3047
CALIBRATION OF HIGH-TEMPERATURE MASSSPECTROMETERS effect on the diffusion of water is, however, correct. If one introduces some order into the system by making gEa - gcc = 0 gaw
=
[uagww
+
awgaal/(aa
+ a,)
becomes larger. For K I solutions this alteration is
sufficient to cause B to become negative but remain much too small in magnitude compared with the experimentally obtained E. Acknowledgment. The authors wish to acknowledge the helpful discussions of D. W. McCall and the aid of R. L. Kornegay with the computer calculations.
A Technique for the Calibration of High-Temperature Mass Spectrometers1 by R. T. Grimley2 and T. E. Joyce3 Department of Chemistry, Purdue Unthersity, Lufayette, Indiana
47907
(Received October 14, 1968)
A calibration procedure for high-temperature mass spectrometers which involves the use of a newly developed dual-cell system is described. Partial pressure data resulting from the application of this technique to the potassium chloride vapor system are reported.
Introduction A number of techniques have been developed which, in principle, can be used to convert intensity measurements obtained via mass spectrometric Knudsen cell studies into pressure or pressure ratio data. Among the procedures proposed to date are the (1) quantitative vaporization of a known mass of a standard substance in conjunction with mass spectrometric intensity data obtained from the system under investigation, (2) quantitative vaporization of a known mass of the substance under investigation in conjunction with mass spectrometric intensity data from the same system, (3) comparison of the ion intensity data of the substance under study and a standard for which accurate pressure data are known, (4) use of the X+/ X f2 ion intensity ratios provided that independent equilibrium constant information for the dissociation reaction is known, ( 5 ) two-temperature Knudsen cell technique, (6) use of mass spectrometric intensity data and independent weight-loss measurements as a function of temperature. Recently other investigations in the laboratory required that we determine the partial pressures of the vapor species in equilibrium with solid KC1. The KC1 system has been the subject of a number of mass spectrometric studies.@-14 These papers have reported the ionic species and the second-law heats of sublimation. It is extremely inconvenient or not feasible to use the established procedures to obtain the mass spectrometric pressure calibration for the potassium chloride and similar type systems. This explains in part the absence of partial pressure data for KC1 derived from mass spectrometric measurements.
In each of the calibration methods, a single Knudsen cell is used except for the two-temperature method in which two cells are interconnected, only one of which has an effusion orifice. Thus any compounds or standards used in a vaporization study with present methods come into contact in either the condensed or gas phase. The use of the single cell with procedure 1is not possible in this instance because of the unavailability of acceptable calibration substances. The quantitative vaporization of KC1 from a single cell, i.e., method 2, is a possible method of choice. However, if a single cell is used, the sample must be of sufficient size such that (1) Work supported by the U. S. Atomic Energy Commission. (2) Person to whom correspondence should be addressed. (3) This paper contains material taken from a dissertation submitted by T. E. Joyce to the Faculty of Purdue University in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Aug 1968. (4) .M.G. Inghram and J. Drowart, “Mass Spectrometry Applied to High Temperature Chemistry,” Proceedings of the International Symposium on High Temperature Technology, Asilomar, Calif., 1959, McGraw-Hill Book Co., New York, N. Y. ( 5 ) R. T. Grimley, “Mass Spectrometry,” “The Characterization of High Temperature Vapors,” John Wiley & Sons, Inc., New York, N. Y., 1967. (6) (a) T. A. Milne, J. Chem. Phys., 28, 717 (1958); (b) J. Berkowita, H. A. Tasman, and W. A. Chupka, ibid., 36, 2170 (1962). (7) P. A. Akishin, L. K . Gorokhov, and L. N. Sidorov, Dokl. A k a d . N a u k SSSR, 135, 113 (1960). (8) E. D. Cater and R. J. Thorn, J. Chem. Phys., 44, 1342 (1966). (9) R. Hobson, {bid,, 23, 2463 (1955). (10) T. A. Milne, H. Klein, and D. Cubicciotti, ibid., 28, 718 (1958). (11) T. A. Milne and D. Cubicciotti, ibid., 28, 846 (1958). (12) J. Berkowita and W. Chupka, ibid., 29, 653 (1958). (13) T. A. Milne, ibid., 32, 1275 (1960). (14) T. A. Milne and H. Klein, ibid., 33, 1628 (1960). Volume 79, Number 9
September 1969
R. T. GRIMLEY AND T. E. JOYCE
3048 equilibrium vaporization is assured and reproducible intensity values are achieved for the various species. If intensity measurements are made at several temperatures, integration of the data and correction to the reference temperature becomes extremely cumbersome. With the large samples required for equilibrium measurements, the integration time frequently becomes unmanageable. Method 3 is difficult to use with the single-cell technique since the standard must have a vapor pressure close to that of the system under study. Furthermore, the system and the standard should not react chemically. In practice this method has seldom been used with a single-cell arrangement. The use of method 4 has been limited to permanent gases such as 02 where the Oz+-O+ ions peaks are used. In view of the fact that independent data on the KC1 monomerdimer equilibrium are not available, the method is not suitable for use with the KC1 system. The information obtained from the two-temperature procedure (method 5 ) is complementary to the other methods in that relative ionization cross sections are obtained. The majority of workers who have reported pressure data on KC1 have used the conventional Knudsen weight loss, transpiration, or hot wire techniques. These studies assumed monomeric vapor species, however, and there is moderate disagreement among these workers. The only attempt at partial pressure measurement of the monomer and dimer species was reported by Miller and Kusch,16who used velocity distribution curves. We have developed a technique which permits determination of the partial pressures of systems such as KCl and which, at the same time, eliminates many of the disadvantages of previous techniques. This method is termed the dual-cell technique. We propose to describe the equipment and its application to the determination of partial pressures of the equilibrium KC1 (gas-solid) system.
Apparatus The mass spectrometer used in this research was a 60" sector field, 30.5-cm radius of curvature, first-order, direction focusing instrument and was operated at an approximate resolution of 1/1000. The high-temperature assembly and source were mounted in the vertical direction to maximize machine stability under hightemperature operating conditions. The analyzer, source, and high-temperature sections of the mass spectrometer were differentially pumped by means of mercury diffusion and ion pumps. The ion pumps could be isolated from the mercury pumps, and thus it was possible to use ion pumping exclusively when desired. Machine pressures of Torr or lower were routinely maintained during high-temperature operation. The dual-cell assembly consists of two separate Knudsen cells which are independently mounted, heated, and shielded. The more prominent features of The Journal of Physical Chemistry
/J
I K
H
E D
G
C A
B
7
I,
12
0
U
Figure 1. Cross-sectional view of the dual-cell assembly: A, rail; B, rail support blocks; C, sled; D, support platform; E, furnace support; F, winding support; G, cell support; H, support rod; I, Knudsen cell; J, heat shields; K, bottom heat shields.
the unit are shown in the cross-sectional view, Figure 1. Either cell can be precisely located below the shutter and entrance slit of the ion source. The assembly was designed to fit our standard mass spectrometer base plate configuration. Except where noted the material used in construction was Inconel 600. The cell and furnace assemblies are mounted on a common sled which is capable of linear motion along a rail. The rail, A, is a bar which is mounted above the base plate by the rail support blocks, B, a t the ends of the rail. The sled, C, surrounds the rail on four sides and is driven from below by a rack and pinion gear arrangement (not shown). The gear is driven by a modified Ultek No. 80-334, direct drive, rotary feedthrough. Precision stops are used to limit the travel of the sled in either direction. Plate, D, which is located immediately above the sled provides a platform to mount the supports, E, for the furnace windings. There are three winding supports, F, to a furnace, and these are made of Lucalox alumina. The furnace windings are bifilarly wound Pt-lO% R h alloy wire. The furnaces were independently controlled by two Hyperion HYSi- 15-10 dc power supplies, With this arrangement cell temperatures were held to *0.lo. Mounted directly on the sled are the cell supports, G, which hold and position the precision ground alumina support rod, H. The Knudsen cell, I, is located on top of the support rod. Both cells were routinely jig aligned prior to a run. The orifice was drilled through 0.002-in. thick tantalum foil and was secured to the cell body by squeezing the foil between a lid with a wide opening and the cell body proper. The cell orifices were 0.040 in. in (15) R. C.Miller and P. Kusch, J . Phys. Chem., 25,860 (1956).
CALIBRATION OF HIGH-TEMPERATURE MASS SPECTROMETERS diameter. The heat shields, J, are constructed of 0.002-in. tantalum foil and are constrained by split rings. The bottom heat shields, K, are supported by 0.060-in. tungsten rods. Chromel-alumel thermocouples used to measure cell temperatures were peened into the bottoms of the Knudsen cells. A gradient of approximately 4' existed between the thermocouple and the interior cell temperature at the sample surface. The working thermocouples were previously calibrated against a Pt--Pt-Rhlo reference thermocouple.
3049
units, u = ionization cross section, y = multiplier efficiency, E = E(measured) - AP (appearance potential). The subscript u refers to the species under study and c refers to a species from the standard calibration substance. To calculate the pressure, P,, the calibration factor ( P c / I c + T c is ) determined from intensity data of the small weighed sample. The Knudsen equation'e for a single species is
Calibration Procedure The three most abundant ion peaks in the mass spectrum of KC1 are K+, KC1+, and K2C1+. The KaCl2+ peak has previously been reported and a very low intensity peak of K4C13+ was also found in this work. Only the three most abundant peaks were considered since the higher mass peaks were of negligible intensity. The dual-cell calibration technique allows substantial flexibility in the use of procedures developed for the single cell. In this work one cell was loaded with a small, weighed sample (approximately 3 mg) of reagent grade KC1 powder. The second cell contained a KC1 single crystal with the (100) face exposed. Prior to the use of the KCl single crystal sample, separate experiments were run in which a finely powdered sample of reagent grade KC1 was placed in one cell and a KC1 single crystal with the (100) plane exposed was placed in the other cell. The orifice diameters, internal geometry, and volume were identical in both cases. When both samples were heated to identical temperatures over the temperature range of interest, the ion intensities for a given vapor species from the two cells were equal. The single crystal sample was used for handling convenience. The cell containing the 3-mg sample was first aligned with the source and then heated. The intensity, I+,of the KSgpeak was followed us. time until the sample was exhausted. During the course of the quantitative vaporization, checks were made on the intensities of the KCF', KtC1113ion peaks. Temperature measurements were made frequently during the course of the calibration. The major part of the vaporization occurred a t the preset reference temperature of 605'. The cell containing the single crystal was then positioned under the source and heated. Intensity measurements were made on the K+, KC1+, and K2C1+ ion species at 20' intervals in the temperature range 530-610". Repeat measurements were made a t each temperature by cycling the temperature at least three times to ensure the reproducibility of the peak intensities for the various ions. The value of the absolute pressure for each species can be determined from the intensity data according to the equation
(&)(2)(:)(%)
P , = I,+T, Ic+Tc
LE,
where g, is the number of grams of species i which vaporize during time, t, through an orifice of s cm2 area, and M e is the molecular weight of species i. The calibration factor is obtained from eq 2 (3)
If we replace the product I,+t by the integral
J0 I , +dt = A , , then (4)
It should be noted that the value for A , must be corrected for the isotope abundance of the appropriate ion species since g, refers to the mass contribution from all isotopes. Data taken at temperatures other than the reference temperature are corrected to the reference temperaturen6 The total number of KC1 ion pairs, Z,, in the solid sample is given by the relation zt
=
ZKCl
+ 2ZKzClz = MKCI - g N
(5)
where ZKCl = the total number of molecules which vaporize as monomer, Z K ~ C=I ~the total number of molecules which vaporize as dimer, g = the sample ~ weight of KC1, N = Avogadro's number, and M K C = the formula weight of KC1. For any species i the kinetic theory shows that
where v, = number of molecules em-* sec-l, E~ = average velocity, and k = Boltzmann constant. It has previously been shown by Honig" that
(7) where K' is a constant. To use eq 7 it is necessary to relate which fraction of the intensity of an ion peak may
(1)
where P = pressure, I + = ion intensity in arbitrary
(16) M.Knudsen, Ann. Phys., 28, 75 (1909). (17) R. E.Honig, J. Chem. Phys., 2 2 , 126 (1964). volume ?'$? Number 9 September 1969
3050
R. T . GRIMLEYAND T. E. JOYCE
be associated with a given neutral precursor. The ionization processes which are commonly proposed for the KC1 system are
+ e +K2Cl++ C1 + 2e KzCh + e +KC1+ + KC1 + 2e KzCl2 + e +K + + KC1 + C1 + 2e KC1 + e +KC1+ + 2e + C1 + 2e KC1 + e +K+ KzClz
(8)
(9) (10) (11) (12)
Sidorov, Gorokhov, and Akishin7J8 have proposed the use of the two-temperature cell to determine the relative contributions of various possible ionization processes for complex systems in general, and in particular for the cesium halide systems. It should be noted, however, that the equations solved for the CsX system have assumed that all reactions similar to eq 8 through 12 contribute to the ion peaks. There is strong evidence which suggests that eq 8, 11, and 12 are the main processes by which K+, KCl+, and KzCl+ are formed. Second-law measurements on the K+, KC1+, and K2CI+ 0.6 kcal ions yield the following values: K+, 49.5 mol-'; KC1+, 50.0 0.7 kcal mol-'; KzCl+, 58.0 f 1.0 kcal mol-'. These results indicate that the heat of sublimation of the dimer exceeds that of the monomer by no less than 8 kcal mol-'. Let us assume that K + peak is derived exclusively from ionization of the monomer. If the KCl+ ion intensity results both from monomer and dimer ionization, then the slope would be intermediate between that observed for K + and K2C1+. Within the error limits of our measurements, the intermediate slope is not observed. Let us now consider the case where dimer and monomer ion products are assumed to contribute to the KC1+ and K + ion intensities. Under these assumed conditions, at a given temperature, the K ion intensity is proportional to the sum of the cross section-pressure products of the monomer and dimer. A similar relationship holds for the KCl+ ion ratio, C~ it ~is intensity. If one examines the I K + / I K apparent that the pressure terms in the relation must be temperature dependent since the heats of sublimation of the monomer and dimer differ. The only condition under which the intensity ratio could be temperature independent wouId be the highly unlikely situation in which the ratio of the dimer cross sections for the processes producing KC1+ and K + is equal to the ratio of the monomer cross sections for the processes producing KC1+ and K+. The I K + / I K C ~ + ratio is observed to be constant with temperature. Further support of these arguments is seen in the angular distribution studies of molecular effusion reported by Grimley and Muenowle in which the distribution curve of the K2Cl+ ion was substantially different from that of the K + ion. Furthermore, the curves for K + and KCl+ were identical. If the KC1+ peak were the result of ion contributions from the mon-
*
The Journal of Physical Chemistry
*
omer and dimer species, differences in the mmomerdimer pressure ratio should cause a change in the shape of the distribution curve as the temperature is varied. Since the AH,,b of the dimer is greater than that of the monomer, the KC1+ curve should shift toward the dimer distribution curve as the temperature is increased. This effect is not observed. Except for inconsequential contributions, we believe the K + and KCl+ peaks are derived from KCl(g). For the species K + and KC1+ an equation will relate the partial pressure of the KC1 monomer to the ion intensity P(KC1) = P(KC1) =
K'I +(K +) T a (K +) y (K +) AE (K +)
K 'I +(KC1+) T (aKCl+)y (KCl+)AE(KCI+)
(13) (14)
where a(K+) and a(KCl+) are the cross sections for the processes projected in eq 11and 12. A decision has to be made at this point in terms of the use of the K+-KCl+ ion intensity data. Since the processes involved in the formation of K + and KzC1+ are similar in nature, we have arbitrarily assigned the cross section for the monomer to the process shown in eq 12 and the dimer cross section to the process shown in eq 8. An alternate choice would have been to assign the total cross section to the sum of the cross sections of eq 11 and 12. If eq 7 is substituted into eq 6, we obtain for the two species the equations ZKCl
ZKCl
=
=
K'sC(KC1) S > + ( K + ) d t (15) 4ka (K +) y (K +) AE(K +) o
K'sC(KZC12) 4ka(K2C1+)y(K&l+) AE(K2C1+) Pt
J o I +(K2Cl+)di (16) For convenience in handling the data, the ratio (ZKC~/ Z K ~= C ~a ~is used. In this calculation the additivity assumption of Otvos and Stevensonz0 is made that u(K2Cl+) = 2a(K+), and the ratio (K2Cl+)/y(K+) used was corrected for molecular effects where necessary. Substitution in eq 15 and 16 results in the relation a =
2.07
AB (K2C1+ ) A2 (K +) AE (K +)A 1 (K&l+)
(17)
Appearance potentials were measured by use of the linear extrapolation technique and yielded the following values: K + , 10.6 eV; KCl+, 10.1 eV; K2C1+, 10.4 eV. (18) L. N. Sidorov and P. A. Akishin, Dokl. Akad. Nauk SSSR,151, 136 (1963). (19) R. T. Grimley and D. W. Muenow, J . Chem. Phys., 46, 3260 (1967). (20) J. W. Otvos and D. P. Stevenson, J . Aner. Chem. Soc., 78, 646 (1956).
CALIBRATION OF HIGH-TEMPERATURE MASSSPECTROMETERS The spectroscopic ionization potential of mercury (10.4 eV) was used as a reference for the energy scale. Measurements were made using 18-eV electrons, and thus the values of AE used were K f , 7.4; KC1+, 7.9; and K2C1+,7.6. We now substitute in eq 5 for Z K ~ C I ~
( + t)
2, = ZRCl 1
where fl = 1
+ 2/a.
=
N
~
= ZKCI@ (18)
MKC~
In addition
3051
log P (dimer) =
-+ 8.256 T 12,635
(23)
The agreement among the runs is seen to be quite excellent, and the scatter is better than one normally observes in high-temperature vaporization studies. Several possibilities exist for the comparison of these results with the data of other workers. The results of the dual-cell studies may be compared with (1) independent Table I1 : Pressure Data for the KCl System
where YKCl = number of grams of sample which vaporize as the monomer. The calibration factor using the monomer is
where A ,(K+) := L ' I + ( K + ) d t .
If we solve the ZKCIin eq 18 using eq 19, we find that = g/P. Substitution for g K C l in eq 20 gives the final calibration equation
gKCl
PKCl
--
I+(K+)T
-
'/2
(Z)
flsA,(K+) .d!f~ciT
(21)
Run no.
T,OK
12-10 12-11 12-12 12-10 12-11 12-12 12-10 12-11 12-12 12-10 12-11 12-12 12-10 12-11 12-12
800.1 800.1 800.1 819.9 819.9 819.9 839.8 839.8 839.8 859.9 859.9 859.9 880.2 880.2 880.2
'O'*11.4
11.6
PKCI, atm
2.54 x 2.67 X 2.80 x 5.62 X 5.91 x 6.00 X 1.18 x 1.25 x 1.21 x 2.32 X 2.40 X 2.41 X 4.53 x 4.67 x 4.70 X
PK~C atm I~,
10-7
2.55 2.86 2.97 6.55 7.31 7.30 1.57 1.60 1.63 3.58 3.65 3.61 7.66 7.93 8.10
10-7 10-6 10-6 10-6
10-6
10-6
x x x x x x x x x x x x x x x
10-8
10-8 10-8 10-8 10-8 10-8 10-7 10-7 10-7 10-7 10-7 10-7 10-7 10-7
Results In this work three separate calibration runs were made. A sampling of the raw I + T data for one run is shown in Table I. The rounded values of the param-
Table I : Raw Z+T Data for the Ionic Species Kas, KCP4, and K&l11a (Run No. 12-11) (in Arbitrary Units) T, "K
800.1 819.9 839.8 859.9 880.2
K8Q
3.72 X 8.24 x 1.75 X 3.35 X 6.51 X
lo7 107 lo8 IO8 lo8
KCIT*
KzCl"*
7 . 4 4 x 106 1 . 6 5 X lo7 3.40 x 107 6.48 x 107 1 . 3 3 X lo8
6 . 0 0 X lo6 1.53 x 107 3.36 x 107 7 . e 5 x 107 1 . 6 6 X 108
eters contained in eq 21 are: run 12-10, g = @ = 1.331, A , = 5.115 X lo9;run 12-11, g = @ = 1.331, A , .- 3.369 X lo9; run 12-12, g = fl = 1.335, A , = 2.661 X lo9. The pressures
3.25 mg, 2.95 mg, 3.00 mg, obtained from the three runs are shown in Table I1 and in Figure 2. Least-squares fits of the log pressure (atm) vs. 104/T plots for the monomer and dimer are given by the equations log P (monomer) and
=
10,793 - T
+ 6.931
(22)
11.8
12.0
12.2
12.4
12.6
I O ~ / TOK Figure 2. Partial pressures (in atmospheres) of the KCl(g) and KtCl%(g)equilibrium vapor species us. lO4/T. Volume 7.9, Number 9 September 1690
R. T. GRIMLEY AND T. E. JOYCE
3052
THIS WORK MILLER AND KUSCH ----__ZlMM AND MAYER MAYER AND WINTNER TREADWELL AND WERNER TOTAL PRESSURE
where iKC1 and refer to the hot wire ion currents arising from monomer and dimer, respectively. Thus one would expect the Zimm and Mayer total pressure data to fall slightly below the actual total pressure. While the Zimm and l‘Iayer data are slightly below our measurements, a quantitative comparison is not possible. The “JANAF Thermochemical Tables”2ahave presented a compilation of data on the KC1 system based on an analysis of P V T data and transpiration and effusion measurements. A comparison of the results of this work with the JANAF tabulation is shown in Table 111. The agreement is seen to be quite good. The Table I11 : A Comparison of the Result,s of This Work with the JANAF Tabulation for the KC1 Syst,em
Figure 3. Comparison of the partial pressures obtained by the dual-cell calibration procedure with the results obtained by other workers.
monomer-dimer partial pressure data, ( 2 ) independent total pressure determinations, and ( 3 ) partial pressure values obtained from combined weight loss and mass spectrometric data. As was previously mentioned, the only independent data on the monomer-dimer partial pressures are those of lliller and Kusch,21who obtained their results indirectly through velocity distribution studies. The monomer pressures reported by Miller and Kusch are higher than the values obtained in this work. I n addition, the dimer pressures and slope are seen in Figure 3 to differ from our results. Knudsen cell studies in which a hot wire detector was used have been reported by Zimm and &Iayer.22 The total pressures obtained from our work are plotted in Figure 3 and are virtually identical with the total pressures reported by Zimm and &.layer. It should be noted, however, that Zimm and &layer assumed only monomeric vapor species. If the assumption is made that both monomer and dimer vapor species contribute one ion per molecule, it may be shown using eq 2 of Zimm and NIayer that the ratio of the pressure assuming dimers, P a o t u a l , to the pressure assuming no dimer, P Z M , is given by equation
~-
Paotual PZM
-
+ 1.414i~~c1~
~KCI
Z‘KC1-k iKlCl2
T h e Journal of Physical Chemistry
(24)
--PKcI, This work
atm-
T,”K
800 900
2.7 X 8.7 x
2 . 3 X lo-’ 7.9 X
-------PK~CI~
JANAF
This work
2.9 X 1.6 X
atm-JANAF
4 . 2 X lo-* 2.3 X
heat of sublimation obtained from slope measurements of the monomer at 850°K is reported by the JANAF tables as 50.6 kcal/mol compared to our 49.4 ltcal/mol. For the dimer the JANAF value is 57.2 kcal/mol, whereas our value is 57.8 kcal/mol. The final basis for comparison involves the method proposed by Cater and Thorn.8 In the CT method two types of measurements are used. Total weight loss data are obtained from effusion experiments, and intensity data are obtained from mass spectrometric measurements. The use of this method eliminates the need for estimated ionization cross sections. To determine the partial pressures by the Cater-Thorn method, the ion intensity data from this study were used in conjunction with the Mnudsen effusion data of Mayer and Wintner (lIW)24and the transpiration studies of Treadwell and Werner (TW) .26 A separate series of r e functions, which are defined by the equation r e = n
W(2nRT)”2= i
i14,”zPp,, were calculated at 10” in2-1
tervals from 800 to 880°K for both MW and TW studies. By use of eq 16 of Cater and Thorn, our mass spectrometric intensity data, and the r functions previously calculated, partial pressure data for the monomer were determined. The dimer partial pressures were similarly calculated. Six separate values for each of the (21) R. C. Miller and P. Kusch, J . Chem. Phys., 25, 860 (1955). (22) B. H. Zimm and J. E. Mayer, ibid., 12, 362 (1944). (23) “JANAF Thermochemical Tables,” First Addendum, PB 168 370-1 (1966). (24) J. E. Mayer and I. H. Wintner, J . Chem. Phys., 6, 301 (1938). (25) W. D. Treadwell and W. Werner, H e h . Chim. Acta, 36, 1436 (1963).
CALIBRATION OF HIGH-TEMPERATURE ~ ~ I A SSPECTROMETERS S monomer and dimer pressures were obtained a t each temperature. Examination of Figure 3 reveals that the monomer pressure values cluster around the partial pressure measurements which were made by the dualcell technique. The agreement among the dimer data resulting from the various possible combinations is seen to be poor. Although there is admitted uncertainty in the dual-cell work due to cross-section uncertainties, the scatter of the dimer partial pressures is considerably less than that obtained using the C T method. I n view of the large uncertainty in the dimer partial pressures as calculated by the CT method, it would be difficult to claim that the absolute accuracy of the CT method is greater than that obtained by the dual-cell procedure. Furthermore, the second-law heats of sublimation as obtained by the CT treatment are lower than the mass spectrometric results. Since the second-law mass spectrometric measurements require no cross-section assumption except for the constancy of the ionization cross section with temperature, we feel these measurements are reasonably accurate. I n the Cater-Thorn procedure slight changes in the slopes of either the mass spectrometric or weight loss data result in a magnification of the dimer data scatter. I n measurements of
3053
systems such as KCl, the dual-cell technique appears to be superior to other existing methods. While we have used the dual-cell technique as a modification of procedure 2 listed in the Introduction, it is obvious that the dual cell may also be used to great advantage with procedures 1 and 3. The problems commonly encountered with the single cell using procedure 1 involve (a) chemical reaction between the sample and the calibration material, (b) unavailability of a calibration material with the desired vapor pressure characteristics, and (c) incompatibility of the sample or calibration substance with the cell. Since the sample and calibration substance are in separate cells in the dual-cell arrangement, the vapor pressure characteristics of neither material are a limitation. I n procedure 3 the calibration constants may be obtained from the mass spectrometer intensity-temperature data and from previously determined vapor pressure data. The use of the single cell in this type of determination is not practicable. The dual cell, however, is particularly suited for use with procedure 3. An obvious and quite useful application of the dual cell in conjunction with procedure 3 is the determination of activities.
Volume 78, Number 9 September 1969
