I
R. W. MOONEY, A. J. COMSTOCK, R. L. GOLDSMITH, and G. J. MEISENHELTER Sylvania Electric Products Inc., Towanda, Pa.
Predicting Chemical Composition in
...
Precipitation of Calcium Hydrogen Orthophosphate Statistical analysis of the calcium to phosphorus mole ratio yields a regression equation which can be used to predict chemical composition as a function of precipitation variables
R E C E N T L Y , THE PRECIPITATION of calcium hydrogen orthophosphate by the reaction,
(NH4)2HPO(
+ CaC12
-c
+
CaHP04 2NH4Cl
(1)
was studied ( 3 ) , using a four-variable central composite design for regression analysis (7). No attempt was made to determine a prediction equation for chemical composition because the analytical data were thought to be “essentially constant over the range of conditions studied.” However, the mole ratio of calcium to phosphorus was found to be somewhat greater than unity in all precipitates. Thus, the presence of some calcium hydroxyl apatite was indicated, and to investigate this ratio of calcium to phosphorus, the analytical data were analyzed statistically. T h e coding equations for the independent variables were the same as those used previously ( 3 ): XI
x2 = xg
=
temp. - 80 = 7.5
CaC12 concn. - 1.25 0.375
(NH1)2HPO4 concn. 0.375
x4
(2)
addition rate = 85
-
-
1.25
Although the above equation is mathematically complete, graphical presentation was made in order to present the results in an easily recognizable form. Therefore, certain variables were held constant and the predicted response (calcium to phosphorus mole ratio) a t various points within the experimental
Table 1. Experimental Analytical Data for the Three Block Design Coded Mole Variables . Ratio xi xa xa 2 4 Ca, % P, % CdP Block I -1-1-1-1 0 0 0 0 -1+1+1-1 +1-I-1+1 +l+l-1-1 -1--1+1+1
+l+l+l+l
o ! l o o
+1--1+1--1 -1+1-1+1
(3) (4)
+1+1-1+1 -1-1+1-1 0 0 0 0 -1+1+1+1 +1+1+1-1
(5)
0 0 0 -1i-1-1-1
+l-l+l+l -1-1-1+1 +1--1-1-1
Results
1.07 1.06 1.04 1.17 1.10 1.07 1.06 1.08 1.09 1.07
29.8 29.7 29.7 29.8 29.4 30.0 29.8 30.5 29.9 30.4
P = 1.0630
0.0150 XI - 0.0183 X Z 0.0150 XQ 0.0050 ~4 0.0113 ~ 1 . ~-2 0.0075 21x3 f 0.0025 XIX~ - 0.0013 X Z X ~0.0038 X Z X ~ 0.0025 ~3x4- 0,0019 XI’
-
~3~
- 0.0044~4~
(6)
0 0 0 0 -2 0 0 0 0 0-2 0 0 0 0 0 0 0 0+2 0 0 0-2 0-2 0 0 04-2 0 0 +2 0 0 0 0 0+2 0
29.7 29.5 31.1 29.8 29.7 29.4 30.9 29.4 30.2 30.0
z
+2
2 21.6 21.7 21.9 21.9 21.9 21.7 21.7 21.2 21.7 21.0
1.07 1.06 1.05 1.05 1.04 1.07 1.06 1.11 1.06 1.12
I-
2
*I
I-
z
W
0 2
0
0 0
-
N
0
-1
0
0
Block I11
Statistical analyses of the calcium to phosphorus mole ratio data (Tables I and 11) lead to the regression equation:
+ + + 0 . 0 0 9 4 ~ 2+ ~ 0.0131
21.7 21.7 22.0 20.9 21.5 21.5 21.7 21.7 21.4 21.7
Block I1
0
180
30.0 29.9 29.5 31.6 30.5 29.7 29.7 30.2 30.1 30.1
region was calculated. Since all of the coefficients involving terms in 2 4 (Equation 6) showed no significance a t the 95’% confidence level (Table 11), x4 was arbitrarily set equal to zero in the following calculations. The prediction equation was then used to calculate values of XIand xz for which the calcium to phosphorus mole ratio had certain arbitrary values with x 3 held constant a t the center of the design-i.e., x3 = 0. These calculations gave rise to the contour diagram shown in Figure 1. If the precipitation of calcium hydrogen orthophosphate with a calcium to phosphorus mole ratio of 1 to 1 is considered desirable and the precipitation of calcium hydroxyl apatite with a calcium to phosphorus mole ratio of greater than 1 to 1, varying u p to as high as 5 to 3, is considered undesirable, then the two temperatures within the experimental design which are most likely to
v
21.5 21.9 20.8 21.7 21.7 21.8 20.8 21.5 21.6 21.4
1.07 1.04 1.16 1.06 1.06 1.04 1.15 1.06 1.08 1.08
x“
-2 -2
-I
0
+I
+2
XI ( T E M P E R A T U R E )
Figure 1. Calcium to phosphorus mole ratio shows a saddle-point configuration as a function of temperature and calcium chloride concentration with x3 =
x4
=
0
VOL. 52, NO. 5
MAY 1960
427
Table II.
A Second O r d e r Equation Gives a Statistically Adequate Fit a t the 95% Confidence Level"
Standard Error for Coefficients
Degrees of
5
Source
Freedom
Blocks Linear Interactions Quadratic (Second order) Lack of fit Error
2
4 6 4 (10) 10 3
Mean Square 5.24
x
F Ratio 5.24 48.67b 4.22 20.52b (11 .58b) 1.90
10-4
48.67 X 4.22
x 10-4
20.52 X (11.58 X 1.90 x 10-4 1.00 x 10-4
20.4 25.0
19.1
x x x
10-4 10-4
10-4
By analyses of variance for the calcium to phosphorus mole ratio. CY
< 0.05.
yield the orthophosphate are 65" C. ( x , = -2) and 95' C. ( x , = +2). However, the orthophosphate is precipated a t 95" C. only if the concentration of calcium chloride is maintained a t the high extreme of the design-Le., x 2 = +2 or 2.00 moles per liter, since precipitation of calcium hydroxyl apatite is strongly favored at high temperatures ( x , = +2) and low calcium chloride concentrations (xp = -2). In view of these results, the calcium to phosphorus mole ratio was plotted as a function of the concentration of reactants, x2 and x3, with the temperature of precipitation set arbitrarily a t X I = -2, 0, and +2, respectively, and the rate of addition set arbitrarily at x4 = 0 (Figure 2). At 65" C. the lowest calcium to phosphorus mole ratio (1.025) is obtained 0 with any trend toward with xp E x3 the extremes in concentration resulting in an increase in the calcium to phosphorus mole ratio. At 80" C. the lowest calcium to phosphorus mole ratio achievable is 1.05 as indicated by the saddle-point configuration with temperature shown in Figure 1. T h e position of the minimum moved to higher concentrations of both calcium chloride and diammonium hydrogen phosphate. Again the precipitation of calcium hydroxyl apatite is favored by the lowest concentrations giving a mole ratio of greater than 1.20 at x2 = x 3 = -2. At 95" C., the minimum calcium to phosphorus mole ratio of 1.025 is found at a calcium chloride concentration of equal to or greater than 2.00 moles per liter (xp 2 +2), whereas the diammonium hydrogen phosphate concentration necessary to give this ratio is approximately 1.72 moles per liter (23 = 1.25). At this highest temperature, formation of calcium hydroxyl apatite is highly favored by low concentrations giving a mole ratio greater than 1.30 at x2 = xa = -2. Thus, there is a continuous trend toward higher concentrations with higher temperatures if the precipitation of calcium hydrogen orthophosphate is to be maintained with minimum formation of calcium hydroxyl apatite.
Discussion The explanation of these results lies in the chemistry of the calcium phosphates. Thus Elmore and Farr ( 4 ) have shown that solubility of calcium hydrogen orthophosphate decreases with temperature. Specifically, the solubility product decreases from 2.8 X 1 0 9 a t 25" C. (5) to 1.23 X 10-b at 90" C. (6). This effect tends to favor the formation of the orthophosphate at elevated tempera12
+I
0
-I
+2
literature Cited (1) Box, G. E. P., Wilson, K. B., J . Roy. Statist. SOC.B13, 1 (1951). (2) Clark, J. S.,Can. J . Chem. 33, 1696
(1955). ( 3 ) Comstock, A . J., .Jurnack, S. J., Mooney. R . W., IND.ENG.CHEM.51,
+
428
tures. Opposing this trend, is the well-known hydrolysis of any calcium phosphate in aqueous solution with the ultimate formation of calcium hydroxyl apatite (7). Since the rate of hydrolysis should increase with increasing temperature. this factor should favor the formation of calcium hydroxyl apatite at elevated temperatures. This trend is evident from Figure 2, where a t low concentrations ( x , = x 3 = - 2 ) , the hydrolysis mechanism predominates leading to calcium to phosphorus mole ratios of greater than 1.10 for 65" C., 1.20 for 80" C., and 1.30 for 95" C. Thus the saddle-point configuration could arise from the increasing hydrolysis of calcium hydrogen orthophosphate to the apatite structure with increasing temperature opposed by the decreasing solubility of the orthophosphate a t elevated temperatures provided the concentrations are increased to prevent hydrolysis. Another factor operating to favor the formation of the orthophosphate as opposed to the apatite at elevated temperatures is the rise in the dissociation pressure of ammonia over diammonium hydrogen phosphate leading to a gradual transition to the nionoammonium salt ( 8 ) . The increase in HzP04- ion concentration at the expense of the HP04' ion concentration in the solution would decrease the PO4= ion concentration, thus decreasing the probability of the precipitation of calcium hydroxyl apatite. The transition from the di- to the monoammonium hydrogen phosphate also tends to lower the pH, thus decreasing the hydroxyl ion concentration and lowering the ion product constant for calcium hydroxyl apatite which according to Clark (2) must only exceed 10-1'5 for precipitation to occur. I n summary, precipitation of calcium hydrogen orthophosphate is favored at 65" C. and medium concentrations of reactants, or 95" C. and high concentrations. Intermediate temperatures are to be avoided.
-2 -2 X,
-I
(CaCI,
0
+I
t2
CONCENTRATION)
Figure 2. Higher concentrations of reactants and higher temperatures (xq = 0 ) give minimum calcium to phosphorus mole ratios
INDUSTRIAL AND ENGINEERING CHEMISTRY
325 (1959). (4) Elmore. K. L., Farr. T. D., Zhzd., 32, 580 (1940). (5) Farr, T. D., "Phosphorus," Chem. Eng. Rept. 8, Tennessee Valley Authority, Wilson Dam, Alabama, 1950. (6) Mooney, R. W., Meisenhelter, G. J., J . Chem. Eng. Data, in press. ( 7 ) Warren, T. E., J . Am. Chem. Soc. 49, 1904 (1927). (8) Wazer, J. R. van, "Phosphorus and Its Compounds," vol. I, Interscience. New York. 1958. RECEIVED for review August 28, 1959 ACCEPTED December 17, 1959
