Inorganic Chemistry, Vol. 15, No. 9, 1976 2187
Lower Oxidation States of Tellurium the y hydride, however, expansion takes place mainly in the a parameter. Interpretation of these interesting structural differences must await neutron diffraction measurements on the RCo3 hydrides. As noted above, the RFe3 compounds form only two hydrides-the a or terminal phases and a second hydride. It is not entirely clear whether this should be designated p or y. We incline to regard it as the y hydride, by analogy with the crystallographic behavior of the RCo3-H systems, since it involves an expansion in both the a and c parameters. The H2 pressures over the RFe3-H systems are consistently lower than those of the RCo3-H system in the two-phase regions. However, the RFe3 phase absorbs less hydrogen at the maximum pressure utilized (400 psig) than the corresponding RCo3 compound. Clearly, the y RFe3-H phase is stabler against hydrogen loss than the y RCo3-H phase at the hydrogen-poor end of the range of stability of the phase, and this order of stability exists for all hydrogen concentrations in the a! phases. There are then three classes of systematic behavior exhibited by the RT,-H systems with regard to affinity for hydrogen: 1, a decrease as the atomic number of R increases; 2, a decrease as x increases; 3, a decrease when Fe is replaced by Co. In each of these three cases the decrease in affinity for hydrogen accompanies a change in chemical composition of stoichiometry which leads to a decrease in lattice size. We shall return to this point below. Several absorption experiments were made to investigate the extent of the hysteresis between absorption and desorption of hydrogen for the 1:3 compounds. The behavior was found to be similar to that of the 1:5 cobalt compounds7 in that the quantity a p I P at different temperatures for the same hydride was essentially constant. AP is the difference in plateau pressure observed in the absorption and desorption experiments. In most treatments of the hysteresis phenomenon the lattice expansion and the degree of hysteresis are interrelatede8 In the 1:3 cobalt case where two hydrides are formed, the value of AP/P was greater for the y hydride than for the /3 hydride. This is as expected since the lattice expansion is greater for the y hydride. The main difference in hydrogen absorption of the 1:3 cobalt or iron phases and that of the RT5 compounds is the temperature at which desorption of hydrogen takes place above atmospheric pressure. The LaNis desorption pressure at room temperature is 2.5 atm. For Lac05 a temperature of 90 OC
is required to generate a hydrogen pressure exceeding 1 atm. The corresponding temperatures are 180 and 215 "C for the RCo3 and RFe3 phases, respectively. The RT3 compounds thus afford a low-pressure hydrogen storage and delivery system which can easily be controlled by temperature. Above, it was pointed out that in the RT, phase the affinity for hydrogen is reduced by increasing the atomic number of R or T or by increasing x; all of these result in a more compact lattice. The work of Kuijpers and Loopstrag shows that molecular H2 (or more exactly D2)in PrCo5 is broken down into the monatomic form and the atoms reside in certain interstitial sites. As the lattice size is diminished, the volume of the interstitial site decreases correspondingly. Superficially one might ascribe the systematics noted to the varying size of the site in which the H is occupied. We doubt that matters are that simple since the size of H+, the species which probably most nearly resembles the dissolved form of hydrogen, is far smaller than that of the interstice. Probably the variations noted affect the band structure in these materials in a systematic way, and it is this which leads to the observed systematic trends noted in the hydrogen affinity of the RT, phases. APW band calculations on selected RT, phases are being carried out in this laboratory, and these may in time be useful in elucidating the receptivity of these phases for hydrogen. Acknowledgment. This work was assisted by a contract with the Energy Research and Development Administration. Registry No. GdCo3, 12017-50-4; TbCo3, 12187-47-2; DyCo3, 12187-40-5; HoCo3, 12140-00-0; ErCo3, 12134-04-2; GdFe3, 12023-46-0; TbFe3, 12268-62-1; DyFe3, 12517-72-5; HoFe3, 12361-81-8; ErFe3, 12400-78-1; H2, 1333-74-0.
References and Notes (1) J. H. N. van
Vucht, F. A. Kuijpers, and H. C. A. M. Bruning, Philips Res. Rep., 25, 133 (1970). (2) F. A. Kuijpers, J . Less-Common Met., 27, 27 (1972). (3) T. Takeshita, W. E. Wallace, and R. S. Craig, Inorg. Chem., 13,2282, (4)
73R111974) ,-- / .
k:H. J. Buschow and H. V. Van Mal, J. Less-Common Met., 29, 203 (1972).
(5) R. Lemaire and D. Paccard, Bull. SOC.Fr. Mineral. Cristallogr., 92, 9 (1969). (6) F. A. Kuijpers, Ph.D. Thesis, Technische Hogeschool, Delft, 1973. (7) F. A. Kuijpers and H. H. Van Mal, J. Less-Common Met., 23,395 (1971). (8) See, for example, N. A. Scholtus, and W. K. Hall, J. Chem. Phys., 39, 868 (1963). (9) F. A. Kuijpers and B. D. Loopstra, J . Phys. (Paris) Colloq., 32, C1-657 (1971).
Contribution from The Technical University of Denmark, Chemistry Department A, DK-2800 Lyngby, Denmark
Lower Oxidation States of Tellurium. 4. Tetratellurium(2+), Hexatellurium(Z+), and Octatellurium(2+) in Chloroaluminate Melts R. FEHRMANN, N. J. BJERRUM,* and H. A. ANDREASEN
Received January 15, 1976
AIC60040L
The solvated entities Te42+, Te,j2+, and Teg2+ have been identified in reaction mixtures of dilute solutions of TeC14 and elementary tellurium by a combination of a spectrophotometric and a potentiometric method. The spectra of the individual tellurium species in the low-melting NaCl-AlCl3 (37:63 mol %) solvent at 250 "C are calculated from the spectra of the experimental mixtures. pK values (based on molar concentrations) for the reactions 2Te4+(soln) -I- 7Te,j2+(SOh) 11Ted2+(soln)and Teb2+(soln) Teg2+(soln) e 2Te,j2+(soln)were found by both methods. The spectrophotometric method (at 250 "C) gave for the two reactions pK values of -12 and -0.4 with nonlinear confidence limits (95%) of -m to -9 and -2.2 to -0.2, respectively. The potentiometric method (at 150 "C) gave for the two reactions pK values of -17 and -0.93 with nonlinear confidence limits (95%) of -m to -10 and -1.03 to -0.84, respectively.
+
Introduction Previously' it has been mentioned that in an NaCl-AlC13 (37:63 mol 96) melt three low oxidation states of tellurium seem
to be formed, when Te(1V) is reduced with tellurium. One of these species has been shown' to be Te42+,whereas the other species have only been suggested to be Teci2+ and Tes2+.2 In
2188 Inorganic Chemistry, Vol. 15, No. 9, 1976
Fehrmann, Bjerrum, and Andreasen
the present paper evidence is given for these species in chloroaluminate melts. The observation of two of these three species is in agreement with work by Corbett and c o - ~ o r k e r s . ~ In this work it was shown that tellurium compounds with oxidation states + l / 2 and + I / 3 exist. The +‘/2 oxidation state was later shown to contain the Te42+ entity in the form of Te4(AlC14)2 or Te4(A12C17)2$ but no x-ray structure has been given for the + l / 3 oxidation state. Tellurium species in the oxidation states + l / 2 and + l / 3 have been found in other highly acidic media.5
Experimental Section Materials and Measurements. The materials used in the present work are purified or made in the same way as in previous An analysis of the TeC14 used gave as an average of four measurements a chlorine content of 52.73 h 0.1 1% (the theoretical values for TeC14 is 52.64%). The experimental technique was the same as in previous ~ o r k . ’ ~The ~ ~same * type of electrochemical cells with inert electrodes of vitreous carbon were used, but NZgas was added to the cells instead of Cl2 gas. In all potentiometric measurements the pressure was the same over the melts in the two cell compartments. The measured potentials were found constant within ca. kO.01 mV (over a period of several hours), when equilibrium conditions were reached.
Methods of Investigation General Considerations. The initial molar amount of one of the added substances (in the present work NaC1, AlC13, TeC14, and Te) dissolved in 1 1. of the melt is defined as its formality. The ratio between two formalities is called the formality ratio for these substances and is denoted by the letter R. The densities of the solutions were calculated assuming ideal mixtures of Te, TeC14, and NaC1-AlC13. This assumption will only give rise to a small error as the amounts of Te and TeC14 added were small compared with the amounts of NaCl-AlC13. The densities of Te, TeC14, and NaCl-AlC13 were obtained from the work of D a m i e n ~ ,Simons,Io ~ and Boston,I1 respectively. Due to the reaction A12C17- C12AlC14- I 2 the melt was well buffered with respect to the chloride activity. Spectra. The formal absorptivity is defined by A(lc’)-l, where A is the absorbance corrected for the absorbance of cell and solvent, 1 is the path length, and c’ is the formality. In the present work all of the measured absorptivities have been divided by the total concentration of tellurium. This is expressed in the formulation A/lC’Te,total, where A and 1 have the meanings given above and C I ~ ~ , t ~iswthe i total concentration of tellurium. It has previously been mentioned14 that it can be shown from the Bouguer-Beer law, the law of additive absorbances, and the mass action relation that straight lines on a plot of the formal absorptivity vs. the formality ratio (for example of Te:TeCl4) can only be obtained for a system with two species; that this is so can be seen from the following arguments. From the Bouguer-Beer law and the law of additive absorbance one obtains the equation
+
species coming from the added tellurium. The formal charge of Te(1V) (Le., 4+) can be expressed as =PlCI/C’Te(IV)
+ PZCZ/C‘Te(IV) + P 3 C 3 / C f T e ( I V )
+ . . . +PnCn/C’Te(IV)
(3)
where Z is the formal charge of Te(1V) and p1 is the stoichiometric amount of tellurium in the first species coming from the added TeC14 times the formal charge of Te(1V). From the law of mass action one obtains
K1K2 -
clll,l
c2k2
c311,3
c212.2
c312.3
c412,1
Kn-z = cn-z
I n - 2 , n-2
ln-2, n-1
Cn- 1
Cn
ln-2, n
(4)
(5)
(6)
where K1 is the equilibrium constant for the first equilibrium and 111,l)is the reaction coefficient for the first species in the first equilibrium. From these equations (which are irreducible) the concentrations of all species up to the nth species can always be calculated from c1 and c2 and all the equilibrium constants from K1 to Kn-2. The concentrations of all of these species can now be introduced into eq 1-3. If we first look at a two-species system, eq 1-3 will contain only two terms with Cl/C‘Te(IV) and C2/dTe(IV) as parameters. Equations 1-3 can be solved by elimination and we will obtain an equation of the form ad(V’)/c’Te(IV)l
+ azR 4-
=o
(7)
where al, a2, and a3 are constants. Since Z is also constant, it is obvious that we have a linear relationship between A(V’)/C’Te(IV)/ and R. The important thing is now that if we deal with a system with more than two species, nonlinear terms will be introduced into eq 1-3. An elimination of the parameters which are now CI and c2 (since it is normally not possible under these circumstance to use Cl/C’Te(IV) and c2/ C’T~(IV) as parameters) will give us a nonlinear equation between A ( Y ’ ) / c ’ T ~ ( I R, v ) ~and , C’Te(IV) (i.e., curved lines at constant C’Te(IV)). In practice it can of course be difficult to distinguish between slightly curved lines and straight lines. By varying the formality of TeC14 the relative concentrations of the different species will, if there are more than two, normally be changed due to the law of mass action, and this will again affect the formal absorptivity. Therefore, by varying the formality of the highest oxidation state (in the present case TeC14) one can identify cases where it is difficult to distinguish between a straight line and a slightly curved line. Finally it is also important to make plots at more than one wavenumber. It can also be ~ h o w n ’ ~from > ’ ~the Bouguer-Beer law and the law of additive absorbances that if we deal with different spectra obtained at different compositions, a general equation involving three matrices can be put forward, i.e.
A(v’ l)/C’T e ( I V ) l = E l(V‘l)c 1/C’Te( I V ) + E2(V’ l)C2/C’Te ( I V )
+ E3(V’l)C3/C‘Te(IV) + . . . -b En(V‘l)Cn/C’Te(IV)
(1)
where A(v’1) is the total absorptivity at the wavenumber u’l, C‘T~(IV) is the formal concentration of Te(IV), ti(v’1) is the molar absorptivity of the first species and c1 is the concentration of the first species. The formality ratio, R, can be expressed as R
= f l C 1/C’Te ( I V ), f2CdC’T + . . . +fncn/c Te(1V)
e (I v )
f$3/c‘T e ( I V )
(2)
wherefl is the stoichiometric amount of tellurium in the first
[ l m c m i I [ c i ( ~ ’ n > I= P m ( v ’ n ) I
(8)
where I, is the path length at the mth composition, cnzris the concentration of the ith species for the mth composition, er(Jn) is the molar absorptivity of the ith species at the wavenumber J n , and A m ( d n ) is the total absorbance of the mth composition at the wavenumber J,,. From the model put forward to explain the spectral changes of the melt and from an arbitrarily chosen equilibrium constant, the concentration of each species cLcan be calculated. This (together with the measured absorbances at different wavenumbers and different compositions) is now introduced in eq 8 and the “best” values of c i ( d n ) (least squares) are calculated. By varying systematically the
Inorganic Chemistry, Vol. 15, No. 9, I976 2
R T I1n -1 u d In [Te,"] - n-'q AE =-=SI F
d In [Terlx+]
- t oNa+ d In [Na'] 4- t o ~ lcl,Z d In [AlzCl;]
+ t 0 ~ 1 c l 4 -d In [A1Cl4-] - -1rk ~ % ~ + [ T e , ~d+In] [Te,"] [TeuXf]d ln [Teux+] - -kTeux+ 1 X
1
- - k ~ ~ ~ z + [ T e d, ~ln+ [Tey"+] ] z
(1 4)
where ON^+, t0AlzC1,-, and toAlC14- are the transference numbers in pure NaCl-AlC13 (37:63 mol %) and kTeq+, kT&, and kTeym are constants, which multiplied by the concentrations of the respective species give the transference numbers for the same species. An integration of this expression gives
l:z::lc4 j 1
solution I1 carbon I Teqrf and TeuX+ porous pin Tear+and TeuXC carbon I1 (9) in NaCl-AlC1, (37:63 mol %) (37:63 mol %)
RT
[Teqr+]IIn" [TeuX+]In-'q F [Te,r+]In-' [TeuX+]IIn-'q RT W + I I I RT [A12C17-1II --- toNa+In - -toA12c1,- In F W+II F [AlzC17-I1 [AlCl -1II--- RT kTeqr+ RT =toAlCl4-In ([Teqr+lII F [A1C1,-lI F r
A E = = In
+
+
or (q/n)TeuX+ 2 (u/n)Teqr++ e-
(11)
where e- is the electron and n is the number of electrons. The potential of the cell can now generallyI5 be given as 1
A,!?=$llxitj(-z
