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A discussion of the paper “solubility of Ca(OH)2 and CaSO4.2H2O in the liquid phase from hardened cement paste” by W. Ma, P.W. Brown and D. Shi
Cement and Concrete Research, Vol. 24, No. 2, pp. 387-388, 1994 1994 Elsevier Science Ltd Printed in the USA. All rights reserved 0008-8846/94 $6.00 + .00
Pergamon
A DISCUSSION OF THE PAPER "SOLUBILITY OF Ca(OH)2 AND CaSO4.2H20 IN THE LIQUID PHASE FROM HARDENED CEMENT PASTE" BY W. MA, P.W. BROWN AND D. SHI*
S.J. Way and A. Shayan CSIRO Division of Building, Construction and Engineering PO Box 56, Highett, Victoria 3190, Australia
This discussion re-examines three aspects considered or implied in the authors' paper: 1 the limit of applicability of the Greenberg and Copeland expression (G-C model) (1) for calculating the solubility of Ca(OH) 2 in (Na,K)OH solutions; 2--the application of the model to describe the solubility of Ca(OH) 2 and CaSO4.2H20 in KOH solutions; and 3--their calculation of the solubility product of CaSO4.2H20. (1) In their paper, the authors argue that as the G-C model estimates solubilities satisfactorily only for ionic strengths less than 0.2, and since the ionic strength of cement pore solutions may greatly exceed this value, the use of the G-C model for assessing the state of saturation of the solutions may not be valid. Their basis for the first premise is a study by Moragues et al. (2). On closer examination of the relevant data (Table II in reference (2)), both the experimental and calculated calcium concentrations at the higher alkali concentrations are found to be in serious error. Table 1 below gives a corrected version of the table together with values calculated using the alternative values for lOgl0 Ksp (log. solubility product) and parameter B', namely, -5.12 (1,3) and 0.322 (3), which are the linear regression values using Fratini's data. The corrected and calculated values are shown in bold type. The experimental values at alkali concentrations of 0.35 and 0.5 M were first reported in a paper by Moragues et al. (4), wherein they are expressed as g/L. The values in Table II of reference (2) need to be increased by a factor of 10 to be correctly converted to mol/L. From Table 1, the experimental and calculated calcium concentrations are seen to be in good agreement to I = 0.5. TABLE 1 Alkali Hydroxide Concentration (M)
I
0.1048 0.212 0.35 0.5
0.12 0.21 0.35 0.5
Concentration of Calcium (M) Exp.
Calc. (a)
Calc.(b)
0.0049 0.0027 0.0018 0.0013
0.0051 0.0030 0.0023 0.0021
0.0048 0.0025 0.0017 0.0013
(a) log Ksp = -5.15, B' = 0.165; (b) log Ksp = -5.12, B ' = 0.322; A = 0.50. * Cement and Concr. Res. 22, 531 (1992). 387
388
Vol. 24, No. 2
Discussions
(2) The authors found the G-C model was unsatisfactory when tested against the solubility data of Hansen and Pressler (5) for the system Ca(OH)2-CaSO4.2H20--K20-H20. This model is based on the use of the extended form of the Debye-Huckel equation:
(1)
lOgl0 y+ = - z+ z_ A "~- + B' I
where T+ is the stoichiometric mean activity coefficient, I is the ionic strength, A = 0.51 at 25°C, z÷ and z_ are the charges on the positive and negative ions, respectively, and B' is an adjustable parameter serving to correct for deviations due to solvation and ion interaction effects in the given system. It ,was of interest to examine whether the solubility data could be fitted with a different value of B. We plotted log([Ca2+] (2[Ca2+] + [K+] - 2[SO42-]) 2) - 6 A "~- against I. The symbols [Ca2+], [K÷] and [SO42-] represent the stoichiometric concentrations of calcium, potassium and sulfate, respectively, and I = 3[Ca 2+] + [K÷] + [SO42-]. A linear regression of six points (the anomalous values at 0.4 M omitted) gave log Kso = -5.10 and B' = 0.506. With a correlation coefficient of 0.992, the experimental and calculhted calcium and hydroxyl concentrations in Table 2 were expectedly in good agreement. TABLE 2 KOH Conc. (M)
0.0 0.02 0.04 0.0802 0.1202 0.2004
SO4 Conc. (M)
0.0123 0.0151 0.0190 0.0289 0.0426 0.0722
Ca Conc. (M)
OH Conc. (M)
Exp.
Calc.
Exp.
Calc.
0.0331 0.0292 0.0240 0.0211 0.0183 0.0161
0.0330 0.0282 0.0247 0.0203 0.0190 0.0173
0.0414 0.0488 0.0502 0.0649 0.0726 0.0888
0.0415 0.0462 0.0515 0.0630 0.0729 0.0907
(3) From the data of Hansen and Pressler (5) the authors have estimated a solubility product for CaSO4.2H20 of 1.03 x 10-5 using the Pitzer-Mayorga (P-M) model (6). Their value is considerably lower than 2.4-2.6 × 10-5, the range reported in the literature. The equation given by the authors for BMX was noticed to be different from that in the paper by Pitzer and Mayorga (6). Repeating the calculations with A, = 0.391, a mean value of 2.90 (SD + 0.07) 10- 5 was obtained. Since the P-M model applies strictly to single electrolyte solutions, we compared calculated stoichiometric mean activity coefficients with reported values for CaSO 4 in water (7,8). Agreement was excellent for a saturated solution and about 4% higher for unsaturated solutions. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
S.A. Greenberg and L.E. Copeland, J. Phys. Chem. 64, 1057 (1960). A. Moragues, A. Macias, C. Andrade and J. Losanda, Cement and Concr. Res. 18, 342 (1988). S. Diamond, Cement and Concr. Res. 5, 607 (1975). A. Moragues, A. Macias and C. Andrade, Cement and Concr. Res. 17, 173 (1987). W.C. Hansen and E.E. Pressler, Ind. Eng. Chem. 39(10) 1280 (1947). K.S. Pitzer and G. Mayorga, J. Sol. Chem. 3,539 (1974). K.S. Pitzer, J. Chem. Soc. Faraday Trans. II 68, 101 (1972). T.H. Lilley and C.C. Briggs, Proc. Royal Soc. Lond. A 349, 355 (1976).
Pergamon
A DISCUSSION OF THE PAPER "SOLUBILITY OF Ca(OH)2 AND CaSO4.2H20 IN THE LIQUID PHASE FROM HARDENED CEMENT PASTE" BY W. MA, P.W. BROWN AND D. SHI*
S.J. Way and A. Shayan CSIRO Division of Building, Construction and Engineering PO Box 56, Highett, Victoria 3190, Australia
This discussion re-examines three aspects considered or implied in the authors' paper: 1 the limit of applicability of the Greenberg and Copeland expression (G-C model) (1) for calculating the solubility of Ca(OH) 2 in (Na,K)OH solutions; 2--the application of the model to describe the solubility of Ca(OH) 2 and CaSO4.2H20 in KOH solutions; and 3--their calculation of the solubility product of CaSO4.2H20. (1) In their paper, the authors argue that as the G-C model estimates solubilities satisfactorily only for ionic strengths less than 0.2, and since the ionic strength of cement pore solutions may greatly exceed this value, the use of the G-C model for assessing the state of saturation of the solutions may not be valid. Their basis for the first premise is a study by Moragues et al. (2). On closer examination of the relevant data (Table II in reference (2)), both the experimental and calculated calcium concentrations at the higher alkali concentrations are found to be in serious error. Table 1 below gives a corrected version of the table together with values calculated using the alternative values for lOgl0 Ksp (log. solubility product) and parameter B', namely, -5.12 (1,3) and 0.322 (3), which are the linear regression values using Fratini's data. The corrected and calculated values are shown in bold type. The experimental values at alkali concentrations of 0.35 and 0.5 M were first reported in a paper by Moragues et al. (4), wherein they are expressed as g/L. The values in Table II of reference (2) need to be increased by a factor of 10 to be correctly converted to mol/L. From Table 1, the experimental and calculated calcium concentrations are seen to be in good agreement to I = 0.5. TABLE 1 Alkali Hydroxide Concentration (M)
I
0.1048 0.212 0.35 0.5
0.12 0.21 0.35 0.5
Concentration of Calcium (M) Exp.
Calc. (a)
Calc.(b)
0.0049 0.0027 0.0018 0.0013
0.0051 0.0030 0.0023 0.0021
0.0048 0.0025 0.0017 0.0013
(a) log Ksp = -5.15, B' = 0.165; (b) log Ksp = -5.12, B ' = 0.322; A = 0.50. * Cement and Concr. Res. 22, 531 (1992). 387
388
Vol. 24, No. 2
Discussions
(2) The authors found the G-C model was unsatisfactory when tested against the solubility data of Hansen and Pressler (5) for the system Ca(OH)2-CaSO4.2H20--K20-H20. This model is based on the use of the extended form of the Debye-Huckel equation:
(1)
lOgl0 y+ = - z+ z_ A "~- + B' I
where T+ is the stoichiometric mean activity coefficient, I is the ionic strength, A = 0.51 at 25°C, z÷ and z_ are the charges on the positive and negative ions, respectively, and B' is an adjustable parameter serving to correct for deviations due to solvation and ion interaction effects in the given system. It ,was of interest to examine whether the solubility data could be fitted with a different value of B. We plotted log([Ca2+] (2[Ca2+] + [K+] - 2[SO42-]) 2) - 6 A "~- against I. The symbols [Ca2+], [K÷] and [SO42-] represent the stoichiometric concentrations of calcium, potassium and sulfate, respectively, and I = 3[Ca 2+] + [K÷] + [SO42-]. A linear regression of six points (the anomalous values at 0.4 M omitted) gave log Kso = -5.10 and B' = 0.506. With a correlation coefficient of 0.992, the experimental and calculhted calcium and hydroxyl concentrations in Table 2 were expectedly in good agreement. TABLE 2 KOH Conc. (M)
0.0 0.02 0.04 0.0802 0.1202 0.2004
SO4 Conc. (M)
0.0123 0.0151 0.0190 0.0289 0.0426 0.0722
Ca Conc. (M)
OH Conc. (M)
Exp.
Calc.
Exp.
Calc.
0.0331 0.0292 0.0240 0.0211 0.0183 0.0161
0.0330 0.0282 0.0247 0.0203 0.0190 0.0173
0.0414 0.0488 0.0502 0.0649 0.0726 0.0888
0.0415 0.0462 0.0515 0.0630 0.0729 0.0907
(3) From the data of Hansen and Pressler (5) the authors have estimated a solubility product for CaSO4.2H20 of 1.03 x 10-5 using the Pitzer-Mayorga (P-M) model (6). Their value is considerably lower than 2.4-2.6 × 10-5, the range reported in the literature. The equation given by the authors for BMX was noticed to be different from that in the paper by Pitzer and Mayorga (6). Repeating the calculations with A, = 0.391, a mean value of 2.90 (SD + 0.07) 10- 5 was obtained. Since the P-M model applies strictly to single electrolyte solutions, we compared calculated stoichiometric mean activity coefficients with reported values for CaSO 4 in water (7,8). Agreement was excellent for a saturated solution and about 4% higher for unsaturated solutions. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
S.A. Greenberg and L.E. Copeland, J. Phys. Chem. 64, 1057 (1960). A. Moragues, A. Macias, C. Andrade and J. Losanda, Cement and Concr. Res. 18, 342 (1988). S. Diamond, Cement and Concr. Res. 5, 607 (1975). A. Moragues, A. Macias and C. Andrade, Cement and Concr. Res. 17, 173 (1987). W.C. Hansen and E.E. Pressler, Ind. Eng. Chem. 39(10) 1280 (1947). K.S. Pitzer and G. Mayorga, J. Sol. Chem. 3,539 (1974). K.S. Pitzer, J. Chem. Soc. Faraday Trans. II 68, 101 (1972). T.H. Lilley and C.C. Briggs, Proc. Royal Soc. Lond. A 349, 355 (1976).