CHARLES E. MESSERAND GILBERTWAN-HOIHUNG
3958 able from 26% estimated from experiments with pure ketene. The similarity of the results in pure ketene and in ketene-butane mixtures leads to the inference that a particular electronic state of methylene is responsible for all free-radical reactions here reported. We choose to call it the normal-state triplet methylene by analogy with the work with near-ultraviolet radiation, but, as noted earlier, it could be some excited electronic
state of methylene not observed upon absorption of near-ultraviolet radiation.
Acknowledgment. This work was supported by the funds provided by the National Science Foundation. T. A. W. was a recipient of National Science Foundation and National Institutes of Health predoctoral fellowships for which he wishes to express his appreciation.
Dissociation Pressures in the System LaH,-LaH,, 250-450' by Charles E. Messer and Gilbert Wan-hoi Hung Contribution No. 961 from the Department o j Chemistry, Tufts University, Medford, Massachusetts 06166 (Received January 18, 1968)
Equilibrium hydrogen dissociation pressures have been measured for the lanthanum-hydrogen system from 250 to 450" in the composition region of continuous solid solutions from n = 2.2 to 2.7 atoms H/atom of La. Partial molal enthalpies R H - l / z H H z oand entropies SH- '/zSH9"have been evaluated. The results have been interpreted in terms of regular-solution theory. The interaction energy between LaHz and LaHs (or between octahedral sites and octahedral hydrogen) is negative, indicating attractive interaction. The negative excess entropy of mixing of LaHz and LaH3is interpreted in terms of partial ordering and vibrational effects. Introduction The equilibrium hydrogen dissociation pressures of rare earth hydrides, for those systems which form continuous solid solutions from MH2 to MH3, have been measured over wide composition ranges in this region for ~ e r i u m , l - ~praseodymium, and neodymium. They have also been measured for plutonium,6 which forms continuous solutions up to PUH,~.,. The metal atoms in these systems form a face-centered cubic lattice, the hydrogens up to MH-2 going into the tetrahedral holes and the rest into the octahedral holes. Dissociation pressures have been measured in the lanthanum-hydrogen system as follows: in the LaLaHz two-phase plateau region by Mulford and Holley' and by Korst and Warf,4in the LaH1.8-LaH2.3 region at 550-800" by Iiorst and Warf,4 and at high pressures in the LaHz,,-LaHz.~region at 400-450" by Warf and Hardcastle.e In the present research, the system was investigated from LaHz,z-LaHz.8,at temperatures of 200-450" and at pressures from 0.01 torr to 1 atm. Libowitz and Lightstone' have interpreted the dissociation pressures in the region LaHl.8-LaH2.z in terms of lattice-defect theory. Several authors8-10 have given statistical mechanical interpretations of metal-hydrogen systems. Libowitzl' showed that a thermodynamic treatment based on regular-solution theory12 gave equations similar to those derived by The Journal of Physical Chemistry
statistical methods for nonstoichiometric uranium and palladium hydrides. The results of the present research are interpreted in terms of regular-solution theory, giving results closely related to those of Takeuchi and Suzukilobut more directly deduced. Experimental Section Equilibrium pressures and temperatures were measured in a standard glass vacuum system calibrated so that the amount of gaseous hydrogen present at any time could be determined from pressure-volume-tem(1) R. N. R . Mulford and C. E . Holley, Jr., J . Phys. Chem., 59, 1222 (1955). (2) R . Streck and K . Dialer, 2.Anorg. Chem., 306, 141 (1960). (3) C. E . Lundin, Trans. Met. SOC.A I M E , 236, 978 (1966). (4) W. L. Korst and J. C. Warf, Inorg. Chem., 5 , 1719 (1966). (5) R. N. R. Mulford and G. R. Sturdy, J . Amer. Chem. Soc., 78, 3897 (1956). (6) J. C. Warf and K . I. Hardcastle, ibid., 5 , 1728 (1966). (7) G. G. Libowitz and J. B. Lightstone, Proceedings of the 6th Conference on Rare Earth Research, Gatlinburg, Tenn., 1967, published as Air Force Office of Scientific Research Report AFOSR 67-1214, 1967, p 132. (8) J. R. Lacher, Proc. Rou. SOC.,A161, 525 (1937). (9) A. L. G. Rees, Trans. Faradag Soc., 50, 335 (1954). (10) S. Takeuchi and K. Susuki, Trans. Jap. Inst. Metals, 3, 41 (1962). (11) G. G. Libowitz, J . A p p l . Phys. Suppl., 33, 399 (1962). (12) J. H . Hildebrand and R . L. Scott, "The Solubility of NonElectrolytes," 3rd ed, Reinhold Publishing Corp., New York, N. Y.. 1950.
DISSOCIATION PRESSURES IN THE SYSTEM LaH2-LaH3, 250-450' perature measurements. l 3 Pressures were measured to *0.2 torr by a mercury manometer from 25 to 760 torr and by a series of RiIcLeod gauges from to 25 torr, to f 2-5y0. Temperature was recorded and controlled to * l o by a Honeywell Elektronik 15 recording controller, actuated by a chromel-alumel thermocouple junction inserted in a thermocouple well positioned very close to the sample. The sample container was a molybdenum boat which was placed in a Pyrex outer tube, surrounded in operation by a 12-in., 750-W tube furnace and connected to the vacuum-hydrogen system by a ground joint. The hydrogen gas was ultrahigh purity grade, about 10 ppm of impurities, from the Matheson Co. The lanthanum metal was obtained from the Ronson Netal Gorp., with a stated purity of 99.6%. Based upon analysis of a solution of the metal in dilute HC1, 0.1% Fe and 0.1% SiOzwere shown to be present. A piece (8 g) was cut under oil, rinsed with anhydrous diethyl ether, and transferred at once to an argon-filled drybox. The excess oxide coating was trimmed off with a stainless steel file, leaving a lustrous surface. The metal was weighted to hl mg in the drybox and transferred anaerobically to the vacuum line, where it was degassed under vacuum at 300". A measured quantity of Hz was exposed to each La sample at room temperature. The sample was heated in succession to each of several ascending temperatures from 200 to 450", by 50" intervals, then cooled in succession to each of these temperatures, and finally cooled to room temperature. ilt each temperature, it was assumed that the sample came to equilibrium when the pressure remained constant to *0.2 torr for 1 hr. At the higher temperatures, this required several hours; at the lower temperatures and pressures, as much as 2 days. Values obtained for the same point on ascending and descending temperatures agreed in almost all cases to h0.005 in the H:La ratio, to h 1% in pressure above 25 torr, and to 5% below 25 torr. The composition of the samples at the end of the measurement cycle, from PVT measurements, agreed to .tO.OOl in the H :La ratio with that at the beginning for four samples of an initial composition of H :La of 2.203 to 2.610. For samples of higher hydrogen content, H :La initially 2.82-2.92, compositions were from 0.02-0.10 lower at the end. The discrepancy was almost entirely due to the failure of the sample to take up as much hydrogen in the last cooling stage as it gained in the first warming stage. The gross final compositions of several samples were checked by a gas-evolution analysis based upon the measurement of the hydrogen produced by hydrolysis with 1 N HC1. The results agreed with the PVT measurements to f3yO.
*
Results Dissociation Pressures and Directly Related Thermo-
3959
Figure 1. Pressure-composition isotherms of LaHt-LaHs ( P is in torr; n is the number of atoms H per atom of La): 0, this research; A, Warf and Hardcastle.6
dynamic Properties. The pressure-composition isotherms are shown in Figure 1. Each single circle represents the average of two equilibrium measurements, one on warming and the other on cooling. Where there are double circles, the rising-temperature and falling-temperature results differed by the amount indicated. The relation between the results of this research and the high-pressure studies of Warf and Hardcastlee is also shown. The more or less uniform displacement of certain sets of experimental points from the isotherm lines is probably due to a systematic error in composition for each of those particular samples. The pressures in the lanthanum-hydrogen system resemble closely those in the cerium-hydrogen system, 1-4 at corresponding pressures and compositions. There is considerable disagreement among the four cerium-hydrogen papers. The lanthanum results of this research compare most closely with the cerium results of Streck and Dialer.2 At 250" the La-H pressures are definitely lower; at 450" the two sets are nearly identical. Van? Hoff plots of the data were made for compositions n = 2.20, 2.30,2 -40; 2.50, 2.60, and 2.70 H :La and are shown in Figure 2 . The linear "deviation-parameter" isotherms of Figure 3 were used to derive the (13) C. E. Messer in "Preparative Inorganic Reactions," Vol. 1, W. L. Jolly, Ed., Interscience Publishers, New York, N. Y., 1964, p 203.
Volume 7.8?Number 12 Nonember 1968
3960
CHARLES E. MESSERAND GILBERTWAN-HOIHUNG
Table I : Relative Partial Molal Enthalpies and Entropies of the System La-H, 250-450' Atoms of H/ atom of La
-@H
2.2 2.3 2.4 2.5 2.6 2.7
Figure 2. Van't Hoff plots, log P us. 1/T, for LaHt.2-LaH2.7.
- (BH - '/28Hz0)
- '/?HHaa), koa1 mol-1
oal mol-' de$-1
11.75 11.02 10.29 9.64 8.98 8.15
13.0 13.3 13.5 13.7 14.0 14.0
for the cerium-hydrogen system at corresponding temperatures and concentrations. The relative partial molal enthalpies become less negative with increasing hydrogen content, and the relative partial molal entropies become more negative. The latter effect would seem to indicate increasing order in the hydrogen positions, but the possible influence of changes in vibrational entropy mill be considered. Interaction Energy and Entropy. Derivation. The dissociation pressure data are interpreted in terms of the interaction-energy parameter w, defined in the theory of regular solutions12as
w =2 ~ ,3
EHH
- EAA
(1)
where E is the interaction energy per mole of H atoms,16 H refers to hydrogen atoms in octahedral sites, and A refers to vacant octahedral sites. The entrance of hydrogen into octahedral sites may be represented in either of two formally equivalent ways LaHds)
+ l/ZJ&(g)
+LaHds)
A
4- '/2H2(g)
-+
H
(2)
(2')
The equilibrium constant for reaction 2' is
2.2
2.3
2.4
I 2.5
2.6
2.7
2.8
n Figure 3. Graph of 2.303(1og P for LaHz.z-LaHz.8.
+ 2 log [(3-n)/(n-2)] 1 vs. n,
where a is activity. The mole fractions of A and H are 3 - n and n - 2, respectively, where n is the number of atoms of H per atom of La, assuming that virtually all of the tetrahedral sites are filled. The activity coefficients, from regular-solution theory, are YH
smoothed-curve values for Figure 2, rather than the nonlinear pressure-composition isotherms of Figure 1. The slopes and intercepts were evaluated by the method of least squares and were used14 to determine the relative partial molal enthalpies RH- ~ / Z H H ;and entropies SH - 1/2,S"20, which are given in Table I. For any given temperature and composition, the partial molal Gibbs free energies may be calculated from the relation14 6~ - 1 / 2 G ~ , a= -l/zRT In PH~. These quantities resemble closely in behavior those The Journal of Physical Chemistry
=e
YA = e
( w / X T )(3 - n ) ?
(4)
(w/RT)(n-2)z
The standard state of H is MH3 and that of A is MHz", a hypothetical lattice in which all of the tetrahedral but no octahedral holes are filled. The system is then symmetrical about 0.5 mol fraction or n = 2 . 5 . (14) G. G. Libowitz, "Solid-State Chemistry of Binary Metal Hydrides," W. A. Benjamin, Inc., New York, N. Y., 1965, p 61. (15) The interaction energy per H-A pair is defined as 2w, but the factor 2 disappears when the energies are redefined as per mole of H atoms.
396 1
DISSOCIATION PRESSURES IN THE SYSTEM LaH2-LaH8, 250-450' The assumption is implicit, and valid, that the volume contraction of about 1% on going from LaHz to LaH3 is negligible as such. Any resulting strainenergy effect might possibly not be negligible. Alternatively, the standard state of H can be taken as that of "infinite dilution" in MH2*. The activities in the two states are related according to the equation aH*
=
squares. Table I1 shows the values of w,log K , and log K * and also of the total and excess Gibbs free energies of mixing at n = 2.5. Table 11: Values of Certain Parameters as Functions of Temperature of the LaH2-LaHa System
aHe - AE*/RT oc
Interaction energy ( w ) , oal mol-1
Log K (eq 3), atm-'/z
Log K* ( e s e),
250 300 350 400 450
-1800 -1620 -1470 -1300 -1080
1.019 0.674 0.375 0,129 -0.078
1.795 1.292 0.891 0.551 0.248
t,
where AE* is the molar energy of transfer of H from MH3to MH2*. This transfer is equivalent to the interchange of H and A, and hence AE* = 20. Equation 3 then becomes
Taking the logarithms and rearranging, this becomes
+ 2 log [(3 - n ) / ( n - 2)]) -(4w/RT)n + (8w/RT) - 2(2.303) log K* (8) Ifweset Y 2.303 {logP + 2 log [(3 - n ) / ( n - 2 ) ] ) ,
2.303 {log p
=
=
then a graph of Y us. n should be a straight line. w is obtained from the slope, and K* is obtained from the intercept. If the standard state of H were taken as MH3, the intercept term in eq 8 would become (10zu/RT) 2(2.303) log K . The choice of states is, in a sense, purely formal, but the "infinite-dilution" standard state will be shown to be the one which is in accord with the usual statistical mechanical treatment. Equation 29 of the statistical mechanical treatment of Talreuchi and Suzukilo is essentially the same as our eq 8. The energy quantity obtained from the slope of This is the interaction their Y us. n - 2 graph is 7". energy between pairs of hydrogen atoms in octahedral sites, and in their treatment it is taken to be the only effective interaction energy in this composition region. by using eq 2 of It may be shown that 20 = -7" Takeuchi and Suzuki to calculate the difference between the energy of formation (from H atoms) of LaH2.5 and the mean of the energies of formation of LaHz and LaH3. If eq 29 of Takeuchi and Suzuki is expressed in a form analogous to eq 8, the interaction term in the intercept is 8w/RT. In their treatment, the H-H interaction is the only composition-dependent interaction in the composition region; in the regular-solution treatment, there are three interaction terms: H-H, H-A, and A-A. If the latter two are zero, then from eq 1 we have w = -WIH = -7". Interaction Eneygg and Entropy. Results and Discussion. Figure 3 shows the fit of the results of this research to eq 8, as determined by the method of least
atm-'/2
AUmiXm
AUmix
(n = 2 . 5 ) , (n = 2 . 5 ) , C S I mol-1 oal mol-1
-450 -410 -370 -320 -270
-1170 -1200 -1230 -1250 -1270
The 200" results were inconsistent, probably due to lack of true equilibrium especially at the lowest pressures, and were not used. The interaction energy, w,is negative at all temperatures, increasingly so at lower temperatures. This is indicative of an attractive interaction between LaHz and LaH3, or between octahedral hydrogen and octahedral sites; that is, LaHz.5 is more stdble than the mean of LaHz and LaH3. The interaction energy is a linear function of the temperature, the following equation fitting the values in Table I1 to within *20 cal mol-l: w = -2690 3.54t cal mol-', where t is in degrees Centigrade. From the values of w and dw/dT, the enthalpy of mixing, the excess Gibbs free energy of mixing, and the excess entropy of mixing may be calculated from the standard relations: AGmixE = XlxzW, A S m i x E = -x1xz dw/dT, and AH,ix = xlxZ[w - T(dw/dT)]. The total AG and AX of mixing may also be calculated, allowing for A S = R In 2 for random mixing. The free energy values are shown in Table 11. The enthalpy and entropy values, which seem to be temperature independent within experimental error, are : A H m i x = -920 cal mol-l, ASmixE = -0.88 calmol-' deg-I, and A S m i x = 0.50 cal mol-l deg-', for x1 = xz = 0.5 ( n = 2.5). Log K and log K* are linear functions of 1/T (where T is in degrees Kelvin) within experimental error. Least-squares evaluation of the slopes and intercepts give the values: AH = -9.52 kcal mol-', A S = -13.6 cal mol-l deg-l, AH* = - 13.33 h a 1 mol-l, and AS* = - 17.3 cal mol-' deg-l. AH and AX represent the integral quantities for the addition of l/zH,(g) to LaH2* to form LaH3, and AH* and AS* for the addition of 1/2Hz(g)to LaH2* to form octahedral-hydrogen interstitials at infinite dilution. The relative partial molal enthalpy values of Table I satisfy a linear relationship with n to within k O . 1 kcal mol-l. This is a necessary condition for a regular solution and may be shown as follows.
+
Volume 79, Number I 9
November 1968
CHARLES E. MESSERAND GILBERTWAN-HOIHUNG
3962 From eq 7 or 8 we have In P = -2(2n - 4 ) ( w / R T ) -
2 In K* - 2 In [(3
- n ) / ( n - 2)]
(9)
Since
RH- '/2HHZ0= -'/pRT2(b In P / b T ) ,
(10)
Then
RH- 2:"/'
=
- (2%- 4) [W - T(dw/dT)] + RT2(d In K*/dT) =
- (2%- 4) [W
- T(dw/dT)]
(11)
+ AH*
The slope of the line should be - 2 [w - T(dw/dl') ] = 2.5) = 7.3 kcal mol-l. The value of HH - '/2HH: at n = 2.0 should be AH* = -13.33 kcal mol-1. This reduces to the equation = -8AH,i,(n
I?H
- '/2HH2'
= -27.9
+ 7.3%kcal mol-'
which fits the values in Table I to *0.1 kcal. The negative excess entropy of mixing would normally be interpreted in terms of partial ordering of the octahedral hydrogens. However, nmr studies on the lanthanum-hydrogen system by Schreiber and Cotts16 indicate that proton self-diffusion is virtually complete
The Journal of Physical Chemistry
below room temperature at compositions from LaH2.2 to LaH2.8. This apparent negative excess entropy of mixing may be interpreted in terms of vibrational effects. Libowitz and Lightstone7 have shown that upon formation of a Frenkel defect (transfer of a hydrogen from a tetrahedral position to a vacant octahedral site) a, temperature-independent entropy decrease of about 8.9 cal mol-l deg-l may occur. They attribute this large decrease to the increase in vibrational frequency resulting from the contraction of the lattice on passage of the hydrogen atom from the tetrahedral to the octahedral position. The apparent excess entropy of mixing of only -0.88 cal mol-' deg-I might be due to the difference between the vibrational entropy of LaH2.6 and the average vibrational entropy of LaHz and LaHa, or more simply to the change in vibrational entropy due to hydrogen-hydrogen interaction.
Acknowledgments. Appreciation is expressed for valuable discussions with Dr. George G. Libowitz on the relations between the statistical mechanical and thermodynamic approaches. This research was supported by the U. s. Atomic Energy Commission under Contract AT(30-1) 1355. (16) D. 8. Schreiber and
R. M.
Cotts, Phys. Rev., 131, 1118 (1963).
