DESALINATION

ELSEVIER Desalination 159 (2003) 107-l 18 www.elsevietcomhcate/desal

Precipitation of calcium carbonate in the presence of citrate and EDTA

Karl-Johan Westin*, Hike C. Rasmuson Department of Chemical Engineering and Technology, Royal Institute of Technology, SE-I 0044 Stockholm, Sweden

Tel. +46 (8) 790-6402; Fax +46 (8) 105228; email: johanw@ket.kth.se

Received 4 July 2002; accepted 14 February 2003

Abstract

The influence of process conditions such as feed rate, calcium/carbonate ratio, pH, complexing agents [ethylenediaminetetetic acid (EDTA), citrate (UT)] and their concentration on the average particle size and shape of precipitated calcium carbonate was studied. The precipitation was performed in a semi-batch operated agitated vessel at constant pH by adding sodium hydrogen carbonate to a solution containing calcium chloride. In the absence of a complexing agent, agglomerates of needle-shaped crystals, probably aragonite, are obtained. Increasing feed time and the calcium/carbonate ratio increases the average particle size, whereas the opposite effect is observed for increasing pH. The observations can be related to the level of supersaturation. In the presence of complexing agents and at a concen- tration ratio of calcium vs. a complexing agent of6, differently shaped and smaller particles were obtained. Furthermore, the effect of the other parameters on particle size becomes much weaker in the presence of complexing agents. In the presence of EDTA mostly spherical particles were obtained, and in the presence of citrate mainly rhombic particles corresponding to calcite were obtained. The effect on particle shape and size is attributed to interactions of the complexing agents with the faces of the crystalline calcium carbonate.

Kwo?u!r: Calcium carbonate; Precipitation; Crystallization; pH-stat; Process conditions; Semi-batch; EDTA; Citrate; Complexing agents; PHREEQC

1. Introduction recirculation of process water in certain indus-

The chemical industry’s effort to improve its environmental sustainability is an ongoing process. A key issue is to reduce the overall outgoing flow of wastewater. To enable the

*Corresponding author.

tries such as the pulping industry, the removal of calcium may become a necessity in order to prevent precipitation of calcium salts (e.g., as oxalate, carbonate or sulfate) onto process equipment and product. Removal can be per- formed by carbonate precipitation followed by,

001 l-9164/03/$- See front matter Q 2003 Elsevier Science B.V. All rights reserved PII: SOOll-9164(03)00575-7

108 K.-J. Westin, A.(:. Rasmuson / Desalination 159 (2003) 107-I 18

e.g., sedimentation or filtration. The efficiency of these down-stream processes depends on the particle size and shape of the precipitate [l-3].

Complexing agents such as EDTA are often used to tackle problems that arise from high levels of metals in process water. In the pulping industry oxidation of peroxides used for totally and elemental chlorine-free bleaching can be overcome by complexing copper, manganese and iron with DTPA or EDTA [4,5]. Complexing agents have the ability not only to form com- plexes with calcium, thus lowering the super- saturation, but also to be adsorbed onto the surface of solid calcium carbonate [6]. Such adsorption may pose a substantial obstacle to crystal growth. Little is, however, known of the surface complexation of a complexing agent such as EDTA on various forms of calcium carbonate. Studies have been performed for similar substances, e.g., outer-sphere adsorption of Pb(II)EDTA on goethite (a-FeOOH) [7].

It has been shown that trace elements like magnesium may influence the growth of calcite substantially [8]. A common method to obtain aragonite instead of calcite is to perform calcium carbonate precipitation in the presence of mag- nesium. Several authors have investigated the distribution of trace elements between carbonate minerals and aqueous solutions in order to determine distribution coefficients [9-l 11.

Davey and Mullin [12] established relation- ships to correlate the effect of the impurities (CrC13x6H,0, FeCl, andAlC1,) on the growth of ammonium dihydrogen phosphate. They reached the conclusion that the observed growth inhi- bition could be attributed to adsorption of the impurities onto growth steps. Specific adsorption onto kinks was found to be unlikely. Growth rate models accounting for the effect of adsorption have also been proposed, for instance, by Cabrera and Vermilyea [ 131 and Kubota et al. [ 141.

In the case of calcium carbonate, the influence of impurities on crystal growth has mostly been studied for the case of calcite. Still Gutjahr et al.

[S] have shown that impurities such as Mg2’, Fe*+, Zn”, Cu*+, ZI?, Sf’ and Ba*’ differ in their effect on the crystal growth of calcite and arago- nite. Remarkably, the inhibition effects observed corresponded well to the fact that Mg”, Fe2’ and Zn2+form crystals isotype to calcite, whereas Sf and Ba” form crystals isotype to aragonite.

The purpose of this study is to determine the effect of two exemplary complexing agents (EDTA, citrate/UT) and certain process para- meters (carbonate/calcium ratio, pH, feed time) on the average crystal size and shape of the precipitate.

2. Theory

2.1. Supersaturation

The driving force for a solid calcium car- bonate phase to nucleate and grow may be expressed by the difference in chemical potential

Ap=p-p* (1)

between the non-equilibrium state and the equi- librium state. Introducing the solubility product as a measure of the equilibrium state, the super- saturation may be written as:

lnS - AP _ ln aco3aca = ln aco3aca RT ado, ala %

(2)

The solubility product of calcium carbonate differs for all its polymorphs. Calcite, being thermodynamically stable, has the lowest [ 15,161. The solubility products below are given for a temperature of 20°C.

K sp,calcite = 1()-8.475

K s*,aragonite = 10-8.36

(3)

(4)

K.-J. Westin, A. C. Rasmuson / Desalination 159 (2003) 107-I 18 109

K sp, vatefite = 10-7.913

K sp, CaCO, * Hz0 = 10-7.149

K sp,CaCO, * 6I$O = 10-6.585

K sp, ACC = 10-6.4

(5)

(6)

(7)

(8)

In order to determine the supersaturation, chemical speciation must be performed to determine the activity of Ca*’ and CO:-. In an ionic solution the deviation from ideal behavior can be accounted for using the Davies equation to correlate the activity coefficients [ 161:

a, = yici (9)

logy. = -AZ? G I - - 0.3 I with I = $ z,yci ’ l+JI

’ (10)

The reactions given in the Appendix are assumed to occur in the system studied.

2.2. Nucleation and crystal growth

Formation of a solid phase from a super- saturated solution is initiated through primary and secondary nucleation. When dealing with precipitation at higher supersaturations, it is often assumed that the effect of secondary nucleation is negligible. As can be seen from the relation- ship derived from the classical nucleation theory [17], the nucleation rate depends on the inter- facial energy, temperature and supersaturation.

3 -f* --

~~~ T31n2S (11)

Thus a higher supersaturation will yield a larger number of crystals [ 181. The crystal growth rate can often be correlated using a simple power law 1191:

G=$ a (s-l)g (12)

The exponent g usually lies within the range of 1 to 2.

3. Experimental

Calcium carbonate was precipitated by adding a sodium hydrogen carbonate solution to a calcium chloride solution. The influence of para- meters such as pH, calcium/carbonate ratio, feed rate, complexing agents and their concentration on the semi-batch precipitation of calcium carbonate was studied and their range is given in Table 1.

Table 1 Parameter ranges

Parameter -

Range

PH 9,10, 11 Calcium/carbonate ratio l/l, l/4, l/8 Feed time, min 10,30,60 EDTA, CIT concentration, mol L“ 0,0.05,0.2,0.5

(based on final volume)

3.1. Apparatus

The experimental set-up is shown in Fig. 1. All reactions were performed in a 1 L glass tank reactor (LFI 00 Glasschliff). The sodium hydro- gen carbonate solution was pumped with a syringe pump (Yale Apparatus Multi Phaser Mode1 YA-12) using a 60 ml plastic syringe. The sodium hydrogen carbonate solution was introduced slightly above the stirrer through a stainless steel tube (OD/ID 3 mm/2 mm). To set or maintain pH, a 1 mol L-r sodium hydroxide solution is added using a pH-stat titrator (Methrohm 718 stat). A Julabo JH thermostat with a PTl 00 stainless steel temperature probe was used to maintain a temperature of 50°C in

K.-J. Westin, .d.C. Rasmuson / Desalination 1.59 (2003) 107-I 18

L

Logger and Confroller

pU- ekctrode

NaOH feed

NaHCO, feed

PTlW sensor

Fig. 1. Experimental set-up.

the reactor. The content of the reactor was stirred using a pitched-blade turbine with the dimensions l/3 of the reactor diameter and blade height of l/8 of the turbines diameter. A Janke & Kunkel IKA-Werk RW 20 DZM was used to actuate the stirrer.

Particle-size distribution was measured with a Malvern 2600C using low-angle laser light scattering. A thermostated Malvern small volume dispersion unit was used to handle the sampled particle suspension. The average particle size measured corresponded to the mass weighted mean particle size according to the equation below:

D C, NiD” 43 = ci N,D’

(13)

The particles were visually inspected with a light microscope coupled to an image analysis system.

3.2. Procedures

A calcium chloride solution of 0.95 L of a 3.16 mol L-’ (or 3 mmol/l based on a volume of 1 L) was emptied into the reactor. The solution in some cases also contained one complexing agent, i.e., either EDTA or citrate. The pH of the solution was then adjusted to the desired level through the addition of sodium hydroxide solu- tion. After enabling the pH-control of the titratror, 50 ml of a sodium hydrogen carbonate was pumped into the calcium chloride solution at a given feed rate. Three different sodium hydrogen carbonate solutions were used, i.e., 60 mol L-‘, 240 mol L-’ and 480 mol L-‘. Imme- diately after completion of an experiment, the particle size distribution was measured and the particles were visually inspected.

4. Chemical speciation

To enable a comparison of the level of super- saturation and theoretical yield of each experi- ment, a calculated maximum supersaturation was introduced. The maximum supersaturation corre- sponds to the supersaturation that prevails, if all of the precipitant is introduced instantaneously, the content of the reactor is well mixed and precipitation does not occur. Based on the acti- vities calculated for calcium and carbonate, the supersaturation of all known solid forms of calcium carbonate can then be expressed. Below, supersaturation with respect to calcite having the lowest solubility is used for a comparison of the experiments. The temperature dependence of the equilibrium constants is accounted for using an analytical expression or a van’t Hoff approach. PHREEQC, a software tool for aqueous geo- chemical calculations, was used for the calcu- lations. [20].

5. Results

The particles obtained varied significantly in shape especially depending on the presence or

K.-J Westin, kc. Rasmuson / Desalination 159 (2003) 107-118 111

Fig. 2. Particles obtained for 60 min feed time at pH 10 and a calcium/carbonate ratio of l/4.

Fig. 3. Particles obtained for 60 min feed time at pH 10, in the presence of 0.5 mol L“ EDTA and a calcium/ carbonate ratio of l/4.

absence of complexing agents. Characteristic particles are shown in Fig. 2 (absence of complexing agents), Fig. 3 (EDTA present) and Fig. 4 (citrate present). The particles shown in Fig. 2 are agglomerates of needle-shaped single crystals suggesting aragonite. For small single crystal sizes these agglomerates had the appear- ance of spheres, but as the single crystal size increased, the agglomerates came to consist of fewer particles. An important observation made visually and with the Malvern 2600C laser

Fig. 4. Particles obtained for 60 min feed time at pH 10, in the presence of 0.5 mol L-’ citrate and a calcium/ carbonate ratio of l/4.

* i 1 Oti _..... L _.__ $-A -._. .& . ..A”_... $L _._.__. .“&- __.__ & _...*&. “A.L. ___.._._. 7.

Feed Time [min]

Fig. 5. Average particle size of precipitate formed at different feed times and calcium/carbonate ratios (* = l/l, n = l/4 and + = l/S, pH 10, calcium concentration 3 mol L-‘, temperature SOYI).

diffractor is that the particle concentration is lower for all solutions that contain complexing agents.

In Fig. 5 the influence of calcium/carbonate ratio and feed time on the average particle size for precipitation in the absence of complexing agent solutions is shown. The experiments were performed at pH 10.

At all calcium/carbonate ratios a prolonged

K.-J. Westin, A.C. Rasmuson /Desalination 159 (2003) 107-l 18

I , . . . , , . , , _.

I 3 , ! I ‘0 i0 20 30 40 50 60 70

Feed Time [min]

725-------------------.--?-----i-----

2 ; ---!

+ooi- 41 : i

‘3 al 75-

5 -1

r r z 5oj-

8’ $ 25i-

4 1 1 / I , I I I

‘0 70 20 30 40 50 60 70 Feed Time [min]

Fig. 6. Average particle size of precipitate formed at Fig. 7. Average particle size of precipitate formed at different feed times and calcium/carbonate ratios in the different feed times and calcium/carbonate ratios in the presence of 0.5 mol L-’ EDTA (0 = l/4 and m = l/8, pH presence of 0.5 mol L-’ citrate (0 = l/4 and m = l/8, pH 10, calcium concentration 3 mol L-‘, temperature 50°C). 10, calcium concentration 3 mol L-‘, temperature 50°C).

8 25- $ cc

‘8

1

/ / 9 10 ;1 12

PH

Fig. 8. Average particle size of precipitate formed at different feed times and pH (0 = 10 min, n = 30 min and + = 60 min, temperature 50°C, calcium concentration 3 mol L-‘, calcium/carbonate ratio l/I).

feed time leads to an increase in average particle size. Reducing the calcium/carbonate ratio reduces the average particle size. The particles obtained are predominantly agglomerates of needle-shaped crystals (indicating aragonite).

Similar experiments were performed for solutions containing 0.5 mol L-’ EDTA and 0.5 mol L-i citrate with respect to a volume of 1 L. A calcium/carbonate ratio of l/l was omitted since the particle concentration was too low to

Fig. 9. Average particle size of precipitate formed at different feed times and pH in the presence of 0.5 mol L-’ EDTA (0 = 10 min, m = 30 min and + = 60 min, calcium concentration 3 mol L-‘, calcium/carbonate ratio l/8).

allow for any representative characterization of the particle size distribution. The results are displayed in Figs 6 and 7.

The average particle size is reduced in the presence of EDTA and citrate. This can partly be attributed to the fact the particles differ in shape. In case of EDTA the particles are predominantly of spherical shape, which points towards vaterite agglomerates. Still a smaller fraction has a rhombic structure suggesting calcite. In case of citrate only rhombic crystals are obtained.

K.-J. Westin, d C. Rasmuson / Desalination I59 (2003) 107-l I8 113

$

1 I 10 11

J 12

PH

Fig. 10. Average particle size of precipitate formed at Fig. 11. Average particle size of precipitate formed at different feed times and pH in the presence of 0.5 mol L-’ different pH and calcium/carbonate ratios (0 = l/l, l = citrate (0 = 10 min, n = 30 min and + = 60 min; calcium l/4 and + = l/8, feed time 30 min, calcium concentration concentration 3 mot L-‘, calcium/carbonate ratio l/8). 3 mol L-‘, temperature SOOC).

EDTA [mmoVij

Fig. 12. Average particle size of precipitate formed at different levels of EDTA and pH (0 = pH 9, n = pH 10 and + = pH 11, calcium/carbonate ratio 8, calcium concentration 3 mol L-‘, temperature 50°C).

In Figs. S-10 the effect of pH and feed time on the average particle size is displayed.

In the absence of complexing agents and with a calcium/carbonate ratio of 1, the average particle size markedly decreases with pH. Again mostly spherical agglomerates of needle-shaped crystals corresponding to aragonite were ob- tained. A greater average particle size coincides with an increase in the thickness of the needle- shaped crystals.

. . . . ..I__..... i l’-.‘J ;a$ __L__ oi;j -.._ “--.tiLq‘; ..- -&-.-..-- _...

~DTA ~mmovlj ’

Fig. 13. Average particle size of precipitate formed at different concentration levels of EDTA and calcium/ carbonate ratios (0 = l/4 and m = l/8, pH 10, calcium concentration 3 mol L-‘, temperature 50°C).

The average particle size is generally lower in the presence of EDTA and citrate. A slight tendency to form larger particles at pH 9 can be seen. However, the same drastic effect on average particle size as observed in the absence of complexing agent cannot be found.

The influence of pH at different carbon/ calcium ratios was studied in the absence of complexing agent and a feed time of 30 min (see Fig. 11). Increasing pH as well as the calcium/

114 K.-J. Westin, ,d. C. Rasmuson / Desalination 159 (2003) 107-I I8

carbonate ratio reduces the average particle size. The largest particles are obtained at a ratio of 1 and pH 9. In all of these experiments aragonite crystals dominate, except at a ratio of 4 and pH 11 where the smallest average particle size was obtained and a notable amount of rhombic crystals corresponding to calcite was observed.

The effect of EDTA concentration and pH is shown in Fig. 12 for a calcium/carbonate ratio of8.

Increasing the EDTA concentration appears to reduce the average particle size ofthe precipitate. This is mainly due to the fact that the crystal shape changes from the left to the right hand side of the diagram. In the absence of EDTA spherical agglomerates of needle-shaped particles are obtained. As the EDTA concentration increases the shape gradually shifts to smaller and denser spherical agglomerates and rhombic crystals. Visual inspection indicated that the particle con- centration decreases with EDTA concentration.

The influence of EDTA concentration and calcium/carbonate ratio is shown in Fig. 13. As can be seen, the average particle size is lowered by a higher concentration of EDTA. Reducing the calcium/carbonate ratio appears to decrease the average particle size.

6. Discussion

In the absence of complexing agents it has been shown that a prolonged feed time increases the average particle size. This can be explained by the fact that a shorter feed time implies a higher feeding rate and hence a higher super- saturation around the feed point where the sodium hydrogen carbonate solution is intro- duced. A higher level of supersaturation is expected to induce a higher nucleation rate according to Eq. (11). Consequently, a larger number of smaller crystals is formed. Yet, the product particles formed are agglomerates of needle-shaped particles. The mechanisms under-

lying agglomeration are quite complex. Agglo- meration is expected to increase at increasing supersaturation [2 1,221. However, it is not clear from the literature whether larger agglomerates can be expected when operating at higher super- saturation levels. Microscopic observation of our particles suggests that larger agglomerates in this case actually contain individual crystals that are larger. A change in single crystal size is coherent with a change in agglomerate size. The use of low-angle laser light scattering to determine the average particle size of complex particles such as these agglomerates is perhaps questionable. Yet visual inspection and average particle size measurement showed a good enough agreement to support a discussion of the influence of process a conditions. In the following the results are discussed partly with respect to the maximum supersaturation level even though the relationship to particle size is not perfectly clear.

The results show a clear influence of pH and calcium/carbonate ratio that may find explanation by considering Eq. (11) combined with chemical speciation calculations. The effect that the calcium/carbonate ratio and pH have on the maximum supersaturation is shown in Fig. 14.

For a fixed calcium concentration the super- saturation decreases as the calcium/carbonate ratio increases. This finding is significant, but perhaps not very surprising. However, it helps explain why larger particles are obtained as the ratio increases. A lower supersaturation induces a lower nucleation rate. A far more interesting finding is that the difference in supersaturation between solutions containing 0.5 mol L-’ EDTA or citrate and complexing agent-free solution is far too small to satisfactorily explain the differ- ence in particle shape and size. At similar super- saturation levels entirely different particle shapes and sizes are obtained. An interaction between the crystal surface and the complexing agents can be suspected. This interaction appears to be polymorph-dependent, which helps explain why for instance citrate favors the formation of

K.-J Westin, d C. Rasmuson /Desalination I59 (2003) 107-l I8 115

01 ” “I’ ‘st,,‘3 aa’ 0 ‘Ok5 .0.5 0.75 1 Ca/C Concentration Ratio

Fig. 14. Supersaturation of calcite in dependence of calcium/carbonate ratio in the absence of complexing agents, presence of 0.5 mol L-’ EDTA and 0.5 mol L-’ citrate (* =-, n = 0.5 mol L-’ EDTA and + = 0.5 mol L-’ CIT, pH 10, calcium concentration 3 mol L“).

500 r-

c ’ I I /

o7- 8

8 $ 70 77 12 PH

Fig. 15. Supersaturation of calcite in dependence of pH in the absence of complexing agents, presence of 0.5 mol L-’ EDTA and 0.5 mol L-’ citrate (0 = -, u = 0.5 mol L -’ .EDTA and + = 0.5 mol L-’ CIT; calcium/ carbonate ratio l/S, calcium concentration 3 mol L-l).

calcite. Citrate is according to Reddy and Hoch [6] only a weak growth inhibitor for calcite. This does not, however, exclude being a strong inhibitor for other polymorphs such as aragonite or vaterite.

In Fig. 15 the effect of pH and complexing agents on the maximum supersaturation is shown. The supersaturation has a strong dependence on pH. A maximum is obtained around pH 10.5.

t 01 .._..L... * .--. L-L.~..-.l.-.A .-.. ?.I... ^.“....i.._. ..I..__... l.... --i.....L .._.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 / EDTA Concentration [mmo/X]

8

Fig. 16. Supersaturation of calcite in dependence of EDTA concentration and pH (0 = pH 9, n = pH 10 and + = pH 11, calcium/carbonate ratio l/8; calcium concen- tration 3 mol L-‘, temperature SOOC).

Since pH has such a strong influence on super- saturation, experiments performed at pH 9 and in the absence of complexing agents have a lower supersaturation than experiments performed at pH 10 and in the presence of either EDTA or citrate. This result may very well explain the fact that larger particles are obtained at lower pH in the absence of complexing agents, since the supersaturation is lower. However, the difference in supersaturation cannot satisfactorily explain the effect that complexing agents have on particle shape and size. If EDTA and citrate only were to influence the supersaturation by binding calcium ions, the observed distinct variation in crystal shape should not be expected for similar super- saturation levels.

In Fig. 16 the influence of EDTA concen- tration on the calculated supersaturation is shown. The supersaturation decreases linearly with EDTA concentration. At the concentration levels studied, pH apparently affects the super- saturation more than the EDTA concentration does. Yet particle shape and size change from the left side to the right side of the diagram in a manner that can only be explained by EDTA inhibiting growth of needle-shaped crystals corresponding to aragonite.

116 K.-J. Westin. XC. Rasmuson i Desalination 159 (2003) 107 II8

7. Conclusions

In the absence of complexing agents and under the chosen experimental conditions, agglo- merates of needle-shaped single crystals suggest- ing aragonite are obtained. The average particle size is influenced by process conditions such as feed rate, calcium/carbonate ratio and pH. The complexing agents citrate and EDTA, however, have a considerable effect on particle mor- phology. Further, their presence limited the influence of other process conditions on the average particle size substantially.

The results obtained in the absence of complexing agents show a clear connection between supersaturation level and average particle size. In simple terms, a higher super- saturation causes smaller product particles.

In the case of solutions containing EDTA and citrate, an analysis of the level of supersaturation using the same maximum supersaturation cannot satisfactorily explain the observed variation in particle shape and size. Many studies have shown that a higher supersaturation favors the formation of vaterite or aragonite in accordance with Ostwald’s law of stages, but solely rhombic particles corresponding to calcite, for instance, are obtained for the case of citrate. It is therefore concluded that complexing agents such as citrate and EDTA limit the influence of other process parameters which play a more important role in their absence. Complexing agents, besides complexing calcium ions, influence the crystalli- zation process by selectively inhibiting growth of certain polymorphs of calcium carbonate. This proposed mechanism coincides with the obser- vations made in other studies that have reported on growth-inhibiting effects of similar substances even at very low concentration levels.

Practical implications of the findings are that unless there is risk of hydroxide precipitation, calcium removal should be performed at around pH 10 to 10.5. The presence of calcium com- plexing agents may, however, hinder the precipi-

tation process by lowering process speed, average particle size and yield.

8. Symbols

A - Davies constant a - Activity, mol L-’ C - Concentration, mol L-’ G - Growth rate, m s-’ g - Growth exponent I - Ionic strength, mol L-’ J - Nucleation rate, mm3 s-’ K - Equilibrium constant L - Length, m R - Avogadro gas constant, J K-’ mol-’ s - Supersaturation T - Temperature, K z - Charge

Greek

P - Chemical potential, J mall’ Y - Activity coefficient Ys - Interfacial energy, kg sW2

Indices

* - Equilibrium state sP - Solubility product

Acknowledgements

This work is part of the Ecocyclic Pulp Mill programme financed by MISTRA, the Swedish Foundation for Strategic Environmental Research.

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Appendix - Equilibrium constants at 25°C:

H,O = OH- + H’ H’ + CO:- = HCO; 2H’ + CO:- = H,CO, H’ + Citrate3- = CitrateH2- 2H’ + Citrate3- = CitrateH; 3H’ + Citrate3- = CitrateH, H’ + Edta4- = EdtaH3- 2H’ + Edta4- = EdtaHi- 3H’ + Edta4- = EdtaHj 4H’ + Edta4- = EdtaH, 5H’ + Edta4- = EdtaHf

lg K= - 13.998 IgK= 10.33 IgK= 16.681 lgK=6.33 IgK= 11.05 Ig K= 14.18 Ig K = 9.96 IgK= 16.21 igK= 18.86 Ig K = 20.93 lg K= 23.464

Ca*’ + H,O = CaOH’ + H’ Ca” + CO;- + H’ = CaHCO’ Ca*+ + CO:- = CaCO, Ca*+ + Citrate3- = CaCitrate Ca*’ + Citrate3- + H’

IgK= -- 12.598 IgK= 11.33 IgK= 3.15 Ig K = 4.73

= CaCitrateH IgK=3.02 Ca2’ + Citrate3’ + 2H’

= CaCitrateHi + Ca*’ + Edta4- = CaEdta2- Ca2’ + Edta4- + H’ = CaHEdta- Na’ + CO:- = NaCO, Na’ + CO:- + H+ = NaHCO, Na’ + Edta4- = NaEdta3-

lgK= 1.29 lgK= 12.4 lgK= 16 IgK= 1.268 IgK= 10.08 IgK=2.5