PHYSICAL - CHEMICAL TREATMENT OF WATER AND WASTEWATER - CHAPTER 11 pdf

Water Stabilization As mentioned in Chapter 10 on water softening, as long as the concentrations of CaCO 3 and Mg(OH) 2 exceed their solubilities, the solids may continue to precipitate. This condition can cause scale to form, a solid that deposits due to precipitation of ions in solution. To prevent scale formation, the water must be stabilized. A water is said to be stable when it neither dissolves nor deposits precipitates. If the pH is high, stabilization may be accomplished using one of several acids or using CO 2 , a process called recarbonation . If the pH is low, stabilization may be accomplished using lime or some other bases. Because of the universal presence of carbon dioxide, any water body is affected by the reaction products of carbon dioxide and water. The species produced from this reaction form the carbonate system equilibria. As discussed later, the stability or instability of water can be gaged using these equilibria. Thus, this chapter discusses this concept. It also discusses criteria for stability and the recarbonation process after water softening. 11.1 CARBONATE EQUILIBRIA The carbonate equilibria is a function of the ionic strength of water, activity coeffi- cient, and the effective concentrations of the ionic species. The equilibrium coeffi- cients that are calculated from the species concentrations are a function of the temperature. This functionality of the coefficients can, in turn, be calculated using the Van’t Hoff equation , to be addressed later. One of the major cations that can form scales as a result of the instability of water is calcium. Calcium plays an important role in the carbonate equilibria. We will therefore express the carbonate equilibria in terms of the interaction of the calcium ion and the carbonate species which are the reaction products of carbon dioxide and water. In addition, since the equilibria occur in water, the dissociation of the water molecule must also be involved. Using calcium as the cation, the equilibrium equa- tions of the equilibria along with the respective equilibrium constants at 25 ° C are as follows (Rich, 1963): (11.1) (11.2) 11 K w 10 14– H + {}OH − {}== K 1 10 6.35– H + {}HCO 3 − {} H 2 CO 3 ∗ {} == TX249_frame_C11.fm Page 513 Friday, June 14, 2002 2:27 PM © 2003 by A. P. Sincero and G. A. Sincero 514 Physical–Chemical Treatment of Water and Wastewater (11.3) (11.4) The K s are the values of the respective equilibrium constants. is the equilibrium constant for the solubility of CaCO 3 . The pair of braces, { }, are read as “the activity of,” the meaning of which is explained in the Background Chemistry and Fluid Mechanics chapter in the Background Prerequisites section. As shown, the equilibrium constants are calculated using the activity. In simple language, activity is a measure of the effectiveness of a given species in its partic- ipation in a reaction. It is proportional to concentration; it is an effective or active concentration and has units of concentrations. Because activity bears a relationship to concentration, its value may be obtained using the value of the corresponding concentration. This relationship is expressed as follows: (11.5) where sp represents any species involved in the equilibria such as Ca 2+ , , and so on. The pair of brackets, [], is read as “the concentration of,” γ is the activity coefficient. 11.1.1 I ONIC S TRENGTH As the particle ionizes, the number of particles increases. Thus, it is not a surprise that activity coefficient is a function of the number of particles in solution. The number of particles is characterized by the ionic strength µ . This parameter was devised by Lewis and Randall (1980) to describe the electric field intensity of a solution: (11.6) i is the index for the particular species and z is its charge. The concentrations are in gmmols/L. In terms of the ionic strength, the activity coefficient is given by the DeBye-Huckel law as follows (Snoeyink and Jenkins, 1980; Rich, 1963): (11.7) (11.8) In 1936, Langelier presented an approximation to the ionic strength µ . Letting TDS in mg/L represent the total dissolved solids, his approximation is (11.9) K 2 10 10.33– H + {}CO 3 2− {} HCO 3 − {} == K sp,CaCO 3 4.8 10 9– () Ca 2+ {}CO 3 2− {}== K sp,CaCO 3 sp{} γ sp[]= CO 3 2− HCO 3 − µ 1 2 sp i []z i 2 ∑ = −log γ 0.5z i 2 µ () 1 1.14 µ ()+ = γ 10 0.5z i 2 µ () 1+1.14 µ () – = µ 2.5 10 5– ()TDS= TX249_frame_C11.fm Page 514 Friday, June 14, 2002 2:27 PM © 2003 by A. P. Sincero and G. A. Sincero Water Stabilization 515 Also, in terms of the specific conductance, sp conduc (in mmho/cm), Russell, another researcher, presented yet another approximation as (11.10) Example 11.1 The pH of a solution is 7. Calculate the hydrogen ion concen- tration? Solution: Example 11.2 The concentration of carbonic acid was analyzed to be 0.2 mgmol/L. If the pH of the solution is 7, what is the concentration of the bicarbonate ion if the temperature is 25 ° C? Solution: Example 11.3 A sample of water has the following composition: CO 2 = 22.0 mg/L, Ca 2+ = 80 mg/L, Mg 2+ = 12.0 mg/L, Na + = 46.0 mg/L, , and . What is the ionic strength of the sample? Solution: Example 11.4 In Example 11.3, calculate the activity coefficient and the activity in mg/L of the bicarbonate ion. Ion mg/L Mol. Mass gmols/L Ca 2+ 80 40.1 0.001995 Mg 2+ 12.0 24.3 0.0004938 Na + 46.0 23 0.002 152.5 61 0.0025 216 96.1 0.0022 µ 1.6 10 5– ()sp conduc= pH log 10 –H + {}= 7 log 10 –H + {} H + {} 10 7– gmols/L Ans== K 1 10 6.35– H + {}HCO 3 − {} H 2 CO 3 ∗ {} 10 7– HCO 3 − {} 0.2/1000 == = HCO 3 − {}8.93 10 4– () gmol/L HCO 3 − []Ans== HCO 3 − = 152.5 mg/L SO 4 2− 216 mg/L= µ 1 2 sp i []z i 2 ∑ = HCO 3 − SO 4 2− µ 1 2 0.001995 2 2 ()0.0004938 2 2 ()0.002 1() 0.0025 1() 0.0022 2 2 ()++++[]= 0.023 Ans= TX249_frame_C11.fm Page 515 Friday, June 14, 2002 2:27 PM © 2003 by A. P. Sincero and G. A. Sincero 516 Physical–Chemical Treatment of Water and Wastewater Solution: 11.1.2 EQUILIBRIUM CONSTANT AS A FUNCTION OF TEMPERATURE The equilibrium constants given previously were at 25°C. To find the values of the equilibrium constants at other temperatures, the Van’t Hoff equation is needed. According to this equation, the equilibrium constant K (K sp for the solubility product constants) is related to temperature according to a derivative as follows: (11.11) T is the absolute temperature; ∆Η ο is the standard enthalpy change, where the standard enthalpy change has been adopted as the change at 25°C at one atmosphere of pressure; and R is the universal gas constant. The value of R depends upon the unit used for the other variables. Table 11.1 gives its various values and units, along with the units used for ∆Η ο and T. By convention, the concentration units used in the calculation of K are in gmmols/L. Enthalpy is heat released or absorbed in a chemical reaction at constant pressure. Table 11.2 shows values of interest in water stabilization. It is normally reported as enthalpy changes. There is no such thing as An absolute value of an enthalpy does not exist, only a change in enthalpy. Enthalpy is a heat exchange at constant pressure, so enthalpy changes are measured by allowing heat to transfer at constant pressure; the amount of heat measured during the process is the enthalpy change. Also, the table indicates enthalpy of formation. This means that the values in the table are the heat TABLE 11.1 Values and Units of R R Value R Units K Concentration Units Used ∆H o Units T Units 0.08205 — °K 8.315 °K 1.987 °K 82.05 — °K From J. M. Montgomery Engineers, Pasadena, CA. γ 10 0.5z i 2 µ () 1+1.14 µ () – 10 0.5 1() 0.023() 1+1.14 0.023() =0.86– == sp{} γ sp[] 0.86 0.0025()0.00215 mg/L Ans== = dlnK dT ∆H o RT 2 = L atm gmmol.K ° gmmols L J gmmol.K ° gmmols L J gmmol cal gmmol.K° gmmols L cal gmmol atm.cm 3 gmmol.K° gmmols L TX249_frame_C11.fm Page 516 Friday, June 14, 2002 2:27 PM © 2003 by A. P. Sincero and G. A. Sincero Water Stabilization 517 measured when the particular substance was formed from its elements. For example, when calcium carbonate solid was formed from its elements calcium, carbon and oxygen, −288.45 kcal of heat per gmmol of calcium carbonate was measured. The negative sign means that the heat measured was released or liberated in the chemical reaction. Also, the state of the substance when it was formed is also indicated in the table. For example, the state when calcium carbonate is formed liberating heat in the amount of −288.45 kcal/gmmol is solid, indicated as s. The symbol l means that the state is liquid and the symbol aq means that the substance is being formed in water solution. Also, note the subscript and superscript. They indicate that the values in the table were obtained at standard temperature and pressure and one unit of activity for the reactants and products. The standard temperature is 25°C; thus the 298, which is the Kelvin equivalent of 25°C. The standard pressure is 1 atmosphere. The super- script o symbolizes unit activity of the substances. This means that the elements from which the substances are formed were all at a unit of activity and the product substances formed are also all at a unit of activity. The enthalpy change is practically constant with temperature; thus ∆H ο may be replaced by . Doing this and integrating the Van’t Hoff equation from K T1 to K T 2 for the equilibrium constant K and from T 1 to T 2 for the temperature, (11.12) This equation expresses the equilibrium constant as a function of temperature. TABLE 11.2 Enthalpies of Formation of Substances of Interest in Stabilization Substance , kcal/gmmol HOH (l) −68.317 0 −54.96 −167.0 CO 2(aq) −98.69 −161.63 −165.18 CaCO 3 (s) −288.45 −129.77 Ca(OH) 2(aq) −239.2 Mg(OH) 2(aq) −221.0 Mg 2+ −110.41 ∆H 298 o H aq() + OH aq() − H 2 CO 3 ∗ CO 3 aq() 2− HCO 3 aq() − Ca aq() 2+ ∆H 298 o K T 2 K T 1 ∆H 298 o RT 1 T 2 T 2 T 1 –()exp= TX249_frame_C11.fm Page 517 Friday, June 14, 2002 2:27 PM © 2003 by A. P. Sincero and G. A. Sincero 518 Physical–Chemical Treatment of Water and Wastewater 11.1.3 ’S FOR PERTINENT CHEMICAL REACTIONS OF THE C ARBONATE EQUILIBRIA Let us now derive the values of the of the various pertinent chemical reactions in the carbonate equilibria as shown in Eqs. (11.1) through (11.4). According to Hess’s law, if the chemical reaction can be written in steps, the enthalpy changes can be obtained as the sum of the steps. Thus, consider Equation (11.1). The corresponding reaction is (11.13) Writing in steps to conform to Hess’s law: The values of the ’s are obtained from Table 11.2. Note that the values in the table indicate of formation having negative values. Thus, if the reaction is not a formation but a breakup such as , the sign is positive. This reaction indicates that to break the water molecule into its constituent atoms +68.317 kcal/gmmol of energy is required. The + sign indicates that the reaction is endothermic requiring energy for the reaction to occur. For the ionization of the water molecule as represented by and using Hess’s law as shown previously, +13.36 kcal/gmol of HOH (l) is required. The Hess’s law steps for the rest of Eqs. (11.1) through (11.4) are detailed as follows: ∆∆ ∆∆ H 298 o ∆H 298 o HOH  H + OH − + HOH l() H 2 1 2 O 2 ∆H 298 o +→+68.317 kcal/gmmol of HOH l() = 1 2 H 2 H aq() + ∆H 298 o → 0= 1 2 H 2 1 2 O 2 + OH aq() − ∆H 298 o →−54.96 kcal/gmmol of OH aq() − = HOH l()  H aq() + OH aq() − ∆H 298 o ++13.36 kcal/gmmol of HOH l() = ∆H 298 o ∆H 298 o HOH l() H 2 1 2 O 2 +→ HOH l()  H (aq) + OH (aq) − + H 2 CO 3 ∗ H 2 C6O 2 ∆H 298 o ++→+167.0 kcal/gmmol of H 2 CO 3 aq() ∗ = 1 2 H 2 H aq() + ∆H 298 o → 0= 1 2 H 2 C6O 2 ++ HCO 3 aq() − ∆H 298 o → 165.18– kcal/gmmol of HCO 3 aq() = H 2 CO 3 aq() ∗  H aq() + HCO 3 aq() − ∆H 298 o ++1.82 kcal/gmmol of H 2 CO 3 aq() = TX249_frame_C11.fm Page 518 Friday, June 14, 2002 2:27 PM © 2003 by A. P. Sincero and G. A. Sincero Water Stabilization 519 Example 11.5 A softened municipal water supply enters a residence at 15°C and is heated to 60°C in the water heater. Compare the values of the equilibrium constants for CaCO 3 at these two temperatures. If the water was at equilibrium at 25°C, determine if CaCO 3 will deposit or not at these two temperatures. Solution: Therefore, HCO 3 aq() − 1 2 H 2 C6O 2 ∆H 298 o ++→+165.18 kcal/gmmol of HCO 3 aq() = 1 2 H 2 H aq() + ∆H 298 o → 0= C6O 2 +CO 3 aq() 2− ∆H 298 o → 161.63– kcal/gmmol of CO 3 aq() 2− = HCO 3 aq()  H aq() + CO 3aq() 2− ∆H 298 o ++3.55 kcal/gmmol of HCO 3 aq() = CaCO 3 s() CaC6O 2 ∆H 298 o ++→+288.45 kcal/gmmol of CaCO 3 s() = Ca Ca aq() 2+ ∆H 298 o → 129.77– kcal/gmmol of Ca aq() 2+ = C6O 2 +CO 3 aq() 2− ∆H 298 o → 161.63– kcal/gmmol of CO 3 aq() 2− = CaCO 3 s() Ca aq() 2+ CO 3 aq() ∆H 298 o +→ 2.95 kcal/gmmol of –CaCO 3 s() = K T 2 K T 1 exp ∆H 298 o RT 1 T 2 T 2 T 1 –()= K sp,CaCO 3 Ca 2+ {}CO 3 2− {}4.8 10 9– ()== K T 1 4.8 10 9– () in gmol units at 25°C== ∆H 298 o 2.95 kcal/gmmol of CaCO 3 s() – 2,950 cal– /gmmol of CaCO 3 s() == R 1.987 cal gmmol.K° T 1 25 273+ 298°K=== T 2 15 273+ 288°K T 2 60 273+ 333°K== == K T 2 at 15°K 4.8 10 9– ()exp 2,950 1.987 298()288() 288 298–()= 4.038 10 9– () in gmol units= TX249_frame_C11.fm Page 519 Friday, June 14, 2002 2:27 PM © 2003 by A. P. Sincero and G. A. Sincero 520 Physical–Chemical Treatment of Water and Wastewater Therefore, Thus, the value of equilibrium constant is greater at 60°C than at 15°C. Ans The value of the equilibrium constant for calcium carbonate at 25°C is 4.8(10 −9 ). At this condition, the ions Ca 2+ and ions are given to be in equilibrium; thus, will neither deposit nor dissolve CaCO 3 . At the temperature of 15°C, the value of the equilibrium constant is 4.038(10 −9 ). This value is less than 4.8(10 −9 ) and will require less of the ionized ion; therefore at 15°C, the water is oversaturated and will deposit CaCO 3 . Ans At 60°C, the equilibrium constant is 8.10(10 −9 ), which is greater than that at 25°C. Thus, at this temperature, the water is undersaturated and will not deposit CaCO 3 . Ans 11.2 CRITERIA FOR WATER STABILITY AT NORMAL CONDITIONS In the preceding discussions, a criterion for stability was established using the equilibrium constant called K sp . At normal conditions, as especially used in the water works industry, specialized forms of water stability criteria have been developed. These are saturation pH, Langelier index, and the precipitation potential of a given water. 11.2.1 SATURATION pH AND THE LANGELIER INDEX Because pH is easily determined by simply dipping a probe into a sample, determi- nation of the saturation pH is a convenient method of determining the stability of water. The concentrations of any species at equilibrium conditions are in equilibrium with respect to each other. Also, for solids, if the condition is at equilibrium no precipitate or scale will form. One of the concentration parameters of equilibrium is the hydrogen ion concentration, which can be ascertained by the value of the pH. Thus, if the pH of a sample is determined, this can be compared with the equilibrium pH to see if the water is stable or not. Therefore, we now proceed to derive the equilibrium pH. Equilibrium pH is also called saturation pH. In natural systems, the value of the pH is strongly influenced by the carbonate equilibria reactions. The species of these reactions will pair with a cation, thus “guiding” the equilibrium reactions into a dead end by forming a precipitate. For example, the complete carbonate equilibria reactions are as follows: (11.14) (11.15) K T 2 at 60°K 4.8 10 9– ()exp 2,950 1.987 298()333() 333 298–()= 8.10 10 9– () in gmol units= CO 3 2 − CO 3 2− HOH  H + OH − K w + H 2 CO 3 ∗  H + HCO 3 − K 1 + TX249_frame_C11.fm Page 520 Friday, June 14, 2002 2:27 PM © 2003 by A. P. Sincero and G. A. Sincero Water Stabilization 521 (11.16) (11.17) c is the charge of the cation that pairs with forming the precipitate Cation 2 (CO 3 ) c(s) . We call the formation of this precipitate as the dead end of the carbonate equilibria, since the carbonate species in solution are diminished by the precipitation. Let us digress for a moment from our discussion of the saturation pH in order to find the dead end cation for the carbonate system equilibria. Several of these cations can possibly pair with the carbonate. The pairing will be governed by the value of the solubility product constant, K sp . A small value of the K sp means that only small values of the concentration of the constituent species are needed to form a product equal to the K sp . This, in turn, means that solids with smaller K sp ’s will easily form the solids. Thus, of all the possible cations that can pair with the carbonate, the one with the smallest K sp value is the one that can form a dead end for the carbonate equilibria reactions. Mg forms MgCO 3 with a K sp of 10 −5 . Ca forms CaCO 3 with a K sp of 4.8(10 −9 ). Table 11.3 shows other carbonate solids with the respective solubility product constants. From the previous table, the smallest of the K sp ’s is that for Hg 2 CO 3 . Thus, considering all of the possible candidates that we have written, Hg 2 CO 3 is the one that will form a dead end for the carbonate equilibria; however, of all the possible cations, Ca 2+ is the one that is found in great abundance in nature compared to the rest. Thus, although all the other cations have much more smaller K sp ’s than calcium, TABLE 11.3 Solubility Product Constants of Solid Carbonates at 25°C Carbonate Solid K sp BaCO 3 8.1(10 −9 ) CdCO 3 2.5(10 −14 ) CaCO 3 4.8(10 −9 ) CoCO 3 1.0(10 −12 ) CuCO 3 1.37(10 −10 ) FeCO 3 2.11(10 −11 ) PbCO 3 1.5(10 −13 ) MgCO 3 1.0(10 −5 ) MnCO 3 8.8(10 −11 ) Hg 2 CO 3 9(10 −17 ) NiCO 3 1.36(10 −7 ) Ag 2 CO 3 8.2(10 −12 ) SrCO 3 9.42(10 −10 ) ZnCO 3 6(10 −11 ) HCO 3 aq() −  H aq() CO 3 2− K 2 + Cation 2 CO 3 () cs() ↓  2Cation c+ cCO 3 2− K sp + CO 3 2− TX249_frame_C11.fm Page 521 Friday, June 14, 2002 2:27 PM © 2003 by A. P. Sincero and G. A. Sincero 522 Physical–Chemical Treatment of Water and Wastewater they are of no use as dead ends if they do not exist. The other cation that exists in abundance in natural waters is magnesium. In fact, this is the other constituent hardness ion in water. Comparing the K sp ’s of the carbonate of these cations, however, CaCO 3 is the smaller. Thus, as far as the carbonate equilibria reactions are concerned, the calcium ion is the one to be considered to form a dead end in the carbonate system equilibria. Cation 2 (CO 3 ) c(s) is therefore CaCO 3(s) . For this reason, Equation (11.4) was written in terms of CaCO 3 . (See Table 11.4). As will be shown later, the saturation pH may conveniently be expressed in terms of total alkalinity and other parameters. The alkalinity of water is defined as its capacity to neutralize any acid added to it. When an acid represented by H + is added to a hydroxide represented by OH − , the acid will be neutralized according to the reaction H + + OH −  HOH. Thus, the hydroxide is an alkaline substance. When the acid is added to a carbonate, the acid is also neutralized according to the reaction . Carbonate is therefore also an alkaline substance. By writing a similar reaction, the bicarbonate ion will also be shown to be an alkaline substance. As we know, these species are the components of the carbonate equilibria. They also represent as components of the total alkalinity of the carbonate system equilibria. They may be added together to produce the value of the total alkalinity. To be additive, each of these component alkalinities should be expressed in terms of a common unit. A convenient common unit is the gram equivalent. [OH − ] is equal to {OH − }/ γ ΟΗ , where γ ΟΗ is the activity coefficient of the hydroxyl ion. {OH − } could be eliminated in terms of the ion product of water, K w = {H + }{OH − }. To establish the equivalence of the component alkalinities, they must all be referred to a common end point when the acid H + is added to the solution. From general chemistry, we learned that this is the methyl orange end point. As far as the OH − ion is concerned, the end point for the reaction H + + OH −  HOH has already been reached well before the methyl orange end point. Thus, for the purpose of deter- mining equivalents, the reaction for the hydroxide alkalinity is simply H + + OH −  HOH and the equivalent mass of the hydroxide is OH/1. One gram equivalent of the hydroxide is then equal to one gram mole. Therefore, (11.18) , where is the activity coefficient of the bicar- bonate ion. From Equation (11.3), ; thus, . Reaction of the acid H + with the bicarbonate given by H + + ends exactly at the methyl orange end point. From this reaction, the equivalent weight of the bicarbonate ion is HCO 3 /1; thus, one gram equivalent is equal to one gram mole. Therefore, (11.19) 2H + CO 3 2− +  H 2 CO 3 OH − [] geq OH − [] OH − {} γ OH K w γ OH H + {} == = HCO 3 − []HCO 3 − {}/ γ HCO 3 = γ HCO 3 HCO 3 − {}H + {}CO 3 2− {}/K 2 = HCO 3 − [] = H + {}CO 3 2− {}/ γ HCO 3 K 2 HCO 3 −  H 2 CO 3 2− HCO 3 − [] geq HCO 3 − [] H + {}CO 3 2− {} γ HCO 3 K 2 == TX249_frame_C11.fm Page 522 Friday, June 14, 2002 2:27 PM © 2003 by A. P. Sincero and G. A. Sincero [...]... by A P Sincero and G A Sincero TX249_frame_C11.fm Page 539 Friday, June 14, 2002 2:27 PM Water Stabilization 11. 8 11. 9 11. 10 11. 11 11. 12 11. 13 11. 14 11. 15 11. 16 11. 17 11. 18 11. 19 11. 20 539 The concentrations of carbonic acid and bicarbonate were analyzed to be −4 0.2 mgmol/L and 8.93(10 ) gmol/L, respectively If the pH is equal to 7, determine the temperature of the solution A sample of water has the... expression produces 2 x – 6.35 - = 10 0.1 – x – 6.35 + ( 10 – 6.35 2 ) + 4 ( 0.1 ) ( 10 – 6.35 ) – 10 x = - = 0.000 211 2 © 2003 by A P Sincero and G A Sincero (11. 53) TX249_frame_C11.fm Page 536 Friday, June 14, 2002 2:27 PM 536 Physical Chemical Treatment of Water and Wastewater Therefore, 0.000 211 φ aH2 CO3 = - = 0.00 211 0.1 Note: In the previous calculation,... s } (11. 25) The Langlier Index (or Saturation Index) (LI) is the difference between the actual pH and the saturation pH of a solution, thus LI = pH – pH s © 2003 by A P Sincero and G A Sincero (11. 26) TX249_frame_C11.fm Page 524 Friday, June 14, 2002 2:27 PM 524 Physical Chemical Treatment of Water and Wastewater A positive value of the Langelier index indicates that the water is supersaturated and. .. Sincero and G A Sincero TX249_frame_C11.fm Page 542 Friday, June 14, 2002 2:27 PM 542 Physical Chemical Treatment of Water and Wastewater Coucke, D., et al (1997) Comparison of the different methods for determining the behaviour of water to calcium carbonate Aqua (Oxford) 46, 2, 49–58 Edwards, M., M R Schock, and E T Meyer (1996) Alkalinity, pH, and copper corrosion by-product release J Am Water Works... mgmol/L, [A]mgeq = 0.4 mgeq/L, temperature = 20°C, and pH = 6.7 The saturation pH was calculated to be equal to 8.67 Calculate the values of γ HCO 3, K2, K spCaCO 3 , γOH, Kw , and γH © 2003 by A P Sincero and G A Sincero TX249_frame_C11.fm Page 540 Friday, June 14, 2002 2:27 PM 540 Physical Chemical Treatment of Water and Wastewater 11. 21 Analysis of a water sample yields the following results: [TDS]... ion that precipitates, Cappt Because the number of moles of Cappt is equal to the number of moles of the carbonate solid CaCO3ppt that precipitates, [ CaCO 3ppt ] = [ Ca ppt ] © 2003 by A P Sincero and G A Sincero (11. 43) TX249_frame_C11.fm Page 532 Friday, June 14, 2002 2:27 PM 532 Physical Chemical Treatment of Water and Wastewater FIGURE 11. 1 A water distribution pipe almost completely blocked with... equilibria in the treatment of natural waters Khimiya i Tekhnologiya Vody 15, 6, 468–474 Gomolka, E and B Gomolka (1991) Application of disk aerators to recarbonation of alkaline wastewater from wet gasification of carbide Water Science Technol Advanced Wastewater Treatment and Reclamation, Proc IAWPRC Conf., Sep 25–27, 1989, 24, 7, 277–284 Polish Soc of Sanitary Engineers Holtzclaw Jr., H F and W R Robinson... Equilibrium constant of CaOH o K CaSO 4 c Equilibrium constant of CaSO 4 Ksp Solubility product constant K sp, CaCO 3 Ksp of CaCO3 KT1 Equilibrium constant at temperature T1 KT 2 Equilibrium constant at temperature T2 Kw Ion product of water © 2003 by A P Sincero and G A Sincero TX249_frame_C11.fm Page 538 Friday, June 14, 2002 2:27 PM 538 Physical Chemical Treatment of Water and Wastewater l LI Pblock... TX249_frame_C11.fm Page 534 Friday, June 14, 2002 2:27 PM 534 Physical Chemical Treatment of Water and Wastewater 3 a distribution main at a rate of 0.22 m /s Determine the length of time it takes to clog a section of the distribution main 1 km in length, if the diameter is 0.42 m Solution: 2+ 2+ 100 ( [ Ca before ] – [ Ca after ] )Q pipe t P block = - ( 100 ) ρ CaCO... 2− ] γ Ca K w 4 1 + - + + K CaSO c γ CaOHc K CaOHc γ H [ H ] 4 4 0.7 –4 [ Ca T ] = - = 7.0 ( 10 ) gmol/L 1000 © 2003 by A P Sincero and G A Sincero TX249_frame_C11.fm Page 530 Friday, June 14, 2002 2:27 PM 530 Physical Chemical Treatment of Water and Wastewater –9 K sp,CaCO 3 4.8 ( 10 ) o –6 [ CaCO 3 ] = - = = 7.97 ( 10 ) gmol/L – 3.22 . Sincero and G. A. Sincero 518 Physical Chemical Treatment of Water and Wastewater 11. 1.3 ’S FOR PERTINENT CHEMICAL REACTIONS OF THE C ARBONATE EQUILIBRIA Let us now derive the values of the of the. by A. P. Sincero and G. A. Sincero 524 Physical Chemical Treatment of Water and Wastewater A positive value of the Langelier index indicates that the water is supersatu- rated and will deposit. == TX249_frame_C11.fm Page 513 Friday, June 14, 2002 2:27 PM © 2003 by A. P. Sincero and G. A. Sincero 514 Physical Chemical Treatment of Water and Wastewater (11. 3) (11. 4) The K s