1496
H. J. L. SCHUURMANS AND J. J. HERMANS
Vol. 61
increased a t high temperature. It does not, however, explain the effects of radiation type, which effects require a second-order process. If the time schedule for track expansion suggested by the theoretical treatment of Gangluly and MageeI4 is correct, it is possible for carbon monoxide to be produced in the tracks and spurs from acetaldehyde produced in these same tracks and spurs by the initial excitation through reactions VII, IX and XVI. As these reactions are very fast, and occur in at most a few vibrational cycles, as far as the track is concerned, during its expansion there is present a concentration of acetaldehyde, decreasing with time, but which initially is quite high. By an hydrogen-abstraction reaction as those previously given as reactions 2, 3 and 4,CO is produced by a second-order process and the yield by this process is dependent on the density of excitations in the tracks and spurs. This same argument, if applied to propylene, would predict a marked difference in propylene yield between helium ions and y-rays. Figure 3 shows this not t o be the case. This lack of gross change as well as the argument previously given for the change of propylene yield with total energy input suggests that propylene may be formed from a long-lived excited state of the isopropyl ether which can largely escape the initial track and spurs be-
fore decomposition occurs. Reactions XXIV and XXVI would predict the production of alpha-methyl-vinyl isopropyl ether. Kharasch, Friedlander and Urry16 suggest reaction XXVI as the principal reaction product from the reaction of such radicals a t 80”. Bromine titration of the residual liquid after separation of the low-boiling components showed a bromine absorption about equivalent to the hydrogen yield, indicating considerable unsaturation. Attempts to separate the component by vapor-liquid gas chromatography yielded a small fraction, the mass spectrum of which was not identified, but which could be the unsaturated ether mixed with a considerable fraction of impurities. Therefore reactions XXIV and XXVI are good possibilities for the production of oxidized products which are missing in the oxidation-reduction balance. Acknowledgments.-The author wishes to acknowledge his indebtedness to the late Dr. Joseph G. Hamilton, the late Mr. Bernard Rossi, and Mr. W. B. Jones and the crew of the Crocker Laboratory cyclotron for aid during the cyclotron irradiations, and to Mr. Duane Mosier for aid in the electron irradiations. Mr. Herbert X. DiGrazia, Mr. Aldo Sciamanna, Mrs. Bobby Mohler, and Mrs. Sylvia Waters aided in the mass spectrometer analyses.
(14) A. K. Gangluly and 1 . L. Magee, J . Chem. Phya., 26, 129 (1956).
( 1 5 ) M. 5. Kharasch, H. N. Friedlander and W . H. Urry, J . Ore. Chem., 16, 553 (1951).
HEATS OF MIXING I N THE SYSTEM POLYVINYL ACETATE-TOLUENE BY H. J. L. SCHUURMANS~ AND J. J. HERMANS Laboratorium voor Anorganische en Physische Chemie, Universiteit, Leiden Received January 86, 1067
A differential calorimeter for measuring heats of mixing is described. It avoids changes in pressure and in vapor phase as in the instrument of Cheesman and Beryl Whitaker. The temperature differences are determined by resistance thermometry. It is found that the heat of mixing polyvinyl acetate with toluene in the concentration range 0.2 to 1.6% polymer is proportional to @(I - a), where @ is the volume fraction of the polymer. The results are used in conjunction with second virial coefficients B obtained by Dykstra to check various theories. The Flory-Huggins equation gives B-values that are too high. Application of the Miller-Guggenheim formula leads to a reasonable coordination number at 25’, but gives less good results at 35’. Staverman‘s theory which takes into account that a polymer chain may bend back on itself gives acceptable results. The application of Longuet-Higgins’ and Prigogine’s theories whjch relate volume changes to heats of mixing gives heats of mixing which agree with experiment as regards order of magnitude.
Introduction Direct measurements of heats of mixing in polymer-solvent systems are scarce. Yet, for a comparison with thermodynamic theories it is essential that the free energy and heat of mixing be determined independently. In many cases the agreement between theoreticad Gibbs free energies AG of mixing and experimental AG values is much better than between the experimental and theoretical heats of mixing AH and entropies of mixing AS. Values of AH derived from the temperature coefficient of AG are not, as a rule, sufficiently accurate. A property of intrinsic interest in itself is the temperature coefficient of AH. A pronounced negative temperature coefficient was found by van der (1) Monsanto Chemical Company, Texas City, Texas.
Waals2 for mixtures of alkanes. Similar results have since been reported by Korvezee, Ruiter and S t ~ y t s . Finally, ~ we may mention that Daoust, Rinfret and Parent4have recently claimed that the heats of mixing in certain polymer-solvent systems when plotted against the polymer concentration give a curve with a pronounced break a t a certain (low) concentration called “critical concentration” which is compared with that where anomalous vis(2) J. H. van der Waals and J. J. Hermans, Rec. Ira% chim., 69, 949 (1950). (3) A. E. Korveaee, L. H. Ruiter and A. L. Stuyts, iMd., 78, 462 (1953). (4) H. Daoust and M. Rinfret, Canad. J . Chem., 32, 492 (1954); € Daoust, I. Master’s degree thesis, Montreal 1951; thesis doctor’s degree, Montreal 1953; M. Parent and M. Rinfret, Canad. J . Chem., 38, 971 (1955).
Nov., 1957
BEATS OF MIXINGIN SYSTEM POLYVINYL ACETATE-TOLUENE
cosity behavior has been reported.5 Daoust and Rinfret mixed the dry polymer with varying amounts of solvent, so that the process studied included that of dissolution. Heat effects had to be, therefore, followed over a long period of time, and the break in the curve corresponded t o a change in the AH which was small compared to its absolute value. For a study of the behavior a t low concentrations it is therefore desirable t o measure heats of dilution rather than heats of mixing. The calorimeter used by us permits measurements of changes in heat content with a precision which is about ten times as high as that claimed by Daoust and Rinfret. However, the system studied was polyvinyl acetate (PVA) in toluene, where the heats of mixing are small. Our relative accuracy was therefore about equal to that of the Canadian authors who investigated the behavior in polar solvents. No break in the curve was found in the system studied by us. Apparatus and Procedure Calorimeters for measurements of heats of mixing or reaction have been described, among others, by Zellhoefer and Copley,e Schulze,? Young and Voge1,a Huber and Woerner,g Vold,lo” Pitzer,lob Southard,11 Williams,12 Coops, Van Nes, Kentie and Dienske,18 Ruiter,14 Tompa,16 Scatchard, Ticknor, Goates and McCartney,’e Cheesman and Beryl Whitaker.17 Differential calorimeters have been used by Lange and Monheim,l* Charuel and TraynardlQto measure heats of reaction, and by Osborne, Stimson, Ginnings and FiockzO and Gucker, Ayres and Rubinzl to measure heat capacities. Calorimeters of a special design were described by Van der Waals* whose apparatus was improved by Brandt,*Z by LienharP and by Adcock and McGlashanz4using the ideas of Tompa. Finally we mention Calvet,26 Daoust and Rinfret4 and A general account of microcalorimetry (i.e., calorimetry involving small amounts of heat) has been given by SwietoslawskP and by S t u r t e ~ a n t . ~ ~ (5) R. F. Boyer and D. J. Streeter, J . Polymer Sei.. 14, 5 (1954). (6) G. F. Zellhoefer and M. J. Copley, J . A m . Chem. SOC.,60, 1343 (1938). (7) W. Schulze, 2. physik. Chem., l9T, 105 (1951). (8) T. F. Young and 0. G. Vogel, J . A m . Chem. Soc., 64, 3030 (1932). (9) W. Huber and A. Woerner, 2. Eleklrochem., 40, 256 (1934). (10) (a) R. D. Vold, J . A m . Chem. Soc., 59,1515 (1937); (b) K. 8. Pitzer, ibid., 59, 2365 (1937). (11) J . C. Southard, Ind. Eng. Chem., 84, 442 (1940). (12) R. B. Williams, J . A m . Chem. Soc., 64, 1395 (1942). (13) J. Coops, K. Van Nes, A. Kentie and J. W. Dienske, Rec. lrau. chim., 66, 113 (1947); J. Coops and K. Van Nes, ibid., 66, 131, 161 (1947). (14) L. H.Ruiter, thesis, Delft, 1955. (15) H. Tompa, J . Polymer Sci., 6, 51 (1952). (16) G. Scatchard, L. B. Ticknor, J. R. Goates and E. R . McCartney, J . A m . Chem. SOC.,14, 3721 (1952). (17) G. H. Cheesman and A. M. Beryl Whitaker, Proc. Roy. SOC. ( ~ ~ ~A md ,~406~ (1951). ) . (18) E. Lange and J. Monheim, 2.phyaik. Chem., 8149,51 (19301. (19) R. Charuel and Ph. Traynard, J . chim. phys., 6 2 , 441 (1955). (20) N . S. Osborne, H. F. Stimson and E. F. Fiock, J . Research N a t l . BUT. Standards, 6 , 411 (1930); N. €3. Osborne, €1. F. Stimson and D. C. Ginnings, ibid., 18, 389 (19371,and 28, 197 (1939). (21) F. T. Gucker, F. D. Ayres and T . R. Rubin, J . A m . Chem. Soc., S8, 2118 (1936). (22) H.Brandt, 2. phyaik. Chem.. 2 , 104 (1954). (23) A. Lienhart, thesis, Mulhouse, 1954. . (24) D. S. Adcock and M. L. McGlashan, Proc. Roy. S O C (London), A226, 266 (1954). (25) E. Calvet, Mem. Serv. chim. d’Etat, 8 2 , 168 (1945). (26) A. Tian, J . chim. phys., S O , 665 (1933). (27) M. Parent, thesis, Montreal, 1954. (28) W. Swietoslawski, “Microcalorimetry,” Reinliold Publ. Corp., New York, N. Y. 1946. (29) J. M. Sturtevant, in A. Weissberger, ”Physical Methods of Organic Chemistry,” Interscience Publishers, Inc., New York, N. Y., 1949.
1497
Experimental Technique.-Our calorimeter was constructed in principle according to the design of Cheesman and Beryl Whitaker,l? in which changes in pressure and in vapor p u r e as a result of mixing are avoided. The main diferences are the use of resistance thermometry to measure temperature differences and the fact that our calorimeter is of the differential type. Two equal vessels are mounted in a Pyrex chamber that can be evacuated. Each vessel is provided with two platinum coils, one for measuring the temperature and one for calibration and eventually compensation heating. Stirring and breaking the tinfoil, that keeps the liquids apart before the measurements, is done with two permanent magnets outside the vessels and a specially designed stirrer inside. The resistance coils for temperature measurement form two arms of a Wheatstone bridge, the other arms of which are 1000 resistors. By a variable shunt over the largest of the f i s t two resistors the current through the galvanometer is adjusted to zero a t the beginning of an experiment. The output of the bridge is a measure of the temperature difference between the vessels; the resulting galvanometer deflection is amplified by the use of a split selenium cell and recorded on a drum. The compensation circuit is a modification of that described by Sturtevant and McGlashan and enables one to measure not only the temperature difference between the vessels but also the absolute value of the temperature. I n principle the instrument may be used also for direct measurements of changes in heat capacity upon mixing. It was found, however, that in the system investigated the accuracy attained was not sufficient to give reliable data. Procedure.-The amounts of liquid brought into the two compartments of each mixing vessel are weighed on a semimicro balance. One of the compartments always contains pure solvent. After testing for leakage in a high vacuum, the vessel is mounted in the Pyrex chamber, then in the thermostat, and left for 12 hours. After evacuating the system, the Wheatstone bridge is adjusted to zero current. From there on temperature changes are recorded. This causes the supply of a small amount of heat, evolved by the measuring coil. If pol and 02 are the (small) heats supplied to vessels 1 and 2 per unit of time during the period 6 t, as a result of the current through the thermometer circuit, and if wl and w2 are the heat capacities of these vessels, the temperature of vessel 1 changes by an amount
6Tl = (p~l/w1)6t- k JOat (TI
- T)dt
where T i s the bath temperature and k a constant depending on the conduction of heat from the vessel to its surroundings. Similarly, for vessel 2
and the temperature difference AT between the two vessels will therefore change by the amount 6 A T = A6t
-k
so8t
AT dt
where
A qoi/wi - qaz/wz (2) The vessels are sufficiently alike to assume that they have the same k value. The integral in eq. 1 can be determined graphically. Thus, by varying 6t and measuring the corresponding 6AT values, one can determine A and k . If now, more generally, the time interval 6t contains a period 6,t during which known amounts of heat pl and q2 per ,unit time are supp!ie.d by the calibration coils and (or) a period during which nuxing takes place in vessel 1, we obtain
where & is the heat of mixing. If mixing takes place in vessel -&. Furthermore, it is possible to determine heat effects due to stirring when no other process takes place and then to correct for them when a process does take place. Also, we must distinguish between the heat capacities tu1 and w z of the vessels before mixing and those 2, & must be replaced by
H. J. L. SCHUURMANB AND J. J. HERMANS
1498
(tul' and 702') after mixing, but all these quantities follow in a straightforward manner from the experiments. Polymers Used.-Polyvinyl acetate was fractionated by a method based on work of Parentz7and van Beek.*o About 50 g. of PVA was dissolved in 2500 ml. of acetone and filtered. Water was added dropwise to the filtrate until the weight percentage of water was 35. This gave a two-phase system in which most of the polymer was precipitated. After standing for several hours the precipitate was dissolved by heating slowly, and the solution was left to cool slowly, thus causing reprecipitation. From the remaining liquid the first fraction was obtained. These manipulations were repeated several times, changing the water content gradually. Altogether seven fractions were obtained, out of which fractions I11 and IV were used in heat of mixing e ~ p e r i r n e n t s . ~ ~ The fractions 111 and IV obtained were dissolved in about 50 ml. toluene per gram polymer, and this solution was added dropwise to an excess of hexane (about 500 ml. per gram polymer) in a large beaker. Some toluene is enclosed in the precipitate formed. For this reason the precipitate was dissolved in benzene (1% solution) and then subjected to freeze-drying. The final product was stored in a desiccator with silica gel. The PVA was of the same stock as that used by Dykstraa2 and van Beek,80who cornoared viscosities with osmotic data and light scattering. Alchough our fractionation procedure was somewhat different, we used the viscosity in toluene to eetimate the molecular weights, M . The results were fraction 111, [ v ] = 73.5 ml./g.; 1 0 - 4 ~= 39 fraction IV, [ v ] = 123.0 ml./g.; 10-4M = 88 Density measurements were made in a pyknometer in the concentration range 0 to 1.6% polymer and led to the conclusion that the density of PVA solutions in toluene at 25" is given by s = (0.85907 f 0.00025) (0.250 f 0 . 0 1 3 ) ~ (4) where c is the polymer concentration in g./ml. The figures added in the brackets are the standard deviations. In the range from 20 to 45" the temperature coefficient of the density proved to be independent of c within experimental error and equal to - 1.10 X 10-8 per degree.
Results of the Calorimetric Measurements The amounts of liquid in the two compartments before mixing varied from 1 t o 3 g. These were corrected for buoyancy of the air and for the amount of liquid in the capillaries not taking part in the mixing process. The volume fraction of polymer in the solution, before mixing with the solvent, varied from 0.008 to 0.016, that after mixing from about 0.002 to about 0.012. The total number of measurements was 17. T o represent the data, let CP be the volume fraction of the polymer before and CPf that after mixing. Further $ = @(I - *); $! = @'(1 - *') (5) It was found that the heat effect 6AH when divided by the total volume V of the solution and by the difference q f - IC. gave an almost constant result (see Fig. 1 and Table I). This suggested that 6 A H / V be represented by the empirical formula SAH/V = A($' - J.) + C(J.'*- J.') (6)
which would mean that the heat of mixing for a solution of volume fraction CP and volume V obeys the relation A H / V = A$ f C$= T o determine the constants A and C in eq. 6 we considered the equivalent equation . ( 6 A H / W / ( J . ' - $1 = A C($' -t- $L.)
+
(30) L. K. H. van Beek, thesis, Leiden, 1955. (31) H. J. L. Schuurmans, thesis, Leiden, 1956.
(321 A. Dykstra, thesis, Leiden, 1955.
TABLEI SUMMARY OF MEASUREMEN TS $' x 108 + x 108 Fraction I11 at 25" 15.760 8.617 15.760 8.484 15.760 11.839 15,760 11.8G8 15,760 5.25G 15.760 5.107 15.760 3.987 15.760 3.935 8.219 2.048 8.219 2.008 8,219 6.179 8,210 6,220
Run
1 2 3 4 5 6
7 8 9 10 11
+
Vol. 61
12 13 14
15 16 17
6AH/V
11.43 12.04 6.00 6.72 17.24 16.66 19.73 19.51 10,57 9.77 2.81 3.46
Fraction IV a t 25" 15.818 8.682 15.818 8.560 15.818 12 I021 15.818 11.992 15.818 5,234 15.818 5.060 15,818 3.983 15.818 3.922 8.161 2.032 8.161 2.007 8.161 6.149 8.161 6.208 13.563 7.441 13,563 7.296 13.563 9.130 13.563 9.324
10 18 10.73 4.74 4.42 15.56 16.27 18.38 17.39 9.79 8.74 2.42 2.81 9.26 9.60 5.22 6.04
Fraction IV a t 35" 15,818 8.628 15.818 8,007 15.818 11.976 15.818 11.917 15.818 5.284 15,818 5.053
9.09 9.13 4.43 4.38 12.10 13,33
and applied the method of least squares to this straight line relationship. The result of the statistical analysis is shown in Table 11, which shows clearly that the standard deviation of C is of the same order as C itself which means that C does not TABLE I1 CONSTANTS A A N D C (CAL./ML.)IN EQ.6 FROM STATISTICAL ANALYSIS;6A AND SC ARE THE STANDARD DEVIATIONS Fraction
Temp., OC.
A
8A
C
6C
111
25 25 35
1.60 1.60 1.38
0.11 0.13 0.20
1.02 9.31 8.04
5.25 6.43 8.20
IV IV
TABLEI11 EQ. 8 FROM EXPERIMENTAL SECOND VIRIALCOEFFICIENT B (ERQC M . a~ - 2 ) AND HEATOF DILUTION. VALUES OF z A N D p CALCULATED WITH USE OF EQS. 8b AND Sc, RESPECTIVELY CY
IN
Frac-
10-
tion
X B
u
111, 25" IV, 25" IV, 35"
0.34 .22 .37
0.63 .54 .45
MillerGug.
z = z = z =
5.4 4.3 3.7
Staverman 6, p = O.OG z = 6, p = 0 . 3 6 z = 6, p = 0 . 5 6
z =
1499
HEATSOF MIXINGIN SYSTEM POLYVINYL ACETATE-TOLUENE
Nov., 1957
0 (Ijl'
Fig. l.-Plot
of A H / V us. ($'
- $1 x loa.
- $);25";the0lines are drawn in accordance with the statistical calculation: , fraction 1V a t 25'; 0 , fraction IV a t 35'.
differ significantly from zero. It is therefore allowed to assume a straight line relationship. The lines represented in Fig. 1 are plotted in accordance with the statistical calculations thereof. Discussion The result obtained means that the heat of dilution can within experimental error be represented by Ah1 = (bAH/dNl)P.T = Avi@
(7)
where N1is the number of moles of solvent in the solution and u1 the partial molar volume of the solvent. Equation 7 assumes that the dependence of the partial molar volumes of solvent and solute on concentration may be ignored. Introducing eq. 7 into the formula derived by F 1 0 r y ~and ~ Huggins,34 Miller36 and Guggenheim,a6Staverman37 and van der W a a l P for the second virial coefficient B, one finds B = (RT/~p'v1)(01/2- V l A / R T )
(8)
where sp is the density of the polymer, while 01 01
= 1 according to Flory-Huggins = 1 - 2/2 according to Miller-Guggenheim = 1 - (2/2)( 1 p / z ) 2 according to Staverman-
+
(Sa) (Sb)
van der Waals (80)
(33) P. J. Flory, J . Chem. P h y s . , 9,660 (1941); 10,51 (1942). (34) M.L. Huggina, J . Chem. Phys., 9,440 (1941); THISJOURNAL, 46, 151 (1942); Ann. N . Y . Acad. Sei., 43, l(1942). (35) A. R. Miller, Proc. Cambridge Phil. Soc., 39, 54, 151 (1943); 43, 442 (1947). (36) E, A. Guggenheim. Proc. Roy. SOC. (London), 8180, 203 (1944). (37) A. J. Staverman, Rec. lTau. chim., 69, 163 (1950). (38) J. H.van der Waals, thesis, Groningen, 1950.
X, fraction I11 a t
Here x is the coordination number and p the fraction of segments in a polymer molecule making contact with a segment of the same molecule. The second virial coefficient was interpolated from Dyk~ t r a ' sdata. ~ ~ The value of B a t 35' was derived from Dykstra's results a t 25' by means of the experimental value of hl using the relation A91
-
T d A g , / d T = Ah,
where Agl is the Gibbs free energy of dilution. The following approximation was made Ag136 = Ag1'' f lO(dAgi/dT)''
For spin eq. 8 we took the density of the dry polymer to be 1.19. The result of the calculation using the slope of the straight lines in Fig. 1 as A , is shown in Table 111, which shows that the FloryHuggins formula is a rather poor approximation (since in their formula a = l), that the MillerGuggenheim formula leads to a reasonable value of x a t 25' but to a less satisfactory result a t 3 5 O , and finally that with x = 6 the theory of Staverman leads to acceptable values of p. We have also investigated the applicability of Long~et-Higgins'~9conformal solution theory. In the notation used by us, the second virial coefficient B according to this theory is related to the cohesive energy el per mole of pure solvent by the relation eidiz
'/zRT
-v
~ s ~ ~ B
(9)
where dlz is a parameter independent of tempera(39) H. C. Longuet-Higgins, Proc. Row. Soc. (London), A205, 247 (1951); Disc. Faradag Soc., 16, 73 (1953).
1500
EDWARD P. EGAN,JR.,AND ZACHARYT. WAKEFIELD
Vol. 61
ture. At the same time the constant A in eq. 7 is related to el as
compared with the heat of evaporation of toluene which according to Timmermans41is 98.5 cal./mole. Hence, the agreement is better than one might ex(€1 - Taai/bT)die = VIA (10) pect. while the volume change on mixing per unit volume Another theory which relates volume changes of the mixture is with heats of mixing has been developed by PrigoA v = (PK - Tp)diz@(l- @) (11) gine and c o - w o r k e r ~ . ~To ~ check this we used the procedure described by Bellemans and ColinK being the coefficient of compressibility: 91 X and p the coefficient of thermal ex- Naar4a and found agreement between calculated pansion: 1.10 X loFadegr.-l according to our own and experimental values of AH as regards the order measurements. The term I)K in eq. 11 is negligible of magnitude. This is all one may expect because compared to Tp. To calculate AV we used the here, as in the application of the conformal solusolution densities measured and the specific volume tion theory, the weak point lies in the use of the of the dry polymer. Applying eq. 11 this gives the specific volume of the dry polymer for the calculavalue 3.55 for d12at 25' and 3.48 a t 35'. It then tion of AV, whereas the volume to be used should be follows from the other data that for fraction TI1 a t that of the (hypothetical) liquid polymer. 25' and fraction IV a t 25' and 35' el is, respecAcknowledgments.-We wish to thank H. L. tively, 80.0, 81.2 and 84.3 cal mole-' and bel/dT, Jalink and R. van Wijk who performed the density respectively, 0.104, 0.129 and 0.156 cal. mole-' measurements and the fractionation. degr.-l. Finally, since we know the heat of dilu(41) J. Timmermans, "Physico-chemical Constants," Elsevier Publ. tion a t 35' for fraction IV, we are in a position to New York, N. Y . , 1950. estimate d2el/bT2for this fraction. Assuming that Co., I. Prigogine and V. Mathot, J . Chem. Phya., 20, 49 (1950); A changes linearly with time over the interval I. (42) Prigogine and A. Bellemans, ibid., 21, 561 (1953); Disc. Faraday studied, this leads to b2el/bT2 = 0.0233 cal. mole Soc., 16, 80 (1953); J . Polymer Sci., 18, 147 (1955); I. Prigogine, degr.-2 a t 25' and 0.0227 cal. mole-' degr.-2 at V. Mathot and N. Trappeniers, J . Chem. Phys., 21, 560 (1953); Faraday Soc., 16, 93 (1953). 35'. The cohesive energy €1 per mole may be Disc. (43) A. Bellemans and C. Colin-Naar, J . Polymer Sci., 16, 121 (40) "Handb. Chem. and Physics," 33rd edition.
(1955).
LOW TEMPERATURE HEAT CAPACITY AND ENTROPY OF CRYSTALLINE ORTHOPHOSPHORIC ACID BY EDWARD P. EGAN, JR.,AND ZACHARYT. WAKEFIELD Division of Chemical Development, Tennessee Valley Authority,' Wilson Dam, Alabama Received January 88,1867
The heat capacities of the two crystalline forms of orthophosphoric acid were measured over the range 10 to 300°K. A t 298.16'K. the heat content of the anhydrous crystals, HaPO~,is 4059 cal. mole-' and the entropy is 26.41 cal. deg. -1 mole-'. The corresponding values for the hemihydrate crystals, 2HaP04.Hz0, are 9569 cal. mole-' and 61.73 cal. deg.-l mole-'.
As part of a continuing study of the thermodynamic properties of the calcium phosphates and related compounds in the technology of phosphate fertilizers, the heat capacities of crystalline anhydrous orthophosphoric acid and crystalline orthophosphoric acid hemihydrate were measured over the interval 10 to 300°K. The entropies and heat contents at 298.16"K. and the heats of fusion were derived from the measurements. Materials Anhydrous Phosphoric Acid.-Reagent phosphoric acid was heated gently until its specific gravity a t 25' was 1.85.e Crystallization of the anhydrous acid (HaPOa; formula weight, 97.999) was init.iated by spot chilling with solid carbon dioxide. The crystals were allowed to grow for 3 dags a t room temperature. Crystals and mother liquor were centrifuged under a blanket of dry nitrogen in ,8. stainless st8eel basket. The crystals were melted at 45 , and the melt was diluted to a specific gravity of 1.85 a t 25". The acid was twice recrystallized. The crystals were transferred to a special container from which the calorimeter was to be charged, and the open con(1) Article not copyrighted. (2) W. H. Ross and R. M. Jones, J . A m . Cham. Soc.. 41, 2165 (1925).
tainer and acid crystals were stored for 5 months over P z O ~ in a vacuum desiccator for completion of crystallization. Phosphoric Acid Hemihydrate .-Phosphoric acid hemihydrate (2HaPO4.H90; 91.58% H3P04; formula weight, 214.014) was prepared by triple crystallization of reagent phosphoric acid. Complete removal of mother liquor from the crystals proved difficult. Storage of the crystals n a drying atmosphere, as was done with the anhydrous acid, was complicated by the fact that a liquid corresDonding in composition to the hemihydrate has a vapor pressure of about 0.8 mm.8 The vapor pressure was not known precisely enough, however, to permit the selection of B, drying atmosphere. Because of the difficulty of obtaining dry crystals, the crystals were melted for final adjustment of the composition, which at this point was 90.5% Hapol. Excess water was removed by a combination of evacuation and vigorous magnetic stirring at room temperature. Two lots of the hemihydrate were prepared. The HaPo4 content of lot A was adjusted on the basis of density.' Preliminary heat capacity measurements on lot A indicated a relatively large eutectic peak, and the best melting point data on the acid indicated a composition of 91.85% H I P O ~ . Lot A was diluted by weight to 91.58% Hap04 and was (3) T. D. Farr, Tennessee Valley Authority, Chem. En& Repl., No. 8, 1950. (4) J. H. Christensen and R. B. Reed, I n d . Eng. Chem., 4'7, 1277 (1955).
.
