31 5
SYSTEhQ CaO-1'2Oj-IIF-I-IzO
:
THERXODYNAMIC PROPERTIES'
BY THADI). PARRAND KELLYL. ELMORE Division oj Chemical Development, Tennessee Valley Authority, Wilson Dam, Alabama Received September 81, 1961
Thermodynamic d:itrt for solutions of the system CaO-P206-HF-&0, saturated at 25" with both fluorapatite arid calcium fiuoride, were used in estimating the activities of water and undissociated phosphoric acid, the activities of the dihydrogen phosphate and ralcium ions, and the activity solubility product of fluorapatite.
For that portion of the system CaO-Pe05-IIFH 2 0 wherc fluorapntitc (FA) and calcium fluoride are thc solid-phase pair in cquilibrium with the solutions12thc activity relationships may be writtcn The act,ivity of thc phosphate ion is represented by K1K2KaaU GPO4
=
--8-
(2)
aA
wherc KlK2K3 is the product of the three dissociation conhtants of orthophosphoric acid and a, is the activity of undissociatcd orthophosphoric acid. Substitution yields Values for the activities of the undissociatcd phosphoric acid, the calcium ion and the hydrogen ion wcre cstimatcd from the cxperimental dataZrelative to composition, vapor prcssure and pH of the pertinent saturated solutions of the quaternary system at, 25'. Values for the thrce dissociation constants of phosphoric acid have been p ~ b l i s h e d . ~The solubility product of calcium fluoride, 1.612 x 10-10, was calculated from frce cncrgy value^.^ Experimental values of thc basic thermodynamic variables and derived values for parameters of the sevcrnl functional relationships are given in Tables I ant1 I1 and Figs. 1 through 4.
TABLE I1 TIIERMODYNAMXC PROPERTIES OF SOLUTIONS S.lTUR.4TED WITH FLUORAP ~ T I T EA N D CALCIUM FLIJORIDE AT 25' UHK)
awm4
UHaW4
0.9933 .9798 .9667 .9516 .9390 .9272 .9028 .8923 8746
0.209 .276 .321 .357 .374 .394 .419 .428 .440
0.506 1.050 1.755 2.653 3.391 4.369 6 339 7.668 9.428
oca
PKF~ X
pII
0 061 1.76 120.859 .097 1 . 5 5 120 908 .134 1.41 120.815 .I85 1.28 120.831 .222 1.20 120.905 .288 1.11 120.845 .447 0 96 120.865 .89 120 .&55 .545 81 120,434 ,764
Kr,t
1.4 1 2 1.5 1.5 1.2 1.4 1.3 1.4 3.7
Activities of Undissociated Phosphoric Acid and to the Dihydrogen Phosphate Ion.-According Gibbs-Duhem equation as developed by Van Ryselb berg he,^ solutions of the system CaO-P20s-€IFHzOmay be represented by the relationship
+
+ +
-55.5062 d In UH*O = mu d In a, mH,po, d In U H ~ P O ~ mIipok d In U H P O ~ mpOI d In UPO, mHF d In UHF VZF d In a~ ma d In a€? mea d In aca (4)
+
+
+ +
The three dissociation products of orthophosphoric acid and that for hydrofluoric acid yield
-
d In C L H ~ P O=~ d In au d In U H d In U H P O ~ = d In au - 2d In a~ d In apo4 = d In au - 3d In U H d In U F = d In UHF - d In a11
TABLE I Substitution in equation 4 and rcarrangemcnt gives EQUILIBRIUM WITH THE ~OLID-P€1,4SE -55.5062 d In U H ~ O = [mu mn2Pol mmo, PAIRFLUORAPATITE AND CALCIUM FLUORIDE AT 25 O PO^] d In au [ m m m ~ 1d In UHF [mn - ??mZPo4 Vauor 2mnpo4 - 3rnp0, - m ~ 1d In U H mea d In aca preshctivity"
h Q i J I D PH.4SES IN
PzO~, % 5.73 9.70 12.97 16.00 17.91 20.01 23.01 24.38 25.78 0
mr 0.8802 1.6080 2.2856 2.9961 3.4883 4.080.1 5.02.55 5.4973 6.0226
CaO,
%
1.330 2.159 2.800 3.562 3.917 4.377 4.966 5.144 6.466
+
F. mca % 0,2604 0.002 .4530 ,004 ,6379 ,005 .8442 ,035 .9656 .019 1.1297 .027 1.3725 .008 1.4681 ,012 1.6162 ,024
PI-I 1.76 1.55 1.41 1.28 1.20 1.11 0.96 .89 .81
sure,
of water,
mm.
a1
23.60 23.28 22.97 22.61 22.31 22.03 21.45 21.20 20.78
0.99.33 ,9798 ,9667 .9516 ,9390 ,9272 ,9028 ,8923 .8746
at = p/po, where po is 23.76 mm., t,ho vapor pressure of
+ +
+
+
+
mH
- n2Hzpok- 2?n~po,- 3mpo4 - mF
=
-2mc,
general equation 4 is reduced to -55.5062 d In
U H ~ O=
+
mp d In a, mp d In a , I F 2mca d In a H mc, d In nc,, (5)
+
From equation 3, or its cquivalent ~r,~ - '&kl'at,'' anF2 (TCiRzKa)' Knr2
2). -.
-
+ +
+
By setting [mu 1- m ~ m , ~ H P O , mp0,1, thc total phosphorus concentration, equal to mp, and IF ~ z F ] ,thr total fluorine concentration, equal t o mF, and by using the elcctroneutrality equation in the form
pure water tLt 25" determined with thc same null-point mercury isoteniscope used for the saturated solutions (ref. ( 1 ) Presentad before the Division of Physical and Inorganic Chernistry, 132nd National Meeting of the American Chemical Society, New York. N. Y.,Saptember 1957. (2) T. D. Farr, G. Turbutton and H. T. Lewis, Jr., J . Phy8. Chem., 66, 318 (1962). (3) KH~PO,= 7.145 X 10-8; R. G . Bates, J . Research Natl. Bur. Standards, 47, 127 (1951). KH~PO, 6.339 X 10"; R. G. Bates and 9. F. Acree, ibid.. SO, 129 (1943). K H P O , = 4.73 X 10-18: N. Bjerrum and A. Unmack, Kgl. Danske Videnskab. Selskabs, Mat.Ius. Medd., 9, 5 (1929). (4) National Bureau of Standards Circiilar 500, U. S. Govt. Printing Office, Washingt,on. D. C., 1952.
+
aI120
is obtained d In acR
+ 3/5 d In au + 1/5 d In
U ~ = F
2 d In
which, when multiplied by calcium and substituted in equation 5, gives -55.5062 d In -
U H ~ O= [ m p
- 3 / 5 mea]d In a, + [WLF - 1/5 mea] d In n r ~ p
(5) P. Van Rysselberghe, J . Phys. Chem., 89, 403 (1935).
log ai X los
=I
5.541~'/*- 21.8039 f 13.369z6/z 2.5857~3 (10)
where al is the activity of mater and the conccntration variable 2 = m p -2/3 mea. The parameters of equation 10 wcre determiricd by the method of least squarcs; its probable error is f 0.00036, and it rcproduces the experimental values in Table I with a maximal dcviation of 0.18% and an average dcviation of 0.08%. The activity of water is p l o t t d in Fig. 1. Substitution of equation 10 into equation 9, and intcgrntion, yields log
-0.02272'/2
0,
+ 2 . 4 2 0 1 ~- 1.2368~'/~+ 0.215322 + I
(11)
The activity of the undissociatcd phosphoric acid is expressed also by log au = log a H f log aHgPO4 - log (12) where K 1 is the first dissociation constant for phosphoric acid. Equating exprcssions 11 and 12, and rearranging, one obtains
+ 4 + I f log or its equivalent log = -log nz1i2po, f pH + 6 + I + log KI log al72Po4 = -log
Fig. l.--ilctivity
of mater.
or the equivalent
aH
k'l
Yn2P04
[z: --
where 3/5 mc"] d In a, = d In 1/5 mcn
~ H F (6)
6 = -0.02272'/~
(13)
+ 3.42042 - 1.23682% + 0 . 2 1 5 3 ~ ~
From the relationship
By use of the Debyc-Hiickel rclationship in the form
or its equivalent
equation 13 may be written
log ~ n ~ = p o-0.509l/r"2 ~ KCaFS ~
- aCa aEF2
KHp2
is obtained
+ 2 d In
d In aca
log ~
UH*O
UHF
= mp d In au
2 d In UH
+ [mF - 2mc.I
d In UHF
[ni55.5062 ] d In 2mca
- 2mca] d In a,,= d In UHF mp
(7)
Equating expressions 6 and 7, and simplifying, one obtains 55.50132 [-915 men] d In U B ~ O= [9/5 mamp 615 mCn2 3/5 mcam~]d In a, -65.5062
+ d In an2o = (mr - 2/3 mn+ 1/3
mp)
- (mr 55'5062 - 213 mc.) d In
+
+ mn ~
I
I
T'alues for the terms on the left-hand side of equation 14, as calculated for each of the nine saturated solutions described in Table I, wcre used in the least-squarcs computation of the linear relationship 21 = -0.6069
- 0.0503 p
In the solutions saturat,cd with fluorapatit,e and calcium fluoride, thcrcforc, the activity of thc undissociated phosphoric acid is rcprcscntcd by
+
d In
UU
(8)
which represcnts the Gibbs-Duhem-Van Rysselberghe relationship for solutions of the system Ca0-P~O6--€IF-H~0 saturated with both fluorapatite and calcium fluoride. As the concentration of fluorine (< 0.04%) in the saturated solution is negligible, the function reduces to d In a, =
pk'i =
I k A H f . . . (14)
n m m 4 = 2mc.
= 3mcn
CLH~O
or
- (I f
UH~O
(9)
The vapor pressures and compositions of the saturated solutions are related by the expression
. .,
Since the saturatcd solutions h a m negligibly small concentrations of fluorine and h a w p H ' s of less than 1.8, the concentration of the dihydrogen phosphate ion is and the ionic strength is
or the equivalent
[m,
p'/*
an2
which, when multiplied by calcium and substituted in equation 5, gives -55.5062 d In
- p ) f - 0.5091
E ~ P O ,
&Ap f
-
= -0.9227 (mp - 2/3 men)'/* 2.4204 (VZP log 2/3 men) - 1.2368 ( m p - 2/3 mcn)'/2 0.2153 (7nP 2,'s mC.)* 0.6069 (15)
+
-
wrhich is plotted in Fig. 2, and the act,ivity coefficient of the dihydrogen phosphate ion is rcprescnted by
+ 0.0503
log yca2por= -0.5091 ~ ' 1 8
@
(16)
which is plotted in Izig. 3. Activity of Calcium Ion.-Equating the two expressions for the activity of the undissociated phosphoric acid (eq. 15 and the logarithmic form of cq. 3), dividing by 1.5, and rearranging, one obtains -log ac. = 2 pH f 2/3 6
- 1/9 log Rp,\
=
15.0387
THERMODYNAMIC P ~ ~ O ~ U ROFTCa0-1'20~-I-II~-I120 IES
I:cb., 1962 or its equivalent -log yca = log mca
+ 2 pH f
2/3 9
317
- 1/9 log KFA15.9387 (17)
where -yea is the activity coefficicnt of thc calcium ion. Since the modificd Dcbye-Hiickel relationship
+
whcre ionic strength p = 3mca mH, has been found toapply for many calcium phosphate systems, cquatioii 17 may be writtcn a!
,..
= A f B p f CpS
whcre 2.0364 p"~
a!=---
1
+ 1.9512
log mca
u1/2
2 pI-1
- 2/3 9 + 15.9387
A plot of a as a function of the ionic strength (Fig. 4) shows a parabolic curve, which was defined by
I
- 0.00729 p Z + 0.00388 p3 (18) has a probablc error of f 0.0002G; it reproduccs thc LY
=
13.429
+ 0.0436
+ 0.00388 p 3
+ 8 log
U , - 18 log U H 6 log (KIK2Kd log
+
0.6
J
(19)
+
KCnFt
1
h'
which is plotted in Fig. 3. Evaluation of &A .-By combining the expcrimental data in Table I with equations 15 and 19, nine values of the activity solubility product of fluorapatitc were calculated through the relationship log K F A= 9 log aca
I
0.5
0 0
0.00729 pz
I
0.4
p
experimental data with a maximal deviation in a of 0.04% and a mean deviation of 0.02%. The activity cocfficiciit of the calcium ion thcrcfore is reprcsented by the function
of undissociated phosphoric acid.
Fig. 2.-Activity
the method of least squares from eight of the nine saturatcd solutions dcscribed in Table I. The point rcpresentiiig the solution with thc greatest ionic strength mas discarded statistically. Thc resultant equation
(20)
which must exist among the activities of calcium Fig. and hydrogcii ions and of the free phosphoric acid in solutions that are in equilibrium with mixtures of fluorapatitc and calcium fluoride. The constancy of eight of the nine values givcri in Table 11, 1.4 =k 0.2 X shows a high degree of consistency of the experimental results and suggcsts that physicochemical lams gcncrally applied to dilute electrolytic solutions can be applied in this system to solutions of high concentrations. It may bc of interest t>ocompare the solubility product of fluorapatite, ~ K F =A 120.86 f 0.05, dcrivcct from the equilibrium data for the quaternary system with some of the values that may be calculated from thcrrnochemical data. For example, ranging from 114.25 to 120.08 werc values of ~ K I ' A calculated from (a) thc avcragc heat of formation of fluorapatite, -3267.2 f 0.4 lical./mole, as dctermined for thc process G I I I P ~ ~ OCa(0H)t f CaFe = C a l ~ ( P 0 4 ) ~+F ~18Ha0 from published data4 for thc heats of formatioil of Ca(OH)Z, CUI'%and €I&, togcthcr with utipublishcd Fig
1
0.7
0.8
0.9 0
I
I
I
I
I
2
3
4
I
I
5
P. cocfkients of calciurn and dihydrogen phosphate ions.
3.--Activity
,
13.9
L W U M I I V I X
13.7
I U
Y 4 -I
+
0 4-VuriiLtion
I
2 of
LY
Pa
3
4
5
as a furiction of ionic streugth.
318
T. D. FARR, GRADYTARBUTTON AND H. T. LEWIS,JR.
TVA data for the heats of solution of the respective calcium compounds and for the heats of formation and Of phosphoric acid; (b) published data for the heats Of formation4 Of 'Oh3- and F-, for the entropies4of Ca++, F-, Ca(s), F2(g) and
SYSTEM CaO-PzOb-HF-HzO:
02(g), for the entropy6 of Po43- (-52 and for the entropy? of fluorapatite.
Vol. 66 f
2 e.u.),
(6) C. C , Stephenson, J. Am. flhem, Sot., 66, 1436 (1944). (7) E. P. Egan, Jr., Z. T. Wakefield and K. L. Elmore, ibid., 75, 5581 (1951).
EQUILIBRIUN AT 25 AND $0''
BYTHAD D. FARR, GRADYTARBUTTON AND HARRY T. LEWIS,JR. Division of Chemical Development, Tennessee Valley Authority, Wilson Dam, Alabama Received September 91,1081
Phase equilibria in the system CaO-Pz06-HF-HaO a t 25 and 50" were determined for the region represented by liquid phases containing 4 to P206, 0.7 to 5,5y0 CaO and less than o.o7yO F. The stable solid phases in equilibrium with the saturated solutions were calcium fluoride and fluorapatite or calcium fluoride and monocalcium phosphate monohydrate. The invariant points representing solutions saturated with all three compounds were located a t both temperatures. Measurements on the saturated solutions included pH, density and vapor pressure.
The presence of fluorapatite, Ca,o(PO&Fz, as a major component in rock phosphate focuses interest on the system CaO-PzOs-HF-HzO in its relation t o the manufacture and use of phosphatic fertilizers. Phase equilibrium in a portion of the system was studied with three major objectives: To determine whether dicalcium phosphate fertilizer can be made directly from rock phosphate and the stoichiometric proportion of phosphoric acid at temperatures in the range 25 to 50°, to determine the relative rates of equilibration from the directions of supersaturation and of undersaturation, and t o determine some of the thermodynamic properties of the saturated solutions. Materials and Methods Monocalcium phosphate monohydrate, dicalcium phosphate and phosphoric acid were crystallized twice from the reagent materials. Hydrofluoric acid was redistilled in platinum and the middle fraction was retained. Calcium fluoride was prepared from twice-recrystallized calcium nitrate and the purified hydrofluoric acid. Tricalcium phosphate and fluorapatite were prepared by methods described previously.2 About half the equilibration mixtures were prepared from phosphoric acid and fluorapatite to approach equilibrium from the direction of undersaturation. The other mixtures were prepared from phosphoric acid and various combinations of monocalcium phosphate monohydrate, dicalcium phosphate, tricalcium phosphate, fluorapatite, calcium fluoride and hydrofluoric acid. The mixtures were equilibrated in 500-ml. hard rubber or polyethylene screw-cap bottles that were rotated end over end in water-baths a t 25 f 0.08" or 50 rt 0.04". The wet solids were identified petrographically, with some confirmations by X-ray diffraction. Slow settling of solids complicated sampling of the liquid phases, which were analyzed in duplicate. The phosphorus content generally was determined by double precipitation as magnesium ammonium phosphate, with ignition t o magnesium pyrophosphate. A few phosphorus determinations were made by a differential spectrophotometric method .a Calcium was determined by double precipitation as the oxalate, generally with ignition to calcium oxide. Some of the precipitates were ignited a t 475 to 500" and weighed as calcium carbonate. Fluorine was determined by a method that has been de~cribed.~ (I) Presented before the Division of Phyeioal and Inorganic Chemistry, 132nd National Meeting of the American Chemical Society, New Y o r k , N. Y., September 1957. ( 2 ) E. P. Egan. Jr., 2. T. Wakefield and X. L. Elmore, J . Am. Chem. Soe., 1 8 , 5581 (1951). (3) A. Gee and V. R. Deitz, Anal. Chem., 26, 1320 (1053).
Densities of the solutions were measured in 25-ml. pycnometers calibrated a t 25 f 0.005' or 50 f 0.005". The pH's of the solutions were measured by means of a Beckman Model H-2 meter, with glzkss and saturated calomel electrodes calibrated at 25 and 50". A few check determinations of p H were made with a hydrogen half-cell in a different system. In measuring the vapor pressure of a saturated solution, a technique of alternate stirring and freezing was used for removal of dissolved extraneous gases without changing the composition of the solution. The solution was stirred in a 25-ml. bulb by means of a perforated platinum disk, lifted magnetically 8 times per min. After 5 to 10 min. of stirring, the liquid was frozen quickly at -78" and evacuated. The solid was melted a t room temperature with the bulb isolated from the vacuum system and the cycle was repeated until the ressure over the solid was 10-4 mm. on a McLeod gage usually 8 to 10 cycles). The bulb with degassed test solution and stirring mechanism, a mercury isoteniscope, and the critical connecting lines were immersed in a water-bath a t 25 f 0.005" or 50 f 0.005". The nitrogen pressure needed to balance the isoteniscope, as indicated by an electronic relay system, was measured with a manometer containing Monsanto Arochlor No. 1242, which gave a magnification factor of 9.78. The manometer was read with a cathetometer. The apparatus was tested by measuring the vapor pressure of conductivity water. The results of replicate determinations, 23.76 f 0.01 mm. a t 25" and 92.58 i 0.01 mm. a t 50°, are compared with the value 0.032287 kg./cm.2 (23.75 mm.) for 25" recommended by Osborne, Stimson and Ginningss from their compilation of published vapor pressures and the value 92.56 mm. for 50" given by Keyes.*
P
Equilibration at 25".--?dost of the complexes at 25' were sampled at 12, 16, 21 and 24 months. Some of the more viscous liquids were sampIed only twice because of slow settling and the difficulty of getting clear samples. Keither the compositions of the liquid phases nor the forms of the solid phases changed significantly after 18 months. Properties of the system at equilibrium are summarized in Table I. The low fluorine content of the liquid phases (
