I748
Vol. 66
YOTES
(“n) molecule, which requires a total energy of about 147 kcal. above the ground state, would be unlikely in view of the substantial potential energy well envisaged* for this bound electronic state. The greater energy content of N,(A) molecules (142 kcal./mole for the zero vibrational level) mould tend to reduce the cross section for energy transfer to NO below the large value (24.7 A.2) observedg for the resonance transfer’ from excited mercury atoms. On the other hand, the greater energy content of the NO(47r) molecules so formed might be expected’o to increase the apparent value of kl over the quite small value deduced by S and G from the low quantum yield of the over-all reaction in their system. The value of ke also should be increased over that for the photosensitized process, owing to the greater energy content of the (NO)z dimer.11t12Indeed, it is possible that, for the active nitrogen reaction, a simple bimolecular rearrangement process is involved. Decomposition of N O induced by an electronically excited NO molecule of appreciable lifetime, as above, could maintain a factor of 2 between N O destroyed and the concentration of N2(A)molecules in active nitrogen, as used previously2 to calculate the lifetime of the excited nitrogen molecule capable of causing NO destruction. (8) J. T. Vanderslice, E. A. Mason, and W. G. Maisch. J . Chem. Phgls., 31, 738 (1959). (9) J. R. Bates, J . Am. Chem. Sac., 64, 569 (1932). (10) J. L. Magee and W. H. Hamill, J . Chem. Piwe., 31,1380 (1959). (11) G. B. Porter and B. T. Connelly, z b d , 33, 81 (1960). (12) H. M. Frey and G. B. Bistiakowsky, J. Am. Chem. Soc., 79 6373 (1957).
THE VISCOSITY OF LIQUIDS FROM THE HL4LF-TIMEOF RISE I S B FIKE VERTICAL CAPILLARY BYLEONARD S. LEVITT Chemistry Department, Seton Hall University, South Orange, New Jersey Receaved A p r d 16, 1.968
The time of rise of a liquid of viscosity 17, surface tension y , and density p, in a vertical capillary of uniform radius r , is given by Washburn’s t =
where g is the acceleration due to gravity, d is the depth of immersion of the capillary below the surface of the liquid, ga is the viscosity of air, E is the total length of the capillary, F, is the height the liquid has risen after time t, and h~ is the final height it can rise due to its surface tension. If the depth of immersion is made very small, d = 0, and if the viscosity of air is regarded as negligible, g?Z ~ i 0; : noting also3 that 2 r / r p g = h ~ the , equation can be greatly simplified to
t = -8,
[
hF
rLPg
111
(ch) hF
- h]
(2)
We can now define a half-time of rise,* &Iz, as the time required for the liquid to rise to a distance h ~ / 2in the capillary. The half-time of rise is seen to be simply
Noting again that be written
hF =
2y/rpg, eq. 3 also can
ti/, = __ “” (0.193) r3p2g2
Thus the viscosity of the liquid is, from eq. 3 , given by r)
= 0.G47r2pgtl/,/l~~
(4)
If the surface tension of the liquid already is known a t the temperature of the experiment, then the radius of the capillary need not necessarily be calculated since r = 2y,/pghF,so that eq. 4 can also be written 2.59t1/,7? rl=
PghF3
(44
The experimental procedure is simply to detwmine h~ for a given capillary and liquid, and then mark off the distance h ~ / 2directly on the capillary, and accurately determine the time, til$, required for the liquid to rise to this mark. The smaller the radius of the capillary, the longer is the time of rise, and the greater the height to be measured. Therefore, the smaller the capillary bore, the more accurate will be the viscosity determined by this method. For practical results, a bore of r 5 0.005 cm. should be used. Theoretically then, the total volume of liquid required for a viscosity determination by this method is very small indeed. For example, using water as the liquid a t room temperature, pw1.0 g . / ~ m . ~4 , = 72 dynes/cm., g = 980 cm./secx2, and with r = 0.0050 cm., h~ is calculated to be about 30 cm. The quantity of water drawn up into the tube is therefore nr2hF = 2.4 X ~ m .or~ about , 1/20 of a drop. But in practice a t least a few drops of the liquid should be used. The half-time of rise for the example under consideration is calculated from eq. 3 to be approximately 17 sec., which is seen to be a time of convenient duration for accurate measurement. For two different liquids whose half-times of rise are measured in the same capillary, the relative viscosity of the liquids is (Ptl,’,’hF) 1 - -___ - (P*tl/,/?’)1 72
(Ptl/,/hF)2
(P2tl/2/y)2
(5)
We have obtained preliminary results6 with
(1) E. W. Washburn, Piiz/s. Rea., 17, 273 (1921). ( 2 ) 5. R. Ligenza and R. B. Bernstein, J . Am. Chem. S a c . , 18, 4636 (1951). (3) We are a s a m i n g here t h a t the liquid makes a contact angle of zerti with the interior wall of the oapillary durlnp the course of t h e
Ilquid’r rise.
called the “time of hrtlf-rise,” but \*e defer to the established usage in the analogous case of chemidal (4) X o r a accurately, this should be
LinPties.
(5) The author wishes to +hank Alr. Wm. Lane io? obt&inin%the ex= gerimsntal data.
Sept., 1962
1749
XOTES
water, methanol, ethanol, benzene, acetone, and chloroform at room temperature, using marine barometer tubing supplied by the Corning Glass Co, The bore radius \vas determined by capillary rise of water to be 2.70 X cm., and was checked by direct examination with a calibrated microscope, which gave r = 2.71 X lom3cm. With water at 27.4', p = 0.996 gJcrn.3, hF was 54.2 em., an.d ti/, was found to be 98.7 and 98.9 see. in two separate runs.6 The viscosity calculated from eq. 4 is 17 = (0.647)(2.70 X 10-3)2(0.99G)(980)(98.8)/ 54.2 = 8.44 X 10-3 poise = 0.844 cp. This value compares quite favorably with the value 0.846 cp. obtained by interpolat'ion of recorded viscosity data7for water a t various temperatures. I n conclusion it may be pointed out that the present work serves as a coilfirmatlionof the validity of Washburn's eqmtion, as well as providing a new rapid method for simply and accurately determining %heviscosity of a liquid, using samples considerably smaller tha.n heretofore possible with other methods. (6) If t,he same capillary tube is to be used again for a second liquid, i t is, of course, necessary to clean the tube carefully with cleaning solution, followed by a few rinsings with distilled water and then acetone. Finally, the tube must be dried thoroughly. When the tube is not in use, i t should be covered a t hoth ends to prevent the smallest traces of dust from entering. If reproducible half-times cannot be obtained, the capillary is not clean, and in some cases t.he only r e m i d r is to take a new section of capillary tubing. (7) Handbook of Chemiatry and Dhysics, 41st E d . , Chemical Rubber Publ. Co., Cleveland, Ohio, 1960, p. 2181.
Experimental DMD-BDS was prepared from DMDClz, made by Houdry, and Eastman HzBDS. After converting the DMDCh t o the sulfate by addition of silver sulfate, the DMDSO4was precipitated from the aqueous solution by evaporation and addition of ethanol, and was recrystallized from methanol containing a little water. These salts are very soluble in water but nearly insoluble in most' other solvents. I n order to remove sulfuric acid from H2BDS, it was converted to the barium salt in aqueous solution by barium hydroxide, and the BaBDS (12.6 g./15 ml.) was recrystallized from water. The DMDS04 was titrated in aqueous solution t o a nephelometric end-point with BaBDS. After filtering off the barium sulfate, the DMD-BDS was precipitated by addition of ethanol. The salt was recrystallized twice from methanol-water, washed with 7: 1 methanolwater, and dried t o constant weight a t 30 p and 138'. Water probably still was present in the salt, but a higher temperature was not risked. Wet test.s for barium and silver were negative and the salt was neutral. For the preparation of DMD-BPDS, the DMDC12 was recrvstallized by dissolving 5 E. in 10 ml. of hot methanol, then adding an kqual amount 4 ethanol, and evaporating to about one fourth the volume. The salt then was ronverted to the hydroxide by silver oxide. Eastman p,p-diphenyldisulfonic acid was converted t o the potaesium salt, which was recrystallized twice from water. The acid then was formed in aqueous solution by passing a solution of the potassium salt through a Duolite C-3 cation exchanger. The acid was titrated to a methyl orange end-point with DMD(OH)2. After reducing the volume of solution, salt was precipitated by the addition of methanol. The salt was dried for two days a t 78" and 30 p . The methods of measurement have been described previously6; the cell used in these measurements had a constant of 1.0109.
Results The data for the conductance of DMD-BDS and DMD-BPDS are given in Table I. TABLR I
CONDUCTANCE OF 2-2 ELECTROLYTES WITH MULTIPLE CHARGE SITES BY JOHN E . LIND,JR.,'A K D
RAYMOND
CONDUCTANCE O F N,N-DIMETHYLTRIETHYLA~IMOFIUM SALTS
IN WATER AT
M. FVoSS
Contrzbutzon N o . 1698 from the Sterlzng Chemistry Labolatory of Yale Unzverszty, New Haven, Connectzcut Eeceived Aprzl 18, 196%
The conductance theory of FLIOSS and Onsager2 has been applied extensively to 1-1 electrolytes, but there has been little examination of higher symmetrical charge types because the inweased electrostatic fields redulce the range of applicability of the theory. Atkinson3-5 and co-workers have investigated a number of metal salts of m-benzenedisulfonic acid (H2BDS)and p,p-biphenyldisulfoiic acid (H2BPDS). However, no 2-2 salts have been investigated whlere the anions and cations are both large and of comparable size. For such salts the electrostatic interactions at contact are smaller and thus they better approximate the theoretical model. The purpose of this note is to present conductance data a t 25' in water for two such salts: the K,K-dimethyltriet hylenediammon ium (DAID) salts of BDS and BPDS. DMD is the dimethyl quaternized ion of 1,4-diaza-bicyclo [2.2.2]octane with the structure MeN+(CH2CH2),Y+Ne. (1) Du Pont Postdoctoral Research Fellow, 1960-1962 (2) R. >I. Fuoss and F. Accascina, "Electrolj tic Conductance," Interscience Publishers, Inc., New York, N. P., 1959. (3) G. A4tk~nson, &! Yokoi, I. and C Jd Hallada, J . A m Chem Sac., 83, 1670 (1961). (4) C. J. Hallada and C.Atkxnsoa, dbzd., 83, 3759 (1961). (6) C . J, Hallada and 6. Atkinaad, ibid., 83, 4367 (tqfit).
104~
DMD-BD8 A
25" DMD-BPDS
lOaAA
27.161 102.53 -2 20.754 105.83 3 15.529 109.22 1 10.996 112.94 -4 5.657 119.09 1 c/m = 0.99707 - 0.32 m
A
104,
lO*Ah
20.747 101.14 -1 16.821 103.07 $2 12.472 105.62 0 8 065 108.98 -2 +I 4 143 113.22 c/m = 0.99707 - 0.29 m
They mere analyzed by the Fuoss-Onsager equation A
=
+
A, - S ( C ~ ) "Ecy ~ log cy
+ Jcy +
Jz(cy)'''
- KACyf2A
The analysis was made on an IBM 709 computer with Kay's' program in Fortran which was modified by the addition of the cs/z term in the conductance equation. h second modification of the program was the addition of the condition that, if the association constant, K A , becomes negative, the fraction of free ions is set equal to unity. This change was made because it appears that a small term in J was neglected which is by this analysis added as a small negative component to K A . I n Table I, AA is the difference between the observed conductance and the value computed from the (6) J. E. Lind, Jr., and R. M.Fuoss, J . P h p . Chem., 66, 999 (1961). (7) R. L. Kay, J . Am. Chem. Sac., 83, 2099 (1960). Jn order t o adapt the program for 1-1 salts to data for 2-2 salts, one simply replaces the dielectric conntant 0 hs 0/4 and th6 vimmitv 7 by q / 2 ,
