Dec., 1963
THERMODYNAMIC P R O P E R T I E S O F hIAGXESIUM PHOSPHATES
1070 to 3400. This material would be strongly held to the water surface by oxygens, and the evaporation (10) S. A. M o s s , Jr., J . Am. Chem. Soc., 66, 41 (1934).
2737
catalyst would consist of CH2groups. It was not possible to purchase materials of these types for test in the experiments described here.
THE THEL‘CM0DI”AMIC PROPERTIES OF MAGNESITJM ORTHOPHOSPHATE ANI) MAGNESIUM PYROPHOSPHATE BY F. L. OETTINGAND R. A. 3 l c D o x s ~ e Thermal Research Laboratory, T h e Dow Chemical Co., Midland, iVzchigan Received Julv 2, 1963 The heat capacity of magnesium orthophosphate from 17 to 320% and the heat capacity of magnesium pyrophosphate from 14 to 378°K. have been measured experinientally pith a low temperature adiabatic calorimeter. The absolute entropies a t 298.15”K. of magnesium orthophosphate and magnesium Pyrophosphate are 45.22 f 0.15 cal./(mole OK.) and37.02 f 0.15 cal./(mole OK. 1. The heat contents of the two phosphates were determined experinientally from 298 to 1700’K. The melting point of magnesium orthophosphate is 1626 f 5°K. with a heat of fusion of 28.84 5: 0.10 kcal./mole. The melting point of magnesium pyrophosphate is 1668°K. zk 5°K. with a heat of fusion of 32.1 zk 0.4 kcal./mole. The pyrophosphate hlts a transition a t 342.2”K. due to a change in crystal structure with an energy of 729 cal./molr. From experimental data the thermodynamic properties of magnesium orthophosphate and magnesium pyrophosphate have been tabulated from 0 to 1700°K.
Introduction The thermal data which have been given in the literature for magnesium orthophosphate, AIgJ’ZOs, and for magnesium pyrophosphate, JIg2P207,are incomplete. The low temperature region has not been investigated for either compound and various values for the melting point of magnesium orthophosphate have been given in the range of 1457to 1703°K.1-6 The recent work of Holmes6 on the heat of formation of PZO; allows revision of the heat of formation of Mg3PaOsrepoi ted by Stevens and ‘Turkdogan4 which brings it in close agreement with the value calculated from the equilibrium data of Bookeye2 Roy, et al.,’ have studied magnesium pyrophosphate, ;Llg2PZ07, and have observed a heat anomaly near 341OK.; they have confirmed a change in crystal structure by X-ray diffraction. This work was undertaken to determine some of the missing data and then to calculate the thermodynamic properties of nzagizesium orthophosphate and magnesium pyrophosphate. Experimental Material.-The magnesium orthophosphate was prepared ac2(NH4),HPO4-+ cording to the following reaction 3Mg0 MgBPzOs 4SH8 3Hz0. Reagent grade magnesium oxide was washed, dried, and ignited a t 1000° and then mixed with a stoichiometric amount of reagent grade diammonium monohydrogen orthophosphate. The mixture was ignited at 950-1000” for 42 hr. Analysis of the product gave 27.82 magnesium, 23.75 phosphorus, and 48.437, oxygen (by difference), compared to the theoretical analysis of 27.75 magnesium, 23.57 phosphorus, and 48.68Yc oxygen. XRay powder patterns indicated this sample to be anhydrous magnesium orthophosphate. The magnesium pyrophosphate was prepared according to the standard procedure for the determination of magnesium as outlined by Koltoff and SandeX1.8 Pure magnesium was dissolved in
+
+
+
(1) J. Berak, Roezniki Chem., 32, 17 (1958). (2) J. B. Bookey, J.Iron Steel Inst. (London), i72,66(1952). ( 3 ) K. K. Kelley, U. S. Bur. Mines Bull., No. 393 (1936). (4) C. G. Stevens and C. T. Turkdogan, Trans. Faradag Soc., SO, 370 ( 1 954). (5) H. Winter, Dissertation, Cniversity of Leipzig. 1913. ( 6 ) W. S. Holmes, Tians. Faraday Soc., 68, 1916 (1902). (7) R. Roy, E. T. RIiddlesworth, and F. A. Hummel, A m . Minevalogist, 33, 458 (1948).
6 A’ hydrochloric acid, diammonium monohydrogen orthophosphate was added in excess, and ammonium hydroxide was added until precipitation was complete. The precipitate was allowed to settle, then it was filtered and washed thoroughly with dilute ammonium hydroxide. A triple precipitation was made to ensure maximum purity and ideal composition of the precipitate. The material was then calcined t o form the pyrophosphate. X-Ray powder patterns showed only crystalline ff-Mg2P207.
Low Temperature Heat Capacity.-The low temperature adiabatic calorimeter and the mechanics of its automatic operation have been deycribed in detail.Q>lOThe calorimeter has been modified since references 9 and 10. Briefly, the essential features of this revised automalic calorimeter are as follows: The calorimetric assembly is of conventional design and is similar to that described by Ruehrwein and Huffman.ll Automatic operation of the adiabatic shield control is provided by feeding the outputs of three twelve junction Chromel-P vs. constantan thermels t o three servoamplifiers. The first thermel indicates the temperature difference between the sample container and the adiabatic shield side, the second thermel indicates the temperature difference between the shield top and shield side, and the third indicates the temperature difference between the shield bottom and shield side. I n each case, a motor fed by the respective servoamplifier is used t o operate a microswitch that controls the respective shield component heating current. The temperature of the shield environment is controlled in a similar fashion. The sample temperature, indicated by a calibrated platinum resistance thermometer, is recorded continuously on a Leeds and Northrup “High Precision” resistance recorder, which has the considerable advantage of providing a complete record of the thermal history of the sample. Electrical power input to the sample heater is obtained by recording, on a Brown electronic voltage recorder, the potential drops across the sample heater and across calibrated standard resistances. The accuracy of the temperature measurement is such that above 60°K. the temperature rise can be determined to better than 0.05% while a t 30°K. the accuracy is about 0.2%. Electrical power measurements are accurate to better than 0.1%. A pendulum operated clock, periodically checked against a Berkeley Time Interval meter, Model 500C, automatically times the duration of the electrical heat inputs. Even for the shortest inputs, these time intervals are known to better than O.Olyc. This master clock also is used to operate a (8) I. RI. Kolthoff and E. G. Sandell, “Text Book of Quantitative Inorganic Analysis,” The Macmillan Company. New York, N. Y., 1948, Chapter XXII. (9) D. R. Stull, A n d . Chrm. Acta, 17, 133 (1957). (10) D. L. Hildenbrand, W. R. Kramer, R.A, McDonald, and D. R.Btull, J. Am. Chem. Soc., SO, 4129 (1S58). (11) It. A. Ruhriiein and H. >I. Huffman, zbzd., 66, 1620 (1943).
2738
F. L. OETTIPI'G AND B. A. MCDONALD
program unit which furnishes the necessary switching to give the desired alternating sequence of heating and equilibration periods. Several programs are available so that by changing programs or varying the voltage drop across the sample heater any desired temperature rise can be obtained. The program unit operates continuously and above 40°K. requires changing perhaps once a day as the sample heating requirements increase. The side and bottom unit of the shield can be removed for direct access to the sample container. The control thermocouple junctions are insulated with mica strips and are fastened t o the outside of the shield with copper lugs. Each pair of thermocouple leads was given several turns around the shield and is lacquered in place with G.E. No. 7031 adhesive. The outer surface is covered with aluminum foil. The copper band, containing the sample control junctions, which is clamped around the middle of the sample container, is suspended from three linen threads attached to the top of the shield. The sample container is gold plated copper and has a volume of approximately 65 A central re-entrant well is provided for the platinum resistance thermometer, around which are clustered ten re-entrant wells for replaceable heaters. The heaters are made of glass insulated constantan wire encased in a copper tube of 3 mm. 0.d. and have a resistance of ten ohms each. A light coating of silicone grease on the thermometer and heaters provides good thermal contact to promote rapid attainment of thermal equilibrium. A vertical heat distribution fin in the shape of an "L" is bonded to each heater well but not to the thermometer well or the container wall. The lid is soft soldered to the container to facilitate removal for loading the sample. The lid also has a short tube for loading of helium gas. The platinum resistance thermometer (Ro = 93 ohms), constructed as described by Southard and Milner12 and Meyers,13 was calibrated by comparing it a t 41 points between 11 and 300°K. with a platinum resistance thermometer calibrated by the National Bureau of Standards. (This calibration is more recent than that mentioned in ref. 10.) Refrigeration is provided by mounting the calorimetric assembly in the experimental cavity of a Collins helium cryostat. The heat capacity of benzoic acid compares with the standard values given by Furukawa, et a1.,14 as follows: =t3.0% below 20"K., & l . O ~ o from 20 t o 30"K., =t0.5y0 from 30 to 80°K., and i:0.3% from 80 to 310'K. The entropy of benzoic acid a t 298.15'K. is 40.11 i:0.15 cal./(mole OK.) as determined with this apparatus. This is in satisfactory agreement with the standard value of 40.055 cal./(mole "K.).l4 While it is understood that the automatic calorimeter, in its present stage of development, is not capable of attaining the high accuracy of a manually operated precision calorimeter, the apparatus is still useful in third-law work. The advantages of the automatic operation are obvious. Two series of determinations were made on a 66.686-g. portion of the magnesium orthophosphate, and four series of determinations were made on one portion of magnesium pyrophosphate weighing 40.372 g., and two series (Series V and VI) of determinations weremade on another portion weighing 15.350 g. (Two portions of the pyrophosphate were used because a change in sample containers with different sealing solders was required for the higher temperature investigation of the solid state transition.) One atmosphere of helium gas was admitted to the sample container before closing to serve as a heat exchange medium. All weights were corrected to vacuum and the heat capacity results were corrected for the helium and for the change in weight of solder used to seal the container. The gram molecular weights of magnesium orthophosphate and magnesium pyrophosphate are taken as 262.91 and 222.59.16 The ice point is taken to be 273.1B"K. and one defined calorie is taken as 4.1840 absolute joules. High Temperature Enthalpy.-The heat content, HT - H ~ 15, w was determined by the drop method using a copper block calorimeter previously A 7.473-g. portion of the magnesium orthophosphate was sealed in a platinum-lOyo rhodium alloy capsule (14.756 g.) by arc weIding under a helium pressure of 8 cm . However, the capsule (12) J. C. Southard and R. T. Milnar, J . Am. Chem. Soc., 56,4384 (1933). (13) C. H. Meyers, J . Res. Natl. Bur. Std., 9, 807 (1932). (14) G. T. Furukawa, It. 6.MoCoskey, and P. J. King, h d . , 47, 256 (1921). (15) E. Wiohers. J. Am. Chem. Soc., 80, 4121 (1958). (IG) R. A. McDonald and D. R. Stull, J . Chem. Eng. Data, 6, N o . 4, 605 (1961).
VOl. 67
was bulged after heating to 1400'K. and a small hole was drilled in the top of the capsule to release the pressure which would develop a t higher temperatures. There was no loss in weight of the sample after melting several times. Part of the magnesium pyrophosphate preparation was fused in a platinum crucible with a gas-oxygen flame to increase the sample density so that more of the sample could be contained in the sample capsule. X-Ray diffraction of the fused material revealed only Or-MgZP~O~.A 5.224-g. portion was transferred to a platinum-10% rhodium alloy capsule (15.293 g.). Considerable degassing of the sample had been observed on freezing even after heating and cooling three times. Therefore, a small hole was drilled in the top of the capsule t o release possible gas pressure. Again, there was no sample loss during the course of the investigation. The platinum us. platinum-10% rhodium thermocouple used to measure the capsule temperature in the furnace was recalibrated just prior to the heat content measurements by comparison with a similar couple standardized a t the National Bureau of Standards. Correction for the heat content of the capsule and heat loss during the drop was obtained from previous empty capsule measurements. Melting Point.-The temperatures of complete melting of the samples were determined by raising the drop calorimeter sample capsules above the normal position in the furnace so that the hot juwtion of the platinum us. platinum-10yo rhodium thermocouple could be bound to the side of the capsule with fine platinum wire; the junction being located lower than the level of the melt. Time us. temperature heating and cooling curves were obtained. Both compounds super-cooled excessively and the heating curves produced more reliable data.
Results Magnesium Orthophosphate.-The experimental lorn temperature heat capacities are listed in Table I ; smoothed values of heat capacity and the entropy, free energy function, and enthalpy from 17 to 320°K. are given in Table 11. The heat capacity curve is normal with no anomalies being observed in this range. The entropy a t 17"K., 0.098 cal./(mole OK.), was calculated using the Debye T 3 law with 6~ = 199.4". The integral of C, d T / T from 17 to 298.15"K. is 45.12 cal./(mole O K . ) . The absolute entropy a t 298.15"Ii. is, therefore, 45.22 =t0.15 cal./(mole OK.). Enthalpy values observed in the range 295 to 1690'K., Table 111, were smoothed by the method of Shomate. l7 Smoothed enthalpies and graphically smoothed average heat capacities are given in Table IT. Kelley3 quotes a m.p. From the work of of 1457°K. and derives an "uncertain value" of 11.3 kcal./rnole for the heat of fusion. Other values reported for the m.p. of magnesium orthophosphate are 1703°K. by Bookey,z 1621°K. by Stevens and T ~ r k d o g a nand , ~ 1630°K. by Berak.l A value of 1626 f 5°K. was determined in the present investigation as the temperature of complete melting which is in good agreement with Stevens and Turkdogan and with Berak. Pre-melting a t least 40" below the final nieltiiig point is indicated by the enthalpy nieasurements. The heat of fusion at 1626°K. is 28.84 f 0.10 kcal./ mole. The experimental data for the liquid covers only very short range, 1626 to 169OoK;.,but an approximate average heat capacity for the liquid is 112.5 cal./(mole "IC). The heat of formation of magnesium phosphate is evaluated from the work of Stevens and Turkdogan4 where they determined the heat of the following reaction. (17) C. H. Shomate, J . Phys. Chem., 5S, 338 (1954).
THERMODYXAMIC PROPERTIES OF MAGNESIUM PHOSPHATES
Dec., 1963
2739
TABLE I EXPERIMENTAL HEATCAPACITY DATA Magnesium orthophosphate Mg,P2O8,mol. wt. 2C2.91 (mole OK.)
CP,
CP? oa1.l
CP,
cnl./
T , OK.
Magnesium pyrophosphate M g 2 P ~ Omol. ~ , wt. 222.59
T,OK.
(mole OK.)
T , OK.
Gal./ (mole OK.)
144.65 149.89 155.88 161.71 167.42 173.00 178.49 183.88 202.70 208.98 215.16 221.28 244.84 250.59 256.28 261.91 267.48 273.01 278.47 297.30 304.33 311.31 318.20
27.63 28.64 29.85 31.08 32.15 33.15 34.17 35.28 38.38 39.50 40.39 41.14 44.46 45.13 45.96 46.78 47.35 47.91 48.62 50.98 51.68 52.66 53.65
Series I1 100.54 106.37 112.44
17.14 18.67 20.10
118.76 124.81 130.62 136.23 141.68 146.98 152.16 160.47 171.76 182.62 193.13 203.35 213.30 223.04 241.34 252.92 258.62 264.26 269.85 275.94 282.52 289.03 295.48 308.20 314.48 320.69
21.45 22.91 24.39 25.65 26.86 27.94 29.07 30.75 32.89 34.89 36.58 38.36 39.91 41.27 44.05 45.32 46.22 46.88 47.40 48.14 49.01 49.88 50.70 52.21 52.95 53.71
Series I 17.20 19.44 21.40 23.61 26.27 29.04 31.79 34.61 38.13 42,22 46.50 51.07 55.78 60.72 66.01 75.95 80.22 85.82 92.63 98.95 104.88 110.51 115.89 121.07 126.06 135.59 140.17
0.299 ,352 .460 .592 .so0 1.063 1.398 1.874 2.436 3 .(a82 3 ,856 4.881 6.041 7.375 8,570 10.94 12.14 13.57 15.22 16.70 18.26 19.59 21.00 21.99 23.28 25.68 26.67
3RIgO(c)
+ Pp05(orthorhombic)
-+ Mg3P20s(c)
(1) AHY480~. = - 3 10.94 f 0.62 kcal. Tlic reaction taking place a t 298.15"K. using the thermal data on l ~ I g 0 , ~P205,19 * and MgSP208 (this work) gives kLH298.15°K = -110.98 f 0.62 kcal., an insignificant correction. Holmes6 has recently reported the heat associated with the following reaction 2P(white)
+ 5/202(g)-+P20B(hexagonal) AH298 150K
(2)
= --356.6 f 0.5 kcal.
Using the data of Hill et U Z . , * ~ in the conversion of PzOs(hexagona1)to P20a(ortliorhombrc). P205(hexagonal) -+ P20a(orthorhombic) AH298.150K = -6.83
f
(3) 1.00 kcal.
and correcting to the reference state of phosphorus (red) l9 2P(red) --+ 2P(white)
AH298.1501~
=
8.34 f 0.4 kcal.
(4)
the heat of formation of P~05(orthorhombic)is obtained. The hLeat of formation of RIgO has been reported by Shomate and Huffman.2l (18) G. S. Parks and K. K. Kelley. J. Phys. Cheni., 80, 47 (1926). (19) JANAF Thermochemical Tables, The n o w Chemical Co., Nldland,
Mich. (20) W. L.Hill, G T. r a u s t , and S. B. Hendricks, J . A m . Chern. Soo., 65, 794 (1943). (21) C. EI. Shomate and E. 13. Huffinan, zbzd., 66, 1626 (1943).
CP,
T, OK.
Series I 13.30 21.52 24.02 26.71 29.60 32.63 36.22 40.37 44.50 54.40 60.01 250.54 257.40 270.88 284.13 290.65 297.12 Series I1 17.43 20.21 22.78 30.32 33.54 37.27 41.09 45.31 49.94 54.97 60.42 66.33 71.94 78.10 84.85 91.02 96.77 102.21 107.39 112.35 118.27 125.12 131.70 138.03 144.18 150.16 155.99
3Wdc)
cal./ (mole OK.)
T,OK. 65.87 85.88 92.01 97.74' 103.82 110.22 116.33 122.19 127.84 133.31 138.62 143.81 161.70 167.28 172.76 178.69 185.04 191.28 197.43 203.48 209.46 215.35 221.17 248.58 255.43 295.11 301.51
,060 .131 .199 .390 .648 1.104 1.583 2.119 2.654 4.402 5.687 37.44 38.17 39.76 40.83 41.70 42.41
0.088 .122 ,170 .738 1.203 1.643 2.283 2.841 3.600 4.716 5.931 6.878 8.003 9.341 11.00 12.28 13.35 14.27 15.47 16.50 17.63 18.85 20.18 21.57 22.46 23.53 24.72
CP, cal./ (mole "K.)
6.892 11.30 12.44 13.49 14.64 15.94 17.20 18.21 19.54 20.54 21.58 22.37 25.58 26.51 27.28 28.33 29.38 30.27 31.08 31.79 32.63 33.50 34.27 37.24 38.01 42.22 42.96
Series 111 238.36 36.29 244.01 36.87 249.61 37.38 260.67 38.66 276.91 40.29 282.25 40.75 287.55 41.41 298.02 42.52 Series I V 233.07 238.60 244.95 251.25 261.59 263.65 271.77 275.81
+ 3/202 --t
35.73 36.39 37.03 37.56 38.75 39.03 39.77 40.08
3h1go(~)
CP
T,OK.
148.87 153.83 164.46 171.09 177.59 183.97 190.23 196.40 208.48 215.12 222.40 243.62 283.82 285.81 297.61 299.56
?
tal./ (mole OK.)
23.31 24.23 26.07 27.03 28.13 29.14 30.13 30.84 32.65 33.41 34.28 36.87 41.05 41.36 42.49 42.83
Series V 303.38 309.58 315.72 321.80 327.81 333.70 338.70 ( a ) 342.20(j?) 345.51 350.64 357.29 364.14 371.05 378.03
43.34 44.37 45.17 46.15 47.54 50.84 65,86 137.68 81.37 60.12 52.76 51.01 50.43 50.14
Series V I 305.81 313.14 320.39 327.54 333.39 337.89 (a) 342.59 (j?) 344.92 348.88 354.41 361.29 368.27
43.79 44.84 45.88 47.42 50.66 60.00 127.74 88.94 64.02 54.77 51.59 50.71
(5) 5 kcal.
(6) 3 kcal.
gives the heat of formation of magnesium orthophosphate. This is compared t o the value of -910.86 f 7.00 kcal. reported by Stevens and T ~ r k d o g a n . ~The difference is due t o the choice of the reference state of phosphorus and the different values used for the heat of formation of P205(orthorhombic). Bookey2 measured the equilibrium in the system
F. L. OETTINGAXD R. A. MCDONALD
2740
Vel. 67
TABLE I1 THERMODYNAMIC FUNCTIONS Magnesium orthophosphate Mg2Pz08,mol. wt. 262.91 CP,
T,OK.
S,
(HT -
Hd/T,
-(FT
-
Ho)/T,
Gal./ tal./ cal./ Gal./ (mole OK.) (mole OK.) (mole OK.) (mole OK.)
hfagnesium pyrophosphate Mg2P2Q7. mol. wt. 222.59 HT
- Ho,
cal.! (mole)
17.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00
0.285 .398 .700 1.208 1.883 2.736 3.681 4.723
0.096 ,151 ,266 ,436 .671 .975 1.351 1.792
0.072 .112 .194 ,318 ,492 .716 ,992 1.312
0.024 ,039 ,072 .118 .I79 .259 ,359 .480
1.2 2.2 4.9 9.6 17.2 28.6 44.6 65.6
55.00 60.00 70.00 80.00 90.00
5.846 7.033 9.547 12.04 14.55
2,294 2.853 4.127 5.564 7.128
1.673 2.070 2.959 3,938 4.978
,621 ,784 1.168 1.626 2.150
92.0 124.2 207.1 315.1 448.0
100.00 110.00 120.00 130.00 140.00
17.05 19.46 21.87 24.23 26.54
8.790 10.53 12.32 14.17 16.05
6.061 7.169 8.294 9.430 10.57
2.730 3.359 4.031 4.740 5.480
606.1 788.6 995 I3 1226 1480
150.00 160.00 170.00 180.00 190.00
28.64 30.68 32.62 34.44 36.17
17.95 19.87 21.79 23.70 25.61
11.70 12.83 13.94 15.02 16.09
6.248 7.040 7.851 8.678 9.519
1756 2052 2369 2704 3057
200.00 210.00 220.00 230.00 240.00
37.88 39.50 40.96 42.38 43.76
27.51 29.40 31.27 33.12 34.96
17.14 18.17 19.17 20.15 21.10
10.37 11.23 12.10 12.97 13.85
3428 3815 4217 4634 5065
250.00 260.00 270.00 273.15 280.00 290.00
45.09 46.37 47.59 47.97 58.81 50.06
36.77 38.56 40.34 40.89 42.09 43.82
22.04 22.95 23.84 24.11 24.71 25.56
14.73 15.61 16.50 16.78 17.38 18.26
5509 5966 6436 6588 6918 7413
298.15 300.00 310.00 320.00
51.02 51.24 52.41 53.57
45.22 45.54 47.24 48.92
26.24 26.40 27.22 28.02
18.98 19.14 20.02 20.90
7825 7919 8437 8967
in the temperature range 1000 to 1250'. Taking his equilibrium values to calculate AF,/T and the free energy functions of H2,19RIgO,l9 P2,19H20,19and Rig,PzOe (from this work), one calculates the AHzg8to be 215.5 kcal. for eq. 7 as w i t t e n (see Table V). Using tlie heats of forniation of lCIg0,21Pz,I9and H20,19the heat of formation of 9!g,P2O8at 298.15"K. is -893.1 kcal./mole. This value is in good agreement with the value of - 897.G kcal.,/mole obtained from calorimetric data. The quantity, -895.1 f 2.5 kcal./mole, is taken as the most probable value for the heat of formation of magnesium orthophosphate. Bookey's value for the melting point of magnesium orthophosphate, 1703'Is out that the transition should be classed as oiie of first order. Contrary to this supposition is the data presented in Fig. 1 where it is apparent that the transition is not isothermal, a term closely associated with transitions of the first order. Roy, et al., took X-ray patterns of the material at small intervals over a 20" temperature range (333353°K.) which showed the coexistence of the a and p forms. They proposed two explanations. They as-
E". L.OETTINGAND R. A. MCDONALD
2742
Vol. 67
TABLE IV THERMODYNAMIC FUNCTXONS 2',
COP,
OK.
cal./(mole
-
-(F' H0298)/T, OK.) , cal./(mole OK.)
SO, OK.)
cd./(mole
HT'
-
Hzss koal./mole
Magnesium orthophosphate 0.00 45.22 45.22 .09 47.35 5.69 51.62 11.99 56.66 18.76
AHOf*
- 839.90 - 839.56 -821 .oo -802.46 - 784.01
615.64 611.59 448.56 350.74 285,56
- 765 .65 -758.02 - 736.10 -713.78 -691.44
239.04 207.07 178.74 155.99 137.37
-669.22 -647.12 -623.71 - 595.27 -567.02
121.88 108.79 97.36 86.73 77.45
- 559.74
75.22 75.22 69.43
45.22 45.54 61.55 75.57 87.90
700 800 900 1000 1100
72.58 75 .00 77.11 79.04 80.86
98.86 108 .72 117.67 125.90 133.52
61.92 67.16 72.29 77.24 82.02
25.87 33.26 40.86 48.68 56.66
1200 1300 1400 1500 1600
82.61 84.29 85.93 87.56 89.17
140.63 147.31 153.62 159.60 165.30
86.61 91.02 95.27 99.36 103.30
64.84 73.19 81.70 90.38 99.22
- 893.78 - 933.93 - 932:73 - 937,86 - 936.51 - 935.10 - 933.63 - 1023.19 - 1020.39 - 1017.44
89.63 (112.5) (112.5)
166.74 184.48 189.49
104.31 104.31 107.91
101.54 130.38 138,65
-1016.66 - 981.82 - 983.87
298 300 340 342.2 (0) 342.2 ( p )
42.53 42.71 46.78 47.01 45.90
37.02 37.28 42.87 43.18 45.30
350 400 500 600 700
46.43 49.49 54.12 57.32 59.70
46.34 52.75 64.33 74.50 83.52
37.60 39.10 43.02 47.43 51.95
3.06 5.41 10.60 16.19 22.04
800 900 1000 1100 1200
61.65 63.27 64.70 66.00 67.21
91.62 98.98 105.72 111.95 117.74
56.42 60.74 64.91 68.90 72.73
28.12 34.37 40.76 47.27 53.95
1300 1400 1500 1600 1668 (P) 1668 (1) 1700
68.33 69.41 70.46 71.47 72.15
123.17 128.27 133.10 137.68 140.66
76.41 79.93 83.32 86.57 88.72
60.71 67.61 74.60 81.72 86.58
(85.8) (85.8)
159.93 161.56
88.72 90,Oi
118.72 121,47
BOOKEY" Equilibrium measured in the system ILI,v~P~O~(C) 5Hz(g) 3RfgO(c) P4g) 5&O(g)
+
1273
1298 1323 1373 1423 1473 1523
-18 -17 -17 -16 -15 -14 -13
50 89 34 11
05 09
29
-
AF/T
84 652 81 861 79 344 73 716 68 866 64 473 60 812
+
+
A(F
-Hd/T
-84 -84 -83 -83 -82 -82 -81
-
- 559.74 - 540.18
Magnesium pyrophosphate 37.02 0.00 37.02 0.08 37.38 1.87 37.42 1.97 37.42 2.70
TABLE V HEATOF REACTION FROM THE EQGILIBRIUM DATAOF
log KP
KP
- 895.10 895.11 895.28 - 894.97 - 894.43
51.02 51.22 59.85 65.63 69.56
T, O K .
LOP
kcal./mole
298 300 400 500 600
1626 ( e ) 1626 (1) 1700
APf,
kcal./mole
AHsss
296 011 730 176 633 105 586
Av.
215,071 215,302 215,747 215,413 215,583 215,909 216,872b
215,503 cal./mole a J. B. Bookey, J. IiOn Steel Inst. (London), 172, 66 (1952). Not included in average. =
sumed that either some of the material a t all these temperatures is at a different temperature from the
rest due to air currents and surface cooling or that the change actually takes place over a sniall range of temperature. The data in Fig. 1 supports the second view in that it shows there is a range of approximately 20 O, where, under thermal equilibrium conditions, the a and /3 form can coexist. The temperature range of the X-ray patterns and the temperature range of the transition (Fig. 1) coincide very closely. The theoretical explaiiation of this type of situation has been put forth by Allen and EaglesZ3 where they describe the possibility of gradual phase transitions in solids. This could well apply in this case as this would explain the shape of the transition curve. However, it is quite possible to assume that there is Eorne orderdisorder effect along with the phase transition which would explain the shape of the curve, although there is no concrete experimental evidence to support this. Consequently, the transition is treated (23) J. W. Allenand 11. 11. Eagles, I'Ik#Istcu 26, 492 (1960).
RADIOLYSIS OF LIQUIDETHYLENE
Dee., 1963
2743
as a first-order transition and the thermodynamic calculations are made accordingly. Thc clear-cut definition of the order of transition as put forth by Ehrenfest is somewhat difficult to apply. Bartenev shares this ~ i e w . 2 ~ Andersonz5 and Berakl found the m.p. of 1\Ig2P207 to be lG56OK. and 1655°K. This work indicates a m.p. of 1668 f 5°K. although there is evidence of premelting. A t 1668°K. the heat of fusion is 32.1 f 0.4 kcal./mole. The average heat capacity of the liquid between the melting point and 1700°K. is about 85.8 cal./(mole "II .). As with the magnesium orthophosphate, the liquid range is very short and the liquid heat capacity is only approximate.
The thermodynamic functions for magnesium pyrophosphate from 14 to 400°K. are given in Table 11. The entropy a t 14°K. was calculated by the Debye T 3 law with 0D = 287' and is 0.018 cal./(mole OK.). The integral of Cp dT/T from 14 to 298.15OK. is 37.00 cal./ (mole OK.) so that x 2 9 8 . 1 5 = 37.02 f 0.15 cal./(mole OK.). Table IV extends the thermodynamic functions up to 1700°K. The entropy of the transition is 2.13 cal./(mole OK.). A thorough search of the literature to find the heat of formation was unsuccessful; consequently, the free energy of formation cannot be accurately calculated.
(24) G. M. Bartenev, Rues. J . Phgls. Chem., 54, 293 (1060). (25) 0. J. Anderson, Wash. Acad. Sei.,4, 318 (19141, a s quoted by A. Silverman. H. Inslpy, G. W. Morey, and F. D. Rossini, Bull. Natl. Res. Council (U. S.) 118, (1949).
H. W. Rinn for the X-ray powder patterns and to C. J.
Acknowledgments.-The
authors are indebted to
Thompson for the preparation of the samples.
RADIOLYSIS OF LIQUID ETHYLENE' BY
RICHARD A. HOLROYD AND
RICHARD
w.FESSENDEN
Radiation Research Laboratories, Mellon Institute, Pittsburgh, Pennsylvania Received July 8, 1963 The radiolysis of ethylene in the normal liquid temperature range, from - 168 to - 110", is characterized by both radical and molecular processes. Butane, 1-hexene, and 1-butene (in p a r t ) are products that are formed by reactions of the radicals which have been observed to be present in irradiated ethylene: ethyl, vinyl, and 3-butenyl. The yield of I-hexene increases with temperature as a result of the addition reaction which forms 3M-'h butenyl radical from vinyl radical, CzH3 CzHa -+ CdH, (reaction 1). At - 165" h/k>/9 is -4 X set.-'/%. GCZHs is approximately 0.9 and GCZH is 1.7. There are molecular processes forming H1, CZHZ, dimer (C,Hs), and trimer (C6H12). The dimers are identified as I-butene and cyclobutane. The CZH, intermediate species leading to cyrlobutane may be either an excited state such as that formed by direct photolysis or the molecule ion providing i t does not rearrange. The molecular trimerization reaction leads mainly to trans-2hexeno. The aum of the yields of all molecular products is greater than or equal to 2.1.
+
1. Introduction A study of the radiolysis products of liquid ethylene a t lorn temperatures was undertaken for comparison with observations on this substance using e.s.r. techniques.2 In these studies only ethyl, vinyl, and 3-butenyl radicals were observed during the irradiation of the liquid with 2.8-Mev. electrons. Further, a temperature effect on the spectrum was reported; the vinyl radical concentration decreased and the 3-butenyl radical concentration increased in a complimentary manner in going from lower to higher temperatures. These studies led Fessenden and Schuler to propose that reaction 1
CzHa
+ C2H4
+ C4H7
(1) occurs readily even a t low temperatures. From the temperature dependence of the ratio (C4H7)/(C2H3),it mas determined that is 3.3 kcal./mole. The products to be expected from reactions of the three radicals observed with e.s.r. are those given in reactions 2 through 6, which include all possible combination and disproportionation steps. C4H7
+ CzH5 + 1-CsH12 1-C4H8 + C Z H ~ -+
-+
1,3-C4H6 -tC2Hs
(2)
(2a) (2b)
(1) This investigation was supported, in part, b y the U. 9. Atomic Energy Commission. (2) R. W. Fessenden and R. H. Schuler, J . Chem. Phys., in press.
As a consequence of reaction 1, the yields of certain products such as 1-hexene, 1-butene, and 1,3-butadiene are expected to be temperature dependent. There have been several recent studies of the radiolysis of ethylene in the gas phase.3-5 These dealt mainly with the mechanism of formation of decomposition products such as hydrogen and acetylene; however, products such as ethane and butane were observed and are presumably formed mainly from ethyl (3) M. C. Sauer, Jr., and I,. 31. Dorfman, J . Phys. Chem., 66, 322 (1962); M. C. Sauer, Jr., Abstracts of the 140th Kational Meeting of the American
Chemical Society, Chicago, Ill., Sept., 1061. (4) P. Ausloos and R. Gordon, Jr., J . Chem. Phys., S6, 5 (1062). (5) G . G. Meisels and T. J. Sworski, Abstracts of the 141st National Meeting of the American Chemical Society, Washington, D. C., March, 19G2.
