RICHARD A. ROBIEAND J. W. STOUT
2252
mated from the tables in Klotz.25 The calculation is summarized as follows. CaC03 (calcite)
+ COZ( P
+ HzO = Ca+2 + 2HCOc
=
1)
m[Ca(HCO3)2] = 9.0 X yca+z =
0.56
YHCO~-=
2.7 X
=
p
(12)
0.86
AF0298(12)= -RT In (4)(9.0 X (10-3)3(0.56)(0.86)2
-RT In 1.21 X
=
JlgCOa (magnesite)
+ CO2 ( P
=
&Ig+'
J. Phys. Chem. 1963.67:2252-2256. Downloaded from pubs.acs.org by UNIV OF CAMBRIDGE on 08/22/15. For personal use only.
m[ilIg(HCO3)~]= 16.5 X 0.52
y.\1~+2=
YHCO~-
=
1)
+ HzO
+ 2HCO3-
1.1 =
0.82
3(0.52)(0.82)
-RT In 6.3 X
CalClg(CO8)z (dolomite)
Ca+2
+ 2CO2 (P
=
1)
+ hIg+2 + 4HCO3x
~ ~ [ C a n l g ( H C 0=~ 3.245 )~] -yca-z =
(13)
4.95 X lo-'
AF0298(13) = -RT 111 (4) (16.5 X =
=
0.60 yiig+z = 0.62
,U
+ 2H20
=
(14) = 1.95
x
7 ~ ~ =0 0.872 ~ -
AF0298(14)= -RT In (256)(3.245 X 10-3)6(0.60) X
(0.62) (0,872)2 = =
AF0298(4)
AH0298(4)
-RT In 6.4 X
AF02g8(14) - AF0z98(13) - AF02g8(12) = 2.83 kcal. =
2.83
+ 0.24 = 3.07 kcal.
This value of AHOzsa(4) is in good agreement with the value 2.94 kcal. which was calculated earlier from the (25) I. 3L Klota, "Chemiral Thermodynamics," Prentice-Hall. Ine., New York, N. P., 1950,p. 332.
Vol. 67
dissociation measurements. However Halla23b has also calculated AFoZg8(4)from the measured solubilities a t the two triple points where dolomite and calcite or magnesite, respectively, are in equilibrium with water saturated with COZ a t 1 atm. pressure. He = 0.710 kcal. from his measurerneiitsz6 obtains AFoZg8(4) and AFoZg8(4)= 1.017 kcal. from the measurements of Y a n a t ' e ~ a . ~ The ' corresponding values of A\H0298(4) are 0.95 and 1.26 kcal. In this calculation the neglect of ionic activity coefficients introduces negligible error since only the ratio of the activity coefficients of Ca + 2 and Mg f 2 is involved. Conclusion The disagreement between the values of AF0298(4) calculated from the solubility measurements leads one to suspect t h d true thermodynamic equilibrium may not be established in these measurements. This would also be expected from the hydrothermal synthesis results of Goldsmith and Graf.' The most reliable values of the enthalpy and free energy changes for the decomposition of dolomite into calcite and magnesite appear to be those calculated from the high temperature equilibrium data, namely AH0298(4)= 2.94 kcal. and AF02g8(4) = 2.70 kcal. A direct calorimetric measurement of the enthalpy change in reaction 4, by measurement of the heats of solution of the various carbonates, would be valuable in establishing these numbers more precisely. Acknowledgments.-We thank Prof. Fritz Laves for obtaining for us the sample of dolomite, Miss 11. C. Batchelder for the chemical and spectrochemical analyses, Prof. J. 0, Hutchens and Dr. A. G. Cole for stimulating discussions of the experimentdl measurements, and Prof. J. R. Goldsmith for advice on the dolomite decomposition. The partial support of this work by the Office of Kava1 Research and by the Kational Science Foundation is gratefully acknowledged. (26) F. Halla, Tschermalcs minera2. petrog. Mttt., 48, 271 (1936). (27) 0.K . Yanat'eva, Z h . Obsch. Khzm., 25, 234 (1956): J . Gen. Chem. U S S R , 2 6 , 2 1 7 (1955).
HEAT CAPACITY FROM 12 TO 305OK. AND ENTROPY OF TALC AND TREMOLITE BY RICHARD A. ROBIE'AND J. W. STOUT Institute f o r the Study of Metals, and Departments of Geology and Chemistry, University of Chicago, Chicago 37, Illinois Received July 1 , 1963 The heat capacities of talc, Mg&Olo( OH)z, and tremolite, Ca&lg,Si8022(0H)2, have been measured between 12 and 305°K. Smoothed values of heat capacity, entropy, enthalpy, and free energy are tabulated. At 298.15' K. the values of the thermodynamic functions are: talc, C," = 76.89 f 0.23 cal. de@;.-'mole-I, So = 62.33 =t 0.19 cal. deg.-l mole-l, H" - H6' = 11,205 f 34 cal. mole-'; tremolite, C,' = 156.7 f 0.6 cal. deg.-l mole-', 8" = 131.2 f 0.5 cal. deg.-l mole-', H " - Ho" = 23,335 90 cal. mole-'. From the equilibrium data of Bowen and Tuttle and the entropy of talc, the heat of formation of talc from MgO, SiOz, and H20 (lis.) is calculated to be AH'fiss = -43.6 f 1 kcal.
The heat capacities of the minerals talc and tremolite were determined in order to provide basic thermochemical data necessary for understanding of the chemical equilibria involved in the formation of some The thermodynamics Common (1) Theoretical Geophysics Brsnoh, ing, Silver Spring, Maryland.
U.S. Geological Survey, Acorn Build-
of these minerals is also important in the field of ceramics. Experimental Apparatus.--The apparatus used to measure the heat capacities and the method of treating the data for heat exchange have been described previously.2a The calorimeter and resistance thermometer-heater are described in the preceding paper.2b
J. Phys. Chem. 1963.67:2252-2256. Downloaded from pubs.acs.org by UNIV OF CAMBRIDGE on 08/22/15. For personal use only.
Nov., 1963
HEATCAPACITY AND ENTROPY O F TALC AKD TREMOLITE
Sample of Talc, Mg,Si4Ola(OH)z.-The sample of talc was obtained through the courtesy of Drs. K. 0 . Bennington and Paul H. Reitan. It was in the form of a dense aggregate of small crystals 0.01 to 1.0 mm. in diameter. The material was chipped into small pieces using a hardened steel srribe point and sieved. Material passing a 20-mesh screen and retained on a 50-mesh screen was saved. Because talc is an exceedingly soft mineral, with a perfect basal cleavage (OOl), it was feared that crushing in a mortar might distort the crystals,as was pointed out by Gruner,a and we therefore did not grind the sample. This method of sample preparation gave rice-shaped particles each composed of possibly 100 or so small undistorted crystals. The sample was passed through a strong magnetic field to remove any iron introduced in the chipping operation and carefully hand sorted under a binocular microscope. The talc had a very faint greenish tint and the aggregate was translucent. Spectroscopic analysis of the material showed all nonessential elements except iron and aluminum to be less than 0.027, by weight. Three independent spectrographic analyses gave a considerably lower valula for iron than the wet chemical analyses. TTe believe the spectrographic analysis to be more nearly corrert and have modified the wet analysis (Table [ ) accordingly. TLBLE 1 CHEMICAL ANALYSES~ O F TALC ASD
Talc, Murphy, North Carolina Calcd for Mg8Sl4OlQ-
Oxide
(OH)z
Found
SiOz TiOz -41208 Fez03 FeO MnO MgO CaO NazO
62 4.7 0 00 .47 n.d. 0 .00 31 76 0 00
63 37
TREMOLITE, T;I'ErG€IT
KnO
57 76 0.00 51 n.d. 0 11 .O1 25 21 12 96 0 43 .12
PZO6
.Ol
31 88
%
Tremohte, Falls Village, N. Y . Calcd. for Ca~IIgsSiaFound Ozz(0H)z
59.17
COZ
31 0 5 l C HzO 4 70 4 75 2 13 2 22 HzO0 06 0 00 99 91 100 00 99 57 100.00 a Wet analysis H. B. Wiik, Helsinki, Finland, unless otherwise specified. I,Spectroscopic analysis: 0. Joensuu, Miami University, Miami, Fla. Independent carbon dioxide analysis: M. C. Batchelder, Institute for the Study of Metals, University of Chicago, Chicago, Ill. +
Prior to filling the calorimeter, the sample was placed in an oven for 12 hr. at 115" to drive off any Eiurface moisture. The calorimeter was 6lled with 198.12 g. (zn vacuo). Sample of Tremolite, CaZMgSSi8OZ2( 0H)z.-Tremolite presented greater difliculties in obtaining a pure single phase material of approximate stoichiometric composition. The sample, provided by Dr. Brian Mason of the American Museum of Satural History, consisted of a radial aggregate of needle-like tremolite crystals 1 to 4 mm. across and up to 2 cm. long, embedded in a matrix of calcite and dolomite. The tremolite-carbonate rock was crushed to pass 30 mesh and was then heated with dilute HCl over a steam bath until no more effervescence occurred. The acid was renewed frequently. The material was dried a t 110" for 2 hr. and sieved; the fraction passing 75 mesh was discarded and the remaining fraction carefully hand-picked under a binocular microscope. The tremolite was crushed again and the acid treatment repeated. I t was sieved and the maberial passing 100 mesh was discarded. Microscopic examination with a petrographic microscope showed that not all the carbonate phase had been removed, approximately 176, by volume, remaining. It would have been possible to remove the bulk of the remaining carbonate by repeated crushings and acid leaching. This was not done since we wished t o avoid the difficulties encountered with very fine grained samples. A random sample wais selected for chemical (2) (a) 8 . G. Cole, J. 0. Hutchens, R. A. Robie, and J. IT. Stout, J . Am, Chem. SOC.,82,4803 (1960); (b) J. W. Stout and R. A. Robie, J . P h y s . Chem., 67.. 2248 1196.11. (3) J. Gruner, 2.Krist., 88, 412 (1934). ~
1
W.
~
~
~
~
analyses. Several independent determinations were made lor COt to accurately determine the carbonate impurity. The results of the analysis are given in Table I. The sample was heated at 115' for 12 hr. prior t o filling the calorimeter. The calorimeter was filled with 207.07 g. ( i n vacuo).
Experimental Results In Table I1 are listed the experimentally measured values of the heat capacity of 379.29 g. of talc of tlhe composition listed in Table I. The heat capacities of 812.4 g. of the tremolite whose analysis is given in Table I are listed in Table 111. These data are uncorrected for curvature or impurities. The measurements are listed in chronological order. Ta, listed in Tables I1 and I11 is the arithmetic mean of the initial and final temperatures of a measurement. The temperature rise in an individual measurement may be inferred from the temperature interval between successive measurements. S o dependence of heat capacity on thermal history was observed. The definied calorie, 4.1840 j., is used. The ice-point temperature is taken as 273.15'K. The 1961 International Scale of Atomic Weights4 is used. Certain values marked TABLE I1 HEATCAPACITY IN CAL. D E G . - ~ OF 379 29 G . OF TALC FROM MURPHY, NORTHCAROLINA [OOC. = 273.15'K.I OK
AH/AT
Tavt
299.39 306.45
76.86 77.96
81.33
14.71
225.37 230 89 236,24 238.53 245.27 251.56 257.81 263.47 269,25 274.77 281.54 288.11 294.38 209.96
Tav,
24.81 13 80
2253
52.74 57.48 61.89 66.37 70.78 74.92 79.12 83.44 87.88 91.53 95.61 99,95 104.20 108.98 113.89 118.71 123.84 128.80 134.24 140.30 146.33 151.93 156.29 161,86 168.14 174.44 180.54 186.28 190.45 196.15 202.23 208.68 214.91 219.56
5.697 6.970 8.248 9.633 11.04 12.42 13.91 15.47 17.10 18.42 19.90 21.52 23.08 24.87 26,71 28.52 30.44 32.22 34.22 36.41 38.51 40.42 41.88 43.67 45.70 47.69 49.51 51.22 52.39 54,08 55.71 57.45 59.08 60.22
OX.
AH/AT
61.63 63.01 64.28 64.87 66.43 67.76 69.19 70.40 71.57 72.72 73,95 75.17 76.24 77.10
11.85 13.45 15.61 18.12 20,02 22.45 24.60 26.79 29.41 32.43 35,83 39.47 42.34 45.71
0.1690 ,2017 .2702 .3809 ,4838 ,6472 ,8123 1.015 1.291 1.673 2.172 2.785 3.314 4,018
45. 73 49.71 53.71
4.017 4.933 5.944
,
(4) A. E. Cameron and E. Wiohers, J . Am. Chem. SOC.,8 4 , 4 1 7 5 (19621,.
RICHARD A. ROBIEASD J. W. STOUT
2254 TABLE 111
HEATCAPACITY IN FROM
Tav,
'IC
J. Phys. Chem. 1963.67:2252-2256. Downloaded from pubs.acs.org by UNIV OF CAMBRIDGE on 08/22/15. For personal use only.
304.22
812.4 G. OF TREMOLITE FALLS VILLAGE,NEW YORK [O'C. = 273.15"K.j CAL. D E G . - ~ OF
AH/AT
158.9
54.16 58.91 64.06 69.39 75.26 79.83 84.28 89.33 94,53 100.17 105.79 110.92 116.34 121.95 127.41 132.63 138.26 144,22 149,98 155.38 161.13 167.02 172.64
13.78 16.71 20.20 23.87 28.07 31.59 35.03 38.99 42.99 47.34 51.76 55.73 59.96 64.24 68.36 72.25 76.33 80.53 84,53 88.21 92.02 95.74 99.24 103.0 178.88 106.5 184.86 109.8 190.75 113.0 196.46 116.0 202.20 119.2 208.24 122.2 214.22 220.03 125.0 225.82 127.9 231.42 130.5 133.0 236.91 136.3 243.04 249.12 138 6 a "Bud vacuum runs "
T,,, 'IC.
AH/AT
254.99 260.82 266.63 272.62 278.33 284.37 289.76 295.48 301.18
141.1 143,s 145.7 148,l 150.2 152.3 154.2 156.2 157.8
249,17 265. 01 260 ; 85 267.13 273.40 279.32 289.13 294.89
138.7" 141.1" 143.5" 146.0" 148.6" 150.6" 153.9" 155.6"
12.37 13.61 13.49 17.64 20.28 21.79 24.08 26.68 29.80 33.38 36.91 40.57 50.31 L54,93
0,1878 .2376 .3450 ,5089 ,8161 1,030 1.428 1.973 2.784 3.887 5.171 6.673 11.57 14.25
42.98 47.57
7.734 10.03
in Table 111 are "bad vacuum runs'' taken to evaluate a correction2a for temperature gradients within the calorimeter. These points are of lower accuracy than the remaining points, whose accuracy has been discussed previously .2a Thermodynamic Properties In order to calculate the heat capacity and other thermodynamic properties of talc and tremolite of ideal composition it is necessary to make correction for the deviations from the ideal of the compositions of the samples whose heat capacity mas measured. From the analytical data in Table I, one calculates that 384.17 g. of the talc sample corresponds to the empirical formula
+
+
MgsSi4010(OH)z 0.0176 FeA1204 0.006FeO 0.004 R.Ig(OH)z O.O27R/IgO
+
+
It is probable that most of these impurities are actually present in solid solution in the talc structure, which for our sample would have the structural formula6 (Rlg3,o0Fe0~ 2 ) (Si3.96A10.04)010(OH)I.H (5) W. L. Bragg, "ktolnic Structure of hIinerals," Corndl University Press, Ithara. N. Y.. 1937. p. 200.
Tol. G7
One may, however, approximately correct to the heat capacity of talc of ideal composition by subtracting from the heat capacity of 384.17 g. of sample the heat capacities of the remaining substances listed in the empirical formula. The substances listed were chosen because their low temperature heat capacities have been measured. References to the original heat capacity measurements are listed by Kelley and King.6 To check the magnitude of the possible error introduced by this method of correction, the heat capacity of 31g3Si4010(OH)2 was compared with the sum of the @io2 RIg(0H)z. The heat capacities of 2MgO heat capacity of this sum is greater than the observed heat capacity of talc by 36% a t 50°K., 11.4% at 10O0K., and 2.6% at 300'K. The correction to the experimental data is 1.5% at 5O'K. and 0.9% at 300'K. Accordingly the maximum error we should introduce in C, by correcting in this fashion would be -0.3% a t 50' and -0.1% at 100'K. Above 100'K. this method of correcting for impurities introduces negligible error. The error in the entropy a t 298'K. will of course be much smaller since the entropy at 100'K. is only about 17% of
+
+
TABLE IV THERMODYNAMIC PROPERTIES OF TALC,Mg3SiaOla( OH)z [ l mole = 379.289 g.; OOC. = 273.15"K.]
- (F" - 2 7 0 0 ) GPO,
T, K. 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 273.15 298.15
oal. de&-' mole-' 0.078 ,229 ,477 ,841 1.352 2.031 2,866 3.849 4.996 6.284 7,686 9,201 10.79 12.46 14.23 17.88 21.54 25.28 29.04 32.72 36,33 39 80 43.11 46,33 49.41 52.35 55.16 57,84 60,39 62,85 65.22 67.52 69.72 71.82 73.77 75.56 77.18 72.45 76.89 h 0.23
SO,
cal. deg.-l mole-1 0.027 ,084
.182 .325 .521 ,778 1,102 1.495 1.959 2.494 3.100 3.775 4.514 5.315 6.176 8.063 10.13 12.36 14.72 17.19 19.75 22,38 26,05 27.76 30.30 33,25 36.01 38.77 41.51 44.25 46.98 49.69 52.38 55.05 57.70 60.32 62.91 55.89 62.33 h 0 . 1 9
T
-
Ho Hao. oal. mole-1 0 204 Y32 65 89 do 69 88 59 63 78
2 5 11 19 31 48 70 98 133 7 175 8 225 8 283 9 350 6 511 2 708 2 942 3 1214 1523 1868 2249 2663 3111 3590 4099 4636 5201 5793 6409 7049 7713 8399 9107 9835 10582 11346 9335 11205 j l 3 4
'
cal. deg.-1 mole-' 0.007 ,022 ,049 .089 I44 .216 .305 .415 ,546 ,698 .873 1.069 1 289 1.530 1.7'23 2.383 3.054 3,7?8 4,608 5.481 6.409 7.385 8.406 9.465 10 56 11.68 12 83 14.00 15.18 16.39 17.61 18 84 20.07 21 32 22.57 23.83 25.09 21.72 24.86 =t0.07
.
I n Table I11 are listed the thermodynamic quantities for talc of ideal composition Mg3Si40~O(OH)2, corrected as described previously for impurity. (6) K. K . Kelley and E. G. King, U S . Bureau of Mines Bulletin No. 592, 1961.
HEATC A P A C I T Y
Yov., 1963
ENTROPY OF TALC AKD
On a plot of C,T--2 us. T for talc, the three lowest experimental points lie above a smooth curve passing through the higher temperature points and through zero a t OOK. with finite slope. We believe these points are high because of magnetic entropy associated with the ferrous ion impurity in the talc and are not representative of pure material. In calculating the thermodynamic functions listed in Table IV these points have belen ignored aiid the extrapolation of the heat capacity was made with the smooth curve of I?,T-~ vs. T d i i c h joins smoothly to the expeiimental points a t 20°K. and above. From the aiialytical data one finds that 861.3 g. of the tremolite samp!e corresponds to the empirical composi0.023Mg3tion CazSIg6SisOzz(013)z 0.061hIgCO3 Si,Olo(OH)z -t. 0.0065Fe2SiO4 0.023KA18i03 0.065SaA102 0.0275SazSio3 4- 0.122lIgSi04 -k 0.03712Ig0, and the heat capacities of the various substances listed were subtracted from that of 8F1.3 g. of our sample to give the heat capacity of tremolite of ideal composition. Jn Table V are listed the smooth values of the heat capacity and other thermodynamic functions for tremolite of ideal composition CazMg5Si802dOW2. TABLE V THERMODYNAMIC PROPERTIES OF TREMOLITE, Ca2MgjSir022(0H)2
+
-+
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AND
+
+
+
[ I mole = 812.410 g.; 0°C. = 273.16"K2.] CpO,
T,
OK 10 15 20 25 30 35 40 45 50 55 60 65
io 75 80 90 100 110 120 130 140 150 160 1i o 180 190 200 210 220 230 240 250 260 27 0 280 290 300 273 1 5 298.15
cal. deg.-' mole-" 0.0946 ,283 ,713 1.522 2.741 4.349 6 319 8.575 11.24 14.12 17.27 20.65 24.09 27.66 31.45 39.24 46.92 54.69 62.44 69.96 77,19 84.17 90 04 S i . 26 103.3 109.0 114.5 119.7 124.7 129.5 134.1 138.6 142.8 146.8 150.5 I53 9 157.2 148 1 156.7 ~ 4 ~ 0 . 6
So, oal. deK. mole-' 0.034 ,103 .235 .474 ,853 1.39 2.10 2.97 4.01 5.21 6.57 8.09 9.74 11.53 13.43 17.59 22.12 26.95 32.04 37.34 42.79 48.36 54.01 59.71 65.44 71.18 76.91 82.63 88.31 93.96 99.57 105.1 110.7 116.1 121.5 126.8 132.2 117.8 131.2 f 0 . 5
H Q - Hoe, cal. mole-' 0.25 1.14 3.47 8.91 19.38 36.94 63.47 100.6 150.0 213,3 291.7 386.4 498.2 627,5 775.2 1128 1559 2067 2653 3315 4051 4858 5734 6675 7678 8740 9858 11029 12251 13522 14841 16201 17612 19060 20547 22069 23624 19527 23335 f 90
( F a - Ho") T ' cal. de,..-! mlsle-1 0,0089 ,0276 ,0614 ,118 ,207 ,336 .485 .733 1.007 1.334 1,713 2.144 2.627 3.160 3.742 5.045 6.523 8.158 9.934 11.84 13.86 15.97 18.17 20.44 22.79 25.18 27.63 30.11 32,62 35.17 37.74 40.32 42.92 45.53 48.15 50.77 53.40 46.26 5 2 . 9 1 1 0.21
Since the specific heats of most of the minerals considered do not differ much from one another, the error introduced by the impurity correction as described is appreciably less than the error in the analytical data on which it is based. We estimate that the errors arising from theimpurity correction increase the error in
2255
rrREMOLITE
the smoothed values of the heat capacity over the temperature range from 40 to 250OK. from the iiorrnal 0.2702ato 0.3% for talc and 0.4% for tremolite. The Heat of Formation of Talc.-Bennington7 has obtained a value for the heat of formation, from the oxides, for the same sample of talc used in the heat capacity measurements reported here. His data are in marked disagreement with thermal weight loss studies8 and with the high pressure equilibrium data of Boweii and Tuttlegfor the reactions
+ MgzSi04
iVIg3Si4010(OH)2
=
5MgSiOa
+ HzO
and pI/Ig~Si~0~0(0€1)~ = 3MgSiOa
+ SiOz + HzO
between 900 and 1 1 0 0 O . In order to resolve this discrepancy the equilibrium data mere subjected to a "third law" treatment'o to check their internal consistency and to see if a resaoiiable value of AHo,f could be obtained. For the equilibrium data we may write AF
=
0
=
AFoy
f
so P
AVsolids
dP
+ R T In
fHto
The term due to the volume of the solid phases is small and may be approximated by ( P - l)AV0tg8 where ~ l V O z 9is~ the volume change a t 298.15OEi. aiid one atmosphere pressure. Subtracting AH0z98 from both sides and rewriting we obtain
1
R ln.fn,o The first term on the right-hand side was calculated from data listed in Kelley5l1 and the eiitropy of Mg3Si40I0(OH)2given above and approximating the heat capacity of fiIg,Si4010(OH)zbetween 300 and 1200°1
