Inorg. Chem. 1987, 26, 345-349
345
Articles Contribution from Battelle, Pacific Northwest Laboratories, Richland, Washington 99352
Chromium(II1) Hydrolysis Constants and Solubility of Chromium(II1) Hydroxide Dhanpat Rai,* Bruce M. Sass, and Dean A. Moore Received June 9, 1986 The solubility of freshly precipitated Cr(OH), was determined in 0.01 M perchlorate solutions over a pH range of 3.8-14 and under a nitrogen atmosphere. Chromium concentrations in 0.0018-pm filtrates at times between 6 and 134 days, when the solubility was approached from both the undersaturationand oversaturation directions, showed that equilibrium is attained in 1 2 were corrected to 0.01 M ionic strength by assuming that mean activity coefficients for NaC104" apply to NaCr(OH),. [Cr(OH); is the dominant Cr species at these pH values; see Figure 2.1
Figure 2. Experimental data (77 points) used for nonlinear least-squares regression analysis. The data were taken from Figure 1 except for samples with Cr concentrations below the detection limit and samples above pH 12 that were equilibrated in solutions for less than 63 days. Lines represent the three-parameter model that best fits the data. (Concentrations of Cr species are indicated by the solid lines, and total Cr concentrations are given by the dashed line.)
the detection limit represent instrumetrt r -adings that cannot be considered accurate. The Cr concentratio, s display a parabolic trend over a pH range of about 4-12, which IS similar for different time periods and directions of approach to equilibrium. This similarity shows that the kinetics of precipitation/dissolution are very rapid and that equilibrium is reached in 6 days or less below pH 12. Steady-state Cr concentrations in suspensions with pH values >12 were reached slowly (in approximately 63 days), especially when solubility was approached from the undersaturation direction. The results of experiments in which Cr(OH),(s) was precipitated from Cr(NO,),.9HzO are similar to those in which [Cr(H2O),CI2]C1~2Hz0 was used. This similarity indicates that the solubilities of the precipitates do not critically depend on the initial composition of the chromium solution. The total aqueous Cr concentrations in 0.0018-pm filtrates in equilibrium with Cr(OH),(s) plotted against pH (Figure 1) show that Cr(OH),(s) exhibits amphoteric behavior; the Cr concentrations first decrease and then, at pH values > l o , increase with increasing pH. The changes in Cr concentrations with the changes in pH can be attributed to the formation of Cr(I1I) hydroxo complexes because other complexing ligands, including carbonates, were absent from these experiments. In general, the Cr concentrations in filtered solutions are more variable at pH values >6. The variability at intermediate-pH values appears to be due to the close proximity of measured Cr to the Cr detection limit. At pH values > 12, the variability appears to be due to the effects of aging in alkaline media, as the Cr concentrations at later times are less erratic and generally have lower values. Therefore, the Cr data that are above the detection limit and those data at pH >12, where Cr concentrations had reached steady state (>63 days equilibration), were selected for further interpretation of Cr(OH), solubility (Figure 2). Chromium(II1) is reported to form several hydroxo species, including CrOHz+, Cr(OH)z+,Cr(OH),O, Cr(OH),; Cr2(OH);+, and Cr3(OH):+.2 In addition, Stunzi and Marty18 have identified a tetrameric species, C T , ( O H ) ~ ~ +The . Cr(OH),(s) reactions involving these species are given in eq 1-8
where Kslo-Ks14and Kszz,Ks34,and Ks46represent the equilibrium constants for the equations. These reactions indicate that, for the Cr solution species in eq 1-8, lines representing log [Cr] vs. pH will have slopes of -3, -2, -1, 0, +1, -4, -5, and -6, respectively, in the regions of dominance for each hydrolyzed species. The data in Figure 2 show that log [Cr] vs. pH is most negative below pH 6. A least-squares linear regression of the data in this region (24 points) gives a slope of -1.98 f 0.15, which is significantly less than -4; thus, the species Cr2(0H)24+,Cr3(0H)45+,and Cr,(OH)66+do not have a region of dominance, and the reactions indicated in eq 6-8 can be ignored. Thermodynamic data reported in the literatureZ indicate that Cr3+ should be the dominant mononuclear species below pH 4. Evidence for the dominance of Cr3+ and its hydrolysis derivatives was tested statistically at pH values above approximately 3.80. Assuming that the Cr species represented by eq 1-5 are the only species present in significant amounts in solution, the total concentration of Cr in equilibrium with Cr(OH),(s) can be expressed as
Cr(OH),(s)
+ 3H+ + Cr3+ + 3 H 2 0
Cr(OH),(s)
+ 2H+
Cr(OH),(s)
+ H+ + Cr(OH)z+ + H 2 0
Kslo
CrOHZ++ 2 H z 0 Ksll
Cr(OH),(s) F= Cr(OH),O
Kslz
Ks13
(1) (2) (3) (4)
2Cr(OH),(s)
+ HzO =eCr(OH),- + H+ Ks14 ( 5 ) + 4H+ + C r z ( O H ) j + + 4 H z 0 Kszz (6)
3Cr(OH),(s)
+ 5H+ + Cr3(OH)4S++ 5 H z 0
KS3, (7)
4Cr(OH),(s)
+ 6H+ F= Cr4(0H)66++ 6 H z 0
Ks46 (8)
Cr(OH),(s)
(18) Stiinzi, H.; Marty, W. Inorg. Chem. 1983, 22, 2145-2150.
+
+
log [Cr(total)] = log [Cr3+ CrOH2+ Cr(OH)z+ Cr(OH),O
+
+ Cr(OH),-]
(9)
Substituting concentrations of Cr3+,CrOH2+,Cr(OH)2+,C r ( 0 H),O, and Cr(OH)4- from the equilibrium expressions (eq 1-5), we obtain
+
+
log [Cr(total)] = log (1010gKslo-3pH ~ O ' O ~ K ~ I I - ~ P H ~ O ~ & I ~ -+P 1010gKs13 H + 1Ob&14+PH) (10) A nonlinear least-squares curve-fitting program (RS/ 1 "FIT FUNCTION"; Bolt, Beranek, and Newman, Inc.) with a noweighting option was used to evaluate the Ksxvparameters from the data in Figure 2. Models with different numbers of parameters were tested to select the model, and hence the values of KUy,that best describes the [Cr] vs. pH relationship shown in Figure 2. In addition to the full five-parameter model, which includes all possible mononuclear Cr species (eq lo), two four-parameter truncated models (excluding either Cr3+or Cr(OH),+) and one three-parameter (excluding both Cr3+and Cr(OH),+) truncated model were tested. Two statistical calculations were used to select the most appropriate model: (1) the multiple coefficient of determination (@) and (2) the residual mean square (SS). Higher Rz and lower residual mean square values (Table 11) for the three-parameter model compared with those of the four- and five-parameter models show that the three-parameter model representing CrOHz+,Cr(OH),O, and Cr(OH),- (eq 2, 4, and 5 ) best describes Cr(OH),(s) solubility. The calculated log K,,,, log Ks13, and log Ks14 values at 0.01 M ionic strength are 5.96 f 0.08, -6.84 & 0.08, and -18.25 & 0.12, respectively (Table 11). The concentrations of different species calculated by using these three log Ksxyvalues are plotted in Figure 2, along with the total Cr concentration.
348 Inorganic Chemistry, Vol. 26, No. 3, 1987
Rai et al.
Table 11. Nonlinear Least-Squares Fitting Parameters (log 5
9.64 f 0.23 6.09 f 0.20 -0.95 f 0.37 -6.82 f 0.10 -18.26 f 0.13 14.4590 0.9944
3
4
4
9.93 f 0.17 6.01 f 0.13
6.02 f 0.1 1 -0.73 k 0.21 -6.83 f 0.10 -18.25 f 0.12 13.5676 0.9947
-6.84 f 0.09 -18.25 f 0.13 14.2013 0.9945
1
5.96 f 0.08 -6.84 f 0.08 -18.25 f 0.12 13.1246 0.9949
"The relationship between log Kuy and total aqueous Cr is given in eq 10. Error terms are standard errors of determination. *Number of data points is 77.
