NtuYruAL DIFFUSION IX NON-IDEAL LIQUIDMIXTURES
May, 1962
899
TABLEI1 EFFECTOF POTASSIUM CHLORIDE CONCENTRATION O N THE SOLUBIL,ITY OF HIPPURIC ACIDAKD HIPPURIC ACIDESTERSAT 25" iSolubility is expressed in terms of molarity 7
Ester of hippuric acid
0.0
0.1
Free acid Methyl Ethyl Propyl Isopropyl Butyl
1.6828 1.2865 1 4742 1.9352 2,2485 2.1777
1.6931 1,3030 1.4941 1.9563 2.2696 2,1994
0.2
Malalitywof KCl0.0
.-..
1.0
2.0
3.0
1.7859 1.4516 1 . 6734 2.1463 2.4593 2.3949
1.8891 1.6166 1.8726 2.3574 2.6701 2.6121
1.9922 1.7817 2,0718 2.5685 2.8808 2,8293
- log solubility ~
1.7034 1.3195 1.5141 1.9774 2.2907 2.2211
chloride increases with the increasing chain length as might be expected from electrost'atic theories such as that of Butler.6 Insufficient da,ta on the physical characteristics of the esters are available a t this time for attempting t o interpret the results in terms of the more sophisticated treatment of Bockris, Bowler-Reed, and Kitchener.' The good agreernent of the temperature dependence studies with previous studies using conventional agitation t'echniquesis encouraging. It must be pointed out, however, that the procedure out(6) J. A. V. Butler, J . Phys. Chem., SS, 1015 (1929). (7) J. 0. ill, Rookris, J. Bowler-Reed, and J. A. Kitchener, Trans. Faraday Soe., 47, 184 (1951).
I.7344 1.3690 1.5738 2.0407 2.3539 2.2863
lined above does not lend itself to studies approaching equilibrium from oversaturation. It \;l.ould seem that this is a small disadvantage when one considers that such a method is a very practical way to study the solubility of relatively unstable solids. The solution suggested for this problem is simple and inexpensive. Achowledgments.-The authors are indebted to t,he National science ~ ~ and to the ~ N ~ - ~ of Health for their support,. The authors also wish to thank Mr. ill. C. Parkinson of the Virtis Company for his helpful advice and suggestions
3XUTUA.L DIFFUSIOS IK SOX-IDEAL LIQUID MIXTURES. 111. &IETHYL ETHYL KETONE-CARBON TETRACHLORIDE AND ACETIC ACID-CARBON TETRACHLORIDE BY D. K. ANDERSON AKD ,4.L. BABB Department of Chemical Engineering, University of Washkgton, Seattle, Washington Received hrovember 17,1961
Mutual tlifliusivities arid viscosities have been measured for the methyl ethyl ketone-carbon tetrachloride and acetic acidcarhon tetrachloride riysteins a t 25.0". The experimental data are discussed in terms of an equation similar in form to that of EIartley and Crank. The prescnt equation was derived by assigning intrinsic diffusivities to the dimer of the associating component as well as to the monomeric species of both components.
Introduction In a previous paper' the anthors presented diffusion data for the diethyl ether-chloroform system in which the non-ideal behavior was explained by assuming bhat a one: one complex forms between components. In this paper, Idiff usivities and viscosities are reported for the systems methyl ethyl ketone-carbon tetrachloride and acetic scidcarbon tetradchlorideat 25.0'. Experimental Diffusivities were measured with the use of a MachZehnder diff usiometer described fully elsewherel and visoosities were determined using an Ostwald viscometer. Temperatures were controlled a t 25.0 f 0.05'. The reagentgrade solvents were obtained from bIallmckrodt Chemical Works and were used without further purification. The experimental diffusivities were obtained by measuring the interdiffusion of two solutions of vel-y nearly equal concentrations. The measured value was taken to be that of a solution with a concentration equal to the average of the
two solutions. The results are given in Tables I arid I1 and in Fig. 1 and 2 . Experimental viscosities are listed in Tables I11 and IT.
Discussion Comparison of Results with Hartley and Crank Equation.-Hartley and Crank3 have shown that for non-ideal systems the concentration dependence of mutual diffusivities could be described by an equation of the form
+
DAB= B A ( ~ B ~ BDB(VACA) )
(1)
where DAB is the mutual diffusivity, a, is the socalled intrinsic diffusivity, V is the molar volume, C is the molar concentration, and the subscripts A and B refer to components A and B in binary solution. They also have shown that if the driving force for diffusion is the gradient of the chemical potential, the intrinsic diffusivity is given by
--
(1) D. K. Anderson and A. L. Bttbb, J . Phye. Chew., 66, 1281 (1961). ( 2 ) C. S . Cttldwell, J. R. Hall, and A. L. Babb, Rev. Sci. Insly., 28, 816 (1957).
(3) G. S. Hartley and K. Crank. Tvans. Faraday SOC.,45, 801 (1949).
D. K. AXDERSON AND A. L. BABB
900
Vol. 66
TABLE I SUMMARY OF EXPERIMENTAL DIFFUSIVITIES FOR METHYL ETHYLKETONE-CARBON TETRACHLORIDE Mole fraction ketone, solution A 0 0.0363 0.1954 0.397 0.499 0.745 0.9894 Mole fraction ketone, solution B 0.0186 0545 .2030 .405 .509 .752 1.000 Av. mole fraction .0093 .0454 ,1992 .401 .504 .749 0.9947 DABx lo5, cm.*/sec. 1.552 1.453 1.436 1.680 1.878 2.363 3.007 I
TABLE I1 SUMMARY OF EXPERIMEKTAL DIFFUSIVITIES FOR ACETICACID-CARBON TETRACHLORIDE Mole fraction acetic acid, solution A 0 0 0 0.00475 0.1820 0.4004 0.6008 0.8011 Mole fraction acetic acid, solution B 0.00427 0.00453 0.00981 .01759 .1920 .4106 .6108 .8105 Av. mole fraction ,00219 .00227 ,00491 .0112 .1870 .4055 ,6058 .SO58 DABX lo6, cm.*/sec. 1.416 1.414 1.365 1.356 1.208 .916 .820 .881
Mole fraction ketone Viscosity a t 25" (cp.)
TABLE I11 VISCOSITIESOF METHYLETHYLKETONE-CARBON TETRACHLORIDE 0 0.1954 0.405 0.397 0.499 0.745 0.752 0.509 0.887 0.736 0.620 0.623 0.576 0.576 0.483 0.472
TABLE IV VISCOSITIES OF ACETICACID-CARBON TETRACHLORIDE Mole fraction % ' aoeticacid 0.00 21.4 41.8 60.8 Viscosity at 25' (CP.) 0.887 0.820 0.804 0.816
80.5
0.920
I
1.000 0.393
Mole fraction acetic acid X I O 2 , 0 0.5 1.0 1.5 ,
100 0 1.126
0.9896 1.000 0.9948 1.277
2.0-
.
.
.
I I
I I
I
1.8-
1
I
02 04 0.6 08 I .o Mole fraction acetic acid. Fig. 2.-Diffusion coefficients for the system acetic acidcarbon tetrachloride: A, O, experimental; - - - -, calculated, eq. 4.
"0
01
0
0.2
0.4 0.6 0.8 Mole fraction ketone.
I .o
Fig. 1.-Diffusion coefficients. for the system methyl 0 , experimental; ethyl ketone-carbon tetrachlorlde: , calculated, eq. 3; - - - -, calculated, eq. 4.
where ai is the activity of the component, 7 is the solution viscosity, and fi is a friction coefficient dependent only on molecular size. These intrinsic diffusion coefficients are defined with respect to a reference frame through which no volume flow by bulk motion occurs. If eq. 1 and 2 are combined, the well-known Hartley and Crank equation is obtained. Equation 3 was tested on the ketone-carbon tetrachloride system by calculating the values
of fa andfB from the intercepts of the experimental diff usivity-mole fraction (X) curve. These values along with activities calculated from data available in the literature4 were used to compute the diffusivity-mole fraction curve shown in Fig. 1. The lack of agreement with the experimental data probably lies in the assumption inherent in eq. 3 that the diffusing species are simple molecules; whereas, in fact, association occurs so that the diffusing species may be dimers, trimers, etc., as well as simple monomers. Modified Form of the Hartley and Crank Equation.-In the previous paper, it was shown that diffusivity data for the system diethyl ether(4) R. T. Fowler and
G.8. Norria, J . A p p l . Chem., 6, 266 (1955).
May, 1962
N.M.R. S T U D I E S OF T H E
P31 NUCLEUS IS
P H O S P H O R U S COMPOUNDS
90 1
Application of the Modified Equation.-It is not chloroform could not be explained by the Hartley and Crank equation unless it was modified by as- possible at present to assign a definite value to signing intrinsic diff usivities to the three species fix since not enough is known about the diffusion present in solution, &e., the two monomers and the mechanism. However, a qualitative check of the ether-chloroform complex. For the system methyl validity of eq. 4 may be obtained by determining ethyl ketone-carbon tetrachloride, hydrogen bond- a single value of fll empirically from the data of ing can OCCULT between ketone molecules. These Fig. 1 and then using eq. 4 to see how well the interactions cause positive deviations from Raoult’s entire diff usivity-mole fraction curve is predicted. The parameters fl and fi as calculated from the law as opposed to the ether-chloroform system where the cross interaction causes negative devia- intercepts ,Of the experimental curve were 29.0 tions. and 34.7 A., respectively. These correspond to For the present investigation, it is assumed that Stokes-Einstein radii of 1.54 and 1.84 A.d respecthe ketone exists in solution as monomers and Using the empirical value of 2.44 A. for the dimers only and that the concentrations of these tively. Stokes-Einstein radius of the dimer, the curve species can be related by an equilibrium constant shown in Fig. 1, which fits the experimental data K = :x -11 very closely, was calculated. XI2 The system acetic acid-carbon tetrachloride where XI1and X1 are the true mole fractions of the also provides an interesting test of eq. 4. Although dimer and monomer, respectively. The methods it is not possible to estimate the degree of associaoutlined by Hildebrand and Scott5were used along tion of the acetic acid in concentrated solutions, with activity data4 t o estimate an equilibrium it dimerizes very strongly in dilute solution. constant of 5.6 for the methyl ethyl ketone in Davies, et al., have found? the dimerization cong.-mole/l. a t 25°,8 so that stant to be 2.07 X carbon tetrachloride. Intrinsic diffusivities were assigned to the over 96% of the acid is associated to dimers a t a dimer as well as to both monomers, in solution and mole fraction of acetic acid of 0.04. Calculations a modified form of the Hartley and Crank equation based on eq. 4 indicated that a very sharp increase in the diffusivity should be observed a t low conwas derived6 centrations of acetic acid. Data taken a t concentrations as low as possible are shown in Fig. 2. It is seen that the diffusivity does increase sharply near the carbon tetrachloride intercept as predicted. This fact is not predictable from eq. 3. It would be of interest to have values a t even lower concentrations. Additional experimental data are being obtained Equation 4 reduces to eq. 3 for the case when no association occurs { ( i e . , XIo = X A and Xl10 = 0). for systems with known degrees of association and Values of XIQand Xl10 can be calculated from the will be reported in future communications. Acknowledgment.-This work was supported by equilibrium constant. the U. S. Army Research Office (Durham). (6) J. H. Hildebrand and R. L. Scott, “The Solubility of Nonelectrolytes,” 3rd. ed., Reinhold Publ. Corp., New York, N. Y., 1950. (6) D. K. Anderson, P h D. Thesis, University of Washington, 1960, Dissertation Ab&., XXI, No. 6, 1388 (1960).
(7) M. Davies, P. Jones, D. Patnaik, and E. A. Moelwyn-Hughes, J . Chem. Soc.. 1249 (1961). (8)Their equilibrium constant was defined as CI~/CII.
NUCLEAR MAGNETIC RESONANCE STUDIES OF THE P31 NUCLEUS I N PHOSPHORUS COMPOUNDS BY LEOC. D. GROENWEGHE, LUDWIG MAIER,AND KURTMOEDRITZER Mmsanto Chemical Company, Research Department, Inorganic Chemicals Division, St. Louis, Missouri Received November $8. 1961
A study of two hundred new Pal nuclear magnetic resonance chemical shifts shows that the Pal relative shift contributions of common organic ligands directly bonded to a quadruply connected phosphorus atom lie in the order CaH6>/ CH&l > CHa > CzHs. Since these contributions are relatively unaffected by other groupings connected to the phosphorus, their value can be used in the estimation of chemical shifts-a fact of considerable interest in the structural analysis by n.m.r. of mixtures of organic phosphorus compounds. Consecutive substitution of one organic ligand for another on triply connected phosphorus leads to approximately equal stepwise changes in the PS1chemical shift. However, the effect of other ligands bonded to the phosphorus is so large that characteristic shift contributions cannot be assigned readily.
Since the discovery of the chemical shift in the nuclear magnetic resonance (n.m.r.) of the P31nucleus by Knie;htl Some ten years ago, about 400 n.m.r. spectra of individual phosphorus compounds have been reported in the literature. Various aut,hor$2-7 (1) W. D. Knight, Phys. Rev., 76, 1269 (1949).
have published impressive lists of P3* chemical shifts and have shown that P31 n.m.r. spectros(2) H. 8. Gutowsky, D. W. McCall, and c. P. Sliohter, J . Chern. P h w . 21.279 (1953). (3) He 6. Gutowsky and D*W. McCall, i b d , 22, 162 (1964). (4) N. Muller, P. C. Lauterbur, and J. Goldenson, J. Am. Chem. SOC.,78, 3657 (1956).
