606
J. B. WESTMORE, K. H. MAKN,A N D A. W. TICKNER
Mass Spectrometric Study of the Nonstoichiometric Vaporization of Cadmium Arsenide1
by J. B. Westmore,2K. H. Mann,2 and A. W. Tickner Division of B p p l i e d Chemistry, National Research Council, Ottawa, Canada
(Receiued October
4, 1063)
Cd3hsz is shown to dissociate thermally in the temperature range 220 to 280" according to the reaction CdaAsz(s) 3Cd(g) O.dAsd(g). The variation of the partial pressures Kith temperature was measured and an energy barrier was found to exist for the vaporization of arsenic with the result that the vapor is nonstoichiometric. For cadmium, the experimental data may be represented by log P c ~= -8083/T constant. The heat of disis found to be 112.0 i= 1.5 kcal./niole, and the heat of formation of CdaAsz sociation, AH298, is calculated as 14.5 f 3.0 kcal. 'mole. Separate experiments with arsenic give a heat of activation of sublimation of 43.0 i. 0.4 kcal./mole of AS^.
+
+
Introduction A general introduction to the method used in this work has been given by lllanii and T i c k ~ i e r . ~The compound CdaXsz has a much lower vapor pressure than either cadmium or arsenic. It can be vaporized and recondensed from the vapor with no apparent decomposition. Xesmeyanov, et al have measured the vapor pressure of Cd3-4szin the range 238 to 37.5' by an effusion method, assuming that the yapor consisted of CdsAsz molecules. Lyons and Silvestri,j working between 434 and 695') compared dew point, measurements with direct pressure measurements made using a quartz Bourdon gage and deduced that the vapor in that temperature range consisted of Cd and As4. They concluded that vaporization occurred according to
-"
Cd3As2(s)
.?Cd(g)
+ 0.5=ls,(g)
(1)
In the present investigation, carried out over the range 220 to 280°, a mass spectrometer xas used to study the vapor over solid Cd3ilis2, and the variation with temperature of the partial pressures of the species found in the vapor was measured.
Experimental The apparatus and method described previously by Nann and Tickner3 were used with a few minor modifications. Samples used in this n-ork consisted of finely divided material in a molybdenum crucible T h e Journal of Physical Ch,emistry
mounted on a quartz support (corresponding to parts D and G of Fig. 1 in ref. 3 ) . The thermocouple junction was screwed to the base of the crucible to ensure good thermal contact. The electron optics were improved by using a stronger magnet (about 400 gauss) to collimate the electron beam and by inserting a grid, maintained a feTv volts positive with respect to the filament, between the filament and the ion source furnace. Since the ions being studied were heavier than in the earlier work, xenon was used as the reference gas instead of krypton. The CdsAsz used was obtained from two sources. One sample was very kindly supplied by SIr. T'. J. Silvestri of the I.B.SI. Research Center, Yorktown Heights, Ii-. I-. It contained stoichiometric proportions of cadmium and arsenic and consisted of clusters of crystals obtained by condensing the vapor from boat-grown CdsL4sz. The other sample was prepared by Dr. R. D. Heyding of this Division and was made by heating together stoichiometric quantities of cadmium and arsenic, each more than 99.99% pure, to 700" for 24 hr. in a sealed quartz tube. The samples (1) Kational Research Council Contribution No. 7845. ( 2 ) National Research Council of Canada Postdoctoral Fellow. ( 3 ) K. H. 3lann and A. ITT, Tickner, J . P h y s . Chem., 64, 251 (1960). (4) A. N. Xesmeyanov, B, Z. Iofa, A. A. Strel'nikov, and V. G. Fursov, Rum. J . P h y s . Chem., 30, 1250 (1956). ( 5 ) V. J. Lyons and V. J. Silvestri, J . P h y s . Chem., 64, 266 (1960).
607
XONSTOICHIOMETRIC VAPORIZATION OF CADMIUM ARSENIDE
-
1
1
were crushed to give particles with an average dimension of about 0.1 mm. before placing in the apparatus. KO significant differences were observed in results obtained with the two samples. The elemental arsenic used in some of the experiments consisted of annealed crystals with an average dimension of about 0.1 mm., prepared by vacuum sublimation. It was considered to have a purity greater than 99.99%.
Results and Discussion I . X a s s Spectrum of Lhe Vapor. The mass spectrum was scanned up to ?n/e = 600 for electrons of 50 v . energy. Ion currents due to the following species were found: Cd+, As+, As2+, Ass+, and As4+. Cd2+ was also detected, its ion current being about 8% of that of Cd+. S o ion heavier than AS^+ (m/e = 300) could be detected at any temperature up 'to 280'. On outgassing both CdaAsz and arsenic samples after exposure to air, significant currents were observed a t first at m/e = 91 and a t about m/e = 290. These were assumed to be AsO+ and Ass04+. No peaks that could be assigned to other oxides were detected. For the arsenic ions the ratio of the ion currents for 45-v. electrons was found to be As4+:As3+:As2+: As+ = 1.00:0.11:0.24:0.18. This pattern is similar to that obtained from the vapor of pure arsenic both as measured in this apparatus and as reported earlier by Kane and Reynolds.@ It suggests that the arsenic ions are formed from As4 rather than from CdsL4sz. I I . Appearance Potentials of the lons. The ionization eficiency curves for Cd+, Asq+,As3+, Asz+, and As+, together with those of X e + and K r + are shown in Fig. 1 for electron energies up to 50 v. Appearance potentials were determined by the method of Lossing, Tickner, and Bryce' and corrected so that xenon had the literature value of 12.13 v . ~In this may the ionization potential of krypton was found to be 14.01 f 0.03 e.v. (spectroscopic value 14.008)and the appearance 0.05 e.v. in agreement potential of Cd+ to be 8.89 with the spectroscopic ionization potential of 8.99 e.vS6 Separate experiments with pure cadmium gave a value of 8.93 f 0.05 e.v. The appearance potential of As4+ was found to be 9.01 f 0.05 e.v. in reasonable agreement with the electron impact value of about 8.8 e.v. for free arsenic obtained from curves given by Kane and Reynolds6 and with the value of 9.07 f 0.07 e.v. for free arsenic determined in the present apparatus. It should be noted that the latter value is considerably lower than the spectroscopic ionization potential of 9.81 e.v. for atomic arsenic.6 The agreement between the values of the appearance potentials of Cd+ and As4+
0.01
IO
so
PO 30 40 ELECTRON ENERGY -volts (uncorractebl
Figure 1. Ionization efficiency curves for ions from the vapor over CdaAsz; Xe and Kr were added as calibrating gases.
4/
-
I80
I85
I I90
I IT x
lo3
I 1.95
I 2 00
P
Figure 2. Temperature dependence curves for cadmium and arsenic ions from the vapor over CdrAsz (experiment no. 5, Table 11).
obtained from the vapor over Cd3Asz with those obtained from the free elements confirms that the ions are formed from Cd and As4 rather than from molecules of CdBAs2. The positions of the Ass+ and Asz+ curves indicate that they are electron impact fragments of As4,although (6) J. S. Kane and J. H. Reynolds, J. Chem. Phys., 2 5 , 342 (1956). (7) F. P. Lossing, A. W. Tickner, and W. A. Bryce, ibid., 19, 1254
(1951). (8) C. E. Moore, Natl. Bur. Standards Circ. No. 467, U. S. Govt. Printing Office, Washington, D. C., 1958.
Volume 68,Number S March, 1964
608
J. B. WESTMORE, K. H. MANN,AND A. W. TICKNER
the shape of the Asz+ curve at low electron energies may indicate the presence of a small concentration of As1 molecules in the vapor. The ,4s+ curve also suggests that this ion is formed by different processes at different voltages. Kane and Reynolds6 have shown that the smaller molecules may arise by decomposition of As4 on the mass spectrometer filament. In any event, our results indicate that As4 is the only significant arsenic species in the vapor at this temperature. I I I . Variation of Partial Pressures with Temperature. The ion current due to a substance can be used as a quantity proportional to its pressure over a considerable range as long as conditions in the ion source do not change. In practice, the efficiency of the ion source was found to vary with temperature and a reference concentration of xenon was maintained by allowing the gas to leak in from a reservoir in the sample line. The ion currents used in determining variations in partial pressure mere obtained from the equation
where I , is the measured ion current a t temperature T , I x e is the Xe+132ion current at temperature T , and reservoir pressure p x e , and the superscript zero indicates the corresponding quantities under the reference conditions. The measured values and corrections are given in Table I for Cd+ for one series of measure-
I o n currents arbitrary units Cd-I14
502 518 538 547 529 509 496
42 130 438 640 271 88 35
3
5 5 1 6 6 7
3
Xe-182
30 28 25 22 5 26 0 34 4 36
9
5 5 5 85 5 9
log Imr& IXr
-1/2
1 626 2 149 2 725 2 944 2 495 1 897 1 472
0 -0 -0 -0 -0 -0 +O
log
log
T
pxB
log
TO
QXeo
ICd
007 015 019 OS2 003 002
0 -0 -0 -0 -0 -0 -0
006 OS2 020 026 032 038
1 626 2 136 2 698 2 905 2 457 1 862 1 436
ments. The corrected values for both cadmium and arsenic ions for the same series of measurements are shown graphically in Fig. 2 . It is seen that for the arsenic fragments As+, Asp+, and Ass+ the temperature coefficients are slightly gr'eater than for the parent ion, As4+. This is consistent with the effect of temperature on the mass spectra of other molecule^.^ Since the fragments constitute a significant fraction of the The .lownal of Phvsical Chernistrg
Table I1 : Slopes of log I us. 1/T Plots for CdrAsz" Expt. no.
Table I : Variation with Temperature of Cd Pressure over CdsAsz(Experiment No. 5 )
Tamp, OK
total arsenic ion current, the partial pressure of As4 is more correctly related to the sum of the arsenic ion currents than to the current for As4+alone. Cadmium arsenide exhibits interesting behavior on vaporization. As mentioned previously, evidence was observed for the evolution of arsenic oxides on first outgassing the sample. However, even when these oxides had disappeared, the arsenic ion currents were still very small although cadmium appeared to be evaporating readily. As the vaporization continued, the amount of arsenic in the vapor, relative to cadmium, increased steadily with time and approached a limiting value. The absolute concentration of cadmium in the vapor did not appear to vary significantly with time. As a result of this gradual attainment of a steadystate condition, the first few experiments with a new sample did not give reproducible results. After a few series of measurements had been made, however, subsequent series showed satisfactory agreement for ion currents ,measured a t ascending and descending temperatures. In all, three main sets of data were obtained, which are summarized in Tables 11, 111, and IV. Slopes were obtained by treating the experimental points in each experiment by the method of least squares. In each set of experiments the arithmetic mean of the slopes has been taken and the standard deviation calculated.
1 2 3
4 5 6
Temp.. OC.
228-272 224-272 218-266 218-269 223-274 229-274 Mean
Cdn4 slope
ZAa slope
slope
7911 8236 8536 8091 7906 7816 8082
8246 8706 8596 8311 8066 7886 8302 & 127
335 470 60 220 160 70 219 i 6 5
.f
110
A
a Sample size = 0.36 g. (approx.). Estimated sample area 3000 mm.%. Total effusion area = 6.3 m m 2 .
=
The results in Table I1 were obtained using the largest sample of CdsAsz. Its weight was not known exactly, but was estimated to be a t least twice as great as that of the sample used in Table IV, the state of subdivision being about the same. Only runs showing good agreement between increasing and decreasing temperatures have been included. (9) See, for example. D. P. Stevenson, J . Chem. P h y s . , 17, 101 (1949), and R. M . Reese, V. H. Dibeler, and F. L. Mohler, J . Res. iVatZ. Bur. Std., 46, 79 (1951).
609
NONSTOICHIOMETRIC VAPORIZATION OF CADMIUM ARSENIDE .-
Table 111: Slope s of log I Expt. no.
1 2
3
4 5
Temp.,
oc. 231-287 239-276 253-280 236-268 228-263 Mean
us. 1 / T Plots for
CdrAs,"
Cdna slope
ZAs slope
slope
'7550 '71650 7550 7660 8250 1'732 If 132
8326 8440 9000 8600 8900 8653 5 130
775 790 1450 940 650 921 i 1140
A
a Sample size = 0.012 g. Estimated sample area mm.2. 'Total effusion area = 4.0 mm1.2. --
=
108
Table IV: Slopes of log I us. 1 / T Plots for CdaAsz" Expt. no.
1 2 3 4 5 6
7
Temp., OC.
224-285 231-257 227-270 220-270 227-2'73 225-2'72 226-274 Mean
Cdiia slope
ZAs slope
7850 8150 7 800
8400 8950 8000 8750 8450 7800 8300 8386 :F.150
8%00 8350 8000 8100 8064 =I72 =
A slope
550
800 200 550 100
-.200 250 321 5 127
Sample size = 0.172 g. Estimated sample area = 15'70 mm.2. Total effusion area = 4.0 mm.2. Q
The data in Tables I11 and IV illustrate the effect of varying the surface area of the sample. For these experiments a modified crucible was used in which Seven holes 3.1 mm. in diameter and 6 mm. deep were drilled in order to contain the samples. The apertures in the ion source furnace were modified so that the total effusion area was reduced from 6.3 to 4.0 mm.2. The samples consisted of particles passing though 100 mesh and retained on 200 mesh screens. Examination under a microscope verified that the particles were reasonably homogeneous in size and regular in shape and the average size was obtained by weighing a counted number. In this way a specific area of sample could be estirnated although, due to irregularities in the surface, considerable uncertainty exists as to the true surface area. The experiments in Table I11 were performed with a small sample placed in a single hole in the crucible and those of Table IV with a much larger sample distributed among all seven holes. The relative effective sample area for the experiments of Table IV will thus lie between the limits of seven and fourteen times the area for the experiments of Table 111,depending on whether the accommodation coefficient is near unity or is very small.lo
It is evident from the data in Tables I1 to IV that the slopes of the log I vs. 1/T plots vary with the surface area of the sample. The difference in slope between cadmium and arsenic is least a t the largest sample area, suggesting that for large enough samples the slopes would be the same and probably close to the cadmium value of about -8100 obtained with the two largest surface areas. This result is in fair agreement with Kesmeyanov, et a1.,4who obtained a slope of -8292 between 240 and 375'. Our result disagrees, however, with that of Lyons and Silvestri,j who obtained a slope of -6600 between 434 and 695'. Although not pointed out by these authors, CdsAsz undergoes a phase transition a t 578'" and, in fact, their dew point data do show a slight change in slope, the slopes being estimated as -6400 above 578" and -6800 below that temperature. This, however, is not sufficient to bring their results into agreement with those reported here. It may be noted that X-ray powder photographs taken a t 20, 200, 400, 553, and 595" showed that no phase transition occurred in the present samples between room temperature and 553O but that a transition did occur between this temperature and 595". This confirmed that the sample was the stable, low-temperature form and not the hightemperature form in a metastable state, The partial pressures of cadmium and arsenic obtained in individual experiments may be related by correcting the data to constant xenon sensitivity, thus allowing for changes in the sensitivity of the mass spectrometer from one experiment to another. In this way the data of Table V were obtained. It is Table V : Values of the Ratio
~0.172
/PO.OI~
1000/T
T,O K .
Cadmium
Arsenic
2.0
500 526 556
2.29 2.46 2.63
3.76
1.9 1.8
3.98 3.55
evident from these data that the partial pressures of both cadmium and arsenic in the ion source increase as the sample size is increased from 0.012 to 0.172 g. This confirms that, for the smaller sample a t least, equilibrium vapor pressures were not attained. Lyons and Silvestri5used static or equilibrium methods to determine the vapor pressures of the cadmium arsenides. In the interpretation of our results which (10) C . I Whitman, J . Chem P h y s , 20, 161 (1952) (11) M.Hansen and K Anderko, "Constitutlon of Binary Alloys," Second Ed., McGraw-Hi11 Book Co , Inc , Xew York, X Y 1968
Volume 68,3'umber 3
March, 1964
J. B. WESTMORE, K. H. MANN,AND -4.W. TICKSER
610
follows, we assume that true equilibrium was not attained in our measurements and that this accounts for most of the difference in slope between the values reported here and those of Lyons and Silvestri. Since Xesmeyanov, et aL14used an effusion technique it seems probable that their results do not represent true equilibrium values. In Table VI the ratio of the arsenic and cadmium ion currents is tabulated at selected values of 1000/T. Table VI : Values of the Ratio z B A s / I C d l l 4
--
Sample size, g.-----
1000/T
T ,OK.
0.012
0 172
0 350 (approx.)
2.0 1.9 1.8
500 526 556
1.41 1.74 2.14
2.46 2.66 2.88
2.69 2.82 2.98
Since the net rate of decomposition of CdsAszis balanced by the loss of material by effusion, and the parameters governing effusion are the same for both cadmium and arsenic, their relative partial pressures in the vapor should be independent of temperature and sample area if the cadmium and arsenic formed in the dissociation vaporize in stoichiometric proportions. As the data of Table VI show, the ratio of arsenic to cadmium in the vapor increases both with increasing temperature and increasing ratio of surface to effusion area. Thus, although the decomposition presumably occurs according to reaction 1, the products do not appear to vaporize stoichiometrically. The relative ionization cross sections for cadmium and arsenic have been estimated by Otvos and Stevenson12 to be &a1= 22.1 and &.A,: = 18.7 for singly charged ions produced by electrons of 50 to 100 v. energy. Ignoring mass discrimination effects in the spectrometer, which are expected to be small, the ratio of the ion currents for stoichiometric vaporization is given by
1 3 ICdII,
PAS,
PCd
X 4 X
x dl x
Q491
=
CdsXsz(s)
3.1’7
3Cd(s)
+ 2As(s)
3Cd(s) I -3Cd(g)
0.289
Table 1‘1 shows that this value is approached only for the highest temperatures and surface areas used. This, together with the initial vaporization behavior, indicates that the arsenic is vaporizing less readily than the cadmium to give an arsenic-rich layer on the surface of the solid phase, in which, at first, the concentration of arsenic increases with time. The phase diagram11 shows no immiscibility in the cadmium-arsenic system for the range 0 to 70 atom T h e Jnitrnal of Physical Chemistry
arsenic. At higher concentrations, no data are available but, assuming that a complete range of solid solutions is possible, it is postulated that a concentration gradient exists in the surface layer ranging from 40 atom % arsenic (Cd3-4s2)at deeper levels to a higher arsenic concentration a t the surface. The surface arsenic concentration will depend on the relative rates of vaporization and condensation of both cadmium and arsenic, as well as on the rate of diffusion of cadmium to the surface. The initial vaporization behavior seems to indicate that the rate of diffusion of cadmium to the surface is not rate controlling and that the rate of vaporization of arsenic increases as the surface arsenic concentration, possibly as the free element, increases. Results obtained with the smallest sarnple (Table 111) suggest that the rate of diffusion of cadmium to the surface may become important when the surface area becomes sufficiently small. Assuming that the accommodation coefficient for cadmium is close to unity, the effective surface area of this sample is only a little greater than the total effusion area and the loss by effusion is therefore relatively large. It follows that the cadmium concentration at the surface is maintained largely by diffusion from the interior and this may explain the low values of the cadmium slope in Table 111. The above explanation requires that there should be an energy barrier to the evaporation of the arsenic. ,4n energy barrier, or activation energy, of about 10 kcal./mole has been observed in the vaporization of elemental arsenic13 and attributed to rearrangement of arsenic atoms into As4 molecules which do not exist as such in the arsenic lattice; neither do they exist in the CdaAszlattice,14so that in this case too an energy barrier for arsenic vaporization seems likely. I Ti. Calculation of Thermodynavaic Quantities. Thermodynamic quantities are obtained from the experimental results by interpreting them in terms of the surface reactions
2-44s)
0.5As4(g)
(3) (4)
(5)
in which the cadmium vaporizes as rapidly as it is formed. It follows that measurement of the variation of the cadmium pressure with temperature will (12) J. R. Otvos and D. P. Stevenson, J . Am. Cham. SOC.,78, 546
(1956). (13) L. Brewer and J. S. Kane, J . P h y s . Chem., 59, 105 (1955). (14) M . Stackelberg and R. Paulus, 2. physik. Chem.. B28, 427 (1935).
NOXSTOICHIOMETRIC VAPORIZATION OF CADMICN ARSENIDE
yield the heal of dissociation of CdsAsz. The variation of the arsenic pressure with temperature will give a result equal to or greater than this depending upon the extent to which the steady-state pressure falls below the equilibrium value. The most reliable eriperimental result is obtained from the data of Table I1 and is represented bj7 log
pCd
== constant
- 8083:'T
from which is follon s that AH = 37.0 i 0.5 kcal. / mole of Cd or 111.0 1.5 kcal., mole of Cd3As2a t 52OoK1.,the mean temperature a t which the measurements were made. This leads to a value of AHzg8== 112.0 f 1.5 kcal.,'mole, based on the heat capacity data of Kelleyl5 and assuming that the specific heat of arsenic does not change in the dissociation. Lyons and Silvestri5 studied the dissociation under equilibrium conditions and interpreted their results in terms of reaction 1. They found AH for the dissociation to be 106 kcal. mole over the temperature range 434 to 696'. If, however, a slight change in slope in their data at 678" is taken into account, their results lead to a value of AH = 109 kcal. {mole for the temperature range 434 to 578", and thus to a value of AH2ga = 113 kcal./rnole, assuming that the specific heats of cadmium and arsenic are unchanged in Cd38sz. This value agrees well with the one obtained in this work. The heat of formation of Cd3Aszcan be calculated from eq. 1 using the heats of sublimation of cadmium and arsenic given by Stull and Siiike16and taking AHzg8 = 112.0 kcal. 'mole. On this basis A H f o is found to be 14.5 * 3.0 kcal. 'mole in reasonable agreement with the value of 101.0 f 2.0 kcal. mole reported by Shchukarev, et al. l7 1'. Ezperzinents with Arsenic. An reported in sections I and 11, seveial experiments were performed using pure arsenic in order to verify that the mass spectrum of the vapor from Cd3As2(arose from ionization of As4 molecules rather than Cd3As2molecules or other arsenic species. In addition, the variation with temperature of the arsenic pressure above solid arsenic
Table VI1 : Slopes of log I
us.
1 / T Plots for Arsenic
Expt no
Temp OC
1
180-258 210-251 207-248 209-246
2 3 4
61 1
was measured and the results are given in Table VI1 These results lead to a heat of sublimation of 43.0 + 0.4 kcal./mole of Asi a t 298°K. This value is in reasonable agreement with the value reported by Kane and Reynolds6 for large orifice sublimation but is nearly 10 kcal. 'mole higher than values obtained by equilibrium methods. l6 As pointed out by Brewer and Kane,13an activation energy of 10 kcal. 'mole would correspond to an accommodation coefficient of about 10W4a t 55O0K.,which they found to be in accord with their experimentally determined vapor pressures using an effusion cell. Consideration of eq. A3 (see Appendix) for the case where a is very much smaller than f shows that the present results give the activation energy of sublimation rather than the true heat of sublimation. Furthermore, it seems unlikely that the present apparatus can be modified to give reliable values for the heat of sublimation of elements having very low accommodation coefficients.
Acknowledgment. The authors wish to express their gratitude to N r . T'. J. Silvestri and Dr. R. D. Heyding for supplying the cadmium arsenide and arsenic used, and to Drs. J. B. Taylor and L. D . Calvert for X-ray diffraction studies and helpful discussion of the crystalline states of these materials. Appendix The experimental apparatus used in this work essentially constitutes an effusion cell and the results are subject to many of the same uncertainties in the relationship between observed steady-state pressures and equilibriurn values which are encountered in effusion experiments. Since, under steady-state conditions. the rate of vaporization is equal to the sum of the rates of condensation and effusion, it can be shown from kinetic theory that
P = p + Pa z
W)
where P is the equilibrium pressure, p is the steadystate pressure in the cell, a is the accommodation coefficient, a is the effective effusion area, and A is the effective surface area of the condensed phase. If a t A is represented byf, eq. A1 becomes
Slope
Mean
9015 9237 9370 9338 9240 i 82
(15) K. K. Kelley, U. 9. Bur. hlines Bull. 584, E. S.Govt. Printing Office, Washington, D. C., 1960. (16) D. R. Stull and G. C. Sinke, Thermodynamic Properties of the Elements, Advances in Chemistry Series. N o . 18, American Chemical Society, Washington, D. C., 1956. (17) S. A . Shchukarer. A I . P. SIoroanva, and SI. hI. Bortnikova, Zh. Obshch. Khim., 28, 3289 (1958).
Volume 68, S u m b e r 3
March. 1964
612
N. A. DAUGHERTY A N D T. W. KEWTON
P
When a is near unity, AH' is very small and
When f is small and a is close to unity, the steady-state pressure will not differ significantly from the equilibrium value, For the case of sublimation the equilibrium pressure, P , is related to the heat of sublimation AH by the ex. The accommodation coefpression P ficient, a , may be similarly related to an activation e-A"'RT . Equation A2 energy, AH', so that a then gives
-
d 10gp _ _ _-- -AH d ( 1 / T ) 2.303B so that a reliable value of the heat of sublimation is obtained. If, however, a is very much smaller than f , then
-
+
and the activation energy of sublimation, AH AH', is obtained. It may be possible in certain circumstances to set limits on the value of a by varying f and utilizing eq. A2 and A3.
The Kinetics of the Reaction between Vanadium(II1) and Vanadium(V)l
by N. A. Daugherty2and T. 711. Newton U n i w r s i t y of California, L o s Alamos Scientific Laboratory, Los Alamos, New Mexico (Reeeiaed October 19, lOF.9)
+
The kinetics of the reaction V(I1T) V(V) = 2V(IV) have been studied in acid perchlorate solutions from 0.02 to 2.0 "I4 in HC104 over a temperature range from 0.2 to 34.2'. The rate law is -d[V(V)]/dt = k'[V(III)][V(V)] where k' is given by 12' = L 2 [ H + I e 2 k-I[H+]-' ko kl[H+]. The k-l[H+l-I term predominates over most of the [H+]range studied; values of AH* and AS* for the path corresponding to this term are 16.5 i 0.1 kcal./mole and 7.1 i 0.5 e.u. The present results are compared with a previous indirect determination of the rate law.
+
+ +
Introduction This paper reports on a continuation of our study of the kinetics of the reduction reactions of the pervanadyl ion, V 0 2 + , in aqueous solutions. The reaction between V02+and Vef2 has been previously de~cribed.~ Some information on the V(II1)-V(V) reaction is already available in the work of Higginson and Sykes* on the kinetics of the oxidation of V(II1) by Fe(111). The rate law for that reaction was found to be T h e Journal of Physical Chemistry
-d[Fe(III)]/dt
-d[V(III)]/dt = IC1 [Fe(III)I [V(III)I kl" [Fe(III) ] [V(III) 1 [V(IV) I/ [Fe(II)] =
+
(1)
(1) Work done under the auspices of the U. 9. Atomic Energy Commission. (2) Lcs Alamos Scientific Laboratory, Summer Staff Member. (3) N. A. Daugherty and T. W. Newton. J . P h y s . Chem., 67, 1090 (1963). (4) W. C. E. Higginson and A. G. Sykes, J . Chem. Soc., 2841 (1962).
