816
NOTES
With the above two points as a motivation, a systematic study of gases of interest has been undertaken. Methyl and ethyl alcohol and methyl and ethyl acetate are herein reported. Methyl and ethyl alcohol were reported on by Cummings and Bleakneye many years ago, but it was felt that the new techniques developed since their study warranted a re-investigation of these molecules, Experimental All measurements were made on a 90" sector type mass spectrometer. The electronics were of conventional design except for the ion gun control unit, which included a built-in potentiometric circuit for the measurement of the electron energy. The electron accelerating potential was obtained across a Leeds and Northrup precision resistance box of 0 to 10K ohms through which a constant current of 10 milliamperes was maintained. This current was continuously stabilized by use of a Weston standard cell as a reference. Simultaneously, the highly stabilized current wa8 used to produce the potentials necessary to operate the other elements in the electron gun. The standardization circuit functioned by comparing the voltage drop across a resistor adjusted to 101.86 ohms with 1.0186 volt output, which is the same as the standard cell. If 10 milliamperes are flowing through the resistance box, the sum of the voltage drops across the 101.86 ohm resistor and the standard cell will be zero. However, if the current should depart slightly from its proper value, a resultant error voltage appears across the contacts of a Brown Converter and is chopped into a 60 cycle square wave by the motion of the armature contacts. The phase of the resulting voltage depends upon the polarity of the error. The error signal was amplified by n narrow band 60 cycle amplifier and was then fed into a phase sensitive detector which produced a d.c. output of similar polarity but of much greater size than the error signal. The output thus derived was used to correct the grid bias of a tube placed in series with the current to be regulated. The action was degenerative and hence tended to reduce the error to zero. A precaution taken to ensure stability of the system waR that a d.c. feedback path was provided which wm capable of correcting the system in the event of a major disturbance. This was necessary as the high gain of the ax. amplifier tended to produce saturation and loss of phase sense when a sudden large signal was applied. A phase correction network was included to fulfill the Nyquist criterion for the frequency phase relations in any feedback circuit. The unknown gas and the calibrating gas were admitted into the gas inlet simultaneously. The ion peak to be studied was adjusted in height to equal the ion peak of the calibrating gas with 50 volts supplied to the electron beam. The ionization efficiency curves for both gases were obtained rapidly and the method of initial breaks was used to determine the appearance potential. Reproducibility from day t o day was better than 0.05 volt and all standards checked against each other were accurate within the same range. The deviations indicated for the results are indicative of the reproducibility of the ionization efficiency curves from day to day. The accuracy of the ionization potentials, in terms of an absolute number, was approximately 0.2 of a volt for all values given. If the ionization efficiency curve of the unknown turns out to be parallel to that of the calibrating gas and the points of initial break fall within 0.1 of a volt of each other, then it is possible to cite an accuracy less than the above value. However, in most cases, the two curves are not parallel, and it is difficult to find calibrating gases that have the proper appearance potential and therefore a value of 0.2 is most realistic. The results of the measurements of the appearance potentials are as follows: Methyl Alcohol.-Mass number 32, 11.36 f 0.08 volt; 31, 12.26 f 0.10 volt; 29, 14.26 f 0.10 volt; 28, 14.31 f 0.05 volt; 15, 14.96 f 0.10 volt. Ethyl Alcohol.-Mass number 46, 10.88 f 0.15 volt; 45, 11.23 f 0.08; 31, 12.28 f 0.15; 29, 13.91 f 0.15; 27, 15.31 f 0.15. Methyl Acetate.-Mass number 74, 10.95 f 0.10 volt; 59, 12.31 f 0.15; 43, 11.86 f 0.10; 42, 11.81 f 0.15; 31, 12.65 f 0.20; 15, 14.26 f 0.10. (6) C. 8. Cummings, 11, and W. Bleakney, Phpe. Rsv., 18,787 (1940).
Vol. 60
Ethyl Acetate.-Mass number 88, 10.67 f 0.05 volt; 61, 11.24 f 0.10; 45, 11.44 f 0.10; 43, 12.31 f 0.20; 29,12.47 f 0.08; 27,15.32 f 0.20. If we compare the values with the appearance potential of argon (15.77), krypton (14.01), xenon (12.14) and other inert gases, we see that all of the gases studied may be used as quenching vapor in conjunction with inert gases. However, as noted in the introduction, the smaller the difference of the potential, but with the polyatomic vapor having the lower value, the more positive will be the quenching action when used in a Geiger-Muller counter. It will be noted that the criterion for good quenching i s more closely satisfied by the fragments of the polyatomic molecules. Thus in the high counting rates where the fragment may be utilized in the quenching action, this factor should be considered. Cummings and Bleakneys have analyzed the data of ethyl and methyl alcohol in terms of the struchre of the molecule. The discrepancies introduced by their data, that is, the appearance potential of mass 45 in ethyl alcohol is lower than mass 46, is removed by these results. Similar analyses may be made for methyl and ethyl acetate and these will be the subject of a future publication.
LONGITUDINAL DIFFUSION IN ION EXCHANGE AND CHROMATOGRAPHIC COLUMNS. FINITE COLUMN BY W. C. BASTIAN AND L. LAPIDUS Contribution from the Department of Chemical Engineen'ng, Princeton University, Princeton, N . J . Received December 8. 1866
In a recent communication' the effect of longitudinal diffusion on the effluent concentrations from an ion-exchange column was considered. The equations developed, however, were only applicable to a column infinite in length. In the present note the authors present the equations for a column of finite length operating under equilibrium conditions. Consider a column of unit cross-sectional are and let c = concn. of adsorbate in the fluid stream, moles/ unit vol. of soh. n = amount of adsorbate on the adsorbent, moles/ unit vol. of packed bed V = velocity of fluid through interstices of the bed z = distance variable along the bed D = diffusion coefficient of the adsorbate in soln. in the bed eo = concn. of soln., admitted to the bed CY = fractional void vol. in the bed kl,k2 = constants in equilibrium relation L = length of bed
A material balance on an elemental section of the bed produces The column is assumed to be operating under equilibrium conditions and to initially be free of adsorbate. This can be described by the equations4
+
n = klc kr n = e = 0,t
=O
(2) (3)
In addition the behavior of the fluid phase must be described at the inlet, z = 0, and at the outlet, z = L, of the bed. One may postulate a number of different representations at these two points but the recent and detailed work of Wehner and Wilhelm2 has shown that those described by Dank(1) L. Lapidus and N. R . Amundaon, THIBJOURNAL, 56,984 (1952). (21, J. F. Wehner and R. H. Wilhelm, personal communication.
wertsa for a similar problem are correct. These are VCO VC- D
ac
-, z az
_ -- 0 , z ?IC
=0
(4)
Use of boundary conditions of this type were shown by Wehner and Wilhelm to be a consistent set which leads to plug flow of material at one extreme ( D = 0) and perfect mixing of material at the other extreme (D = w ). Making the change of variable c - co w e ( V d 2 D - VPt/4yD) (5) Equations 1, 2 , 3 and 4 become 3
- w coe-Vz/2D,f = O - -bw + 2--wV0 = 0 , z = 0 bz 3 w V -+-w=o,z 20
0 0
If we now let D / r = k and V/2D = h then the system of equations becomes identical to that describing one-dimensional heat flow in a pJane with radiation from each face and an arbitrary initial distribution. From Carslaw and Jaeger4 the solution can immediately be written as e-hmPt OrncosOrnx
+ h sin Ornx
+ h*)L + 2h --COe-hZ(Orncosa,,x + h sin amx) dx (CY:
1
JoL
an L
20r h
= R ant
- h2
(10)
Carrying out the indicated integration in equation 9, returning to the original variables (equation 5) and letting 2) = volume of solution = Vta there finally results
UL
,Cm -
(45
+:a+]
(11)
where the a n are the roots of 0r.L cot a,L
40
Fig. 1.-Values
+ hL = 0
0/2 tan 0/2
- hL
=
100
80
of C / ( ~us. O v, the volume of solution, 3 cm., V / D = 2.0 and y = 25.
L
=
to perfect mixing than to plug flow. As also shown the finite column calculations do not deviate to any large extent from those for an infinite column. This cannot, however, be construed as a general situation. TEMPERATURE DEPENDENCE OF VISCOSITY OF LIQUIDS BY K. KEITHINNES Vanderbill Univeraty, Naahville, Tenn. Received December $3,1066
Viscous flow of liquids is commonly interpreted as a rate process. Thus, the fluidity, 9, by analogy with the rate constant of chemical kinetics, is expected to show an exponential dependence on temperature. It has, indeed, been widely illustrated‘ that within the accuracy of most experimental data the Viscosity, 8, is given by = 1
(12)
Equation 11 represents the effluent adsorbate concentration from the bottom of a column of length L as a function of the volume of solution into the column. While the roots of equation 12 are not readiiy available a5 such, Carslaw and Jaeger tabulate the first six roots of 812 cot 8/2
60
V,Crn.8.
~
VL a L)a + 40 - = (5...vL/D
and of
20
(9)
where the an are the roots of tan
0.4
= L
bz
co
0.6
0.2
3
c
.o
1
=L
bz
=
817
NOTES
June, 1956
0
From these two sets of roots the first twelve roots of equation 12 may be obtained and all those following will increase by a factor of T. The accompanying figure illustrates the use of equation 11. The effluent distribution is closer (3) P. V. Dankwerts, Chem. Eng. Sei., a, 1 (1953). (4) H. 8. Carslaw and J. C. Jaeger, “Conduction of Heat in Solids,” Oxford Prem, 1847.
AreB’IT
(1)
where A’ and B’ are taken as constants. Two of the few cases for which accuracy and sufficient range of temperature justify refinement of (1) are the interesting ones of water and mercury. Previous simple refinements for these substances have considered variation of B’ with temperature.2 We wish to point out that further analogy with chemical kinetics,* particularly for low values of B‘, recommends the form
,
= ATneBIT
(2)
where n is a third constant specific to the given liquid. In addition to relative simplicity, this form may offer information about temperature dependence of liquid structures. It is our impression that equation 2 has not preSee, as examples, E. N. da C. Andrade, Nafure, 126,309 (1930); Kierstead and J. Turkevich, J . Chem. Phys., 12, 24 (1944). For example, T. A. Litovits, ibid., 90, 1980 (1952). A. A. Frost and R. G. Pearson, “Kinetics and Mechanism,” John Wiley and Sons, Inc., New York. N. Y., 1953, p. 24. (1) H. A. (2) (3)
