1826
ARNULF MUANAND W. C. HAHN,JR.
Vol. 63
1.40 1.30 1.20
1.10 1.00 3,3 d l - b
0.80 I
'
-0.400 -0.200 0 0.200 0.400 0.600 0.800 p-OH p-OCHs p-CH3 p-Br Sigma. Fig. 1.-Half-wave potentials vs. U-values: (1) 1st step, furfurylideneacetophenone; (2) 2nd step, furfurylideneacetophenone; (3) 3rd step, furfurylideneacetophenone; (4) benzophenone, 0.1 N acetate bufferpH 5.2 (R. W. Brockman and D. E. Pearson, J. Am. Chem. Soc., 74 4128 (1952)); 15) 1st step, chalcone, (CH3)aNOH-acetk acid buffer T. A. Geissman and S. L. Fries, J. Am. Chem. Soc., 71, 3893 (1949)).
However, the electron attack and protonation in this case would not be a t the carbonyl site. Though this reduction mechanism is not conclusive, the second wave does represent the formation of the saturated ketone VI1 a t the electrode surface. The first two waves are simple diffusion controlled reductions representing one electron transfers, whereas the third wave does not represent such a simple reduction. The id/C values for this wave are about half those for the first and second waves. I n addition, a change in the concentration of the buffer used in this investigation results in decided differences in the heights of the third wave. The polarographic characteristics of this third wave as a function of the buffer are being investigated.
SOME ENERGY RELATIONS IN SOLID STATE REACTIONS INVOLVING CRYSTALLINE PHASES OF VARIABLE COMPOSITIONS BYARNULF MUANAND W. C. HA",
JR.
Contribution No. 68-101 from College of Mineral Industries, The Pennsylvania State University, University Park, Pennsylvania Received March 19,1969
In a recent experimental study of the equilibrium between hausmannite and manganosite according to the approximate 021, it was observed that manganosite used as starting material reacted with oxygen of the equation 2MnaOd = 6Mn0 atmosphere to form hausmannite as a metastable phase a t conditions of temperature and 02 artial pressure within the stability field of mangrtnosite but close to the manganosite-hausmannite boundary curve. $his apparently anomalous reaction is explained in terms of a free energy-composition diagram for the system Mn-0 Implications of this observation on criteria used for judging equilibrium in some solid state reactions are indicated.
+
Introduction The equilibrium between hausmannite and manganosite according to the approximate equation' 2MnsO4 = 6Mn0
+ 02
was studied recently by Hahn and Muan,2 using an open system in which the desired 0 2 partial pressures of the gas phase were attained by mixing COzand O2or COZ and HZ. The method consisted in equilibrating two samples side by side a t constant temperature and chosen constant O2 partial pressure, the starting material in one sample being manganosite and in the other hausmannite. The manganosite had been prepared in advance from Mn02under strongly (1) Hausmannite has approximately stoichiometric MnrOi composition and occurs in two modifications, a low temperature ( c l l 6 0 " ) tetragonal and a high temperature ( > l l 6 O o ) cubic form. Manganosite, with sodium chloride structure, has variable composition, Mnl-.O.~~' (2) W. C. Hahn, Jr., and A. Muan, Am. J. Sci. (in press). (3) M. LeBlano and G. Wehner, Z. phyaik. Chem., A168,59 (1934). (4) T. E. Moore, M. Ellis and P. W. Selwood, J. Arner. Chem. Soc., 18, 856 (1950).
reducing conditions (pO2 = atm. a t llOOo), and hausmannite had been prepared by thermal decomposition of MnOz in air a t 1100". After equilibrium was attained among gas and crystalline phases, the samples were quenched rapidly to room temperature and the phases present determined by using X-ray diffraction. I n some cases, supplementary data were obtained by using only one starting material, either manganosite or hausmannite, and following the progress of the reaction by frequent weighing of the sample in a simple thermal balance setup. The results of the investigation are summarized in Fig. 1, where the solid line represents conditions for coexistence of the two phases hausmannite and manganosite in stable equilibrium. I n preliminary experiments for determination of the equilibrium between the two crystalline phases, the transformations of manganosite to hausmannite and vice versa were studied under conditions of constant temperature and partial pressures of Oa which were later found to be well within the regions
Nov., 1959
ENERGY RELATIONS IN SOLIDSTATE REACTIONS OF CRYSTALLINE PHASES
of stability of the respective oxides. The complete transformations in both directions took place in 3 to 4 hr. in tests run a t 1300’. (The transformations were called complete when the sample had reached a constant weight and consisted of only one phase according to X-ray analysis.) It was later discovered that when the two starting materials, manganosite and hausmannite, were equilibrated side by side under conditions of temperature and O2 partial pressure in the stability field of manganosite but close to the manganositehausmannite boundary curve, both quenched samples turned out to be mixtures of manganosite and hausmannite as determined by X-ray analysis. Experience showed that if both samples were a mixture the first time they were removed from the furnace, the amount of manganosite increased and that of hausmannite decreased in every case upon further time in the furnace. On the basis of this observation it was assumed that manganosite is the truly stable phase under these experimental conditions. Results of weighing experiments carried out in the thermal balance are shown in Fig. 2. Illustrated here is the weight change as a function of time for a sample of manganosite starting material, as it is kept in the furnace at 1443” in a n atmosphere of 0 2 partial pressure of 10-1.99atm. A small part (0.230 g.) of the sample was removed after 130 hr. in order to check the progress of the reaction by X-ray analysis. The portion of the curve to the right of this point on the horizontal axis was obtained by allowing for the amount taken out and recalculating to the original weight of the sample. It can be seen from the curve that the weight increases rapidly a t first, then it levels off and remains nearly constant for some time before finally decreasing. This weight decrease could not be accounted for by vaporization from sample and container. The X-ray observations showed peaks of hausmannite and manganosite of approximately equal intensities after 130 hr., whereas only traces of hausmannite peaks were present in the pattern of the sample a t the conclusion of the experiment (215 hr.). The presence of hausmannite in the quenched sample which originally was manganosite cannot be explained simply by assuming that exsolution of hausmannite from the oxygen-rich manganosite phase close to the boundary curve took place during quenching. The X-ray evidence as well as the weight-time curve indicate clearly that the content of hausmannite first increases and subsequently decreases with time a t constant temperature and 02 partial pressure. It is concluded that manganosite of low oxygen content does not transform directly to manganosite of higher, equilibrium, oxygen content, but first forms a mixture of manganosite and hausmannite. Energy Relations.-The stability relations existing among phases in the system Mn-0 can be illustrated in a free energy-composition diagram (1443’) such as shown in Fig. 3. (For a general discussion of free energy-composition diagrams, see for instance Darken and Gurry.6) In the (5) L. S. Darken and R. W. Gurry, “Physical Chemistry of Metals,”
McGraw-Hill Book Co., Inc., New York, N. Y.,1953.
1827
- 1600
- 1500 v W
a
3
-1400
% E a
5c - 1300
I
I
I
I
-4
-3
-2
I
-I
I
0
log Po,.
Fig. 1.-Diagram showing stabilities of the phases hausmannite and manganosite as a function of 02 partial pressure (log scale in atm.) and temperature (inverse OK. scale), after Hahn and Muan.2
$
0.78
Y 0.76
i
; 100 200
0
XK,
TIME (HOURS).
Fig. 2.-Diagram showing weight changes as a function of time as a sample of manganosite of low oxygen content transforms to manganosite of higher, equilibrium, oxygen content under conditions close to the mangrtnosite-hausmannite boundary curve, as explained in detail in the text.
diagram in Fig. 3 are plotted atom fractions of 0 along the horizontal axis, and along the vertical axis free energy values F* = F - (NI * F o M n 4N2 FOo). Here F is the free energy per g. atom of material and F o M n and F0o the free energies per g. atom of manganese and oxygen, respectively, in their standard states.6 We will choose as standard states metallic Mn and O2gas of 1 atm. pressure, respectively. Hence F* will be zero for metallic Mn as well as for O2gas of 1 atm. pressure. . The other free energy values used in the graph were taken from the data tabulated by Coughlin7 in (6) The free energy-composition diagrams discussed by Darken and Curry6 were constructed for closed systems. However, the relations apply equally well t o a chosen part of an open system. I n the present case we are dealing with a total amount of 1 g. atom of material (Mn 0). (7) J. P. Coughlin, Bulletin 542, U. S. Bureau of Mines, Washington, D. C.. 1954.
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ARNULFMUANAND W. C. HA”, JR.
1828
-10,000O r \ \
\
-20,000-
z0 +c 0%
% z5
-30,000-
I
5
-40,000-
LL
\
-60,000
Mn NO
__L
Fig. 3.-Diagram showing free energy as a function of composition for the phases manganosite and hausmannite in the system Mn-0 at a constant temperature of 1443’. The meanings of the various lines and symbols used are explained in detail in the text. (Diagram based on data, compiled by Coughlin? as well as recent data by Hahn and Muan.2)
conjunction with data contained in Fig. 1. It will be noticed that hausmannite is represented in the diagram by a point (m) because the composition of this phase is essentially constant. The manganosite phase, on the other hand, is represented by a curve (a--b). The exact shape of this curve and the exact location of its end-points a and b are unknown. However, we know that the oxygen content of the manganosite phase increases with increasing 0 2 pressure of the atmosphere. Hence, the curve must be concave upward and the slope of the tangent to the curve must vary continuously. Furthermore, the intercepts of this tangent with the two vertical axes measure the partial molal free energies of Mn and 0, respectively, of the manganosite phase. Therefore, the shape of the curve must be such that its tangent at the extreme left end (a) (representing manganosite in equilibrium with metallic Mn) must go through the zero point on the left side vertical axis. Similarly, the tangent t o the curve a t its extreme right end (b) , representing composition of manganosite in equilibrium with hausmannite, must pass through point m (and also through point w on the right side vertical axis corresponding to a value of F* of ‘/z RT In pop,where PO, is the 0 2 partial pressure of the gas phase in equilibrium with hausmannite and manganosite). I n order to illustrate more clearly the relations probably causing the anomalous behavior of manganosite, a distorted free energy diagram in conjunction with a distorted temperature-com-
Vol. 63
position-pressure diagram for the system Mn-0 is presented in Fig. 4. I n both diagrams in this figure the part of the diagram between the MnO and MnaO4 composition points has been greatly enlarged for sake of clarity. The upper diagram shows qualitatively phase relations at subsolidus temperatures in a part of the system Mn-0. Attention is drawn to the dash lines representing 0 2 isobars. (For a detailed discussion of the significance of such lines, see for instance a recent paper by Muan.8) These are horizontal lines through the two-phase (two condensed phases) regions, but traverse one-phase areas, such as that of manganosite, a t an angle. Only two such O2isobars have been indicated in Fig. 4, one marked “high poi’ and the other marked (‘low pori." It is obvious that the composition of manganosite made up a t a chosen temperature will depend on the 0 2 partial pressure of the atmosphere, the oxygen content of manganosite increasing with increasing 0 2 partial pressures. Assume that the manganosite used as starting material in the investigation of the hausmannite-manganosite equilibrium2was made up a t ‘(lowPO,” and a t temperature ti shown in Fig. 4. The composition of this manganosite is therefore, assuming that equilibrium was reached, represented by point D1. Now consider the situation when manganosite of this composition is introduced into the furnace under conditions of temperature and O2 pressure close to the boundary conditions (the equilibrium curve shown in Fig. 1) for the hausmamite-manganosite equilibrium. Let this situation be represented by the “high PO;’ isobar and temperature tz in Fig. 4. It is evident from the sketch that the equilibrium phase under these conditions is manganosite of composition represented by point C while the starting material is in a condition represented by point Dz, which is obtained by projecting the composition point Di to the higher temperature level tz. Hence the starting material is unstable in the new surroundings, and in order to obtain stability it must change its composition to C. This does not necessarily occur as a simple reaction between the manganosite starting material and oxygen of the atmosphere to form a manganosite phase increasingly rich in oxygen. A demonstration of this is offered by the sketch in the lower half of Fig. 4. Here the free energy F*, a t constant temperature tz, is plotted along the vertical axis and composition along the horizontal axis. The free energy of hausmannite is represented by point m, whereas the free energy of the manganosite phase of varying composition is represented by the curve a--b. The dash line x‘cx is the tangent corresponding to “high pop”. Also shown is the straight line w’bmw which passes through point m and a t the same time is tangent t o the manganosite curve a t point b. The system has at least two alternative ways of reaching the equilibrium state of minimum free energy, characterized by the coexistence of mangnnosite (represented by point c) and gas (represented by point x), One possible way would be for manganosite to change composition continuously along the (8) Arnulf M a u n , Anaer. J . Sci., 256, 171 (1958)
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-
Nov., 1959
ENERGY RELATIONS IN SOLID STATEREACTIONS OF CRYSTALLINE PHASES
curved path a--b from d to c. The free energy of the system (condensed phase plus gas phase) a t any instant would be represented by a point on a straight line anchored to point x and whose other end slides along the curve a--b from d to c. Another possibility is the following: Because point m, representing free energy of hausmannite, is located below the straight line connecting d and x, the system could also decrease its free energy from the original by forming hausmannite. It is easily recognized from the diagram that if manganosite of composition d and 0 2 gas of partial pressure represented by point x react in the proportions required to form stoichiometric hausmannite, the free energy is lowered, as indicated by the arrow in the diagram. With manganosite, hausmannite and gas coexisting, the free energy of the system at. any instant is represented by a point in the triangle outlined by the straight line m--x and the two straight lines connecting some point on the a--b curve below d with points m and x, respectively. As the manganosi te composition slowly changes along a--b during this process, the free energy gain caused by formation of hausmannite gradually diminishes and becomes zero as the manganosite composition reaches point e. From here on a reversal in the process is to be expected: The free energy of the system will be lowered by the hausmannite formed during the first stages of the reaction reverting to manganosite of compositions gradually changing from e toward c. The weight versus time curve shown in Fig. 2 can be explained on this basis. The initial steep portion of the curve marked by relatively rapid weight increase corresponds to the situation where hausmannite forms while t,he manganosite composition is close to point d. The curve levels off as the manganosite composition moves toward point e. Here the weight reaches a maximum, and with increasing time the weight decreases slowly because of the very slow decomposition of hausmannite to manganosite of composition continuously changing from e toward c. The X-ray evidence also supports this interpretation. It is evident from the sketch in Fig. 4 that the anomalous behavior of manganosite, that is, the intermediate formation of metastable hausmannite, is to be expected only a t combinations of temperature and O2 partial pressure close to the boundary conditions. At the chosen temperature ( t z ) for which the sketch in Fig. 4 applies, point w represents O2 partial pressure a t the boundary curve where hausmannite and manganosite coexist in equilibrium. Point z, the intersection with the 0 axis of a line through point m drawn from the extreme left end of the manganosite composition curve (a), represents the largest distance from equilibrium a t which the observed phenomenon should be expected. As the oxygen content of the manganosite used as starting material increases, this maximum distance from boundary conditions decreases. With point d representing the manganosite used in our experiments, the maximum distance from boundary conditions for observing the anomalous behavior is represented by point y. It is also evident that when the composition of the
1829
Fig. 4.-Diagrams presented in order to explain observations made as manganosite of low oxygen content transforms to manganosite of higher, equilibrium, oxygen content under conditions close to the manganositc-hausmannite boundary curve, as explained in text. The upper diagram is a distorted sketch of phase relations at subsolidus temperatures in the system Mn-0. Solid lines are boundary curves, and dash-dot lines are OZ isobars. The lower diagram illustrates free energy relations of the manganosite and hausmaniiite phases a t temperature tz. Solid dots labeled D!, Dn and C in the upper diagram and a, b, c, d, e, m, in the lower diagram represent compositions of manganosite and hausmannite phases whose reactions are discuyed in the text. Open circles labeled w, x, y, a, w’, x , in the lower diagram are points pertaining to discussion in the text.
manganosite ‘starting material is such that its free energy falls to the right of point e on the line a-b, the formation of hausmannite as a metastable phase should not take place at the “high pop’’ and temperature t z used as an example in the present discussion.
1830
0. W. EDWARDS AND E. 0. HUFFMAN
The formation of metastable phases as intermediate products during heterogeneous chemical reactions is, of course, a well-known phenomenon expressed in "Ostwald's Stufenregel."g However, the present case seems to be different from any observation reported previously in the literature. Our case is one in which a phase of one structure first transforms to a metastable phase of a different structure which then in turn reverts back to the original structure, all at a constant temperature and constant 0 2 partial pressure. This is made possible because compositional variations occur in one of the structures involved in the equilibrium. The observation has a very significant bearing on criteria used for judging what the true equilibrium phase is in heterogeneous reactions. It is generally assumed that when a crystalline phase A of a certain struc(9) W. Ostwald, Z . physik. Chem., 22, 289 (1897).
Vol. 63
ture is observed experimentally to convert to a second phase B of a different crystalline structure under a given set of experimental conditions, then structure B is stable relative to structure A under these conditions. The present investigation has shown that this is not necessarily so. Compositional variations in one of the phases may cause formation of the metastable phase B although A is the truly stable crystalline structure under the prevailing conditions. The present experience has shown that very critical evaluation of observations made in phase equilibrium studies is necessary in order to avoid wrong conclusions. Acknowledgments.-The ideas presented in this paper resulted from experimental work carried out as part of a research project on phase equilibrium relations in oxide systems sponsored by the American Iron and Steel Institute.
DIFFUSION OF AQUEOUS SOLUTIONS OF PHOSPHORIC ACID AT 25' BY 0. W. EDWARDS AND E. 0. HUFFMAN Division of Chemical Development, Tennessee Valley Authority, Wilson Dam, Alabama Received March 81. 1969
Diffusion coefficients of phosphoric acid solutions at 25" were measured with a two-lens Gouy diffusiometer over the concentration range 0.036 to 16 M . The c,oefficienta decrease from 10.41 X 10-6 cm.2 sec.-l at 0.036 M to 8.29 X 10-6 at 1 M, remain nearly constant between 1 and 5 M , and decrease from 7.84 x 10-6 cm.2 sec.-l a t 5 M to 1.32 X 10-6 cm.2 sec.-l a t 16 M. The recision of the D values is f0.3%. An extrapolation leads to 7.6 X 10-6 em.* sec.-1 for Do,, the hypothetical limiting difksion coefficient for undissociated phosphoric acid a t 25'. This value, along with hydrodynamic considerations, suggests that a hydration shell surrounds the undissociated molecule. The ratio D o ~ * ~ , - / D oism1.15.
Extensive inquiry1-'8 into the physicochemical properties of phosphoric acid has paralleled a remarkable growth in the industrial importance of the acid in recent years. Study of the diffusion of aqueous solutions of phosphoric acid offers means for gaining additional insight into the nature of this complex electrolyte. Of particular interest are the relative mobilities of the phosphate anion and the neutral molecular species-a comparison of the type recently reported for the weaker electrolytes acetic acid14and citric acid. l5 (1) J. H. Christensen and R . B. Reed, Ind. Eng. Chem., 47, 1277 (1955). (2) E. P. Egan, Jr., B. B. Luff and Z. T . Wakefield, THISJOURNAL, 62, 1091 (1958). (3) K. L. Ellnore, C . M . Mason and J. H. Christensen, J. A m . Chem. Soc., 68, 2528 (1946). (4) N. N. Grenwood and A. Thompson, Proc. Chem. Soc. (London), 352 (1958). (5) E . 0. Hnffman, J. D. Fleming and A. J. Smith, Ind. Eng. Chem.. Chem. Eng. Data Series, 3 , 17 (1958). ( 6 ) 0 . W. Edwards and E. 0. Huffman, ibid., 3, 145 (1958). ( 7 ) C. M . Mason and J. B. Culvern, J . A m . Chem. Soc., 71, 2387 (1949). (8) A. J. Smith and E . 0 . Huffman, Ind. Eng. Chem., Chem. Eng. Data Series, 1, 99 (1956). (9) C . M . Mason and W. M . Bluni, J . Am. Chem. Soc., 69, 1246 (1947). (10) R . Ripen and C. Liteanu, Acad. Rep. Populare Romdne, Bul. StiinL., A l , 387 (1949). ( 1 1 ) H . Sadek, J . Indian Chem. Sac., 29, 84G (1952). (12) RI. Kerker and W. F. Espenscheid, J. A m . Chem. Soc., 80, 776 (1958). (13) K . N. Bransoombe and R. P. Bell, Disc. Faraday SOC.,NO.24, 158 (1957). (14) V. Vitagliano and P. A. Lyons, J. A m . Chem. SOC.,7 8 , 4538 (1950).
Here we describe measurements of diffusion coefficients of phosphoric acid at 25" over the concentration range 0.036 to 16 M . Made by means of a Gouy interferometer, the measurements led to a value for the limiting diffusion coefficient of undissociated phosphoric acid. The results expand greatly upon the few integral values heretofore available. l6 Measurements Apparatus.-A two-lens Gouy diff usiometer was constructed by modifying a diffractometer that was similar in design and dimensions to Buerger's apparatus .I7 The light source, slit, filter and cell masks of the interferometer were essentially identical to those described14*18for single-lens instruments, whereas the camera and the plate masks were modified for convenience of operation. The two lenses were almost identical plano-convex air-spaced doublets, 6 in. in diameter, corrected for chromatic and spherical aberration. The components were mounted on an H-beam that was supported, through intervening cushiona of cork and of rubber, by a continuous concrete pier. The water-bath was mounted d!rectly on the beam between the lenses by means of an adjustable foot assembly that fit holes in the beam. The windows of the bath were single optical flats in holders that were adjustable about the two axes erpendicular t o the optic axis. The temperature of the batg was 25 f 0.005". The diffusion cell was a tall-form Tiselius cell whose top section extended above the bath liquid. The cell holder was of standard design18JQwith the usual cell masks and a rack(15) G . T. A. M W e r and R. H. Stokes, Trans. Faraday Soc.. 53, 642 (1957). ( l G ) L. W. bholm, Finska Kemistsamfundets Medd., 30, 09 (1921). (17) M . J. Buerger, J. A p p l . Phus., 21, 909 (1950). (18) L. J. Gosting, E . M . Hanson, G . Kegeles and M. S. Morris, Rev. Sci. Instr., 20, 209 (1949). (19) L. J. Gosting, Thesis, University of Wisoonain, 1947.
