Constituents of Water and Wastewater Given a wastewater, what process should be applied to treat it: biological, chemical, or physical? Should it be treated with a combination of processes? These questions cannot be answered unless the constituents of the wastewater are known. Thus, before any wastewater is to be treated, it is important that its constituents are determined. On the other hand, what are the constituents of a given raw water that make it unfit to drink? Are these constituents simply in the form of turbidity making it unpleasant to the eye, in the form of excessive hardness making it unfit to drink, or in the form bacterial contamination making it dangerous to drink? Water and wastewater may be characterized according to their physical, chemical, and micro- biological characteristics. These topics are discussed in this chapter. 2.1 PHYSICAL AND CHEMICAL CHARACTERISTICS The constituent physical and chemical characterizations to be discussed include the following: turbidity (physical), color (physical), taste (physical) temperature (phys- ical), chlorides (chemical), fluorides (chemical), iron and manganese (chemical), lead and copper (chemical), nitrate (chemical), sodium (chemical), sulfate (chemi- cal), zinc (chemical), biochemical oxygen demand (chemical), solids (physical), pH (chemical), chemical oxygen demand (chemical), total organic carbon (chemical), nitrogen (chemical), phosphorus (chemical), acidity and alkalinity (chemical), fats and oils and grease (chemical), and odor (physical). The characterization will also include surfactants (physical), priority pollutants (chemical), volatile organic com- pounds (chemical), and toxic metal and nonmetal ions (chemical). These constituents are discussed in turn in the paragraphs that follow. 2.1.1 T URBIDITY Done photometrically, turbidity is a measure of the extent to which suspended matter in water either absorbs or scatters radiant light energy impinging upon the suspen- sion. The original measuring apparatus that measures turbidity, called the Jackson turbidimeter , was based on the absorption principle. A standardized candle was placed under a graduated glass tube housed in a black metal box so that the light from the candle can only be seen from above the tube. The water sample was then poured slowly into the tube until the candle flame was no longer visible. The turbidity was then read on the graduation etched on the tube. At present, turbidity measure- ments are done conveniently through the use of photometers. A beam of light from a source produced by a standardized electric bulb is passed through a sample vial. 2 TX249_Frame_C02.fm Page 125 Friday, June 14, 2002 1:51 PM © 2003 by A. P. Sincero and G. A. Sincero 126 Physical–Chemical Treatment of Water and Wastewater The light that emerges from the sample is then directed to a photometer that measures the light absorbed. The readout is calibrated in terms of turbidity. The unit of turbidity is the turbidity unit (TU) which is equivalent to the turbidity produced by one mg/L of silica (SiO 2 ). SiO 2 was used as the reference standard. Turbidities in excess of 5 TU are easily detected in a glass of water and are objectionable not necessarily for health but for aesthetic reasons. A chemical, for- mazin, that provides a more reproducible result has now replaced silica as the standard. Accordingly, the unit of turbidity is now also expressed as formazin turbidity units (FTU). The other method of measurement is by light scattering. This method is used when the turbidity is very small. The sample “scatters” the light that impinges upon it. The scattered light is then measured by putting the photometer at right angle from the original direction of the light generated by the light source. This measure- ment of light scattered at a 90-degree angle is called nephelometry . The unit of turbidity in nephelometry is the nephelometric turbidity unit (NTU). 2.1.2 C OLOR Color is the perception registered as radiation of various wavelengths strikes the retina of the eye. Materials decayed from vegetation and inorganic matter create this perception and impart color to water. This color may be objectionable not for health reasons but for aesthetics. Natural colors give a yellow-brownish appearance to water, hence, the natural tendency to associate this color with urine. The unit of measurement of color is the platinum in potassium chloroplatinate (K 2 PtCl 6 ). One milligram per liter of Pt in K 2 PtCl 6 is one unit of color. A major provision of the Safe Drinking Water Act (SDWA) is the promulgation of regulations. This promulgation requires the establishment of primary regulations which address the protection of public health and the establishment of secondary regulations which address aesthetic consideration such as taste, appearance, and color. To fulfill these requirements, the U.S. Environmental Protection Agency (USEPA) establishes maximum contaminant levels (MCL). The secondary MCL for color is 15 color units. 2.1.3 T ASTE Taste is the perception registered by the taste buds. There should be no noticeable taste at the point of use of any drinking water. The numerical value of taste (or odor to be discussed below) is quantitatively determined by measuring a volume of the sample A (in mL) and diluting it with a volume B (in mL) of distilled water so that the taste (or odor) of the resulting mixture is just barely detectable at a total mixture volume of 200 mL. The unit of taste (or odor) is then expressed in terms of a threshold number as follows: (2.1)TON or TTN AB+ A = TX249_Frame_C02.fm Page 126 Friday, June 14, 2002 1:51 PM © 2003 by A. P. Sincero and G. A. Sincero Constituents of Water and Wastewater 127 where TON = threshold odor number TTN = threshold taste number 2.1.4 O DOR Odor is the perception registered by the olfactory nerves. As in the case of taste, there should be no noticeable odor at the point of use of any drinking water. The secondary standard for odor is 3. Fresh wastewater odor is less disagreeable than stale wastewater odor but, nonetheless, they all have very objectionable odors. Odors are often the cause of serious complaints from neighborhoods around treatment plants, and it is often difficult for inspectors investigating these complaints to smell any odors in the vicinity of the neighborhood. The reason is that as soon as he or she is exposed to the odor, the olfactory nerves become accustomed to it and the person can no longer sense any odor. If you visit a wastewater treatment plant and ask the people working there if any odor exists, their responses would likely be that there is none. Of course, you, having just arrived from outside the plant, know all the time that, in the vicinity of these workers, plenty of odors exist. The effect of odors on humans produces mainly psychological stress instead of any specific harm to the body. Table 2.1 lists the various odorous compounds that are associated with untreated wastewater. The determination of odors in water was addressed previously under the discus- sion on taste. Odors in air are determined differently. They are quantitatively mea- sured by convening a panel of human evaluators. These evaluators are exposed to odors that have been diluted with odor-free air. The number of dilutions required to bring the odorous air to the minimum level of detectable concentration by the panel is the measure of odor. Thus, if three volumes of odor-free air is required, the odor of the air is three dilutions . It is obvious that if these evaluators are subjected to the odor several times, the results would be suspicious. For accurate results, the evaluators TABLE 2.1 Malodorous Compounds Associated with Untreated Wastewater Compound Formula Threshold (ppm) Odor Quality Ammonia NH 3 18 Odor of ammonia Butyl mercaptan (CH 3 ) 3 CSH — Secretion of skunk Crotyl mercaptan CH 3 (CH 2 ) 3 SH — Secretion of skunk Diamines NH 2 (CH 2 ) 4 NH 2 , NH 2 (CH 2 ) 5 NH 2 — Decayed fish Ethyl mercaptan CH 3 CH 2 SH 0.0003 Decayed cabbage Hydrogen sulfide H 2 S < 0.0002 Rotten eggs Indole C 8 H 7 N 0.0001 — Methyl amine CH 3 NH 2 4.6 Fishy Methyl mercaptan CH 3 SH 0.0006 Decayed cabbage Methyl sulfide (CH 3 ) 2 S 0.001 Rotten cabbage Phenyl sulfide (C 6 H 5 ) 2 S 0.0001 Rotten cabbage Skatole C 9 H 9 N 0.001 Fecal matter TX249_Frame_C02.fm Page 127 Friday, June 14, 2002 1:51 PM © 2003 by A. P. Sincero and G. A. Sincero 128 Physical–Chemical Treatment of Water and Wastewater should be subjected only once, to avoid their olfactory nerves becoming accustomed to the odor thus making wrong judgments. 2.1.5 T EMPERATURE Most individuals find water at temperatures of 10–15 ° C most palatable. Groundwaters and waters from mountainous areas are normally within this range. Surface waters are, of course, subject to the effect of ambient temperatures and can be very warm during summer. The temperature of water affects the efficiency of treatment units. For example, in cold temperatures, the viscosity increases. This, in turn, diminishes the efficiency of settling of the solids that the water may contain because of the resistance that the high viscosity offers to the downward motion of the particles as they settle. Pressure drops also increase in the operation of filtration units, again, because of the resistance that the higher viscosity offers. 2.1.6 C HLORIDES Chlorides in concentrations of 250 mg/L or greater are objectionable to most people. Thus, the secondary standard for chlorides is 250 mg/L. Whether or not concentra- tions of 250 mg/L are objectionable, however, would depend upon the degree of acclimation of the user to the water. In Antipolo, a barrio of Cebu in the Philippines, the normal source of water of the residents is a spring that emerges along the shoreline between a cliff and the sea. As such, the fresh water is contaminated by saltwater before being retrieved by the people. The salt imparts to the water a high concentration of chlorides. Chloride contaminants could go as high as 2,000 mg/L; however, even with concentrations this high, the people continue to use the source and are accustomed to the taste. 2.1.7 F LUORIDES The absence of fluorides in drinking water encourages dental caries or tooth decay; excessive concentrations of the chemical produce mottling of the teeth or dental fluorosis. Thus, managers and operators of water treatment plants must be careful that the exact concentrations of the fluorides are administered to the drinking water. Optimum concentrations of 0.7 to 1.2 mg/L are normally recommended, although the actual amount in specific circumstances depends upon the air temperature, since air temperature influences the amount of water that people drink. Also, the use of fluorides in drinking water is still controversial. Some people are against its use, while some are in favor of it. 2.1.8 I RON AND M ANGANESE Iron (Fe) and manganese (Mn) are objectionable in water supplies because they impart brownish colors to laundered goods. Fe also affects the taste of beverages such as tea and coffee. Mn flavors tea and coffee with a medicinal taste. The SMCLs (secondary MCLs) for Fe and Mn are, respectively, 0.3 and 0.05 mg/L. TX249_Frame_C02.fm Page 128 Friday, June 14, 2002 1:51 PM © 2003 by A. P. Sincero and G. A. Sincero Constituents of Water and Wastewater 129 2.1.9 L EAD AND C OPPER Clinical, epidemiological, and toxicological studies have demonstrated that lead exposure can adversely affect human health. The three systems in the human body most sensitive to lead are the blood-forming system, the nervous system, and the renal system. In children, blood levels from 0.8 to 1.0 µ g/L can inhibit enzymatic actions. Also, in children, lead can alter physical and mental development, interfere with growing, decrease attention span and hearing, and interfere with heme synthesis. In older men and women, lead can increase blood pressure. Lead is emitted into the atmosphere as Pb, PbO, PbO 2 , PbSO 4 , PbS, Pb(CH 3 ) 4 , Pb(C 2 H 5 ) 4 , and lead halides. In drinking water, it can be emitted from pipe solders. The source of copper in drinking water is the plumbing used to convey water in the house distribution system. In small amounts, it is not detrimental to health, but it will impart an undesirable taste to the water. In appropriate concentrations, copper can cause stomach and intestinal distress. It also causes Wilson’s disease. Certain types of PVC (polyvinyl chloride) pipes, called CPVC (chlorinated polyvinyl chloride), can replace copper for household plumbing. 2.1.10 N ITRATE Nitrate is objectionable for causing what is called methemoglobinemia (infant cyanosis or blue babies) in infants. The MCL is 10 mg/L expressed as nitrogen. Before the establishment of stringent regulations, sludges from wastewater treat- ment plants were most often spread on lands and buried in ditches as methods of disposal. As the sludge decays, nitrates are formed. Thus, in some situations, these methods of disposal have resulted in the nitrates percolating down the soil causing excessive contaminations of the groundwater. Even today, these methods are still practiced. In order for these practices to be acceptable to the regulatory agencies, a material balance of the nitrate formed must be calculated to ascertain that the contamination of the groundwater does not go to unacceptable levels. 2.1.11 S ODIUM The presence of sodium in drinking water can affect persons suffering from heart, kidney, or circulatory ailments. It may elevate blood pressures of susceptible individuals. Sodium is plentiful in the common table salt that people use to flavor food to their taste. It is a large constituent of sea water; hence, in water supplies contaminated by the sea as in the case of Antipolo mentioned earlier, this element would be plentiful. 2.1.12 S ULFATE The sulfate ion is one of the major anions occurring naturally in water. It produces a cathartic or laxative effect on people when present in excessive amounts in drinking water. Its SMCL is 250 mg/L. 2.1.13 Z INC Zinc is not considered detrimental to health, but it will impart an undesirable taste to drinking water. Its SMCL is 5 mg/L. TX249_Frame_C02.fm Page 129 Friday, June 14, 2002 1:51 PM © 2003 by A. P. Sincero and G. A. Sincero 130 Physical–Chemical Treatment of Water and Wastewater 2.1.14 B IOCHEMICAL O XYGEN D EMAND Biochemical oxygen demand (BOD) is the amount of oxygen consumed by the organ- ism in the process of stabilizing waste. As such, it can be used to quantify the amount or concentration of oxygen-consuming substances that a wastewater may contain. Analytically, it is measured by incubating a sample in a refrigerator for five days at a temperature of 20 ° C and measuring the amount of oxygen consumed during that time. The substances that consume oxygen in a given waste are composed of carbon- aceous and nitrogenous portions. The carbonaceous portion refers to the carbon content of the waste; carbon reacts with the dissolved oxygen producing CO 2 . On the other hand, the nitrogenous portion refers to the ammonia content; ammonia also reacts with the dissolved oxygen. Even though the term used is nitrogenous, nitrogen is not referred to in this context. Any nitrogen must first be converted to ammonia before it becomes the “nitrogenous.” Generally, two types of analysis are used to determine BOD in the laboratory: one where dilution is necessary and one where dilution is not necessary. When the BOD of a sample is small, such as found in river waters, dilution is not necessary. Otherwise, the sample would have to be diluted. Table 2.1 sets the criteria for determining the dilution required. This table shows that there are two ways dilution can be made: using percent mixture and direct pipetting into 300-mL BOD bottles. Normally, BOD analysis is done using 300-mL incubation bottles. Because BOD analysis attempts to measure the oxygen equivalent of a given waste, the environment inside the BOD bottle must be conducive to uninhibited bacterial growth. The parameters of importance for maintaining this type of environment are TABLE 2.2 Ranges of BOD Measurable with Various Dilutions of Samples Using Percent Mixtures By Direct Pipetting into 300-mL Bottles % mixture Range of BOD 5 mL Range of BOD 5 0.01 35,000–70,000 0.01 40,000–100,000 0.03 10,000–35,000 0.05 20,000– 40,000 0.05 7,000–10,000 0.10 10,000–20,000 0.1 3,500–7,000 0.30 4,000–10,000 0.3 1,400–3,500 0.50 2,000–4,000 0.5 700–1,400 1.0 1,000–2,000 1.0 350–700 3.0 400–1,000 3.0 150–350 5.0 200–400 5.0 70–150 10.0 100–200 10.0 35–70 30.0 40–100 30.0 10–35 50.0 20–40 50.0 5–10 100 100 100 0–5 300 0–10 TX249_Frame_C02.fm Page 130 Friday, June 14, 2002 1:51 PM © 2003 by A. P. Sincero and G. A. Sincero Constituents of Water and Wastewater 131 freedom from toxic materials, favorable pH and osmotic pressure conditions, optimal amount of nutrients, and the presence of significant amount of population of mixed organisms of soil origin. Through long years of experience, it has been found that synthetic dilution water prepared from distilled water or demineralized water is best for BOD work, because the presence of such toxic substances as chloramine, chlorine, and copper can be easily controlled. The maintenance of favorable pH can be assured by buffering the dilution water at about pH 7.0 using potassium and sodium phosphates. The potassium and sodium ions, along with the addition of calcium and magnesium ions, can also maintain the proper osmotic pressure, as well as provide the necessary nutrients in terms of these elements. The phosphates, of course, provide the necessary phosphorus nutrient requirement. Ferric chloride, magnesium sulfate, and ammonium chloride supply the requirements for iron, sulfur, and nitrogen, respectively. A sample submitted for analysis may not contain any organism at all. Such is the case, for example, of an industrial waste, which can be completely sterile. For this situation, the dilution water must be seeded with organisms from an appropriate source. In domestic wastewaters, all the organisms needed are already there; conse- quently, these wastewaters can serve as good sources of seed organisms. Experience has shown that a seed volume of 2.0 mL per liter of dilution water is all that is needed. Laboratory calculation of BOD. In the subsequent development, the formu- lation will be based on the assumption that the dilution method is used. If, in fact, the method used is direct, that is, no dilution, then the dilution factor that appears in the formulation will simply be ignored and equated to 1. The technique for determining the BOD of a sample is to find the difference in dissolved oxygen (DO) concentration between the final and the initial time after a period of incubation at some controlled temperature. This difference, converted to mass of oxygen per unit volume of sample (such as mg/L) is the BOD. Let I be the initial DO of the sample, which has been diluted with seeded dilution water, and F be the final DO of the same sample after the incubation period. The difference would then represent a BOD, but since the sample is seeded, a correction must be made for the BOD of the seed. This requires running a blank. Let I ′ represent the initial DO of a volume Y of the blank composed of only the seeded dilution water; also, let F ′ be the final DO after incubating this blank at the same time and temperature as the sample. If X is the volume of the seeded dilution water mixed with the sample, the DO correction would be ( I ′ − F ′ )( X / Y ). Letting D be the fractional dilution, the BOD of the sample is simply (2.2) In this equation, if the incubation period is five days, the BOD is called the five- day biochemical oxygen demand , BOD 5 . It is understood that unless it is specified, BOD 5 is a BOD measured at the standard temperature of incubation of 20 ° C. If incubation is done for a long period of time such as 20 to 30 days, it is assumed that all the BOD has been exerted. The BOD under this situation is the ultimate; therefore, it is called ultimate BOD , or BOD u . BOD IF–()I′ F′–()X/Y()– D = TX249_Frame_C02.fm Page 131 Friday, June 14, 2002 1:51 PM © 2003 by A. P. Sincero and G. A. Sincero 132 Physical–Chemical Treatment of Water and Wastewater BOD u , in turn, can have two fractions in it: one due to carbon and the other due to nitrogen. As mentioned before, carbon reacts with oxygen; also, nitrogen in the form of ammonia, reacts with oxygen. If the BOD reaction is allowed to go to completion with the ammonia reaction inhibited, the resulting ultimate BOD is called ultimate carbonaceous BOD or CBOD. Because Nitrosomonas and Nitrobacter, the organisms for the ammonia reaction, cannot compete very well with carbonaceous bacteria (the organisms for the carbon reaction), the reaction during the first few days of incubation up to approximately five or six days is mainly carbonaceous. Thus, BOD 5 is mainly carbonaceous. If the reaction is uninhibited, the BOD after five or six days of incubation also contains the nitrogenous BOD. BOD is normally reported in units of mg/L. Experience has demonstrated that a dissolved oxygen concentration of 0.5 mg/L practically does not cause depletion of BOD. Also, it has been learned that a depletion of less than 2.0 mg/L produces erroneous results. Thus, it is important that in BOD work, the concentration of DO in the incubation bottle should not fall below 0.5 mg/L and that the depletion after the incubation period should not be less than 2.0 mg/L. Example 2.1 Ten milliliters of sample is pipetted directly into a 300-mL incubation bottle. The initial DO of the diluted sample is 9.0 mg/L and its final DO is 2.0 mg/L. The initial DO of the dilution water is also 9.0 mg/L, and the final DO is 8.0 mg/L. The temperature of incubation is 20°C. If the sample is incubated for five days, what is the BOD 5 of the sample? Solution: 2.1.15 NITRIFICATION IN THE BOD TEST The general profile of oxygen consumption in a BOD test for a waste containing oxygen-consuming constituents is shown in Figure 2.1. As mentioned previously, because the nitrifiers cannot easily compete with the carbonaceous bacteria, it takes about 5 days or so for them to develop. Thus, after about 5 days the curve abruptly rises due to the nitrogenous oxygen demand, NBOD. If the nitrifiers are abundant in the beginning of the test, however, the nitrogen portion can be exerted immediately as indicated by the dashed line after a short lag. This figure shows the necessity of inhibiting the nitrifiers if the carbonaceous oxygen demand, CBOD, is the one desired in the BOD test. The reactions in the nitrification process are mediated by two types of autotrophic bacteria: Nitrosomonas and Nitrobacter. The ammonia comes from the nitrogen content of any organic substance, such as proteins, that contains about 16% nitro- gen. As soon as the ammonia has been hydrolyzed from the organic substance, Nitrosomonas consumes it and in the process also consumes oxygen according to BOD IF–()I′ F′–()X/Y()– D 92–()98–()300 10–[]/300()– 10/300 == 183 = mg/L TX249_Frame_C02.fm Page 132 Friday, June 14, 2002 1:51 PM © 2003 by A. P. Sincero and G. A. Sincero Constituents of Water and Wastewater 133 the following reactions: (2.3) (2.4) Adding Eqs. (2.3) and (2.4) produces (2.5) Equation (2.4) is called an electron acceptor reaction. Equation (2.3) is an elector donor reaction, that is, it provides the electron for the electron acceptor reaction. Together, these two reactions produce energy for the Nitrosomonas. The produced in Equation (2.5) serves as an electron source for another genus of bacteria, the Nitrobacter. The chemical reactions when Nitrobacter uses the nitrite are as follows: (2.6) (2.7) Adding Eqs. (2.6) and (2.7) produces (2.8) FIGURE 2.1 Exertion of CBOD and NBOD. Days of incubation 5 days or more Oxygen consumed, mg/L CBOD NBOD 1 6 NH 4 + 1 3 H 2 O 1 6 NO 2 − 4 3 H + e − ++→+ 1 4 O 2 H + e − 1 2 H 2 O→++ 1 6 NH 4 + 1 4 O 2 1 6 H 2 O 1 6 NO 2 − 1 3 H + ++→+ NO 2 − 1 6 NO 2 − 1 6 H 2 O 1 6 NO 3 − 1 3 H + 1 3 e − ++→+ 1 12 O 2 1 3 H + 1 3 e − 1 6 H 2 O→++ 1 6 NO 2 − 1 12 O 2 1 6 NO 3 − →+ TX249_Frame_C02.fm Page 133 Friday, June 14, 2002 1:51 PM © 2003 by A. P. Sincero and G. A. Sincero 134 Physical–Chemical Treatment of Water and Wastewater As with Nitrosomonas, the previous reactions taken together provide the energy needed by Nitrobacter. The combined reactions for the destruction of the ammonium ion, , (or the ammonia, NH 3 ) can be obtained by adding Eqs. (2.5) and (2.8). This will produce (2.9) From Equation (2.9), 1.0 mg/L of is equivalent to 4.57 mg/L of dissolved oxygen. 2.1.16 MATHEMATICAL ANALYSIS OF BOD LABORATORY DATA The ultimate carbonaceous oxygen demand may be obtained by continuing the incubation period beyond five days up to 20 to 30 days. To do this, the nitrifiers should be inhibited by adding the appropriate chemical in the incubation bottle. The other way of obtaining CBOD is through a mathematical analysis. In the incubation process, let y represent the cumulative amount of oxygen consumed (oxygen uptake) at any time t, and let L c represent the CBOD of the original waste. The rate of accumulation of the cumulative amount of oxygen, dy/dt, is proportional to the amount of CBOD left to be consumed, L c − y. Thus, (2.10) where k c is a proportionality constant called deoxygenation coefficient. In the previous equation, if the correct values of k c and L c are substituted, the left-hand side should equal the right-hand side of the equation; otherwise, there will be a residual R such that (2.11) At each equal interval of time, the values of y may be determined. For n intervals, there will also be n values of y. The corresponding Rs for each interval may have positive and negative values. If these Rs are added, the result may be zero which may give the impression that the residuals are zero. On the other hand, if the residuals are squared, the result of the sum will always be positive. Thus, if the sum of the squares is equal to zero, there is no ambiguity that the residuals are, in fact, equal to zero. The n values of y corresponding to n values of time t will have inherent in them one value of k c and one value of L c . Referring to Equation (2.11), these values may be obtained by partial differentiation. From the previous paragraph, when the sum of the squares of R is equal to zero, it is certain that the residual is zero. This means that when the sum of the squares is zero, the partial derivative of the sum of the squares must also be zero. Consequently, the partial derivatives of the sum of R 2 with respect to k c L c and k c are zero. Thus, to obtain k c and L c , the latter partial derivative of the sum of the squares must be equated to zero to force the solutions. The method NH 4 + 1 6 NH 4 + 1 3 O 2 1 6 NO 3 − 1 6 H 2 O 1 3 H + ++→+ NH 4 −N dy dt y′ k c L c y–()== Rk c L c y–()y′– k c L c k c y– y′–== TX249_Frame_C02.fm Page 134 Friday, June 14, 2002 1:51 PM © 2003 by A. P. Sincero and G. A. Sincero [...]... 2 10 4 20 6 23 8 25 10 28 Solution: 2 ∑y′∑y – ∑y∑yy′ L c = - y′∑y – n∑yy′ ∑yy′ k c = – 2 ∑y – L c ∑y y m+1 – y m−1 y′ = t m+1 – t m−1 t (day) y (mg/L) y′ 2 y yy′ a b 2 10 4 20 a 3 .25 400 65 3 .25 = 23 – 10 6 2 68 = 20 + 23 + 25 © 20 03 by A P Sincero and G A Sincero 6 23 1 .25 529 28 .75 for 1 ≤ m ≤ n 8 25 1 .25 625 31 .25 10 28 b ∑y = 68 ∑y′ = 5.75 2. .. R13 and those of MPN2 are R21, R 22, and R23 The corresponding mean readings are, respectively, R1ave and R2ave as shown in the equations below: R 11 ( D 1 ) + R 12 ( D 2 ) + R 13 ( D 3 ) R 1ave = -D1 + D2 + D3 (2. 41) R 21 ( D 1 ) + R 22 ( D 2 ) + R 23 ( D 3 ) R 2ave = -D1 + D2 + D3 (2. 42) From Eqs (2. 40), (2. 41), and (2. 42) , we form... Out of 5 of 10-mL 5 of 1-mL 5 of 0.1 mL MPN per 100 mL 0 1 2 3 3 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 0 1 1 1 2 1 2 3 1 2 2 3 3 3 4 4 4 4 5 5 5 5 5 0 1 1 1 1 1 1 1 1 1 2 1 2 3 1 2 3 4 1 2 3 4 5 . 10 20 23 25 28 t (day) 2 4 6 8 10 y (mg/L) 10 20 23 25 28 ∑y = 68 b y′ 3 .25 a 1 .25 1 .25 ∑y′ = 5.75 y 2 400 529 625 ∑y 2 = 1554 yy′ 65 28 .75 31 .25 ∑yy′ = 125 a 3 .25 = b 68 = 20 + 23 + 25 Hydrogen electrode Switch KOH CO 2 absorbent container Electrolyte Stirrer Oxygen. heat Cr 3+ CO 2 H 2 O++ ++ TX249_Frame_C 02. fm Page 141 Friday, June 14, 20 02 1:51 PM © 20 03 by A. P. Sincero and G. A. Sincero 1 42 Physical Chemical Treatment of Water and Wastewater Kjeldahl nitrogen. Of. 129 Friday, June 14, 20 02 1:51 PM © 20 03 by A. P. Sincero and G. A. Sincero 130 Physical Chemical Treatment of Water and Wastewater 2. 1.14 B IOCHEMICAL O XYGEN D EMAND Biochemical