L. S.DARKEN AND K. W. GURRY
798
for the meter, and thus to maintain it and the sample of gas at the calibration temperature. The gas to be tested niay be drawn or forced at the r:tte of a few cubic centimeters per minute through the test chamber, which in present models has a volume of about 4 ml., or it may be introduced after cvacuating the test chamber. The instruincnt iridicates correctly the magnetic susceptibility of the gas in the test chamber within a few sr:ccinc!s; the main delay in reading the instrument is caused by the time required to introduce the gas. lleters have been constructed to cover various ranges uf putin1 pressure of oxygen, irduding 0 to 20 mm. ( i f mercury, 0 to SO, 0 to 160, 110 to 190, and 0 to 800. Dr. A. 0. Beckrnan has also deyised a meter which can be switched from one partial-pressure region to another. Calibr:iti(.)l1 curves for a typical “Model P” meter a t three different temperatures are shown i n Figure G . This meter has been compensated for temperature changes in the ininner described above. The accuracy of a meter is usually about 1% of the range covered. ‘ilie instrunlent may also be used for determining the magnetic susceptibility of paramagnetic and diamagnetic gases or for any analysis dependent on magnetic susceptibility, such as the determination of nitric oxide or nitrogen dioxide in a gas n o t containing oxygen.
Several dozen meters were constructed at the California Institute of Technology before the summer of 1942. Dr. Arnold 0. Beckman, 11 West State Street, Pas;irlena 3, California, who then took over the production of the meter, has manufactured several hundred. Descriptions of the various models will be published elsewhere. Some recording models of tlie instrunlent are available. We are glad to acknowledge the assistance of David P.Shoemaker, James B. Edson, H:trolti Herd, Dr. Herbert Sargent, Dr. Charles D. Wagner, and Beckie Bradford in the developrncnt of this instrument. at +he California Institute of Technology. Summary A simple instrument for determining the partial pressure of oxygen in a gas is descrited. This instrument, the use of which as an oxygen meter depends on the fact that the magnetic susceptibil.ity of oxygen is very much greater than that of other common gases, consists of a small glass dumbbell with attached mirror suspended on a stretched fused-silica fiber in an inhomogeneous magnetic field produced by a small permanent magnet. In the simpler models of the instrument the partial pressure of oxygen is indicated on a scale by a beam of light reflected from the mirror. PASADENA 4, CALIFORNIA RECEIVED JANUARY 7, 1946
\ C O Y rKIBUTIOU F R O M T H E RESEARCH LABORATORY,
The System Iron-Oxygen.
Vol. 68
r.s.STLEL COKPORATIOS]
11. Equilibrium and Thermodynamics of Liquid Oxide and Other Phases BY L. S. DARKEN AND R. W. GURRY
This paper, an extension of a previous paper’ on the equilibrium between iron, oxygen and wiistite throughout its field of stable existence, deals with the results of similar measurements at the higher temperatures at which a liquid phase appears. The data, in conjunction with those in paper I, suffice not only for the construction of phase diagrams showing the relation between temperature, gas composition (oxygen pressure) and composition of the oxide phases, liquid or solid; but also for evaluation of the following thermodynamic quantities : activity and partial molal heat of iron and of oxygen throughout the several homogeneous fields, heat of formation and of fusion of iron oxide of any composition realizable at oxygen pressures up to one atmosphere. The general method was, as before, to pass a gas mixture of constant known composition over the condensed phase, maintained a t one of a series of constant temperatures, until equilibrium was (1) L . S. Darken and R . W. Gurry, THISJ O U R N A L , 67, 1398 (1945); hereafter referred t o as papet I .
attained, then to quench the iron oxide phase and determine its composition. The temperature ranged up to 1640‘; the equivalent partial pressure of oxygen in the gas phase from 10-lo up to 1 atm.; the atom ratio of oxygen to iron in the liquid oxide from about 1.03, that in equilibrium with iron, to about 1.38, somewhat beyond FelOl. In the region studied there are several distinct, though related, equilibria, each of which must be considered separately; the system as a whole is therefore somewhat complex. For this reason, and so that the reader may more readily apprehend the precise inter-relations, it was deemed best to begin by presenting as a summary diagram, in Fig. 1, our final temperature-composition diagram for the iron-oxygen system, solid as well as liquid, a t an oxygen pressure ranging up to one atmosphere and a total pressure of one atmosphere throughout. The other phase diagrams have been lettered to correspond as far as possible thereto. It is to be remarked that change in composition of the condensed phase, a t least at its surface, follows quite rapidly any
May, 1946
IRON~XYG EQUILIBRIA EN INVOLVING LIQUIDOXIDE
change in effective oxygen pressure of the gas phase in immediate contact with it; further, and as a consequence of the rate of adjustment of the reaction, that the observed melting of an “iron oxide” may begin a t any temperature from 1371 to 1597’) depending on the prevailing oxygen pressure. For the sake of clarity, all experimentally determined points have been omitted from this phase diagram ; they appear in the several special figures or in the tables. Because the scale of Fig. 1 as reproduced is, unavoidably, small, the coordinates of each point on it designated by a letter are given in the appended table; and these letters are used to identify each field or boundary discussed later. The significance of each of these points or lines, in Fig. 1, from pure iron (left) to ferric oxide (hematite, right) and the sources of the data on which they are based, are summarized below. The solubility of oxygen in solid iron is, according to Diinwald and Wagner2 less than 0.0170 a t 800-1000°; according to Slomanl 0.003-0.006~0 at “low temperature”; as calculated from the lowering of freezing point of &iron (line AB) on the usual assumptions, it is less than 0.01% a t that temperature. Consequently, Fig. 1 was drawn on the ‘basisthat this solubility line practically coincides with the vertical axis. The solubility of oxygen in liquid iron is represented by the line BB’, according to Taylor and Chipman4; the percentage of oxygen a t B (0.16%) agrees with that (0.1.570) reported by Sloman.s Line CGN, the composition of liquid oxide in equilibrium with 6-iron, is determined by the results in Table 111. The boundaries JQ, QH of the wiistite field a.re taken from Fig. 9 of paper 1.6 The third boundary, the solidus JH, was derived by reading, from appropriate graphs of the data in Table V of paper I, the composition of wiistite in equilibrium with each of the several atmospheres a t each of the melting temperatures in Table I\‘ of this paper. The liquidus curves NI, IV, VR were derived similarly from Tables I and IV, and the three boundaries VR’, UT, TV of the magnetite field likewise from Tables I1 and IV. Points 011 the line R’Y, representing compositions in equilibrium with pure oxygen, are from Table I1 and the data of Greig, Posnjak, Merwin and Sosman,6 according to whom the composition of ferric oxide (line 22’) is essentially constant. In the construction of Fig. 1 and of the several diagrams upon which it is based, use was made not only of the direct measurements, but also of ( 2 ) Ddnwaldand Wagner, 2.anorg. allgem. Chcm., 199,321 (1931). (3) H. A. Sloman, J. Iron Sled Inst., London, 149,298P (1941). (4) Taylor and Chipman, Trans. A m . Inst. M i n i n g M e t . Engrr., 154, 228 (1943). (5) Ref. 1, p. 1410. (6) Greig, Posnjak, Merwin and Sosman. A m . J . Sci., SO, 239 (1935): their temperatures, on the Geophysical Laboratory scale, have been corrected to bring them to the slightly different international temperature scale.
799
00.20.422
24 26 28 30 Wt. % ’ oxygen. Fig. 1.-The temperaturecomposition phase diagram of the iron-oxygen system a t a total pressure of one atmosphere. Recommended values for certain fixed points are as follows: IRON-OXYGEN SYSTEM AT ONEATMOSPHERE PRESSURE POP
Point OC. A 1535 B 1524 C 1324 G 1400“ H 1424 I 1424 J 1371 L 911‘ N 1371
% 0 Poo2/Peo Point OC. % 0 PcoJPCO (atm.) Q 0.16 22.60 22.84 25.60 25.31 23.16 23.10 22.91
0.209 0.209 0.263 16.2 16.2 0.282 0.447 0.282
R
R’ S V
Y 2
560 1583 1583 1424 1597 1457 1457
Z’
23.26 28.30 28.07 27.64 27.64 28.36 30.04 30.06,
1.05
1 1 16.2 0.0573 1 1
’Value lor pure iron.
thermodynamic relations derived from them, as an aid in interpreting and collating the data of the more recent investigators of this system. The pertinent thermodynamic calculations of the changes in heat content and free energy and of activity are discussed in detail following the presentation of the experimental results of this investigation.
Experimental The general procedure for determining the equilibrium was the same as was described in paper I, the only differences being a consequence of the fact that me are here dealing with a liquid instead of a solid phase: and that additional atmospheres of somewhat different composition were required. Starting materials, gas mixer, furnace and temperature controller were idectical. The air atmosphere was air freed from water arid carbon dioxide by passage over ascarite and activated alumina; the oxygen atmosphere was commercial oxygen (99.9%) similarly treated. The carbon dioxide atmosphere was commercial material, thoroughly dried, passed over copper at 600” and again dried. A special device was needed to mix gas with water vapor
L.S. D A R ~ EAND N R. W.GURRY
800
in known ratio. This was a positive displacement rotary micro-pump, gear-driven by a synchronous motor, which was specially designed and calibrated; it delivered the gas into a thermos bottle containing water heated by a coil of platinum wire, all connections thence t o the furnace being heated t o obviate condensation. The rate of production of steam was measured by the watt-input, corrected for the small loss of heat and checked by condensing the output; these calibrations agreed within 1%. This same bottle supplied the steam atmosphere, the gas inlet being then closed. The results of analyses of melts which had been equilibrated with an atmosphere lean in oxygen, then either quenched in mercury or merely pulled quickly up into the cool head of the furnace tube, were the same; but when the,atmosphere was air or oxygen, the samples tended to pick up oxygen unless quenched. The results on samples quenched in mercury were erratic and are not here recorded. Consequently recourse was finally had to water as quenching liquid, despite the danger of loss of oxygen
Fez03 Wiistite Fez03 Wustite
i
1601 1601 1610 1610
Vol. 68 4.5 4.5 2 2
1.429 1.427 1.431 1.427
G. COz-H?, initial P C O ~ / P H =~28.3 4 1485 1.698 1491 3 1.710 1496 6 1.708 1496 6 1.719 1.720 18 1535 18 1535 1.710 2 1594 1.732 ziy:ite 2 1594 1.707 1.752 5 1598 Fe20s Wiistite 5 1598 1.758 TABLE I 2 1603 1.766 COMPOSITION OF LIQUID IRON OXIDE IN EQUILIBRIUM Ei:iite 2 1603 1.777 WITH SEVERAL ATMOSPHERES AT VARIOUS TEMPERATURES H. Steam, 1 atmosphere Time at Starting temp., (Fe++ + Fe+++)/Fe++ Temp., 1594 12 2.074 j FeOx materiala OC. hours r Wiistite 1594 12 2.080 A . COrCO, pco,/pco = 0.376 1601 18 2 045 FeaOt lx‘iistite 1383 41 1.096 Wiistite 1601 18 2.055 48 1.097 Fe,03 1395 Wiistite 1445 75 1.091 I. Cot-1 atmosphere Wiistite 1479 72 1.088 1577 5 2.304 Fez03 Fe.203 1500 23 1.086 1578 2 2.309 Fe203 B. COz-CO, Pcor/Pco = 1.00 1590 3 2.302 FetO3 1591 5 2.291 Wiistite 5 1.183 Fez03 1403 1592 5 2,286 FenOa 6 1.178 FezOa 1450 1634 4 2 2.58 Fe?03 1575 4 1.169 Fez03 1575 6 1.169 Wiistite J . COz-O?, 3.91y0 oxygeti Wiistite Wiistite Fe;Oa Wiistite Fez03 Wiistite
{
i {
1 1
1
C.
i
Fe20a Wiistite Fez03 (Wiistite ,I~ez03 lwiistite
COz-H?, 1395 1395 1500 1500 1600 1600
initial P C O ~ / P H=~2.23 5112 1.241 51/2 1,238 18 1.230 18 1.227 3l/4 1.227 31/, 1.227
D. Hz0-Hz, PE~o/PH,= 7.10 18 1,273 1428 .1428 18 1.267 1605 4 1.250 1605 4 1,245
Fez01 Wiistite ,I ~e203 U’iistite
1
E. CO?-CO-IISO, initial P C O ~ / ~ C O / = ~ E1~:1O:1 4 . 1 FeaOs 1598 4 1.386 Wiistite 1.598 4 1,382 1633 4 1.392 ~e203 4 1,392 1Wiistite 1633
1
F. Fez03 \h’iistitc:
{ g;yL: Fez03 Fen03 Wiistite
C02-H2, initial p c o , / p ~ , = 7.13 1444 5 1,428 1444 5 1,427 1469 5 1.426 1-109 5 1’.425 1172 5 1.426 1535 3 1.430 1535 3 1.427
Fez03
1605
7
Fez03
1606
3
Fez03 Fe203 Fez03 F~t03 FQO~
j~ e 2 0 a
1Wiistite
K. Air. 1 atmosphere 1595 2 1602 2 3 1619 1 1630 (i 1630 4 1635 3 1635
2.838 3.529 3.492 3.439 3,338 3.308 3.301 3.281
L. Oyygen, 1 atmosphere 6 4.237 1589 (i 4.216 1589 ~ea04 1 4.067 1596 FezOs 1603 1 4.053 Fe2Or 4 4.023 1007 j’~e,03 4 4 007 ltj07 Wiistite I(i1,; 1 3 881 Fes03 4 033 5 ,I F ~ : O ~ 1632 \( Wiistite 3 958 1632 5 FeiOI 1036 1 3 998 Fez03is Riedel.and de Haen’s “titrimetric standard”; the wiistite was prepared b y partial reductio11 of this material. Paired samples were in the furnace simultaneously, in separate crucibles. J’~ e t 0 3
1 1
May, 1946
I R O N ~ X YEQUILIBRIA GEN INVOLVING LIQUIDOXIDE
with the evolved steam; these results are reasonably consistent and show no systematic departure from those on the samples quenched in mercury. Since the platinum crucible picked up iron from the sample, particularly a t the higher temperatures and lower pressures of oxygen, especial care was taken either (a) to use a crucible which had previously taken up about the appropriate amount of iron, or (b) t o make the equilibration period long enough to ensure that any further removal of iron from the liquid should not affect the determination. No platinum was detected in melts when thc atmosphere was low in oxygen. The largest concentration ever detected was 0.2'30 in a liquid equilibrated with l atm. of oxygen a t 1830"; since in this region the precision is somewhat smaller than elsewhere, it is deemed that the presence of platinum was without measurable effect on the result, as should be the case according to the phase rule. Since the melting temperature of platinum is lowered by iron, this method could not be used at very high temperature and low oxygen pressure. For instance. a t 1575" in a 50-50 CO-CO? atmosphere, the crucible in six hours picked up enough iron so that it melted in part and undoubtedly would soon have melted completely.
Direct Determination of Composition in the Liquid Oxide Field.-In general, simultaneous measurements were made on pairs of samples, one of which was initially ferric oxide, the other ferric oxide which had been partially reduced (or in a few cases, electrolytic iron) so that equilibrium was approached from either side; and, after preliminary measurements, each experiment was continued until equilibration was assured, when each pair of determinations agreed. The use of such pairs proved less advantageous than had been anticipated, for the reason that each sample disturbed the atmosphere appropriate to reaction with the other, and consequently a longer time was needed to ensure that both had come to equilibrium with the specified atmosphere; toward the end of the work, therefore, this procedure was abandoned and single, or duplicate, samples were used. The results thus obtained on the composition of liquid oxide, expressed directly as the measured ratio ( I ) of ferrous plus ferric to ferrous iron, in equilibrium with the several atmospheres at various temperatures, are given in Table I; all preliminary measurements have been omitted. The composition range covered in the liquid field is from 22.5 to 28.5y0oxygen by weight. A direct plot of this ratio r in liquid oxide against temperature (Fig. 2 ) shows that all points for each gas composition lie very close to a straight line (each when produced ending on one of the liquidus curves NI, TVR which are derived later from Table IV). The precision is not quite so good as for the solid solution (Fig. 4, paper I ) ; it is, as would be expected, best in the region of low oxygen pressure where the ratio of the components of the gas mixtures is not far from unity. When the proportion of carbon monoxide, or of hydrogen, is small, a trace of oxygen would cause a large error. In the high oxygen range the difficulty of preventing change in composition of the sample while it cools-in other words, the large temperature coefficient of the equilibrium and the rapidity of its adjustment-detracts from the precision;
801
this is considerably exaggerated in Fig. 2 by use of r as coordinate. % Oxygen. 26
24
28
k'
I I 2.0 3.0 4.0 (Fe++ Fe+++)/Fe++. Fig. 2.-Composition of liquid iron oxide, in terms of I (ratio of ferrous ferric to ferrous iron) in equilibrium with various atmospheres, a t temperatures down to the liquidus curves NI, IVR. 1.o
+
+
From a large plot of the data in Table I in which the composition of each atmosphere was expressed in terms of the equivalent' (a) ratio of partial pressure of carbon dioxide to monoxide, (b) partial pressure of oxygen, the several values of r a t 1400, 1500, 1600' were read off; these are plotted in Fig. 3 in which the composition of the oxide is expressed in terms of the ratio N 2 / N l , N2 and N I being the atom fractions of oxygen and iron, respectively [N2N1 = (3r - 1)/2r]. In Fig. 3A, the ordinate is log pco,/: CO,yielding isotherms which, being nearly coinc' lent, provide a more accurate basis for thermodynamic calculation and apply more directly when low oxygen pressures are being considered. Figure 3B. in which the ordinate is log pol better illustrates the situation a t higher oxygen pressures. I t includes, for comparison, data of WhiteX of Krings and Schackmanno and of the Geophysical Laboratory investigators6; also the several phase boundaries, lettered as in Fig. 1, as derived either from paper I, or from a later section of this paper. In this type of diagram the fields may overlap, as happens in the upper right of Fig. 3B where the field designated "magnetite -I- liquid oxide" is also part of the homogeneous fields of liquid oxide and of magnetite. Direct Measurements in the Magnetite Field VR'YT.-Although in this region the equilibrium in presence of air or oxygen has been thoroughly (7) Computed by use of the constants, as listed in paper I , footnote 7 , p. 1401 (8) J. White, J . Iron Steel I n s f , London, Carnegic Schol. M e m . 17, l(1938). (9) Krings and Schackmann, Z. Glcktrochrm., 41, 479 (1935).
L. S. DARKEN AND R. W. GURRY
SO2
This group of measurements, carried out in precisely the same way as those on the liquid oxide, yielded the results in Table 11. These are plotted in Fig, 4 in which, for ease of subsequent calculation, the abscissa is the mole fraction of FeaOa on the basis of Fe30c and Fen03as components [NFerOc = 2 / ( r - l)]. The results of VL'hitea in this region are so scattered that they have been omitted. The phase boundaries are the best smooth curves through the points representing the continuation of the curve for each atmosphere to the melting temperature or the magnetite-hematite inversion temperature, as given in Table IV and indicated in Fig. 4. These are the least precise of our results, because of the relatively large error caused by possible lack of purity of the gas (carbon dlcxide) a t lower oxygen pressures, and at higher oxygen pressures by change of composition during quenching of the
3
,g . 6
A
!2
A
I
0
-1
Vol. 68
~~
TABLE I1 COMPOSITION OF MAGNETITE IN EQUILIBRIUM WITH SEVERAL ATMOSPHERES AT VARIOUS TEMPERATURES Starting materiala
A.
{
Ciz:ite Fez03 Wustite Fez03 Wiistite
i
r{
-2
E Z t e Fez03 Wiistite
i
Temp., 'C.
M
s
-6
1189 1294 1294 1296 1296 1390 1390 1479 1479
- 10
{
(Fe++
108 18 18 18 18 18 18 18 18
+ Fe+++)/Fe++ 1
3.01 3.00 3.01 3.01 3.01 3.01 3.01
3.01 2.98
B. Steam, 1 atmosphere 18 18
C. COz, 1 atmosphere Fe, electrolytic 1128 240 Wiistite 1147 72 Wiistite 1147 72 Fe, electrolytic 1148 48 Fez03 1177 60 Fe, electrolytic 1180 64 Wiistite 1198 72 Wiistite 1210 96 Fee08 1244 72 Fe, electrolytic 1256 18 FezOa 1306 24 Wiistite 1306 24 Fez03 1321 18 Wiistite 1321 18 Fe, electrolytic 1335 1 1392 18 Fez03 Wiistite 1443 72
i
-8
NzINi. Fig. 3B.-Relation between partial pressure of oxygen and composition of liquid oxide, expressed as the atom fraction iV*/Ni, as read from Figure 2 at 1400, 1500,1600'; with data of other recent investigations for comparison, and outlines of the several phase boundaries.
hours
c02-H~; initial f i c o , / f i ~ , = 28.3 1189 108 3.03
1521 1521 -4
Time at temp.,
1542 1542
18 18
3.00 3.01 3.147 3.205 3.257 3.124 3.121 3.121 3.146 3.074 3.080 3.102 2.999 2.993 3.046 3.019 2.994 2.999 3.012 2.955 3.005
IRON-OXYGEN EQUILIBRIA INVOLVING LIQUIDOXIDE
May, 1946 'TABLE Starting materiala
I). FezOa Fe wire Fe wire Fez03 Fez03
11 (CO%ClUdcd)
Temp., OC.
Time at temp.,
hours
+ Fe+")/Fe++ r
(Fe++
02-CO2, PO, = 0.0391 atmosphere 72 m 11-14 1286 18 m 1320 18 3.560 72 3.397 1388 5 3.195 1505
E. Air, 1 atmosphere 1502 1502
Fez03 Magnetite Fez03 U;iistite I;e?Oa IViistite
1545 1545
i
1589 1589 1593 1593
{
ci:;ite
i i
Fen03 1493 Wiistitc 1493 Fe.Oa 1512 Wiistite 1512 a See note to Table I.
23 23 18 18 18 18 3 3
3.513 3.495 3.328 3.332 3,299 3,280 3.314 3.305
E;. Oxygen, 1 atmosphere 45 45 7 7
4.108 4.090 3.827 3.870
803
Determination of the Equilibrium Iron-Liquid Oxide: Line CN.-These measurements were made by heating an oxide, enclosed in a closed iron crucible in an atmosphere of purified nitrogen, to one of a series of temperatures from about 1370 to 1520°, then analyzing the product. The results, in Table 111, are somewhat less concordant than those in Table I (which were equilibrated with a gas instead of a solid), but less erratic than those observed when wiistite was heated in an iron crucible (paper I). As an independent check, a small (1-g.) sample of electrolytic iron was suspended, at the thermal center of the furnace through which passed a constant carbon dioxidemonoxide mixture such that it would just oxidize iron a t this temperature, 1455'; the liquid oxide dropping off slowly was caught in a platinum crucible below the furnace, about twenty-four hours being required to collect enough for snalysis. hlicroscopic examination disclosed no metallic iron; the result ( r = 1.067) is in satisfactory accord with the other data in Table IIIA. TABLE 111 A. COMPOSITION OF LIQUIDOXIDEIN EQUILIBRIUM WITH IRON (LINE CN) Tzmp.,
sample. Within the range covered, there is no indication of a stable magnetite with less oxygen than the formula Fea04,but a considerable range (up to 0 : F e = 1.38) of solid solution of oxygen in magnetite.
Starting material'
C.
Time a t temp, (Fe++f Fe+++)/Fe++ hours I
FQO~
1390 1390
4 18
Wiistite
1392
2
Fez03
Fe304 1393 Wiistite magnetite 1397 Fez02 1454 Fez03 1461 FetO3 1495 FeDa 1501 FesOa 1502 Fez03 1502 Fe 1455 a See note to Table I.
+
6.5 2.2 4.5 18 1 3.5 2.5 2 24
{
1.081 1.076 1,052 1.056 1.077 1.069 1.057 1,055 1.056 1.051 1.045 1.049 1,067
B. COMPOSITION OF CO-C02 MIXTURES IN EQUILIBRIUM WITH IRON A N D LIQUIDOXIDE
1100
-
1.o
"J 0.9
I
I 0.8
0.7
NF~~o,. of magnetite, expressed as
0.6
Fig. 4.-Composition in equilibrium with various atmospheres, up to the phase boundaries; transition temperatures indicated are from Table 111.
Temp., 'C.
fiCOJPC0
1376 1436 1493
0.268 ,233 I199
The composition of the carbon dioxide-monoxide mixture in equilibrium with iron and its liquid oxide a t several temperatures was determined in precisely the same way as in the analogous case of iron and wiistite (paper I ) . A strip of lightly oxidized electrolytic iron was held in a known carbon dioxide-monoxide mixture, with its lower tip a t the thermal center of the furnace, a t a temperature such that it was oxidized only a short distance at the lower end but the remainder was reduced. 'The boundary between the oxidized and the deoxidized zone was not sharp but its indeterminacy was judged to correspond to about
L.S. DARKEN AND R. W. GVRRY
804
-
L . . .
5.2
5.4
Fig. 5.-Gas composition in equilibrium with iron and ils liquid oxide; direct determinations by this investigation shown as circlcs, by Chipman and Marshall as squarer. The upper line is drawu with the slope corresponding to the more reliahle heal of reactiooa calculated as described latcr in the text.
;'1 its temperature, which coincided within 1' with that of the thermal center, was taken as that for equilibrium with this particular atmosphere since at lower temperature the tip was reduced. The results, in Table IIIB. when plotted in ternis of log pco,/pco against 1/T, lie close to the straight line which also represents the data of Chipman and lMarshall.1° Yet, despite this agreement, we doubt their accuracy; in part because the slope of this line corresponds to a heat effect which differs unduly from that calculated (on a later page) from other experimental data; mainly, however, because we believe all of them to be vitiated by the experimental fact that the oxide became contaminated by silica which somehow volatilized from the porcelain tube." T o surmount this difficulty we tried, though without success, to procure an alumina tube, as was used by Chipman and hlarshall; but in it they had a radiation shield of clay, overlooked this possible source of contamination, and did not look for silica in their product. For this reason, we preferred t o draw line CN from point NJ in Fig. 5 at an angIe in agreement with the computed heat effect. Melting Temperatures of Wiistite and Magnetite (Lines NI, IVR),-The melting point (N) of wiistite in equilibrinin with iron lins been measured by sevcral investigators, most recently by Chipmail and .\larshall,"' who give it as l:l(i9' We redetermined it by enclosing ferric oxide in a n (electrolytic) iron crucible, closed by pinching its top, held at a controlled temperature for half an hour in an atmosphere of purified nitrogen; after the sample was cooled it was examined. The samples which had been at 1372' had melted completely, those a t or below 1370' showed no sign of melting; a sample held at 1371' had par(10) Chipman and bhrihnll. T H ~ S1 o a r w A L . S I . 2!18 negram atom of oxygen from ture the partial pressure of oxygen (from Table (15) “International C r i t t c d Tables,” Vol. 111, 205. 1700
+ +
+
+
+
(14) This sample analyzed 98 170(FeO being principally oxides of molybdenum.
+ FetCh), the remainder
( 1 B ) Marshal, Dornte 2nd Norton, Tms JOURNAL. 59, 1161 (1937); Jones, Lannmuir and Mackay, Phrs. Rev., 30, 201 (1927).
LIQUIDOXIDE
IRON-OXYGEN EQUILIBRIA XNVOLVING
May, 1946
a carbon monoxide-dioxide mixture to a liquid oxide is 4.575 times the slope of the linear plot of log Pco,/i)co a t round compositions, as read from Fig. 3A, against 1/T. % differs from 2 2 by the heat of formation of CO? from CO and ‘/z 0 2 , taken as 66,660 cal. per mole COZ a t 1500’. The results for several compositions of the oxide are given in Table VI and may be represented within the experimental error (the greatest discrepancy being about 200 ca1.3 by the equations
-
Hi
-
Hz
-79,100 = -145,660
f25
I
I
807 1
I
Nz + 69,500 Nz + 69,500 F, Nl
where, as before, N I and Nz are the atom fractions of iron and oxygen, respectively, in the oxide. From Fig. 2 it is evident that a satisfactory 1.o 1.1 1.2 1.3 1.4 temperature coefficient cannot be obtained when NzIK. N 2 / N 1is greater than 1.2 (7 > 1.7), since beyond Fig. 8.-Partial molal heat of addition ofone gram atom this level the temperature range covered is short. of one gram atom of oxygen (H)Z,_and heat of Although the data of WhiteEin the high oxygen of iron range i r e somewhat erratic, and appear not to be formation of one gram mole of ferrous oxide (HI H2)as in too good agreement with those of this investi- functions of the composition of liquid oxide. gation on an isothermal plot (Fig. 3B), it is of corresponding activity (a)of oxygen (or from some interest to derive g2by combining his pcor/pco). If the integration is performed from temperature coefficients with data from our the composition of oxide in equilibrium with iron 1600’ isotherm. White uses as composition to the composition under consideration, the acvariable the number of moles ferrous oxide ( x ) tivity thus calculated is relative to metallic iron formed from one mole ferric oxide, whence, in our as unity. Although from many viewpoints this notation x = 2 / r = 6 - 4Nz/N1. From a funda- is the most desirable standard state, the accuracy mental theorem of partial derivatives and the of all values based upon the measurements of usual expression for in terms of partial pressures pc~,/pco in equilibrium with oxide and iron is it f0llow:j that seriously impaired by the suspected error in these data, and by the necessity of extrapolating above the melting point of iron. This disadvantage can be overcome by integrating from some arbiThe first of these two partial derivatives was trarily chosen composition as standard, except measured a t 1600’ from the plots given by White, that the activity of metallic iron would then be and the second from Fig. 3B. Values of BZthus uncertain; this is discussed later. The activity derived are shown in Fig. 8; the points fall fauly of iron in liquid oxide relative to the liquid oxide well on the extension of the straight line represent- in which N2,”; = 1.07 is given in Table VI; this ing our results in the lower oxygen range. Similar composition was selected as being near the iron treatment of the air isobar in Fig. 2 leads to a side of the liquid field and in the region where the value of Ir, := -;j0,200 calories (at N , / N ~ = experimental error is least. The activity of ferrous oxide in molten iron 1.357) which d s o is in good agreement with the oxides is similarly derived from the Gibbssame extended line. Duhem equation, which in this case reduces to
(z),
+
Z
TABLE V PARTIAL MOLAL HEATOF SOLUTION OF OXYGEN IN LIQUID IRONOXIDE OF SEVERAL COMPOSITIONS AT 1500’ Composition oxide
NdNi
1.04 1.07 1.10
From COS, cal.
d, -ti860
-4430 -2830
1.15
+ 640
1.20
+4530
Fiom 0 2 . H t , cal.
-73,520 -71,090 -69,490 - 66,020 -62,130
The activity of iron (al) in liquid oxides is calculated by means of the Gibbs-Duhem equafrom the tion: log a1 .:= - J N z / N I d log
N¶/NI
log ~
F
- I [ ( N z / N i ) - 11 d log Po,’/*
= ~ O
Nr/Ni
-
1.07
Although U F ~ O , relative to the composition in equilibrium w i t h iron, is less sensitive than a1 to experimental error in the ratio pco,/pco in equilibrium with iron and molten oxide (since in this vicinity the integrand is small), the integration limits were again from N ~ / N I= 1.07 to each cornposition. The values obtained are given in Table VI. The partial molal heat of solution of metallic iron (El)in liquid iron oxide is obtained, except
L.S. DARKEN AND R. W.GURRY
808
TABLE VI" ACTIVITYOF OXYGEN,IRON(al) AND FERROUS OXIDEIN LIQUID IRON OXIDERELATIVE TO OXIDEIN WHICH Nz/N,= 1.07 AS STANDARD STATE, AT 1400, 1500,1600" Log
-Log
ficop/$co $02 (atm.) Temperature -0.579 9.73 1.034 - .470 9.51 1.04 - ,077 8.73 1.07 ,257 8.06 1.10 .450 7.67 1.117 (G.93)b (1. 15)b (+ , 8 2 3 ) b (1.20)b (fl .396)b ( 5 .78)b NI/NI
+
+
1:0225 1.04 1.07 1.10 1.15 1.20 1.216
-Log ai
Temperature 1500" -0.639 -0.1563 8.92 - ,415 8.42 -0.383 - . I152 7.70 0 7.04 0.358 ,278 5.95 0.968 ,820 4.87 1.60 1.36 4.52 1.82 1.54
+
-Log aFeO
1400' -0.528 -0.0255 -0,415 -0.0215 0 0 +0.362 +o. 0284 0.576 ,0494 (0.999)b ( .0991)b (1.f172)~ ( . 1994)b -0.0279 -0.0199 0 +o. 0280 .0957 .190 .229
Temperature 1600' -0.736c -0.0291' -0.728" 8.20' 1.012; -0,0191 -0.369 - .371 7.46 1.04 0 0 - ,021 6.76 1.07 +O ,0268 $0.343 .295 6.12 1.10 .0914 5.09 0.924 .812 1.15 ,177 4.11 1.50 1.30 1.20 3.11 2.11 .290 1.80 1.25 2.01 2.81 .439 [2.35Id 1.30 ,565 1.23 3.33 [2.74Id 1.333 ,593 3.14 [2.825Id 1.06 1.34 ,733 0.27 3.98 [3.22Id 1.37 a The values in the first row for each temperature ( 2 . e . , a t equilibrium with metallic iron) are taken from Table VIII; thc inethod of derivation is described later in the text. b Values outside the range of stability of liquid Unattainable oxide. c Equilibrium with liquid iron. at 1 atm. pressure.
+
Vol. 68
ferrous oxide from solid wiistite to liquid iron oxide both of this same composition. Since this difference is very sensitive to experimental error in equilibrium with iron and in the ratio p c ~ / p c o liquid oxide and its extrapolation to 1600°, the "probable error" must be regarded as large. The part of this error attributable to the absorption of silica by the sample may be estimated in the following way. From the data of Korber and Oelsen" saturation of liquid ferrous oxide with silicon dioxide (corresponding to about 50% silicon dioxide in the vicinity of 1600') decreases the activity of ferrous oxide by a factor of about 3, or 0.5 log unit. In view of the unexpectedly large volatility of silica from porcelain noticed in this temperature range, it would not be surprising if the film of oxide formed were 10% saturated with silica (i. e., contained 5% silicon dioxide) which would correspond to an error of about 0.05 unit in log a F e O or log pc&/pco. Over the temperature range of the equilibrium measurements (1371 to 1494') 0.05 log unit corre= sponds to an error of (4.575) (0.05)/0.42 X 5,400 cal. in the heat of fusion; and the difference of 12,300 cal. may, from this source alone, be high by an amount of the order of 5,000 cal. This heat of fusion will now be obtained in a different way which, being independent of the large error just discussed, is regarded as more accurate. For the reaction FeO (in wiistite) a FeO (in liquid iron) we may write
where U ' F ~ O ( I ) is the activity of ferrous oxide in liquid iron relative to a standard state of some fixed composition where the activity is u*F,o(~), and U ' F ~ O ( is ~ )likewise that of FeO in wiistite relative to a standard wiistite where the activity is a°FeO(w); aFeO(1) and aFeO(w) are relative to any standard state. The standard state is again selected as Nz/Nl = 1.07 for both solid and liquid for an additive constant I, from HZby the equa- Values of log K F e O were determined a t each uf the tion mqlting temperatures of wiistite listed in Table z 1 = - f NZ/N! d H Z = I - 34,750 (N2/N1I2 IV in the following way. At each of these temIf values of a1 relative to metallic iron are avail- peratures the corresponding compositions of solid able, I may be evaluated by inserting in this and liquid were derived by graphical interpolation (or slight extrapolation) from tables of the ratio equation values of H I = 4.575 (d log al/d ~ / T ) N ~ , N ,pco,/pco . as a function of composition and temThe average value of I thus calculated from the perature. The activity a t each of these composimeasurements of ~,o,/Pco in equilibrium with tions was then obtained by interpolation (extrapmetallic iron and molten oxide (Table IIIB) is olation) from Table VI and from Table I X of 60,420. Other methods of determining it will be paper I ; these values were checked by reading didiscussed later, rect plots (not shown) of log a F e 0 V S . log pco,/pco. Heat of Fusion of Wustite.-The heat of The resulting values of log K F e O are given in fusion of ferrous oxide is the difference between Table VI1 and are plotted against 1/T in Fig. 9. the heat of formation of ferrous oxide in liquid The maximum departure from the straight line oxide and that in wiistite. For example, a t NZ/N, drawn corresponds to a little over lo. The heat = 1.07 the value of i?~ gz (from the equations of fusion of ferrous oxide, the slope of this line given) is 50,800 cal. per mole in the liquid; the multiplied by 4.575, is 7,000 cal. per mole; corresponding value in solid wiistite, from paper strictly, this figure represents the heat absorbed I, is 63,100 cal. The difference, 12,300 cal., cor(17) Korber a n d Oelsen, Mill. Kaiser- Wilhclm Insi. Eiscnforsch. responds to the heat of transfer of one mole of Diisscldorf, 16, 271 (1933).
+
0.04
TABLE VI1 EQUILIBRIUM OF W~STITE WITH LIQUIDOXIDE Composition of Solid Liquid
M. p.,
OC.
1371 1374 1386 1392 1411 1421
809
IRON-OXYCEN EQUILIBRIA INVOLVING LIQUIDOXIDE
May, 1946
NdNi
NdNi
Log K F ~ O
1.052 1.060 1.094 1.112 1.164
1.038 1.045 1.077 1.096 1.149 1.175
0 0098 0106 0191 ,0227 ,0328 ,0383
1.191
by the transfer of one gram-atom each of iron and of oxygen from solid wiistite to liquid oxide both of the composition N z / N I = 1.07. The precision of this value may be estimated as follows: The total temperature range covered is 50°, so that an error of 1' of opposite sign a t each extreme corresponds to 4% or 300 cal. The "probable error" of the activity of solid wiistite, as estimated previously, is about 0.0003 log unit; that of the relative activity in liquid oxide is about 0.001 log unit, which is about 4% of the range covered by log K F e O , hence corresponds t o 300 cal. error in the heat of fusion. Since these are the largest known errors (and they are not independent), we estimate that 7,300 cal. as the heat of fusion of ferrous oxide is probably correct within 500 cal. This m o r is independent of the absolute error in tabulated activities, that is, of any error in the determination of the equilibrium of oxide with metallic iron and of the extrapolation above the melting point of iron. This same quantity is derived from a different source later, and this agreement indicates that as obtained by the first method is high by 12,300 - 7,300 = 5,000 cal. In other words, as obtained from the relative activities of Table VI and the melting temperatures of wiistite (Table VII) is represented by the equation (obtained by subtracting 5,000 cal. from the equation derived above and rounding to the nearest 100 calories) Hi 55,400- 34,750(Np/N,)' Evaluation of the Equilibrium between Iron and Liquid Oxide by Means of the Free Energy of Formation of Magnetite.-This free energy a t temperatures 110O-14OO0 was calculated in paper I, and may be estimated a t temperatures up to its melting temperature by extrapolation of the linear plot of Fig. 8 of that paper. Since in the following discussion considerable weight will be placed on these extrapolated values, we make use of other available data as a check on their reliability. The free energy of formation of magnetite and carbon monoxide from iron and carbon dioxide a t 25' may be evaluated from calorimetric measurementsls and from the entropies calculated from the low temperature specific heats and from spectroscopic data. l9 The equilibrium Fe-Fe304(18) Roth and Wienert, Arch Etscnhullcnw , 7 , 455 (1933-1934). (19) K K Kelley, U S Bur. M r n c s , Bull , 434 (1941)
0.03 c
$ M
3 0.02
0.01 5.90
5.95
6.05
6.00 1041~.
6.10
Fig. 9.-Variation with temperature of the distribution coefficient of ferrous oxide between wiistite and liquid oxide, leading to the heat of fusion of ferrous oxide.
Hz0-H2 at 400, 500, 600' was investigated by Emmett and SCfiultzZ0whose data were converted to, pca/pco by means of from the ratio P H ~ o / ~ H the appropriate constant.21 The several data were collated in the following way: For any reac-
tion from which, by integrating, inserting the identity @ = (AIT'and the definition Agm = ( - Ae9J/298, and rearranging, we have
+
AFd -
f (AH'
- AH&)d 1/T
- AS& T
I
+
For the reaction 3Fe (pure, stable form) 4Coz(g) = Fea04 (magnetite) 4CO(g), A P / T was calculated in the usual manner from the data of Emmett and Schultz and from the measurements a t 1100-1400' reported in paper I. The integral was evaluated graphically by use of data on relative heat content from sources mentioned in paper I. Unfortunately there are no data on the heat content of magnetite above 1OOO'; the required values were obtained by graphical extrapolation. A plot of the left-hand side of this equation versus l / T should be a straight line with a slope equal to AIT'm and an intercept equal to AP,,. Such a plot of the data from the sources mentioned is shown in Fig. 10, from which it appears that the least certain data are APmzz and AH^^,. Moreover, uncertainty in the heat content of magnetite (which was extrapolated above 1000°) (20) Emmett and Schultz, THIS JOURNAL, 66, 1976 (1933).
+
(21) From the sources referred t o in paper I (page 1401).
values of the water-gas constant
The
PCOPHIO used in this conversion are: PCOzPEr
550' 1400' 1500' 1600° 0.0838 0.284 3.32 3.72 4.09 (22) This uncertainty derives from the uncertainty in the low temperature specific heat of magnetite, .S& being 35.0 * 0.7 a3 given by Kelley (ref. 19). 400"
500" 0.200
L.S. DARKEN AND R. W. GURRY
810
VOI. 68
substitution of the appropriate values of log of Pco,/Pco in equilibrium with magnetite and liquid oxide, as obtained from Fig. ?A, and of a F e O from Table VI. Pco,/p~oin equilibrium with metallic iron (i. e., &iron from 1400 to 1524' and liquid iron from 1.24' up) as thus calculated is given in Table VI11 and compared with direct experimental data in Fig. 5. The foregoing equation yields results which are rather insensitive to a variety of experimental errors. For example, a 170 error in the experimental determination of p c ~ , l in p ~equilibrium ~ with liquid oxide and magnetite leads to only O.33y0 error in p , ~ ~ / p c oin equilibrium with liquid oxide and metallic iron (because of the coefficient 3 in the equation) ; errors in measurement of pco,/pco near the low oxygen side of the field produce only a small error in the activity of ferrous oxide (because the integrand in the Gibbs-Duhem e q w tion is very sniall in this regionz3). The maximum probable error occurs a t the highest temperature, 1600'; it is estimated as being between 1 and 2% in pco~lpco. The activity of iron (al)in liquid oxide of the conlposition AVz/AV~= 1.07 relative to metallic iron may now be determined from these new values of pcoZ,'pco, and is given in Table VIII. A plot of these values of log al (relative to al for &iron as unity) vs. 1/T is nearly linear with a slope which corresponds to B,= 16,290 cal., for the transfer of one gram-atom of iron from 6iron to liquid oxide of the composition N2/Nl = 1.07. When this value is inserted in the equation for glon an earlier page the constant I is 56,080; that is, on this basis KFeaO,,
20 30 104/T. Fig. 10.-Extrapolation of lower temperature data on the formation of magnetite from iron in order to fix the activity of iron in liquid oxide relative to iron as standard. 0
10
may lead to considerable error in the ordinate in the sense that deparhre of the curve from strict linearity need not be interpreted as error in the free energy or entropy measurements. Extrapolation, in the range 140O-1G0Oo, of the best line through the points from this investigation, or of any line passing through the mean of our experimental results and within range of the other points shown, yields values of A P / T which differ by not more than 0.1 uiiit; this corresponds to 0.02 unit in log K, 0.005 unit in log pca/pco, or about 1% in the ratio pco,/pco. The line in Fig. 10 is that which fits best the mean of our results and of those of Emmett and Schultz; its equa-
B1 = 56,080- 34,750(L~2/i!J1)2
This equation represents our best determination tion is A P / T (A@ - AH&*) d 1/T = 1.73 Values resulting from the original inof J 1/298 1IT 4330/T, whence AH& = 4,330 cal. for the tegration of (N*/N,)&z in combination with reaction as written (corresponding t o a heat 56,080 for I are plotted in Fig. S; in the range of formation of magnetite of 266,200 cal. a t 25', as composition shown the quadratic term introcompared to the calorimetric value 266,900 tal.'* duces but little curvature. A t the composition and 267,200 cal. obtained in paper I. N 2 / N 1 = 1.07, HZ is (from the equation previously given) - 71,300 cal, whence r?l jf2is Log K F ~ ~ which O , , we define as log - ~ F Pco ~ ~ o ~ -55,010 cal. The corresponding value for solid where the activity of iron is relative to that of the wiistite from paper I is -63,070 cal. The differpure form stable a t the temperature and that of ence, 8,OGO cal., is the heat of transfer of one mole FeaOc is relative t o magnetite of composition ferrous oxide from solid wustite to liquid oxide, Fea04, calculated from AFo, as given by the fore- both of the composition NZ/iVl = 1.07; in other words, this is the heat of fusion of wustke, going equation, is included in Table VIII. Combination of this definition of log KF~,o, (23) Actually a method of successive approximations was used; ~ 0equilibrium with iron (relafirst approximate value of ( 2 ~ in with the isothermal proportionality aFeO 0: the tive to the value at h't/\'i = 1.07) was obtrioed b y iutegration of U F , ( ~ C O , / ~ C O ) (to evaluate the activity of iron) curves similar to those shown in Fig. 3A, but passing through points leads to the equation representing the direct measurements of PcoJpco in equilibrium
zl.
+
+
3 log
(PCOI/fiCO)l. &de
+ Fe = log
KFOsO4
-
This equation may now be used to evaluate
pcoZ/pcoin equilibrium with metallic iron and its liquid oxide, the term on the left-hand side, by
with iron and liquid oxide (at 1600°, the extrapolation thereof). Insertion of these values of activity in the above equation then yielded the new values for pcol/pco in equilibrium with iron and its. liquid oxide. The curves were then altered on their lower extremities (to the positions shown in Fig. 3A) to correspond therewith, and the integration was performed again. The new value thus obtained for log U F ~ Odiffered i r o m the first appruximation by less than 0.0020 (about 0.5% in UF.O) in the worst case.
IRON-OXYGEN EQUILIBRIA INVOLVING LIQUIDOXIDE
May, 1946
811
TABLE VI11 EVALUATION OF LOGpco,/pco
IN
EQUILIBRIUM WITH IRON AND LIQUIDOXIDE; ESTABLISHMENT OF ACTIVITYOF IRON AT Nz/Ni = 1.07 Log
Log KFeaOd
OC.
Pcoz/Pco equilibrium of I-Fe
oxide with
liquid
1-Fe
Log a1 in liquid oxide of comp. N ~ N =I 1.07 relative t o 6-Fe
1-Fe
1400 -1.158 -0.579 -0.528 ( - ,622)" ( - .583)0 1150 -1.189 - ,663 - ,639 1500 -1.215 -1.227 ( - ,682)' (-0.682)" ( - ,666)" (-0.666)' 1524 (In. p . Fe) -1 215 - .724* - ,713 .724b - ,713 1575 -1.208 - .745b - .728 .753b .736 1600 Obtained by interpolation. * Value corresponding to metastable equilibrium or metastable standard state.
-
0
by this method. This compares reasonably well with 7,300 cal., as calculated from the melting curve. of wiistites, but differs markedly from 12,300 cal., derived from the measurements of f ~ c a / p c oin equilibrium with iron and its liquid oxide. Since the methods yielding these two results, 7300 and 8060, are essentially independent and are based on data regarded as reliable, whereas the value 12,300 is derived from data on which suspicion has already been cast, it seems reasonable to conclude that the heat of fusion of wiistite in the vicinity of this composition is approximately 7,500 cal. Moreover, the activity of iron and the heat changes derived by this later method are deemed more reliable than those from the direct measurements of pc~,/pcoin equilibrium with iron and wiistite; consequently all subsequent calculations in this paper are based on Table VIII. From the final equations for and for B2
Ei + Bz =
-89,580
-
two heats of fusion and the heat of transfer are plotted on Fig. 11; on extrapolation to the composition N2,"I = 1 all yield the heat of fusion I
I
I.
1
7.0
+ 69,5OONz/Ni - 34,750 (N*/Ni)'
This equation gives, over the range from equilibrium with iron to N2/Nl = 1.20 and from 1400 to 1600' the heat of formation of one mole of ferrous oxide from metallic iron and gaseous oxygen. Its value for several compositions is given in Table IX; the second row is the corresponding quantity for wiistite, the fourth row the difference, which is the heat of transfer of one mole of ferrous oxide from wustite to liquid oxide a t each of these compositions (this transfer cannot be performed isothermally a t equilibrium). The fifth and sixth rows are the heat of fusion of wiistite, per gram atom of iron and of oxygen, respectively, to a liquid of the same composition (not strictly, isothermal since there is a melting range). These
I
6.511
6.0
NdNi.
Fig. 11.-Heat of transter of one gram mole of ferrous oxide from wiistite to liquid oxide (heat of fusion) A ( P 1 H2); expressed also per gram atom iron AHr/Nl and per gram-atom oxygen AHf/N2, where AH{ = NiAHI
+ +
iV2AHs.
of the unstable (and unattained) compound ferrous oxide, which is clearly in the vicinity of
TABLE IX HEATOF FORMATION OF FERROUS OXIDEIN WUSTITEAND LIQUIDIRON OXIDE; HEATOF FUSION OF WUSTXTE (KcAL.) NdNi1.055 1.07 1.09 1.11 1.11 1.16 fi, HZ(wiistite) -63.15 -63.07 -62.99 -62.98 -63.03 -63.08 f fi, (liquid) -54.93 -55.00 -55.11 -55.25 -55.51 -55.72 A(Bi BL?) 8.22 8.06 7.88 7.73 7.52 7.36 Heat of fusion of wiistite per g. atom Fe 7.63 7.48 7.34 7.24 7.14 7.08 per g. atom 0 7.23 6.99 6.74 6.51 6.26 6.11 @I 18.84 16.36 13.69 12.11 10.17 8.94 AR, 10.62 -8.29 -5.81 -2.65 -1.58 -4.38
+
+
-
812
L.S. DARKEN AND R. W. GURRY
8,500 cal. The last two rows of Table I X are the partial molal heats of fusion, which show a marked variation with composition; and it is surprising that the partial molal heat of fusion of oxygen is negative over the entire range. It is generally accepted that the crystal lattice of wiistite is of the sodium chloride type, with all sites for oxygen atoms fully occupied but a greater or smaller number of iron sites unoccupied. The energy change on fusion may be interpreted, in part, as the energy required to break some of the bonds thus giving rise to empty "lattice sites" in the liquid. Since crystalline wiistite already has empty lattice sites and their number increases with NJN1, it would be reasonable to expect the heat of fusion to decrease as N2I.471 increases, as illustrated by Fig. 11. Further, since the empty sites in wiistite are all iron sites, it might be expected that this increase in heat of fusion might be reflected in nl?, more markedly than in B z . Table I X shows that this anticipation is also realized; whereas a 1 decreases by 9,900 cal., increases by 9,040 cal. over the range covered. It is to be noted that if one of these quantities decreases, it is a thermodynamic necessity that the other increase. This same line of reasoning leads to the conclusion that the entropy of fusion also should be I The entropy of smaller the higher N ~ / N is. transfer of one gram-atom oxygen and one gramatom iron from wiistite to liquid oxide of the same composition is readily calculable from corresponding values of AH and AF. AH [= A(B1 Ez)] is given in Table I X ; AF [ = A(E Fz)] is equal to the difference in the quantity RT In al Pa'/'for wiistite and for liquid oxide, of the same composition at the same temperature (a1 being relative to metallic iron). The quantity (AH- A F ) / T , the entropy of fusion or, more strictly, of transfer of one mole of FeO from wiistite to liquid oxide of the same composition, at 1400', is given in Table X, and does decrease with increase of NZ/Nl, as anticipated.
Vol. 68
TABLE X ENTROPY OF TRANSFER OF ONE MOLEOF FERROUS OXIDE FROM WUSTITETO LIQUID OXIDEOF SAME COMPOSITION AT 1400 O
Composition NdNi
1.055 1.07 1.09 1.11
!.14 1.16
AS
5.04 4.95 4.82 4.72 4.59 4.49
Heat of Fusion of Magnetite.-For the equilibrium FesO4 (magnetite) e FesO4 (in liquid iron oxide), we may write, since the compositiqn of magnetite in equilibrium with molten oxide of lower oxygen content is fixed (within the experimental error)
The additional subscript (liquid) may be dropped, and
where AH is the heat of transfer according to the above reaction, a t the composition of the standard state a t which aFe@4 is unity. It would be desirable to choose this standard state to correspond to the composition Fe304, but liquid of this composition does not exist (except as a metastable supercooled liquid) in the range in which this equilibrium can be measured, i. e., from the peritectic (1424') to the melting point of Fe304 (1597'); hence, the heat of fusion a t the melting point of FeaO4 cannot be determined (except by extrapolation) from the data of this investigation. In order to have the greatest possible range for the plot of log aFerO4 VS. 1/T, the composition of the peritectic liquid (N2/NI = 1.1825) is chosen as standard. The activity of Fe304 relative to this standard state is then equal to the o , ~U F ~ O ~ $ J O ~a' /t~ equilibrium ) with quantity a ~ * $ J(or magnetite divided by its value a t the composition NZ/N1 = 1.1825. The compositions of the 0.4 liquid oxide in equilibrium with magnetite a t 1500, 1575 and 1597' were read from the phase 0.5 diagram and the corresponding activities required from Table VI; the plot of log U F ~ , O ~as , d thus obtained, against l / T proves to be a line a 0" 0.2 (Figure 12) whose slope corresponds to a molar M heat of fusion of 30,400 * 1,000 cal. The heat of 2 transfer of FesOl from the peritectic composition 0.1 to any other composition in the range measured may be found from the equations given for RIand %; it is the difference in the quantity (3B1 0 5.3 5.4 5.5 5.6 5.7 5.8 5.9 BZ) between the particular composition and the W/T. peritectic composition. This quantity when Fig. l2.-Change with temperature of activity of FeaO, added to the heat of fusion of magnetite is the in liquid oxide in equilibrium with magnetite, leading to the heat of solution of magnetite in iron oxide of the composition considered. Although the extrapolad heet of fusion of magnetite,
+
+
+
IRON-OXYGEN EQUILIBRIA INVOLVING LIQUIDOXIDE
May, 1946
813
tion is somewhat uncertain, the molar' heat of fusion of FesOc to a liquid of the same composition at 1597' is about 33,000 cal., with a probable error estimated as not more than 2,000 cal. The Activity of Fes04 in magnetite may be represented as proportional to the product a13ppck2 which, with the Gibbs-Duhem equation, gives log ~ F ~ , O=,
J;k''" 3Nz/NI) d log
#o,'/S
Na/Ni-3
In order to perform this integration the quantity (4 - 3N2/N1) was plotted (Fig! 13) against log pOrf/a a t three temperatures, selected to include as many points as possible, and to be close to the experimental points in Fig. 4; its zero points corresponding to the composition Fe304 are from Fig. 7B. The form these curves would have if magnetite behaved as an ideal solid solution of Fez03 in FelOc i s illustrated by the line designated "Raoult's Law" in Fig. 13. 28.2
28.0
$
k
6 &3 27.8
-2
-1 0 Log Por'/2. Fig. 13.---Isothermal plots of data in the magnetite field whose integration yields the activity of FelOd in magnetite. The contour which the isotherms would have if the solid solution of ferric oxide in magnetite were ideal is the line designated "Raoult's Law."
-3
It is rather surprising that these isotherms (at least that for 1575') exhibit little curvature in the major portion of the magnetite field but break abruptly near the composition Fe@4, and then run horizontally for a considerable distance. This means that in this vicinity the change of composition of magnetite corresponding t o an order of magnitude change in partial pressure of oxygen, is immeasurably small, a type of behavior which is characteristic of traditional chemical compounds (for example, the composition of sodium chloride is independent of the partial pressure of chlorine above it). No explanation is offered for the fact that magnetite behaves in this way on the low oxygen side yet as a typical solid solution on the high-oxygen side. Integration of the curves in Fig. 13 gives the activity of Fer04 in magnetite solid solutions; the curve a t 1575O (the curve for the other temperatures is not significantly different) is reproduced in Fig. 14, which again shows that the departure from Raoult's law is large.
0
0.1.
0.2
0.3
0.4
NF~~o,. Fig. 14-Variation of activity of FelO4 with composition of the magnetite solid solution, from integration of the 1575' isotherm Fig. 13.
The heat of solution of oxygen in magnetite of any composition may be obtained from the value of d log poJd 1/T a t that composition, The only composition common to more than two curves on Figure 4 is N F ~ O=, 0.760 (allowing a slight extrapolation); a plot (Fig. 15) of log Poaus. 1/T a t this composition is a straight line. Its slope corresponds to -67,200 cal. as the heat of addition of one mole of gaseous oxygen to magnetite of this composition, or to -33,600 cal. as the heat of transfer of one gram-atom oxygen from oxygen gas t o magnetite of this composition. This is considerably smaller than the partial molal heat of oxygen in wiistite (-61,720 to -63,460 cal.).
-0.5O
r
it M
3
- 1.0
- 1.5
L
6.0 6. 104/~. Fig. 15.-Change of log Po2 with 1/T at the composition N F ~ ~= O ,0.760 within the magnetite field, serving to evaluate the heat of addition of oxygen to magnetite. 5.5
The activity of ferric oxide in magnetite is proportional to a12po,*/'; choosing as standard state a t each temperature the composition in equilibrium with hematite we found (from a plot of log
L. S. DARKEN AND R. W. GURRY
814
Vol. 68
vs. 1/T) that the heat of solution of hematite in magnetite ( N F e : O , = 0.760) is +6,900 cal. The Magnetite-Hematite Equilibrium.-For the reaction
0.25, but its lower part departs by as much as a factor of ten (in PO,) from the curve thus calculated. Not only is there no value of k p which covers the whole isotherm, but even limited portions of the lower half cannot be represented by 2FerO4 (mag.) ~ / z O (gas) Z _r 3FezOa (hem.) any positive value of k2. In general, this mode of the e uilibrium constant may be written K = interpretation calls for an isotherm which differs l/po,'q. a2p,,o., since hematite is of essentially from the experimental curve by having more constant composition and its activity may be marked inflection, considerably greater curvature taken as unity. This K was calculated from PO, in the lower half, and an asymptotic approach to as given in Table IV, and aFerO, as read from Fig. the vertical axis (Nz/Nl = 1); it seems unprom14 at the appropriate conipositions from Fig. 4, ising. and log K was plotted versus 1/T. The three Nevertheless, as it was thought that considerahigher temperature points were colinear within the tion of more molecular species might improve the experimental error (1% of the partial pressure of agreement, we investigated at great length the oxygen, or 2') and yielded a heat of - 54,500 cal. form of the isotherm calculated similarly but on for the reaction as written. The fourth point (cor- the basis of additional molecular species including responding to the measured transition in carbon Fe, (FeO)z and FedOs. A method was devised to dioxide atmosphere-the least precise of these indicate the formula of the compound (or commeasurements) is considerably off the line deter- pounds) needed to force agreement; the disturbmined by the other three; the discrepancy ing result was that negative mole fractions were amounts-to about 50' as compared to the esti- called for unless a prohibitively complicated mated precision error of 20" in the measurement. array of molecular species is postulated-. Our From this value, -54,500 cal. combined with final conclusion is that the system is essentially the heat of formation of FeaO4 a t 1250' (-260,900 non-ideal and that no set of postulates involving cal.), the diRerence in temperature being ignored, the assumption that activity is equal to mole the heat of formation of one mole of hematite from fraction is capable of yielding an adequate intery F e and gaseous oxygen is -192,100 cal. It is pretation of the isotherms. This might be coninteresting to note that the heat of formation of jectured from the fact that the isotherms for the wiistite per gram-atom of oxygen, as given in liquid oxide are somewhat similar in form to those paper I, is -63,100 cal., that of magnetite is for wiistite, and from the difficulty of ascribing -65,200 cal., and that of hematite is -64,000 any physical significance whatsoever to molecular cal. In other words, the heat of formation of species in this solid solution, with a sodium chlosolid iron oxides per atom of oxygen is nearly ride type lattice, in which the variability in comindependent of the oxide formed. position arises from a deficiency of iron atoms. Another semi-empirical mode of attack is based The Liquid Oxide Equilibria on the fact that if the logarithm of the activity I t is of interest to consider whether the oxygen coefficient (n)of one component in a binary pressure isotherms in Fig. 3 may be interpreted solution is represented (at constant temperature) in terms of a simple picture of the constitution by a power series in the mole fraction of the other of the liquid. Whites interpreted his data, on a componen t-namely relatively small portion of the system, in terms log 71 = CYNZ @NzZ of the law of mass action; in essence he assumed it may be shown that a = 0 if Raoult's law is that the liquid oxide is composed of three moN2 = 1, and that then the single approached at lecular species, FeO, Fez03and FesO4, and that the activity of each is equal to its mole fraction in term PNZ2is in some cases sufficient. It then accord with Raoult's law. He then considered follows, from the Gibbs-Duhem equation, that if log y1 '= PNz2, then log 7 2 = P N l z . A similar the equilibria relation may be deduced by the methods of statistical mechanics for regular solutions-those for which the entropy of mixing is equal to that (FeO) (Fezor) for an ideal solution-and was applied by KiellandZ4 FeaOc = FeO FeeOa; kl = (FetOJ to the data of Krings and Schackmann9included in the parentheses representing mole fraction ; and Fig. 3B. If ferrous and ferric oxides are taken as was able to find values of k, and kz which repro- components of the liquid oxide, the equilibrium duced his measurements within the experimental constant for the reaction FezOq(l) = 2Fe0(1) error. On the other hand, our 1600' isotherm, l / 2 0 2 may be expressed as covering a much greater range, as shown in Fig. log K = log (UFe02P0z1/z/UFezO:) = 3B, is not reproduced, even reasonably well, by log ( N F ~ O ~ P O ~ ' / ~ / N ~F ( ~~ N ~O Fw ~)o N : ~F ~ o ~ ) any choice of k l and kz, the position being fixed by kl, the form being completely determined by k z . Thus, if this approach is correct, a plot of log :) (~ N * F ~-, No2~F e 0 ) for Its upper one-third, with a generous allowance ( N Z F e O ~ 0 ~ / ' / N F e , Oagainst for experimental error, is reproduced by k2 = (24) J. Kielland, Z Elckfrochcm , 41, 8 3 4 (1935).
aF-0,
+
+
+
+
+
+
May, 1946
IRON-OXYGCK EQUILIBRIA INVOLVI~\~C LIQUIDOXIDE
isothermal measurements, should br: linear, as Kielland found for the limited range covered by Krings and Schackmann. However, when a11 our data for 1600' (Fig. 3B) were plotted in this way, the curve departed considerably from linearity, principally at t.he low oxygen pressure end; a straight line represented satisf:ictorily the high oxygen end (as found by Kir-11and) but this region is less than liali' the range covered. The reversc calculation, to predict the form of the curves in Fig. 3 U from the foregoing equation, leads to an isotherm which, when forced to agree with that observed a t its upper end, rises higher than observvd IICX the center and falls again a t the lower end ; the iiiaximurn discrepancy amounts to a factor of about four in Poz. I t must be concluded, therefore, that this is a poor way of interpreting the data. In fact, a much closer approximation is to consider the isotherms themselves (i. e., the plot of log pol vs. N,/N1) as straight lines. As mentioned previously, there is reason to donbt if :-I fruitful interpretation of the behavior of liquid iron oxide in the range investigated can be based on the concept of molecular species. If this be true, it is meaningless to compare the actual behavi0.r with that expected for an ideal solution, :sincethe concept of an ideal solution presupposes the existence of molecular species; in special cases, such as molten alloys, the atoms of the elements may be considered as molecules, but obviously the present system behaves very differently from an ideal solution of iron and oxygen. Consequently we are forced to the opinion that adequate interpretation of the partial pressure and activity isotherms must await the development of a more satisfactory theory for this type of solution based on the methods of statistical mechanics. It is worth noting that the relation between oxygen and iron is not reciprocal; although the plot of log PO, (or F,) vs. N*/Nl is nearly linear, that of log u1 (or TI) vs. N2/N1 (or-N1/N2) exhibits marked curvature. The calculated heats of solution, considered previously, indicate that Hz is also a linear function of N z / N lwhereas glis not. Thus F, and gzare both approximately - that linear functions of N2/Nl, whence i t follows the partial molal entropy 3 2 = (gz - F2)/T is also a nearly linear function of A72/N1over the range covered. Similarly Fl, and 3 1 are approximately parabolic functions of N?/Nl. The similarity in the form of each of these three functions, although rather striking, possibly may not be of significance for the following reasons: Hl and E2 were determined over a rather limited range in this investigation, the precision is not sufficiently great to determine unambiguously the form of the relation with N2,"1, and F2 is linear with N2/N1only as first approximation. Acknowledgment.-The authors acknowledge with thanks the assistance of Mark C. Lindsay, Jr., who performed some of the analyses.
815
Summary Ry equilibration of liquid iron oxide with several controlled gas mixtures the equilibrium relations between partial pressure of oxygen, tcrnperature and composition of oxide were determined. The range of temperature covered was from tlic incltirig curves to 1640'; of oxygen press"ure f r o i i i that i n cquililriuni with iron to one atiiic?sl)hcre; of oxide coiiiposition froin a ratio of 0: Fe of 1.02 to 1 .:8. The magnetite field was investigated in the same wxy, arid the inelting curves oi wiistite and magnetite arid the equilibrium of iron with liquid oxide and of ningnetite with hematite likewise. From thesc data, topcther with therniodyiianiic quantities calculated from thein the phase diagrams (Figs. 1, 3, 7 ) were constructed. The magnetite field was found to comprise compositions with considerably niore oxygen than corresponds to the forniula Fe304but none with appreciably less. This iiitiicates that magnetite of high oxygen content behaves as a typical solid solution whereas magnetite of low oxygen content behaves as a typical compound; this conclusion is verified by its therniodynamic behavior, The therniodynamic activity of iron and of ferrous oxide was computed and tabulated over the composition range investigated a t 1400, 1500 and 1600'. The heat of transfer a t 1500" 3f one gr,?inatom of oxygen from gaseous oxygen to liquid oxide of cornposition A ~ 7 2 , f l ~ lis l (in caI. * 300) I72 = - 145,660 69,5G0i?L72/iv1. The corresponding heat of transfer of one gram atom of iron from 6-Fe to liquid oxide is = 56,080 - 34,750. (i~*/Nl)'. The heat of fusion of wiistite (the heat of transfer of one mole of ferrous oxide from wiistite to liquid oxide-both of the composition N2/LVl = 1.07) was determined from the solidus and liquidus curves to be 7,300 cal.; this same heat as determined from the partial molal heat content is S,OGO cal. The heat and also the entropy of fusion decrease with increasing oxygen content, as expected from the crystallographic nature oi wiis tite. The heat of solution of magnetite (Fe304)in liquid oxide of peritectic composition is 30,400 * 1,000 cal. From this the heat of fusion at the niaximum melting point (1597') is 33,000 * 2,000 cal. The heat of formation of ferric oxide from y-Fe and O2 (at 1400') is -1992,100 * 1,000 cal. No adequate solution theory is available to interpret the form of the oxygen pressure coniposition isotherms. T o a first approximation log PO, for liquid oxides is a linear function of N2/Nl. The departure from ideal solution behavior is wide for liquid oxides and magnetite as well as.for wiistite. The heat of addition (1450') of one gram atom of oxygen (from 0,) to magnetite (of composition N F ~ ~=o ,0.760, NF~,o, = 0.240) is -33,600 cal.,
+
E. F. LANDAU, w. F. WHITMORE AND PAUL DOTY
816
much smaller than the corresponding heat for wiistite. At the same temperature for the reaction 2Fe304 (mag.) l/202(g) + 3FezOs (hem.), AH is -54,500. By evaporation of iron oxide in a vacuum furnace a t 1600O it was found that the total vapor pressure passes through a minimum a t an atomic
+
Vol. 68
ratio of 0 : F e = 1.116 (24.23% oxygen). From this composition of the azeotropic mixture it is calculated that the vapor pressure of liquid iron a t 1600’ is 5.8 X atm. and it is shown that the vapor pressure of molecular FeO is small in comparison thereto. KEARNY,
N. J.
RECEIVED NOVEMBER 1 4 , 1945
I CONTRIBUTION FROM THE DEPARTMENT OF CHEMISTRY, POLYTECHNIC INSTITUTE OF BROOKLYN]
The Kinetics of the Reaction of Sodium 2-Haloethanesulfonates with Aqueous Alkali BY E. F. LANDAU,^ W. F. WHITMORE AND PAUL DOTY
A monomolecular reaction (El) would be expected from an electrophilic attack by the solvent on X to form a carbonium ion. The hydroxide ion would then accept a proton in a fast reaction to give the olefin. A bimolecular reaction (E2) would conceivably result from a nucleophilic attack by the hydroxide ion on a &hydrogen atom. The mechanism for this reaction will be discussed later. In the case of primary alkyl halides the elimination reac5ons studied have been of second order6 while for halides containing secondary and tertiary halides the reactions are predominantly lo*l1 first ~rder.’.~,~. Hughes and Shapiro9in their study of the mechanism of substitution a t a saturated carbon atom have discovered that the two substitution reacR f + OH- +ROH (fast) tions and the bimolecular elimination reaction OHRX+ ROH Xsa2 have comparable velocities for the case of the isoThese reactions differ fundamentally only in the propyl halides in a water-alcohol medium. They degree of the solvolytic ionization whose pre- have evaluated the A and E parameters in the dominance is responsible for the Snl reaction. It Arrhenius equation and find that these quantities has been shown that a decrease in the electro- are only slightly dependent upon the particular negativity of the alkyl group favors the ionization halogen present. However, when the ethyl broand increases the speed of the S,1 reaction. In mide reaction is studiedI2 (in anhydrous alcohol) the S,2 reaction the higher the electronegativity it is found that only the bimolecular reactions of the alkyl group the faster the reaction should occur with the substitution reaction predominatbe because of the increased tendency of the alkyl ing to the extent of about 99%. On the other group to share the electrons of the hydroxide hand, t-butyl halides yield mostly isobutylene via group. This situation has been illustrated by a bimolecular reaction (E2) in anhydrous alcohol. Gleave, Hughes and Ingolds and others4 by showThus, with the course of these alkyl halide reing that in the series-methyl, ethyl, isopropyl, actions apparently so dependent upon the prest-butyl iodide-the Sn2 reaction predominated for ence or absence of a relatively electropositive the first two thembers while the Snl reaction is group on the &carbon, it is of interest to record a dominant for the latter two iodides. kinetic study of the reaction in water medium of The elimination reactions which frequently sodium 2-chloro- and 2-bromo-ethanesulfonate accompany these substitution reactions have (CH2XCH2S03Na)with hydroxide ions. the form6 Experimental
The kinetics of the reactions of various alkyl halides with hydroxide ion2 has been the subject of intensive and fruitful investigation, especially by the Hughes-Ingold group, for more than a decade. These researches demonstrated that in some cases the reaction proceeded to the alcohol (substitution) or to the olefin (elimination), but more frequently t o the simultaneous occurrence of both types with the substitution reaction predominating. Moreover, two different mechanisms are possible for each of the above categories; one is monomolecular, the other bimolecular. The two nucleophilic substitution mechanisms are RX +R + + X- (slow) Snl
+
OH-
+
+ HCRnCRX +XnO + RsC=CRn + X-
(1) Taken in part from a thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Polytechnic Institute of Brooklyn, 1945. Present Address: Celanese Corp., Newark, N. J. (2) Remick, “Electronic Interpretations of Organic Chemistry,” John Wiley and Sons,New York,N. Y., 1943. (3) Gleave, Hughes and Ingold. J . Chcm. Soc.. 236 (1935). (4) Koskoski, Thomas and Fowler, THISJOURNAL. 65, 2451 (1941). (6) Hanhart and Ingold, J . Chcm. Soc., 997 (1927).
It has been reported elsewherel*that this reaction can be remesated as (6) Hughes and Shapiro, ibid., 1177 (1937). (7) Hughes, Ingold and Scott, ibid., 1271 (1937). (8) Bodendorf and Bohme, Ann., 616, 1 (1935). (9) Hughes and Shapiro, J . Chcm. Soc., 1192 (1937). (lo) Cooper, Hughes and Ingold, ibid., 1280 (1937). (11) Hughes and McNulty, ibid., 1283 (1937). (12) Grant and Hinshelwood, ibid., 258 (1933). (13) E. F. Landau, T h u i s , Polytechnic Institute of Brooklyn. 1946.
