236
W. 0. EVERBOLE AND D. L. DEARDORFF
perature of 310"C., a pressure of 1500 pounds, and a time of run of 2 hr. A metallic bismuth catalyst prepared by the redKction in hydrogen of bismuth hydroxide at 320" to 340OC. was studied under the same conditions as the metallic lead catalyst. The maximum yield obtained was 45 per cent of aniline a t 31O'C., a pressure of lo00 pounds, and a time of run of 2 hr. CONCLUSIONS
1. The copper catalysts studied gave yields of aniline as high as 89.5 per cent to 94 per cent over a temperatw-e range of 242' to 300"C., the pressure being lo00 pounds and the time of run 2 hr. 2. Copper catalysts reduced from the oxide at either 260" or 360°C. gave, within experimental error, the same yield of aniline. The best results were obtained at a temperature of 27OOC. This is approximately the temperature, 260" to 265"C., that gives the best results in the vapor phase (3). 3. A metallic lead catalyst and a metallic bismuth catalyst prepared and studied under the conditions described are nobgood producers of aniline. REFERENCES (1) ADKINS,HOMER: Reaction of Hydrogen w i t h Organic Compounds over CopperChromium Oxide and Nickel Catalysts, p. 95. Vniversity of Wisconsin Press, Madison, Wisconsin (1930). (2) BROWN, 0. W., ETZEL,G., AND HENKE, C. 0.:J . Phys. Chem. 88, 831-5 (1928). (3) BROWN, 0.W., AND HENKE,C. 0.:J. Phys. Chem. #, 161-90 (1921).
FLOW POTENTIALS THROUGH METALS W. G . EVERSOLE AND D. L. DEARDORFF Division of Phyeical Chemistry, State University of Iowa, Iowa City, Iowa Received March
1 , 19.40 '
In connection with attempts to measure potential differences set up by a stream of liquid flowing through a gas (I), it became necessary to measure potentials set up by flow through a small hole in a platinum disc. Thqse potentials increased with increasing pressure, and the deviations from a linear relationship between the potential difference and the pressure were such as might be,expected from the failure of Poiseuilie's law to apply to this type of flow. Such potential differences set up by the flow of liquids through metals have been measured by other investigators (3, 4), but their significance has not been satisfactorily explained. The
FLOW POTENTIALS THROUGH METALS
23 7
conclusion of Kruyt and Oosterman (3) that they do not permit a calculation of electrokinetic potentials does not seem to be justified. The purpose of this paper is to present an analysis of this situation which leads to an equation that can be used for this calculation in any case where a measurable potential difference is set up by the liquid flow. Figure 1 is a diagram representing the situation esisting in a flow potential apparatus using any capillary which is negative with respect to the liquid. el and e2 are any identical unpolarizable electrodes which are reversible to an ion of the solution. K designates the potential difference between e2 and el and therefore the potential difference between the solu-
SOLID
High P upstreom
downsimm
+ + + + + + L+(4
l;t!
c
i
FIG. 1 Diagram of apparatus for det,ermination of flow potentials
tions “downstream” and “upstream” from the capillary. 11,Is, I*, 14, IS are various components into which the total current through the cell may be divided. These currents will be discussed in order. Consider an equilibrium state in which the liquid is a t rest and all currents in the system are zero. If pressure is applied to the upstreim side, the positive-ion atmosphere is swept downstream by the flow of liquid. This constitutes the positive current ZI. We may define this current as: 11
= KV
(1)
K is the charge in the ion atmosphere per unit length of capillary, and V is the average velocity with which this charge is swept downstream. I I
238
V-. G . EVERSOLE AND D. L. DEARDORFF
may bc rrgardcd as being dependent on the distribution of charge in the liquid and on the conditions of flow but independent of T . As a result of I,, the solution downstream becomes positive with respect to the solution upstream. The currents 12,Z3,Zl,and 1 5 arc sccondary effrcts resulting from this potential difference. IZand 1 3 arc, respc,cti\cly, a poqitivc-ion current upstreani and a negativc-ion current downstream through the capillary, the ions being those prcsrnt in thr solution. Ohm’s Inw may bc applied and
I?
+
7r
= --
(2) R, \\-her(. Ti, ih the resistnncc~of tlw column of solution filling the capillary. Physically, Iz is a movcmcnt of positiw ions downstream with a velocity slightly lcss than thc d o c i t y of liquid flow, and Z3a corresponding mowment of ncgative ion- with n velocity slightly greater than that of the liquid. In gciieral tlic niigration velocity of thc ions due to 7r will be of a much lowcr order of magnitude than thc velocity with which they are swept downstream by thc moving liquid. I , i R an electron currcvit downstream through the wall of the capillary. This current is associated with an clectrocheniical reaction a t the points whcrt. it enters and leaves the capillary. C designates a cathode reaction occurring a t the downstream cnd of the capillary and A an anode reaction a t the upstream end. In many cascs this mill lead to polarization a t the ends of the capillary. I t is thcrefore not permissible to apply Ohm’s law to 1 4 in the general case. For example, if dilute potassium chloride flows through a platinum capillary, I4leads to the discharge of H30+ ions a t the downstream end of the capillary and OH- ions a t the upstream end. The accumulation of hydrogen and oxygen a t the ends of the capillary leads to a counter electromotive force ( E ) which opposc~sI,. Thus the value of I4in general may be represented by equation 3. 13
where R, is the resistance of the capillary. Z6 is an electron currcnt downstream through an estcrnal resistance (R2).Usually such an external resistance is omitted. However, in order to include certain experiments of Bruyt and Oosterman (3) .in the discussion, we ’may consider el and e2 to t c connected through an ohmic resistor, R,, in parallc.1 with the Ineasuring circuit which draws a negligible ccrrent. A
I6
sincc rl and
e2
=K,
arc uiipolariznble elcctrodes.
(4)
FLO\V POTENTLiLS THllOUGH MET.\LS
23'1
As liquid flow continues a t a constant rate, n- will incrmse to an upper limiting value A * , and the back cJlcctromotivcforcc 11 ill also increase to nn upper limiting value E* 7 r* In this steady state I1
=
I;
+ I,* + I : + I t
(5)
or, from equations 1, 2, 3 and 4 and 5 .
In the general case we may definc the flow potential (S) by the equation S = KVR,
and therefore
s = A*
+It,
(7)
[T* ;-E* +g] ___
+
S is evidently the potential necessary to make I2 I 3 equal to 1 1 , and for the usual case of an insulating capillary with R , omitted, S is a*. Equation 8 involves no assumptions in regard to the distribution of the space charge in the liquid and it is therefore valid for any type of double layer. TYie electrokinetic potential may then be calculated from the general form of the Smoluchowski equation
where S is given by equation 8. The usual simplified derivation of equation 9 is given in terms of a Helmholtz double layer. However, the equation can be derived independently of any special assumptions whatever as to the distributions of ions in the liquid (2). Equations 8 and 9 may therefore be regarded as general. However, the following special cases are of interest: Case A: R, is omitted; R, is finite; E* = 0 This corresponds to a conducting capillary in 'the absence of polarieation effects which oppose Id. We may take as an example a dilute solution of silver nitrate flowing through a silver capillary. The electrochemical reaction associated with 14 is the reversible deposition of silver ions at the downstream end of the capillary and their reversible solution at the other end. In general, this classification would also include other cases where the electrochemical reaction is not associated with an increase
240
N-. G. EVERSOLE AND D. L. DEARDORFF
in free energy or irreversible effects. I n this case equations 8 and 9 l e d to the equation
However, the use of this equation is justified only if E* = 0. It reduces to the equation for an insulating capillary when R, > > R.. Equation 10 was improperly applied to rases where E* > 0 by Kruyt and Oosterman (2);
Case B: an insulating capillary; R, i s jinite Equation 9 becomes
This equation has exactly the same form as equation 10 for a conducting unpolarizablc capillary. Kruyt and Oosterman (3) “imitated” wall coaduction in essentially this way, using a glass capillary, and found ‘that equation 11 would apply.
Case C: R, omitted; R, is $nile; E* > 0 ThirJ situation corresponds to a capillary which is a conductor or an imperfect insulator where the electrochemical reaction resulting from I , involves an increase in free energy or irreversible effects or both. (1) If the rate of depolarization is zero, i.e., the electrolysis products are unable to escape from the surface where they are liberated, x* = E* and I4 = 0 in the steady state. Equation 9 becomes for this case
This is the same as the equation for a perfect insulator. It may be pointed out that if a steady state has been attained and the flow of liquid is suddenly stopped, the polarized capillary will behave essentially as a shortcircuited storage cell of relatively small capacity but high internal resistance. It will be discharged by 1 2 , Is,and Id,the direction of Id being reversed. The decay of this back electromotive force may be measured by R after flow stops. The results of Kruyt and Oosterman (3) for the flow of dilute potassium chloride through a platinum capillary indicate that in the steady state E* = R*, for values of T * much less than the decomposition voltage of water. Equation 12 may, therefore, reasonably be used to estimate a t this boundary from their K* values. Equation 10 is not applicable. (3) If the rate of escape of the electrolysis products is finite, then in the
SIZE DISTRIBUTIOiV OF PARTICULATE MATERIAL6
241
steady state 1 4 will approach a lower limiting value I,* > 0. If 1: < < 1: I:, equation 12 may be used, or equation 10 if R, is a fictitious resistance defined as #/IT. This value mill in general be much greater than the ohmic resistance of the capillary. In general, 1: will be larger if n large surfacc area is involved and if rip is greater than the decomposition voltage of the electrochemical reaction resulting from 1;. However, in many cases where the rate of depolarization is slow or the resistance of the capillary wall is high, a satisfactory measurement of flow potential should be possible, using a conducting capillary.
+
REFEREXCES (1) EVERSOLE,W. G . , A N D DPARDORFF, D. L.: Proc. Iowa .\cad. Sci. d,177 (1536); 44, 109 (1937). (2) KOEUIG,F. 0.: “Dic Elektrokinetischcii Erscheinungen”, in Wen-Harms Handbuch der Ezpen‘mentalphysik, Vol. XII, Part 2 (1933). (3) KRCYT,11. R., A N D OOSTPRMAN, J.: Proc. Acad. Sci. Srnsterdarn 40,4004 (1937), 41, 370 (1938); Kolloid-Beihefte 48, 377 (1938). ( 4 ) S W T H , G. w., . 4 S D REYER5ON, 12. H.: J . Phys. Cheln. 38, 133 (1934).
ST.lTIST1CAI. .%NALYSIS OF SIZE DISTRIBUTION OF YARTICULATE IVIATERIALS, WITH SPECIAL REFERENCE TO BIJIODAL AKD FREQUENCY DISTRIBI‘TIONS. C0RRE;IA’I’IOS O F CJUAIRTII,EWITH STATISTICAL VALUES’ PAUL S. ROLLER2 Bit, enu o/ ill?nes, Eastern Ezpertment Statzon, College Park, Maryland
Recezied March $8) 1.9@
Size data foi a particulate material are properly evaluated solely by a statistical m e t h t d a i this alone take5 into account the contribution of all sizes in the ensem1)lr. Statistical analysis of the data yields certain conbtants, such as euriiice aica per gram, coefficient of uniformity, coefficient of regression, and iiiimber of particles per gram, wliich properly summarize the distributioii and define the material as t u size. Knowledge of these constants is important for the correct physical valuation of a product rtnd of the mode and method of its preparation. The fruitfulness of the result easily justifies the effort involved in calculating the constants from dze data. Published by permission of the Acting Directoi, Bureau of Mines, Department
of the Interior. ?
Physical chemist, Bureau of Mines, Eastern Experiment Station.
