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Thermochemistry of ammonium fluozirconates
J. inorg, nucl. Chem., 1967. Vol. 29, pp 951 to 955. PergamonPress Ltd. Printed in Northern Ireland
THERMOCHEMISTRY OF AMMONIUM FLUOZIRCONATES H. HULL and A. G. TURNBULL Division of Mineral Chemistry, C.S.I.R.O., Melbourne
(First received 10 August 1966; in revisedform 20 October 1966) Abstract--Heats of solution of ZrF4'nNH4F (n = 1, 2 and 3) have been measured in 3.83 N H F at 25° to find heats of formation of ZrF4-3NH4F (c) = --809.2 ± 0-7 kcal/mole, ZrF4"2NH4F (c0 = --697-5 4- 0"7 kcal/mole, and ZrF4"NH~F (c) = --581.2 4- 0.7 kcal/mole. The heat of the ~ --+ fl transition of ZrFc2NH4F at 138°C was found by differential thermal analysis to be 1.7 -4- 0.3 kcal/ mole. From measured heats of formation and estimated heat capacities and entropies, the heats and equilibrium temperatures for the three stages of thermal decomposition of the fluozireonates were calculated and found to agree with approximate values obtained by differential thermal analysis. INTRODUCTION
AMMONIUMfluozirconates are useful in the electrolytic recovery of zirconium, since they precipitate from aq.HF solutions as anhydrous salts which decompose to zirconium tetrafluoride below 400 ° as follows: ZrF4.3NH4F (c) --* ZrF4"2NH4F (c) q- NH 3 (g) + HF (g)
(1)
ZrF4.2NH4F (c) --* ZrF4.NH4F (c) + NH a (g) ÷ HF (g)
(2)
ZrF4-NH4F (c) --* ZrF 4 (c) q- NH 8 (g) + HF (g)
(3)
The chemistry of the solid phases of the ZrF4-NH4F system has been recently reviewed and extended by GAUDR~_~U.(1) The compounds so far characterized are cubic ZrF4"3NH4F, orthorhombic ZrF4.2NH4F and also another form of lower symmetry, and monoclinic ZrF4"NH4F. The occurrence of a single phase region, 2"0--1.7 NH4F/ZrF4 at 200 °, makes the system of especial interest. No thermodynamic properties have yet been reported, but HAENDLER e t aL (~) measured decomposition temperature at four controlled pressures by differential thermal analysis and reported 21, 21 and 25 kcal respectively for reactions (1), (2) and (3). In view of the low accuracy of this method, heats of formation were obtained in the present work from the heats of solution in 3.83 N HF at 25°C of Zr metal, NH4F and ZrF4"nNH4F, where n is 1-3. The heats of formation, together with estimated entropies and heat capacities, enabled the calculation of free energy changes and equilibria for the thermal decompositions. EXPERIMENTAL
Materials The starting materials were reactor-grade Zr turnings (99.65 ~ Zr, 0'01 ~ Hf, 0.04 ~o Mg, 0.125 Fe, 0.01 ~o C, 0"05 ~ CI, 0"090 ~o O, other metals 0.03 ~ by wt.) and A R grade 48 y. H F and NH~F. The products were analysed by pyrohydrolysis in steam at 950 °, zirconium weighed as ZrO2, and fluorine precipitated as PbC1F. Nitrogen was determined by Kjeldahl method on separate samples. cxl B. GAUDI~AU, Rev. Chim. miner. 2, 1 (1965). (~) H. M. HAENDLER,C. M. WHEELERand D. W. ROBINSON,f. Am. chem. Soe. 74, 2352 (1952). 951
952
H. HULL and A. G. TURNBULL
(NH,)sZrF7 was made by dissolving Zr in excess 10Yo H F and adding a large excess of NH4F. Slow evaporation, washing and drying over molecular sieves gave 1-2 mm crystals which analysed found, 32-7 YoZr, caled., 32.77 Yo,found, 47.5 ~o F, calcd., 47-78 ~ and found, 15.13 ~ N, calcd., 15.10 ~ . The X-ray powder pattern showed only lines reported '8~for the cubic phase and the density measured with a helium densitometer, 2.25 -4- 0.02 g]ems, agreed with the X-ray density, t3~ 2.213-2.238 g/cm 3. (NI-~)~ZrFe was made in a similar way using the theoretical amount of NH4F. Slow evaporation at room temperature gave rectangular prisms (typically 0.5 × 1 × 5 ram) which analysed found, 37.8 Yo Zr, ealcd., 37.80 ~o, found, 11.5 YoN, calcd., 11-61 ~o. The X-ray powder pattern of this phase (here named ~) was very similar to that reported for the orthorhombic phase prepared from solution t4~ and the measured density, 2.65 ± 0.02 g/cm s, agreed with the reported X-ray density, 2"653 g/cm 3. The same powder pattern and density were reported by GAUDREAU~1~ for material made from ZrF4.3NH4F at 200 ° and quenched. Differential thermal analysis of ~-ZrF,.2NH4F in a sealed tube showed a reversible transition at 138° to a high-temperature phase (here named fl). The transition heat was found to be 1.7 4- 0-3 kcal/mole, by calibration of the DTA apparatus with NH4Br, transition heat 0.882 kcal/mole at 137"2°.tS~ Z r F c N H , F was prepared by heating ZrF4"3NI-I~F at 250 ° under nitrogen to the calculated weight loss. The X-ray powder pattern agreed with that of pure y-ZrFcNH4F made in a similar way by GAUDRF_AU,~x~and no line broadening due to small particle size or strain was detected. ZrFcNH4F was also prepared by slow crystallization from aq.HF containing 75 ~o of the theoretical NH,F, as reported by HAENDLER.c6~ The X-ray powder pattern agreed with that of the pure 7ZrF,.NH4F given by GAUDREAU,tl~ but single crystal studies ~ in this laboratory showed the true cell to be monoclinie with a -----13.57/k, b = 7.90/k, c = 7.99/k and fl = 87°. Pseudo-orthnrhombic symmetry is also displayed by twinning along the b axis. The measured density, 3.18 q- 0.01 g/cm s, agreed with the calculated value, 3.17 g/crn~, for 8 moles per cell. N H , F was purified by recrystallization at pH 8, drying under NHz, and high vacuum treatment just before use. Analysis gave 51.3 ~o F found, 51.29 ~o calcd. Method
Heats of solution were measured in the platinum calorimeter previously described, cs~ Temperatures were measured with a Dymec digital quartz thermometer coated with paraffin wax and immersed directly into the calorimeter. Temperatures were read to 1 × 10-4 °C at 30-see intervals for 30 min before and after reactions, which were complete in 1-3 min. Samples at room temperature (24°) were dropped directly into 110.0 g of 3.83 N H F at 25 ° ± 0"5°C, small corrections being made for temperature differences between sample and solvent. Electrical calibrations were constant within -4-0.1 ~o for repetitive fillings of the calorimeter and agreed with a value calculated from heat capacities of calorimeter and contents. Results in Table 1 are given in terms of the thermochemical calorie TABLE 1.--HEATS OF SOLUTIONIN" 3"83 N H F AT 25°C Compound NH4F (c) ZrF4.3NH4F (c) ZrF¢2NH4F (~) ZrF4"NH4F (c)
No. of runs 5 6 4 4
A H ± 2 S.D. (kcal/mole) 1.015 11.85 9.95 3.60
-4- 0.02 -4- 0-3 ± 0-1 ± 0.3
(4.1840 J) and based on the 1961 scale of atomic weights. Error limits are estimated as twice the standard deviation of repetitive experiments. X-ray diffraction techniques have been previously c8~ H. E. SWANSON, N. T. GILFRICH and M. I. CooK, U.S. Natn. Bur. Stand. Circ. 539, Vol. 6, 14 (1956). t4~ H. BODE and G. TEUFER,Z. anorg, allg. Chem. 283, 18 (1956). c5~A. ARELL, Ann. Aead. Sci. fenn. Ser. AVI, 42 (1960). c6~H. M. HAENagLERand D. W. ROBINSON,J. Am. chem. Soe. 75, 3846 (1953). tT~j. A. WATTS.Personal communication. ,8~ A. G. TURN'BULL,Aust. J. Chem. 17, 1063 (1964).
953
Thermochemistry of ammonium fluozirconates
described.~g} For transition heat measurements sample and reference was sealed in glass tubes having re-entrant thermocouple wells and held in a brass block heated at 4°/min. RESULTS The following reaction scheme was used to find the heat of formation of ZrF4.nNHaF, where n = 1, 2 or 3: Zr (c) q- [1000 HF, 13,900 H20] --~ [ZrF~ 996 HF, 13,900 H20 ] q- 2H 2 (g)
(4)
[nNH4F , ZrF4, 1000 HF, 13,900 H20] -+ ZrF4"nNH4F (c) q- [1000 HF, 13,900 H20 ] (5) nNH4F (c) q- [ZrF 4, 1000 HF, 13,900 H20 ] -~ [nNHaF, ZrF 4, 1000 HF, 13,900 H20]
(6)
2Ha (g) + 2F 2 (g) q- [ZrFa, 996 HF, 13,900 H20] --~ [ZrF,, 1000 HF, 13,900 H20 ] (7) Zr (c) -t- 2F2 (g) + nNH4F (c) --~ ZrF4"nNH4F (c)
(8)
Reaction (4) represents the solution ofzirconiumin 3"83 N HF, for which -- 158.4 --0.2 kcal/mole has been reported, (8~ including corrections for metal impurities and vaporization of solvent by evolved hydrogen. Reaction (5) represents the solution of crystalline ammonium fluozirconates in 3-83 N H F to give the same final Zr concentration as reaction (4) (Table 1). The macro-crystalline samples used should contribute negligible surface or strain energies to the heats of solution. Reaction (6) represents the solution of crystalline ammonium fluoride in 3.83 N H F containing a negligible amount of ZrF a. This was taken as the value in 3.83 N HF alone, +1.015 4- 0.02 kcal/mole. The variation with n, i.e. between concentrations 1"13,900 H20 and 1:4633 H20 was found to be negligible. Finally, reaction (7) represents the partial molar heat of formation of H F in 3.83 N HE containing a negligible amount of ZrF a. This was calculated from recently revised integral heats of formation of aq'HF (x°) to be --77.34 4- 0.14 kcal/mole. Then reaction (8) could be evaluated, using AH~zgs NHaF (c) = --110.89 4- 0"1 kcal/mole, (u) to obtain the heats of formation of the three ammonium fluozirconates (Table 2). These values and their uncertainties depend largely on the value adopted for aq.HF tl°) which requires further confirmation. Heat capacities given in Table 2 were estimated by simple addition of the values for ZrF 4 and NHaF. Entropies were estimated using the formula: S~gs -----S°(ZrF4) + nS°(NH4F) -k AS.
(9)
TABLE 2.--THERMODYNAMIC PROPERTIES OF FLUORIDES
Compound ZrF4.3NH4F (c) ZrF4"2NH4F (u) ZrF4-NH4F (c)
AH;.2,s
C~.29s*
S~'os
AG~.29s
--809.24- 0.7 --697.54- 0.7 --581.2 4- 0-7
(71.6) (56.0) (40"4)
(80.5) (62) (43.5)
--703-6 --619.0 --529-9
* Figures in brackets estimated. c9) I. J. BEAR and A. G. TURNaULL, Aust. J. Chem. 19, 751 (1966). ix0) j. D. Cox and D. HARROP, Trans. Faraday Soc. 61, 1328 (1965). c11~D. D. WAGMAN, W. H. EVANS, I. HALOW, V. B. PARKER, S. M. BAILEY and R. H. SCHUMM, U.S. Bur. Stand., Tech. Note 270-1 (1965).
954
H. HULL and A. G. TURNBULL
The excess entropy, AS, was taken to be 3.9 cal/deg, mole for n = 3, on the basis of the measured entropies of cryolite AIF3-3NaF and its component fluorides, and 2.6 for n = 2, 1.3 for n = 1 by proportion. DISCUSSION
From the measured heats of formation at 298°K and that of fl-ZrF4, --456.8 ± 0.25 kcal/mole, {x2}the stepwise heats of reacting 1, 2 and 3 mole of solid NH4F with solid/~-ZrF 4 were calculated to be --13.5, --5.4, and --0.9 kcal/mole respectively at 298°K. This marked diminution of stability as more NH4F is added suggests that higher complexes (comparable to UF4.4NH4F) will not form at room temperature. When combined with the heat of sublimation of NH4F to give ideal gases N H 3 and HF, 35"1 kcal/mole at 298°K, (lz) the above values gave the heats of the thermal decomposition reactions (1), (2) and (3). A constant value of AC~ -----+ 1, as reported for the sublimation of NH4F, cm was then used to correct these heats to higher temperatures. In actual decompositions, DTA evidence showed that t3-ZrF4.2NH4F is the phase formed above 138°C. Thus the ~ --* fl transition heat, 1"7 kcal/mole, was added to AH(1) and subtracted from AH(2) to find decomposition heats (Table 3) TABLE 3.--REACTION HEATS AND EQUILmRIA
Reaction (1) (2) (3)
Tea. 1 atm (°C) calr. DTA * 225 303 410
297(297) 357(362) 410(425)
calf.
AH~ (kcal) DTA
37.8 -4- 0.5 39.0 -4- 0.5 48.9 4- 0.5
39.8 -4- 3 39.0 4- 3 47.2 -4- 7
• Figures in brackets from least squares/~ -- T fit.
comparable to those derived from DTA. X-ray analysis of DTA residues showed the subsequent products to be well-crystallized ZrFcNH4F and ~-ZrF4. The estimated entropies of the fluozirconates were then combined with their heats of formation (Table 2) to calculate free energies vs. temperature. Since NH4F is completely dissociated in the gas phase, the free energy change for reactions (I), (2) and (3) is given by: A G = - - R T l n (P~14) (10) where P atm is the total pressure. From this relation the equilibrium temperatures for P = 1 atm were calculated (Table 3). These predictions were then compared with the DTA results, c2} The start-of-peak temperatures at 760, 515, 120 and 20 mm Hg ambient pressure were fitted by least squares to the relation In (e*/4) = A - b A H / R T (I 1) to find the heats of reactions (1), (2) and (3) at average temperatures of 523, 583 and 627°K respectively. The values (Table 3) were found to agree with the calorimetric values, within the rather large error limits of 3-7 kcal/mole. However the observed temperatures for P = 1 atm were 15-72 ° higher than the predicted equilibrium ,1,~ E. GREENBERG, J. L. SETTLE, H. M. FF.Dm~ and W. N. HUBBARD, J'.phys. Chem. 65, 1168 (1961). axs~ T. L. t-IxG~Ir~Sand E. F. Wr_s'muM, J.phys. Chem. 65, 830 (1961).
Thermochemistry of ammonium fluozirconates
955
temperatures. This was not unexpected, since the use of a 10°/min DTA heating rate must have caused some lag behind equilibrium. Apparently such lags are constant enough to allow reasonable reaction heats to be derived in favorable cases. A comparison with the previous study (t4) of zirconium fluoride hydrates showed the free energy charge to be always negative for the reaction: ZrF4"mH20 (c) + n(NH4)(aq) --~ ZrF4nNH4F (c) + mH20(aq)
(12)
Thus the N H 4 complexes will crystallize preferentially from aqueous solution containing NH4F, as observed in the present preparations. The hydrates are also much less thermally stable, reaching 1 atm decomposition pressure at temperatures about 150° lower than the corresponding NH4F complexes. ~t4~H. HULLand A. G. TURNBULL,J. inorff, nucl. Chem. 28, 281I (1966).
THERMOCHEMISTRY OF AMMONIUM FLUOZIRCONATES H. HULL and A. G. TURNBULL Division of Mineral Chemistry, C.S.I.R.O., Melbourne
(First received 10 August 1966; in revisedform 20 October 1966) Abstract--Heats of solution of ZrF4'nNH4F (n = 1, 2 and 3) have been measured in 3.83 N H F at 25° to find heats of formation of ZrF4-3NH4F (c) = --809.2 ± 0-7 kcal/mole, ZrF4"2NH4F (c0 = --697-5 4- 0"7 kcal/mole, and ZrF4"NH~F (c) = --581.2 4- 0.7 kcal/mole. The heat of the ~ --+ fl transition of ZrFc2NH4F at 138°C was found by differential thermal analysis to be 1.7 -4- 0.3 kcal/ mole. From measured heats of formation and estimated heat capacities and entropies, the heats and equilibrium temperatures for the three stages of thermal decomposition of the fluozireonates were calculated and found to agree with approximate values obtained by differential thermal analysis. INTRODUCTION
AMMONIUMfluozirconates are useful in the electrolytic recovery of zirconium, since they precipitate from aq.HF solutions as anhydrous salts which decompose to zirconium tetrafluoride below 400 ° as follows: ZrF4.3NH4F (c) --* ZrF4"2NH4F (c) q- NH 3 (g) + HF (g)
(1)
ZrF4.2NH4F (c) --* ZrF4.NH4F (c) + NH a (g) ÷ HF (g)
(2)
ZrF4-NH4F (c) --* ZrF 4 (c) q- NH 8 (g) + HF (g)
(3)
The chemistry of the solid phases of the ZrF4-NH4F system has been recently reviewed and extended by GAUDR~_~U.(1) The compounds so far characterized are cubic ZrF4"3NH4F, orthorhombic ZrF4.2NH4F and also another form of lower symmetry, and monoclinic ZrF4"NH4F. The occurrence of a single phase region, 2"0--1.7 NH4F/ZrF4 at 200 °, makes the system of especial interest. No thermodynamic properties have yet been reported, but HAENDLER e t aL (~) measured decomposition temperature at four controlled pressures by differential thermal analysis and reported 21, 21 and 25 kcal respectively for reactions (1), (2) and (3). In view of the low accuracy of this method, heats of formation were obtained in the present work from the heats of solution in 3.83 N HF at 25°C of Zr metal, NH4F and ZrF4"nNH4F, where n is 1-3. The heats of formation, together with estimated entropies and heat capacities, enabled the calculation of free energy changes and equilibria for the thermal decompositions. EXPERIMENTAL
Materials The starting materials were reactor-grade Zr turnings (99.65 ~ Zr, 0'01 ~ Hf, 0.04 ~o Mg, 0.125 Fe, 0.01 ~o C, 0"05 ~ CI, 0"090 ~o O, other metals 0.03 ~ by wt.) and A R grade 48 y. H F and NH~F. The products were analysed by pyrohydrolysis in steam at 950 °, zirconium weighed as ZrO2, and fluorine precipitated as PbC1F. Nitrogen was determined by Kjeldahl method on separate samples. cxl B. GAUDI~AU, Rev. Chim. miner. 2, 1 (1965). (~) H. M. HAENDLER,C. M. WHEELERand D. W. ROBINSON,f. Am. chem. Soe. 74, 2352 (1952). 951
952
H. HULL and A. G. TURNBULL
(NH,)sZrF7 was made by dissolving Zr in excess 10Yo H F and adding a large excess of NH4F. Slow evaporation, washing and drying over molecular sieves gave 1-2 mm crystals which analysed found, 32-7 YoZr, caled., 32.77 Yo,found, 47.5 ~o F, calcd., 47-78 ~ and found, 15.13 ~ N, calcd., 15.10 ~ . The X-ray powder pattern showed only lines reported '8~for the cubic phase and the density measured with a helium densitometer, 2.25 -4- 0.02 g]ems, agreed with the X-ray density, t3~ 2.213-2.238 g/cm 3. (NI-~)~ZrFe was made in a similar way using the theoretical amount of NH4F. Slow evaporation at room temperature gave rectangular prisms (typically 0.5 × 1 × 5 ram) which analysed found, 37.8 Yo Zr, ealcd., 37.80 ~o, found, 11.5 YoN, calcd., 11-61 ~o. The X-ray powder pattern of this phase (here named ~) was very similar to that reported for the orthorhombic phase prepared from solution t4~ and the measured density, 2.65 ± 0.02 g/cm s, agreed with the reported X-ray density, 2"653 g/cm 3. The same powder pattern and density were reported by GAUDREAU~1~ for material made from ZrF4.3NH4F at 200 ° and quenched. Differential thermal analysis of ~-ZrF,.2NH4F in a sealed tube showed a reversible transition at 138° to a high-temperature phase (here named fl). The transition heat was found to be 1.7 4- 0-3 kcal/mole, by calibration of the DTA apparatus with NH4Br, transition heat 0.882 kcal/mole at 137"2°.tS~ Z r F c N H , F was prepared by heating ZrF4"3NI-I~F at 250 ° under nitrogen to the calculated weight loss. The X-ray powder pattern agreed with that of pure y-ZrFcNH4F made in a similar way by GAUDRF_AU,~x~and no line broadening due to small particle size or strain was detected. ZrFcNH4F was also prepared by slow crystallization from aq.HF containing 75 ~o of the theoretical NH,F, as reported by HAENDLER.c6~ The X-ray powder pattern agreed with that of the pure 7ZrF,.NH4F given by GAUDREAU,tl~ but single crystal studies ~ in this laboratory showed the true cell to be monoclinie with a -----13.57/k, b = 7.90/k, c = 7.99/k and fl = 87°. Pseudo-orthnrhombic symmetry is also displayed by twinning along the b axis. The measured density, 3.18 q- 0.01 g/cm s, agreed with the calculated value, 3.17 g/crn~, for 8 moles per cell. N H , F was purified by recrystallization at pH 8, drying under NHz, and high vacuum treatment just before use. Analysis gave 51.3 ~o F found, 51.29 ~o calcd. Method
Heats of solution were measured in the platinum calorimeter previously described, cs~ Temperatures were measured with a Dymec digital quartz thermometer coated with paraffin wax and immersed directly into the calorimeter. Temperatures were read to 1 × 10-4 °C at 30-see intervals for 30 min before and after reactions, which were complete in 1-3 min. Samples at room temperature (24°) were dropped directly into 110.0 g of 3.83 N H F at 25 ° ± 0"5°C, small corrections being made for temperature differences between sample and solvent. Electrical calibrations were constant within -4-0.1 ~o for repetitive fillings of the calorimeter and agreed with a value calculated from heat capacities of calorimeter and contents. Results in Table 1 are given in terms of the thermochemical calorie TABLE 1.--HEATS OF SOLUTIONIN" 3"83 N H F AT 25°C Compound NH4F (c) ZrF4.3NH4F (c) ZrF¢2NH4F (~) ZrF4"NH4F (c)
No. of runs 5 6 4 4
A H ± 2 S.D. (kcal/mole) 1.015 11.85 9.95 3.60
-4- 0.02 -4- 0-3 ± 0-1 ± 0.3
(4.1840 J) and based on the 1961 scale of atomic weights. Error limits are estimated as twice the standard deviation of repetitive experiments. X-ray diffraction techniques have been previously c8~ H. E. SWANSON, N. T. GILFRICH and M. I. CooK, U.S. Natn. Bur. Stand. Circ. 539, Vol. 6, 14 (1956). t4~ H. BODE and G. TEUFER,Z. anorg, allg. Chem. 283, 18 (1956). c5~A. ARELL, Ann. Aead. Sci. fenn. Ser. AVI, 42 (1960). c6~H. M. HAENagLERand D. W. ROBINSON,J. Am. chem. Soe. 75, 3846 (1953). tT~j. A. WATTS.Personal communication. ,8~ A. G. TURN'BULL,Aust. J. Chem. 17, 1063 (1964).
953
Thermochemistry of ammonium fluozirconates
described.~g} For transition heat measurements sample and reference was sealed in glass tubes having re-entrant thermocouple wells and held in a brass block heated at 4°/min. RESULTS The following reaction scheme was used to find the heat of formation of ZrF4.nNHaF, where n = 1, 2 or 3: Zr (c) q- [1000 HF, 13,900 H20] --~ [ZrF~ 996 HF, 13,900 H20 ] q- 2H 2 (g)
(4)
[nNH4F , ZrF4, 1000 HF, 13,900 H20] -+ ZrF4"nNH4F (c) q- [1000 HF, 13,900 H20 ] (5) nNH4F (c) q- [ZrF 4, 1000 HF, 13,900 H20 ] -~ [nNHaF, ZrF 4, 1000 HF, 13,900 H20]
(6)
2Ha (g) + 2F 2 (g) q- [ZrFa, 996 HF, 13,900 H20] --~ [ZrF,, 1000 HF, 13,900 H20 ] (7) Zr (c) -t- 2F2 (g) + nNH4F (c) --~ ZrF4"nNH4F (c)
(8)
Reaction (4) represents the solution ofzirconiumin 3"83 N HF, for which -- 158.4 --0.2 kcal/mole has been reported, (8~ including corrections for metal impurities and vaporization of solvent by evolved hydrogen. Reaction (5) represents the solution of crystalline ammonium fluozirconates in 3-83 N H F to give the same final Zr concentration as reaction (4) (Table 1). The macro-crystalline samples used should contribute negligible surface or strain energies to the heats of solution. Reaction (6) represents the solution of crystalline ammonium fluoride in 3.83 N H F containing a negligible amount of ZrF a. This was taken as the value in 3.83 N HF alone, +1.015 4- 0.02 kcal/mole. The variation with n, i.e. between concentrations 1"13,900 H20 and 1:4633 H20 was found to be negligible. Finally, reaction (7) represents the partial molar heat of formation of H F in 3.83 N HE containing a negligible amount of ZrF a. This was calculated from recently revised integral heats of formation of aq'HF (x°) to be --77.34 4- 0.14 kcal/mole. Then reaction (8) could be evaluated, using AH~zgs NHaF (c) = --110.89 4- 0"1 kcal/mole, (u) to obtain the heats of formation of the three ammonium fluozirconates (Table 2). These values and their uncertainties depend largely on the value adopted for aq.HF tl°) which requires further confirmation. Heat capacities given in Table 2 were estimated by simple addition of the values for ZrF 4 and NHaF. Entropies were estimated using the formula: S~gs -----S°(ZrF4) + nS°(NH4F) -k AS.
(9)
TABLE 2.--THERMODYNAMIC PROPERTIES OF FLUORIDES
Compound ZrF4.3NH4F (c) ZrF4"2NH4F (u) ZrF4-NH4F (c)
AH;.2,s
C~.29s*
S~'os
AG~.29s
--809.24- 0.7 --697.54- 0.7 --581.2 4- 0-7
(71.6) (56.0) (40"4)
(80.5) (62) (43.5)
--703-6 --619.0 --529-9
* Figures in brackets estimated. c9) I. J. BEAR and A. G. TURNaULL, Aust. J. Chem. 19, 751 (1966). ix0) j. D. Cox and D. HARROP, Trans. Faraday Soc. 61, 1328 (1965). c11~D. D. WAGMAN, W. H. EVANS, I. HALOW, V. B. PARKER, S. M. BAILEY and R. H. SCHUMM, U.S. Bur. Stand., Tech. Note 270-1 (1965).
954
H. HULL and A. G. TURNBULL
The excess entropy, AS, was taken to be 3.9 cal/deg, mole for n = 3, on the basis of the measured entropies of cryolite AIF3-3NaF and its component fluorides, and 2.6 for n = 2, 1.3 for n = 1 by proportion. DISCUSSION
From the measured heats of formation at 298°K and that of fl-ZrF4, --456.8 ± 0.25 kcal/mole, {x2}the stepwise heats of reacting 1, 2 and 3 mole of solid NH4F with solid/~-ZrF 4 were calculated to be --13.5, --5.4, and --0.9 kcal/mole respectively at 298°K. This marked diminution of stability as more NH4F is added suggests that higher complexes (comparable to UF4.4NH4F) will not form at room temperature. When combined with the heat of sublimation of NH4F to give ideal gases N H 3 and HF, 35"1 kcal/mole at 298°K, (lz) the above values gave the heats of the thermal decomposition reactions (1), (2) and (3). A constant value of AC~ -----+ 1, as reported for the sublimation of NH4F, cm was then used to correct these heats to higher temperatures. In actual decompositions, DTA evidence showed that t3-ZrF4.2NH4F is the phase formed above 138°C. Thus the ~ --* fl transition heat, 1"7 kcal/mole, was added to AH(1) and subtracted from AH(2) to find decomposition heats (Table 3) TABLE 3.--REACTION HEATS AND EQUILmRIA
Reaction (1) (2) (3)
Tea. 1 atm (°C) calr. DTA * 225 303 410
297(297) 357(362) 410(425)
calf.
AH~ (kcal) DTA
37.8 -4- 0.5 39.0 -4- 0.5 48.9 4- 0.5
39.8 -4- 3 39.0 4- 3 47.2 -4- 7
• Figures in brackets from least squares/~ -- T fit.
comparable to those derived from DTA. X-ray analysis of DTA residues showed the subsequent products to be well-crystallized ZrFcNH4F and ~-ZrF4. The estimated entropies of the fluozirconates were then combined with their heats of formation (Table 2) to calculate free energies vs. temperature. Since NH4F is completely dissociated in the gas phase, the free energy change for reactions (I), (2) and (3) is given by: A G = - - R T l n (P~14) (10) where P atm is the total pressure. From this relation the equilibrium temperatures for P = 1 atm were calculated (Table 3). These predictions were then compared with the DTA results, c2} The start-of-peak temperatures at 760, 515, 120 and 20 mm Hg ambient pressure were fitted by least squares to the relation In (e*/4) = A - b A H / R T (I 1) to find the heats of reactions (1), (2) and (3) at average temperatures of 523, 583 and 627°K respectively. The values (Table 3) were found to agree with the calorimetric values, within the rather large error limits of 3-7 kcal/mole. However the observed temperatures for P = 1 atm were 15-72 ° higher than the predicted equilibrium ,1,~ E. GREENBERG, J. L. SETTLE, H. M. FF.Dm~ and W. N. HUBBARD, J'.phys. Chem. 65, 1168 (1961). axs~ T. L. t-IxG~Ir~Sand E. F. Wr_s'muM, J.phys. Chem. 65, 830 (1961).
Thermochemistry of ammonium fluozirconates
955
temperatures. This was not unexpected, since the use of a 10°/min DTA heating rate must have caused some lag behind equilibrium. Apparently such lags are constant enough to allow reasonable reaction heats to be derived in favorable cases. A comparison with the previous study (t4) of zirconium fluoride hydrates showed the free energy charge to be always negative for the reaction: ZrF4"mH20 (c) + n(NH4)(aq) --~ ZrF4nNH4F (c) + mH20(aq)
(12)
Thus the N H 4 complexes will crystallize preferentially from aqueous solution containing NH4F, as observed in the present preparations. The hydrates are also much less thermally stable, reaching 1 atm decomposition pressure at temperatures about 150° lower than the corresponding NH4F complexes. ~t4~H. HULLand A. G. TURNBULL,J. inorff, nucl. Chem. 28, 281I (1966).