NOTES
892
Results and Discussion The results of conductance measurements on solutions of KBH4 dissolved in 0.0118 N potassium hydroxide are given in Table I ; parallel results on solutions of KBr dissolved in the same standardized potassium hydroxide are shown in Table 11. In both cases, "apparent" equivalent conduct'ances were calculated from the expression 11
=
1000(L - Lo)/c'
TABLE I CONDUCTANCE OF KBHn IN 0.0118 N KOH C' 103~ 10'(L Lo) A(KBH4)
-
.om .loo0 .1500
3.07 5.87 9.7'2 15.92 21.85
0 2.80 6.65 12.85 18.78
... 136.0 133.1 128.5 125.2
TABLE I1 COSDECTANCE OF KBr IN 0.0118 N KOH C'
l0SL
0 0.0190 ,0486 ,0969 ,1544
3.03 5.58 9.41 15.50 22.48
SMOOTHED
1Os(L
- Lo)
0 2.55 6.38 12.47 19.45
TABLE I11 DIFFERENCES IN EQUIVALEXT
bromide ion are quite similar the equivalent conductances of the KBH4 and KBr solutions should be affected in almost exactly the same way by the presence of KOH. Thus a t>reatmentof the data based on the diflerences, AKBH, - AKBr, should permit an extrapolation to infinite dilution. If we apply the Shedlovsky equation4
(1)
where c' is the concentration of KBH4 or KBr in equivalents per liter, L the specific conductance of the mixed electrolyte and Lo that of the pure KOH solution. The conductance measurements present'ed in Table I1 were made several weeks after those shown in Table I, and this may explain the
0 0.0206
Vol. 65
h(KBr) .
I
.
133.9 131.6 128.6 125.9 CONDUCTANCE
C
A ( KB tI4)
A(KBr)
Ah'
0.0306 .0625 .lo56 ,1600
136.2 133 .O 129.0 ,125.2
133.8 131.4 128.8 126.1
2.5 1.7 0.2 -1.0
to solutions of two different electrolytes, 1 and 2, we obtain where M = A, - dland both A2 and AI are values at the same temperature and at the same concentration in a given solvent. A plot of A&' against c should be linea? at sufficiently low concentration and the intercept will givegthe difference between the limiting equivalent conductances at infinite dilution. The value4 of CY* for water at 25.0' is 0.229. In effect, eq. 3 permits one to obtain a fair A, value from data at relatively high concentrations (say 0.02 to 0.2 N ) if data are available for another similar solute at both high and low concentrations. A test of this method with literature data for potassium chloride and potassium nitrate gives Ah0 to within 0.2 unit of the accepted value. Values of A K B H ~and AKBr read from smooth curves of the apparent equivalent conductance against ciI2 are given in Table I11 together with the quantities A&'. A plot of AAo' against c is linear as predicted by eq. 3 and has an intercept of 3.3 =t0.2. Using the known value of A, for potassium bromide, we obtain 155.0 as the equivalent conduct,ance of potassium borohydride at infinite dilution. However, this value is too high because of the hydroxide impurity in the sample. We finally take AOfor KBH4 as 153, with an estimated uncertainty from all sources of f 3. Thus Xo for the borohydride ion at 25" is 80 f 3 ohm-1 cni.2 equiv.-', which may be compared to the values 76.4, 78.2 and 76.9 for C1-, Rr- and I-, respectively.
slight difference in the Lo values. Any small change in the hydroxide concentration can be ignored, however, in computing the total ionic concentration, c. A plot of these apparent equivalent conduct(8) We consoiously ignore the very small known term in E In c. ances versus the square root of the t'otal ionic con- Cf the work of Fuoaa and Onsager described in reference 4, pp. 254centration gives a smooth curve, but the limiting 271.(9) This statement is not exact, but since tho equations for three-ion law cannot be expected to apply to data in the con- systems are known (reference 4, pp. 114-117) it would be entirely centration range studied. Indeed, the accepted feaaible, though tedious. to estimate the small error involved. T h e value of AOfor potassium bromide is 151.7 and this precision of our results seems not to justify the labor. I t can b e that linear extrapolation to eero total concentration c is the value cannot be obtained by conventional extrap- shown most nearly correct procedure for eliminating the B terms. olation of the data in Table 11. Moreover, these solutions of KBH4 and KBr cannot be treated as single electrolytes since there is a LONG RSXGE ATTRACTIVE POTENTIALS third ionic species (OH-) present in appreciable FROM MOLECULAR BEAM STUDIES OK concentration. The Onsager theory predicts4 THE SYSTEMS K,N*(g) AND KCl,Ns(g)' variations from the Kohlrausch principle of indeBYRICHARD C. SCHOONMAKER* pendent ionic mobilities for solutions containing ions of the same sign and very different mobilities. ColumMa Radiation Laboratory, Department of Physics, Columbia University, Mew York, New York Experiments by L o n g s ~ o r t hfor , ~ example, show an Received October S4, 1960 effect of the order of 2.5% in mixed solutions of HC1 and KC1; and our eqiiivalent conductance values in The molecular beam technique is well suited to Table I1 are from 1.5 to 3T0lower than the values determinations of total cross sections for scatterfor pure KBr at the same total ionic concentration. ing of beam molecules by dilute gasesa3 The However, if the mobilities of the borohydride and introduction of velocity selection for the beam molecules facilitates a determination of the de (7) L. G.Longeworth, J . Am. Cham. Soc., 14, 1897 (1930).
NOTES
May, 1961 pendence of the total scattering cross section on the relative velocity of the interacting particles. From such information, the nature of interaction potentials in the dilute gas phase may be inferred. I n the present study velocity-selected molecular beams of K and KCl have been scattered in a defined region by Np(g). Theory Massey and hf0hr4 have considered long range attractive forces which result in predominantly small angle quantum scattering where the interaction potential is of the form V ( r )=
-
(1)
For potentials which fall off more rapidly than the inverse third power, they have derived the following equation which relates the total scattering Cross section to the relative velocity of the interacting particles Q = B(C/vr)*’(*-l) (2) where Q is the total cross section for scattering particles with an interaction potential given by equation 1 and with a relative velocity v,. B is a constant which depends upon s. It should be noted that equation 2 is not exact but is an approximation from quantum theory. For a velocity selected molecular beam interacting with a scattering gas characterized by a Maxwellian distribution, the total scattering cross section may be related to experimentally measureable quantities by the expressions
n
where r
= Bv, 8 =
(4)
(~2/2kT)’/~and t’r = *(I)/?T’h/3
(6)
d is the scattering path length, rn and T are the mass and temperature of the Scattering gas, v is the velocity of beam particles, Z?r is the average relative velocity of the interacting particles, lo is the measured intensity of the molecular beam with no gas in the scattering chamber, and I is the intensity of the beam after introduction of scattering gas a t density ?I molecules per cubic em. If the attenuation of the velocity-selected molecular beam is measured as a function of the scattering gas pressure, the slope of a plot of In I / I o us. p may be used t o determine the quantity A . Combination of equations 2 and 3 and rearrangement results in an expression which allows determination of the exponent for the interaction potential (1). (1) Work supported in part under a joint service contract with the U. S. Army Signal Corps, the Office of Naval Research, and the Air Force Office of Scientific Research, and also in part under a contract with the U. S. Air Force monitored b y the Air Force Office of Scientific Research of the Air Research and Development Command and in part under a contract with the Office of Naval Research. (2) Department of Chemistry, Oberlin College, Oberlin, Ohio. (3) E. W. Rothe and R. B. Bernstein. J . Chem. Phya., 31, 1619 (1958). References t o earlier work are also summarized here. (4) H. S. W. Maslrey and C. B. 0. Mohr, Proc. Roy. SOC.(London), Al44, 188 (1934).
893
where the subscripts refer to runs a t beam velocities 1 and 2, respectively. An estimate of the angular resolution of the apparatus, based on conservative riter ria,^ indicates that in the present experiments equations 2 and 7 are applicable.2 Experimental Details of the high resolution velocity selector used in this study have been described previously/ The essential feature of the alteration to the apparatus is the placement of an additional, separately pumped vacuum chamber, which contains the scattering cell, between the rotor and detector chambers. All chambers are connected only through narrow slits. The Scattering cell, machined from OFHC copper, is bolted to a cold trap. The cold trap has vertical, horizontal and rotational degrees of freedom to facilitate alignment. The geometrical features of the apparatus, which are similar to those previously described for the velocity selector, have the following additions and dimensional changes: ovenscattering cell, 63.5 cm ; scattering cell-detector, 31.8 cm.; oven slits, 0.005 X 0.318 cm.; surface ionization detector. 0.0025 cm. diameter tungsten. The scattering cell consists of a rectangular box with a length of 0.635 cm. which is connected a t both ends with the vacuum chamber through high impedance channels w-hich have a length of 0.635 cm. and a cross section of 0.02 X 0 356 cm. Thus, the total effective scattering path-length, d . is taken as 1.27 cm. The scattering cell is connected t o an external vacuum and gas inlet system through two 0.475 cm. diameter stainless steel tubes, one of which may be connected to a McLeod gauge for pressure calibration. The McLeod gauge was designed for a sensitivity corresponding to P = 3.305 X 10-7A2when P is the ressure in mm. and h is the difference in height in mm. of tge mercury columns in the closed and open capillaries. h wm measured with a cathetometer which could be read reproducibly to within 0.05 cm. Runs were made with ?;2 as scattering agent and K and KC1 as beam molecules. In all runs the ecattering cell temperature was maintained a t the boiling point of liquid nitrogen. Operating pressures in the mm. and no inapparatus were generally about 2 X crease was observed when gas was admitted to the scattering cell a t the highest pressures employed during the runs (about 5 X mm.). Scattering gas pressures were measured on an ion gauge which was calibrated against the McLeod gauge and a transpiration effect correction was made it1 order to take into account the difference in temperature. between the McLeod gauge and the scattering cell.
Results Typical data obtained for one run with R a i heam atom and N2as scattering medium are show11 in Fig. 1. Least squares determinations of t h c slopes and application of equation 7 to these data give an exponent, s = 6.18, in the potential fun(*tion represented by equation 1. From a large number of runs an average exponent of 6.23 (stanclard deviation, 3~0.17)was obtained for the I < Dispersion or van der Waals forcm arc x T 2 system. postulated as those affecting long range interactioii (predominantly small angle scattering due to interaction of particles with thermal energies) for thih system and these lead to a potential of the fornl v = - C / P . Thus, within the limits of experimental uncertainty the results presented here may be taketi as verification of the potential function which is inferred from theoretical considerations. Recently, Pauly,’ using a similar method, demonstrated that an inverse sixth power dependence gives the best ( 5 ) P. Kusch, “Note8 on Resolution in Scattering h.Ieasurarnents,” private communication, 1960. (6) R. C. Miller and P. Kusch, Ph98. RBV.,99, 1314 (1955). (7) H.Pauly. 2. Natwforeh., lSa, 277 (1960).
NOTES
894
0.2
Vol. 65
ported by Rothe and Bernsteinl when a correction for differences in average relative velocity (equation 2) is applied (t% = 6.4 X lo4cm./sec. this work). I n similar runs witho KCl,K2 mi average total cross section of 787.0 A.2was obtained. I t is proposed to undertake further experimental studies to investigate scattering involving dipoleinduced dipole interactions. Acknowledgment.-I wish to express my appreciation t o Professor P. Kusch for many helpful discussions relating to this work, and also t o acknowledge the contribution of Mr. Isaac Bass in assisting with many of the experimental measurements.
’
SORPTION OF AAIINES BY MONTMORILLONITE 0
20
40
60
80
100
P X 106, mm.
BYJAY PALXER AND NORMAX BAUER~ Chemzstry Department, Utah State Cnizersitii, Logan, Utah
Fig. 1.
results if a potential of the foim of equation 1 is postulated for the K , S 2interactioii. I:or the II;C1,S2system, however, an unexpected result has been obtained. The value for the exponent which was derived from the average of qeveral runs, s = 5.30 (standard deviation, &0.23), implies an inverse fifth power dependenre of the potential on the particle separation. I n all of the runs on this syqtem a double chamber oven8was employed and data were taken with oven chamber temperature differentials in the range 5-265’ so that the contribution of polymeric species to the results could be studied. \Vith the larger temperature differentials the polymer concentration was negligible. No dependence of results on temperature differential was observed. The detectable forces to be expected for the I
