Department of Civil, Water Resource and Environmental Engineering King Fahd University

1. Department of Civil, Water Resource and Environmental Engineering King Fahd University Water Stabilization

2. Water Stabilization • As in water softening, when the concentrations of CaCO3 and Mg(OH)2exceed 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.

3. CO2 H2O • If the pH is high, stabilization may be accomplished using one of several acids or using CO2, 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.

4. 1. Carbonate Equilibria • The carbonate equilibria is a function of : • the ionic strength of water, • activity coefficient, • and the effective concentrations of the ionic species.

5. Carbonate Equilibria: • Calcium is one of the major cations that can form scales as a result of the instability of water. • 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.

6. Carbonate Equilibria: • Since the equilibria occur in water, the dissociation of the water molecule must also be involved. • Using calcium as the cation, the equilibrium equations of the equilibria along with the respective equilibrium constants at 25ºC are as follows (Rich, 1963):

7. Carbonate Equilibria:

8. Carbonate Equilibria: • The Ks are the values of the respective equilibrium constants. • Ksp.CaC03 is the equilibrium constant for the solubility of CaC03. • The pair of braces, { }, are read as "the activity of,"

9. Carbonate Equilibria: • the equilibrium constants are calculated using the activity. • Activity: is a measure of the effectiveness of a given species in its participation in a reaction. • It is an effective or active concentration and has units of concentrations.

10. Carbonate Equilibria: {sp} = γ [sp] • Where sp represents any species involved in the equilibria. • The pair of brackets, [], is read as "the concentration of,“. • γ is the activity coefficient.

11. 1.Carbonate Equilibria: 1.1 Ionic Strength: • As the particle ionizes, the number of particles increases. • the activity coefficient is a function of the number of particles in solution. • The number of particles is characterized by the ionic strength μ.

12. 1.1 Ionic Strength: • 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-Huckellaw as follows (Snoeyink and Jenkins, 1980; Rich, 1963):

13. 1.1 Ionic Strength: Langelier estimated  as (TDS  2.5  10-5) Russell estimated  as (specific conductance 1.6 10-5)

14. Example 1

15. The pH of a solution is 7. Calculate the hydrogen ion concentration? Solution: pH = -log10{H+} 7 = -log10{H+} {H+} = 10-7 gmmols/L Ans.

16. Example 2

17. The concentration of carbonic acid was analyzed to be 0.2 gmmols/L. If the pH of the solution is 7, what is the concentration of the bicarbonate ion if the temperature is 25°C? • Solution:

18. Example 3

19. A sample of water has the following composition: CO2 = 22.0 mg/L, Ca2+ = 80 mg/L, Mg2+ = I2.0 mg/L, Na+ = 46.0 mg/L, HCO3- = 152.5 mg/L, and SO42- = 216 mg/L. What is the ionic strength of the sample? • Solution:

20. μ = 1/2[0.001995(22) + 0.0004938(22) + 0.002(1) + 0.0025(1) + 0.0022(22)] = 0.023 Ans.

21. Example 4

22. In Example 3, calculate the activity coefficient and the activity in mg/L of the bicarbonate ion. • Solution: {sp} = γ [sp] {HCO3-} = 0.86(0.0025) = 0.00215 mg/L Ans.

23. 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;

24. Where: • T: is the absolute temperature. • ΔHº: is the standard enthalpy change, where the standard enthalpy change has been adopted as the change at 25°C at one atmosphere of pressure. • 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

26. Table 11.2 shows values of interest in water stabilization. It is normally reported as enthalpy changes.

27. The enthalpy change is practically constant with temperature; thus ΔHº may be replaced by ΔHº298 Doing this and integrating the Van't Hoff equation from KT1 to KT2for the equilibrium constant K and from T1 to T2 for the temperature, “This equation expresses the equilibrium constant as a function of temperature”.

28. 1.3. ΔH298o, For Pertinent Chemical Reactions Of the Carbonate Eq.: According to Hess's low, if the chemical reaction can be written in steps, the enthalpy changes can be obtained as the sum of the steps;

30. The values of the ΔH298o’s are obtained from the previous Table 11.2. • The values in the table indicate ΔH298o of formation having negative values. • If the reaction is not a formation but a breakup such as; , The sign is positive.

31. Example 5

34. Hand-off • Any questions?

35. 2. Criteria For Water Stability at Normal Conditions: • In the preceding discussions, a criterion for stability was established using the equilibrium constant Ksp. • At normal conditions, as especially 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.

36. 2.1. Saturation pH and Langelier Index: • Because pH is easily determined the determination of saturation pH is convenient method of determining the stability of water. • If the condition is at equilibrium no precipitate or scale will form. • If the pH of the sample is determined , this can be compared with the equilibrium pH to see if the water stable or not. • Therefore, we now proceed to derive the equilibrium pH. “Equilibrium pH is also called saturation pH”.

37. In natural systems, the value of the pH is strongly influenced by the carbonate equilibria reactions. • The CO32- species of these reactions well pair with a cation, thus the equilibrium reactions into a dead end by forming a precipitate. • For example, the complete carbonate equilibria reactions as follows:

38. c is the charge of the cation that pairs with CO32- forming the precipitate Cation2(CO3)c(s). • We call the formation of this precipitate as the dead end of the carbonate equilibria, since the carbonate species in solution are removed by the precipitation.

39. In order to find the dead endcation , several cations can possibly pair with the carbonate. • The pairing will be governed by the value of Ksp. • The cation with smallest Ksp value is the one that can form a dead end for the carbonate equilibria reactions. • however, of all the possible cations, Ca2+ is the one that is found in great abundance in the nature compared to the rest. • Thus, although all the other cations have much more smaller Ksp’s than the calcium, they are of no use as dead ends if they do not exist (see Table 11.3).

41. As will be shown later, the saturation pH may conveniently be expressed in terms of total alkalinity. • The species which 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. • A convenient common unit is the gram equivalent. Letting [A]geqrepresent the total alkalinity;

42. Equations to calculate the carbonate equilibria species:

43. Then the total alkalinity equation becomes; Let Solving for {H+},

44. thus, the saturation pH, pHs is • The Langlier Index (or Saturation Index) (LI) is the difference between the actual pH and the saturation pH of the a solution, thus;

45. Example 6

50. Example 7