample add 1 ml manganous sulfate solution and 1 ml alkali-iodide-azide reagent, cap and shake. Be careful to avoid trapping any air bubbles. If this occurs, remove cap, add a small amount of distilled water and re-cap.

2. Allow precipitate to settle to about half the hight of the bottle and add 1 ml conc. sulfuric acid. Re-stopper and mix.

3. Titrate 200 ml of this sample with the 0.025M sodium thiosulfate solution until a very pale yellow color is obtained. Add a few drops of the starch solution and titrate until the blue color disappears.

E. Winkler Reagents

1. Manganous surfate solution - Dissolve 400 g MnSO₄^.2H₂O in distilled water and dilute to 1 liter.

2. Alkali-iodide-azide reagent - Dissolve 500 g NaOH and 150 g KI in distilled water and dilute to 1 liter. Add 10 g NaN₃ dissolved in 40 ml distilled water.

3. Sulfuric acid concentrated

4. Sodium Thiosulfate titrant - (0.025M) Dissolve 6.205 g Na₂S₂O₃^.5H₂O in distilled water. Add 0.4 g NaOH and dilute to 1 liter. Standardize with the primary-standard Potassium Biniodate or Potassium Dichromate solution using starch to define the endpoint.

5. Starch Solution - Dissolve 2g soluble starch and 0.2g salicylic acid (preservative) in 100ml of hot distilled water.

4. CHEMICAL OXYGEN DEMAND

The chemical oxygen demand (COD) of a waste is measured in terms of the amount of potassium dichromate (K₂Cr₂O₇) reduced by the sample during 2 hr of reflux in a medium of boiling, 50% H₂SO₄ and in the presence of a Ag₂SO₄ catalyst.

The stoichiometry of the reaction between dichromate and organic matter is:

(16.65)

where:

(16.66)

The oxidation is accompanied by the reduction of dichromate:

6e^- + 14H⁺ + Cr₂O₇^-2 -----------> 2Cr⁺² + 7H₂O (16.67)

E_o = 1.33 volts

Chloride ion interferes, being precipitated as AgCl and subject to unpredictable oxidation when Ag₂SO₄ is used as a catalyst, or being oxidized to Cl₂ when Ag₂SO₄ is not used:

6Cl^- + 14H⁺ + Cr₂O₇^-2 -----------> 3Cl₂ + 2Cr⁺² + 7H₂O (16.68)

Free chloride is largely removed by complexation with mercury as HgCl₂(aq). Autooxidation of Cr₂O₇^-2, and organic impurities in the reaction system can be accounted for by running a blank with distilled water.

Upon completion of the reaction with organic matter, it is necessary to determine the residual dichromate in the reaction flask. A reducing agent, in this case Fe⁺², can be used to titrate the dichromate.

Fe⁺² ------------> Fe⁺³ + e^- (16.69)

E_o = -0.77 volts

However, because of the various ionic interactions which occur in electrolyte solution, the oxidation potential for iron in 1M sulfuric acid is -0.66 volts (formal potential). The endpoint of the ferrous titration of dichromate can be determined colorimetrically using Ferroin indicator. Ferroin contains 1,10-phenanthroline, which forms a colored complex with the ferrous ions. At the endpoint after the dichromate has been reduced, the color changes from blue-green to reddish brown (Fe-phenanthroline complex).

The COD test is faster than BOD analysis, so it is commonly used as a quick assessment of wastewater strength and treatment performance. Like the BOD, it does not measure oxidant demand due to nitrogeneous species. However, it cannot distinguish between biodegradable and non-biodegradable organic matter. As a result COD's are always higher than BOD's.

REFERENCES

APHA, AWWA, and WPCF, Standard Methods for the Examination of Water and Wastewater, APHA, Washington (14 ed) pp. 273-282, or (15 ed) pp. 249-257, or (16 ed) pp. 265-273.

Flaschka, H.A. (1959) EDTA Titrations, Pergamon Press, New York.

Kramer, J.R. (1982) "Alkalinity and Acidity", Chapter 3 in Water Analysis: Volume 1, Inorganic Species, R.A. Minear & L.H. Keith editors, Academic Press, pp.85-135.

McQuaker et al. (1983) Environ. Sci. & Technol., 17:431-435.

Perdue, E.M. (1985) Acidic Functional Groups of Humic Substances, in Humic Substances in Soil, Sediment and Water: Geochemistry, Isolation, and Characterization, Aiken et al., eds., Wiley, Publ., New York, pp. 493-526.

Sawyer, C.N. and P.L. McCarty (1978) Chemistry for Environmental Engineering, 3rd Edition, McGraw-Hill Publ., pp. 24-29, 168-188, 343-376.

Schwarzenbach, G & H.A. Flaschka (1969) Complexometric Titrations, Methuen, London.

Snoeyink, V.L. and D. Jenkins (1980) Water Chemistry, Wiley, pp. 86-145, 156-196.

PROBLEMS

16.1 An EDTA solution is added to water sample containing a low concentration of calcium (20^oC). If the total EDTA concentration (all forms) in the water is 0.1M, and all metal species that might form complexes are several orders of magnitude lower in concentration that this. What percentage of the calcium is complexed with the EDTA at:

a) pH 4?

b) pH 10?

16.2 A sample of Wisconsin River water at Muscoda (May, 1952) gave the following analysis (Hem, 1959). Calculate the total hardness, Calcium hardness, magnesium hardness, carbonate hardness, and non-carbonate hardness in mg/L as CaCO₃.

Constituent	Concentration (mg/L)
Silica (SiO2)^o	4.2
Aluminum (Al)^+3	trace
Iron (Fe) total	trace
Calcium (Ca)^+2	18
Magnesium (Mg)^+2	8.5
Sodium (Na)^+	2.5
Potassium (K)^+	2.4
Bicarbonate (HCO3)^-	90
Sulfate (SO4)^-2	9.5
Chloride (Cl)^-	1.5
Fluoride (F)^-	trace
Nitrate (NO3)^-	0.8
Total Solids (measured)	106
Specific Conductance (umhos/cm)	165
pH	7.0
Color (Co-Pt Units)	35

Conductivity = Alk_tot

In order to account for changes in ionic conductances with changing concentrations, the Onsager equation may be employed:

A = A_o - (60.2 + 0.229A_o)C^0.5 (4)

Here "C" represents the equivalent concentration of the salt. For a pure solution of calcium and bicarbonate this would just be equal to the alkalinity (in mg/l as CaCO₃) divided by 50,000. Also, the equivalent conductance, A, is related to the conductivity according to:

Conductivity = CA(1000) (5)

when conductivity is in umho/cm. We can combine equations 4 and 5 to get an expression for conductivity in terms on alkalinity only.

Conductivity = 2.08(Alk_tot)-1.68(Alk_tot)^1.5 (6)

Over the concentration range from 0-200 mg/l alkalinity, this relationship is nearly linear, so that :

Alk_tot = (Conductivity)/2 (7)

For pure solution of carbonate (e.g., Na₂CO₃) the counter ion concentration will be twice the molar carbonate concentration. When titrating a pure carbonate solution of known concentration, C_B will be know.

C_B = 2C_T (19)