2371
Isothermal Diifusion Measurements on H2O-Choline Chloride-KCI
isothermal Diffusion Measurements on the System Water-Choline Chloride-Potassium Chloride ;at 25"' Robert Fleming** and Louis J. Gosting The lnstitute for Enzyme Research, University of Wisconsin, Madison, Wisconsin 53706 (ReceivedJuly 26, 1972; Revised Manuscripf Received July 20, 1973) Publication costs assisted by the School of Pharmacy, Universify of London
The Gouy diffusiometer has been used to study the isothermal diffusion process at 25" in the binary system HzO-choline chloride and in the ternary system HzO-choline chloride-KC1. Values for the mutual diffusion coefficient for choline chloride in water are reported over the concentration range 0.0073-0.2232 g cc-1. The diffusion in a ternary system can be described by four volume-fixed diffusion coefficients, and these were obtained at each of four compositions of the system. For a ternary system a measure of the deviation of the flow of each solute from Fick's first law is given by a cross-term diffusion coefficient. One of these coefficients was found to be large, and the other small, and this is in accordance with the predictions of the first-order equations of O'Donnell and Gosting. Density data and refractive index derivatives for both the binary and ternary systems are reported, together with the partial specific volumes for the ternary system.
Introduction The purpose of this investigation was to study the deviations of solute flows from Fick's first law for the ternary system HzO-choline chloride-KC1 by measuring the main and cross-term diffusion coefficient^.^-^ It was thought that these diffusion coefficients should be of help in the understtanding of diffusion processes that occur during nerve conduction. Isothermal diffusion in one dimension in a ternary solution can be described along the x coordinate by the two flow equations
where the solute concentrations p1 and p2 are expressed in g cc-1. Throughout this article subscript 1 will denote choline chloride and subscript 2 will denote potassium chloride. The solute flows (J,)" are referred to the volume-fixed frame of reference and have units of g cm-2 sec-1. The four volume-fixed diffusion coefficients (D,,)" have units of cm2 sec-l. For the small concentration differences used in these experiments the volume-fixed frame of reference may be considered identical with the cellfixed (or apparatus-fixed) reference frame.6,' The size of the cross-term diffusion coefficients ( D 1 2 ) ~ and (Dp1)" can be predicted qualitatively from the limiting equivalent conductances of the ions present in the system.8 The choline ion has a much lower limiting equivalent conduct~mcegthan either the K+ or C1- ions, which have almost equal values. Consequently the flow of choline chloride, (Jl)", produced by a concentration gradient of KCl will be small, hence (DIP)" is small. Because of the large difference between the limiting equivalent conductances of the 61- and choline ions, the flow of KC1, (Jz)",produced by a concentration gradient of choline chloride will be relatively large, and accordingly (D& will be much larger than (D& and quite different from zero.
The ternary system was studied a t four compositions with the following concentrations of the solutes: 61 = 0.05, 6 z = 0.05; 61 = 0.05, 5 2 = 0.025; 6 1 = 0.025, 6 2 = 0.05; 51 = 0.025," 6 2 = 0.025. Here and throughout this paper 61 (with i = 1 or 2) denotes a particular solute concentration chosen for experimental investigation.
Experimental Section Only a brief outline of the experimental procedure and information specific to this study is given here. For a full description of the standard experimental details and procedures the reader is referred to a paper by Woolf, Miller, and Gosting.lo Materials. Choline chloride for the binary experiments was purchased from Eastman Organic Chemicals Department of Distillation Products Industries, and was recrystallized five times from a solvent consisting of a mixture (volume basis) of 70% absolute ethanol and 30% dry acetone. The crystals were dried in vacuo over magnesium perchlorate. Volumetric assay of the material for chloride content, and calculated as choline chloride, showed it to be 100% pure within the limits of experimental error (*0.25%). Choline chloride for the ternary experiments was purchased from the British Drug Houses, Ltd., En-. gland (99% pure with reference to the dried material). It was recrystallized twice using a solvent mixture of the same composition as described above and then dried in uucuo over magnesium perchlorate. In all ternary experiments the KC1 was part of a batch recrystallized by Woolf, et u1.,10 and was used without further purification. For preparation of the ternary solutions distilled water from a Barnstead steam-heated still was further purified by passing through a Barnstead purification system. The latter consisted of an organic removal column, a mixedbed ion-exchange column, a submicron filter, and a 5-galion reservoir tank. It was designed so that water could continuously circulate through the columns, filter, and tank. The water was allowed to circulate for 12 hr and was The Journal of Physical Chemistry, Voi. 77, No. 20, 1973
Robert Fleming and Louis J. Gosting
2372
then drawn off (specific resistance 12-14 megohm cm) and put in a glass carboy. I t was then saturated with air. Molecular Weights. The molecular weights ( M , ) of HzO, choline chloride, and KC1 were taken to be 18.016, 139.627, and 74.557, respectively. Solutions. Water used in the preparation of the binary solutions had been previously purified by Woolf, et a1.10 For the ternary experiments the solutions were made up with water purified according to the procedure described above. The density of each solution a t 25 k 0.003’ was measured in triplicate in 30-ml single-necked pycnometers, which were always weighed against a sealed tare of similar volume. The measurements for each solution were averaged and are recorded as experimental densities in Tables I and 11. All solutions were prepared by weight, and the weights of choline chloride, KC1, and the final solutions were each converted to weights in vacuum using the density values 1.155,11 1.984, and the solution density, respectively. The concentrations in g cc-l were calculated using the experimental densities. Diffusion Experiments. All diffusion experiments were performed with a Gouy diffusiometer which has been described p r e v i ~ u s l y$.1~2,13 The optical lever arrn,l4 b, from the center of the cell to the emulsion of the photographic plate, was 307.055 cm. The thickness, a, of the 11-ml quartz Beckman/Spinco electrophoresis-diffusion cell was measured with a special internal caliper and was found to be 2.5059 cm. The positions of the fringe intensity minima and maxima on the photographs were measured with a photoelectric null indicator, mounted on a Gaertner M2001RS toolmakers’ microscope. This has been described in detail by Wendtle and Albright.17 Approximately 18-20 fringe minima throughout each Gouy photograph, including the lower 7 (j = 0 through 6), were measured in accordance with the procedure described previously. Each value of Ct (the maximum displacement of light on a photograph according to ray optics) was obtained by the usual extrapolation procedure.l5JsJg Values of DA’,at time t’, which are preliminary values for the reduced height-area ratio, 33.4, for each experiment, were calculated using the following expression.
(3) The plot of D.4’ us. l/t’ was extrapolated to l/t’ = 0 to obtain D A , which is the reduced height-area ratio corrected for initial imperfections in the boundary.20 The starting time correction At, which was found from the slope of the graph, ranged from 7 to 29 sec. A fringe deviation graph for each experiment was made by calculating the average values of 9 , the reduced fringe deviation of each f({), and plotting them against f( {), the reduced fringe number.z2 The area of this graph gZ1
was obtained by applying Simpson’s 113 rule for numerical integration; values of 9 were read at intervals of 0.025 along the f({) axis from a smoothed curve drawn through all the average values of { on the graph. Calculation of the Four Diffusion Coefficients ( D i j ) ~ . These coefficients were calculated according to the method developed by Fujita and Gosting19 which utilizes the areas, Q, of the fringe deviation graphs, The Journal of Physicai Chemistry, Vol. 77,
No. 20, 7973
Results Experimental results for the binary system HzO-choline chloride are shown in Table I. The mean solute concentrations, p l (line 2), were obtained (eq 5) from the initial concentrations of the upper solutions, (PI)*, and the lower ~ , are given on lines 3 and 5 . The exsolutions, ( p ~ ) which perimental densities of the initial solutions, da and d B (lines 4 and 6, experiments 4-8), show reasonable agreement (average deviation 0.0013’70) with the corresponding values calculated from the polynomial equation d = 0.997048 4- 0.11725~~ - 0.03133~1~ f O.09595pl3 (5) which was fitted by the method of least squares23 to the experimental densities using the Atlas computer. The concentration differences, Ap1 (line 7), between the initial solutions in the first two experiments were sufficiently large to give approximately 100 fringes (J, line 8) so that accurate values of D ~ a n dQ could be determined. However, the areas of the fringe deviation graphs (line 10) for each of these experiments were significantly different from zero. This could be due to (a) optical imperfections in the apparatus, (b) solute impurity, or (c) the dependence of certain properties of the solution on solute concentration.lsJ4 The first possibility was considered to be remote, as previous experiments in the same cell and apparatus with pure solutes having negligibly concentration dependent properties gave values of Q = 0 r 2 X 10-4, which indicated an absence of optical imperfections. Also a preliminary test experiment with 1.5’70 sucrose in water a t the start of the present study yielded a value of Q which was approximately 2 X Possibilities b and c can be distinguished because if p 1 is held constant, and A p l is decreased, Q should remain constant for b, and Q should approach zero for e. Therefore experiment 3 was performed with a smaller value of Ap1, using solute from the same batch as in the first two experiments. In this experiment Q became nearly zero (within experimental error) thus ruling out possibility b and indicating that values of A p l between 0.008 and 0.0110 should be the best compromise for the remainder of the experiments. With these concentration differences the effects of concentration-dependent properties of the solution are minimized, yet J is large enough for reasonable accuracy. Furthermore, in acapproximately in cordance with e x p e ~ t a t i o nQ~ decreased ~ proportion to (Ap1)2. If & (line 9) from experiment 1 is adjusted slightly t o correspond to p l = 0.00816 (by using data from other experiments in Table I to estimate the slope of 3JA us. d p 1 ) a value of DA = 1.2245 X is obtained. When this value of DAtogether with those from experiments 2 and 3 are plotted against the corresponding (Ap1)2, the graph is found to be approximately linear in agreement with theory,lsJ4 and it has a very small slope. Thus Q for experiments 3-8 may be identified with the mutual diffusion coefficient, D, within the limits of experimental error. In the study of the ternary system, four sets of experiments were performed corresponding to the four compositions specified by the values of /51 and /52 in line 1 of Table 11.26 For each experiment the mean concentrations of the solutes, p l and p z are listed on lines 3 and 4; they are seen to be very close to the corresponding values of and 5 2 . The experimental densities (lines 7 and 10) were determined as previously described, and the method of least squares was used to evaluate the constants H1 and HZ in eq 6; the results of these calculations are shown in Table 111.26 In all experiments the values of
Isothermal Diffusion Measurements
on HZO-Choline
2373
Chloride-KCI
TABLE I: Data for the Binary System HpO-Choline Chloride at 2 5 0 a
1 Expt n0.b 2 P1 3 (P1)A 4 dA 5 b1)B 6 dB 7 APi 8J 9 DA x 105 1 0 0 X lo4 11 A n l A p ,
1 0.00730g 0
2 0.008134 0
0.014619 0.99875' 0.014619 100.53 1.2274 9.14 0.14986
0.016268 0.99894' 0.016268 111.89 1.2240 10.94 0.14988
5 0.027164 0.023164 0.00753 0.031165 1.000676 0.008001 54.77 1.1738
3 0.008178 0.004111 0,99749' 0.012245 0.99846' 0.008133 55.92 1.2252 3.67
5.21
0.14983
0.14917
8 0.049972 0.0044632 1.002245 0.055313 1.003468 0.01 0682 73.30 1.1367 2.75 0.14954
7 0.065122 0.060292 1.00401 1 0.069951 1.005121 0.009659 66.16 1.1214 2.81 0.14923
4 0.1 23849 0.118876 1.010735 0.128822 1.01 1820 0.009946 68.45 1.0904 3.96 0.14998
6 0.223167 0.219188 1.022255 0.2271 45 1.023192 0.007957 55.12 1.0702 7.16 0.15095
a Units: concentrations and densities, g c c - l ; D A , cm2 sec-l; A n l a p , , cc g - l , For all experiments except 1 and 2, A p l was sufficiently small that DA should be numerically equal to the mutual diffusion coefficient, D , with experimental error: this D is defined by Fick's first law in the form ( J l ) v = -D(apl/ax) and corresponds to the concentration p1 = p i . Similarly A,/Apl may be identified with R1 for the composition p l = p 1 and p2 = 0. Experiments nlJrnbered chronologically. Interpolated from a large graph of experimental densities measured at other concentrations.
TABLE I I : Datal for the Ternary System H20-Choline Chloride-KCI at 250aqb
1 Composition 2 Expt no.c 3 (P1)A 4 (P2)A 5 d.4 6 (PI)B 7 (P2)B 8 dB 9J I O D A x 105 11 Q x 104 1 2 ( D ~ x ~105) 1 3 ( D ~x ~105) 1 4 ( D ~x ~105) 15 ( D ~x ~105)
= 0.05, 5 2 = 0.05 12 11 0.0456825 0.0489650 0.0488190 0.0455233 1.032233 1.030609 0.0543181 0.0510292 0.051 1844 0.0544695 1.034587 1.036217 65.72 72.04 1.66& 1.2200 25.53 57.07 0.9890 0.0519 0.2325 1.7812
Set I : 51
9 0.0499870 0.0444908 1.0301 15 0.0499975 0.0554979 1.036715 63.73 1.8670 -15.18 ~ ~ ~ ~ ~ ~
10 0.0445007 0.0500007 1.032816 0.0555001 0.0499777 1.033992 74.47 1.1245 43.18
= 0.025, 52 = 0.05 24 22 23 0.020731 7 0.0240201 0.0195003 0.0454771 0.0487702 0.0500015 1.029801 1.027801 1.030110 0.0259785 0.0292693 0.030501 2 0.0545182 0.0512349 0.0500018 1.031917 1.033535 1.031307 65.89 72.04 74.17 1.6621 1.2303 1.1227 30.09 60.04 45.99 0.9790 0.0254 0.2463 1.8161
Set I I I: 51
1 Composition
2 Expt no. 21 0.0249985 3 (P1)A 0.0444985 4 (P2)A 1.027333 5 dA 0.0250003 6 (Pi)B 0.0555024 7 (P2)B 1.034023 8 dB 9J 64.18 10D.4 x 105 1.8588 11 Q x 104 -6.17 12 ( D ~x ~105) ~ 13 pl2lV x 105 1 4 ( D ~ x ~105) ~ ~ 1 5 ( D ~x ~105) ~ ~
Set 1 1 : 51 = 0.05, 6.~ 2 = 0.025 17 18 13 0.0490130 0.0457230 0.0499981 0.0204899 0.0237760 0.0194999 1.015404 1.017043 1.01491 g 0.0542770 0.0499976 0.0509856 0.0295168 0.0262250 0.0304983 1.021142 1.019497 1.021624 66.86 73.03 65.46 1.8185 1.6296 1.2107 24.36 48.10 -7.13 1.0102 0.0295 0.1628 0.7699
14 0.0444989 0.025001 1 1.01 7667 0.0554944 0.0249975 1.018895 74.90 1.106~ 29.40
Set I V : p1 = 0.025, 5 2 = 0.025 16 15 19 20 0.0250025 0.0240055 0.0207161 0.01 94965 0.0195032 0.0204950 0.0237857 0.0249956 1.012106 1.012599 1.014249 1.014862 0.0250048 0.0259950 0.0292843 0.0304946 0.0305084 0.0295054 0.0262204 0.0249961 1.018860 1.018356 1.016710 1,016085 65.89 67.41 72.55 74.76 1.8194 1.6291 1.2138 1.1117 -0.41 32.21 46.37 35.65 1.002~ 0.0063 0.1791 1.8076
DA, cm2 sec-': R L , cc g-': D i i , cm2 s e c t (see eq 1 and 2 for their complete definition). 0 = H 2 0 , Experiments numbered chronologically.
a Units: concentrations and densities, g ccrl;
1 = choline chloride, 2 = KCI.
GI)
d(il,i,) + H ~ - ( + ~ H~ ~ - i (, ~) (6) ~ Apl + Apz were close to 0.0110 g c r i . Since choline chloride is a hygroscopic substance and difficult to weigh accurately the agreement between the experimental and the calculated number of fringes, J, was considered to be satisfactory. The partial specific columes, Ek, of the solutes and (lines 8, ', and lo Of Table 111) for the ternary solutions were calculated using the equation27 d(p,, ,)
uk
=
=
1-
d
H k
- HIPI - HZP2
(h
=
1,2)
(7)
Here Hk are the coefficients given in Table 111, d is the ) , pJ = j J 0' = experimental density given as d ( p ~ , p ~and 1,2) is the concentration of each solute expressed in g
.
Fp-i vu
Discussion The three-dimensional graphs of the ( D , J ) v in Figure illustrate the relationships between (a) previous data for diffusion in the binary system Hz0-KC1,28,29 (b) the new binary diffusion data in Table I for HzO-choline chloride, and (c) the new data in Table 11 for diffusion a t four comThe Journal of Physical Chemistry, Voi. 77, No. 20, 7973
2374
Robert Fleming and Louis J. Gosting
(DZ1 IO5
Figure 1. Variation with solute concentrations of the volume fixed diffusion coefficients, ( D i j ) ~defined , by eq 1 and 2 for the system HZO-choline chloride-KCI at 25". Circles represent the ternary data. These ternary data for the main diffusion coefficients are connected to data for the appropriate binary system by solid curves. Solid curves also represent the data for binary systems in their respective planes. The scales of the vertical axes in the graphs of the cross-term diffusion coefficients, ( D 1 2 ) ~and (D2i)~7,have been expanded. All the ( D i j ) have ~ u n i t s of cmz sec- and correspond to solute concentrations expressed in g cc- I. As PI- 0 in this plane the Nernst limiting value TABLE I l l : Constants of Eq 6 for the Densities, and Values of the Partial Specific Volumes, for the System H20-Choline [(~Jm+ l p0, (01O)m (9) Chloride-KCI at 25" a may be calculated from the equation32
-
1 Set
)I
Ill
0.050
0.025
5 Hi 6 Hz 7 % errorb
0.025 1.018274 0.11207 0.61026
0.050
1.033414 0.10829 0.60043
1.03069, 0.1 0873 0.60899
0.0005
0.0005
0.0015
8 Po 9 P,
1.00203 0.8935
10 'v2
0.4004
1.00259 0.8902 0.3908
1.00249 0.8935 0.3920
2 P1 3 52 4 d(Fi&)
I 0.050 0.050
iV 0.025 0.025 1.015477 0.1 1179 0.61401 0.0003 1.00267 0.8906 0.3870
a Units conceitrations and densities g cc-', partial specific volumes, cc g - ' Per cent error = [average deviation/d(b,,F2)] X 100
positions of the ternary system HzO-choline chlorideKCl. In addition, certain limiting values of these (&)\, in regions where no experimental data are yet available were computed from values of the limiting equivalent ionic conductances, h,O, and are also shown. Because choline chloride and KC1 are both electrolytes, the diffusion coefficients were plotted against pL1 2 rather than p L to avoid infinite slopes as p 1 and pz approach zero. Data for the curve in the (D& - p 1 1 I 2 plane were taken from Table I, because as pz 0 in the ternary system, with p1 constant, (D& becomes identical with the , choline chloride mutual diffusion coefficient,30 ( D I ) ~for in water at that value of p l
-
A value of (DIO), = 1.355 x 10-5 cmz sec-1 was obtained with F = 96493 C equiv-I, R = 8.3146 X l o 7 erg deg-l mol-I, T = 298.16", A10 (choline ion19 38.2 and A30 (chloride ion)S3 = 76.35 cm2 ohm-1 equiv-1. It is seen that the decrease of ( D l ) , as p l increases from 0.000 to 0.007 g cc-1 is greater than its decrease over the entire concentration range studied in this investigation. The dependence of this mutual diffusion coefficient on p l is seen more clearly in Figure 2, where the data may be compared with the limiting slope predicted by the Onsager-Fuoss t h e o r ~ . ~ ~ , ~ ~ The adjustable parameter b in the equation
was found by fitting the above equation to the experimental activity coefficient data of Lindenbaum and Boyd.36 Equation 5 was used to convert their molal concentrations to molar, and the values of A, B, and a were taken to be 0.5115,0.3291 X 108, and 4 X 10-8 cm, respectively. Theoretical diffusion coefficients over the concentration range 0.001-0.01 M were calculated using the equation of Onsager and F U O S S . ~ ~
-
D The Journai of Physical Chemistry, Voi. 77, No. 20, 7973
=
M
16.629 X 10IOT~ - (4-l c d In y+/dc)
(12)
2375
Isothermal Diffusion Measurements on H2O-Choline Chloride-KCI
+
where &?/c is the mobility term and (1 c d In y*/dc) is the thermodynamic term and is represented by the dashed line in Figure 2. Diffusion coefficients were also calculated according to the equation
D
=
Do(l
+ c d lny+/dc)
(13)
Do (1.3558 x 10-5 cmz sec-1) was calculated from the
q.10'
limiting equation of Onsager and Fuoss38 and the thermodynamic term was estimated using the value b of 11 together with eq 6-10-2 and 6-10-3 of ref 29. Since the solutions are very dilute, the density term c$(d) was omitted. The results of these calculations are represented by a dotted line in Figure 2. Diffusion coefficients calculated ac0 0.1 0.2 0.3 04 0 5 cording to eq 13 deviate only slightly from the straight line joining DO and the lowest experimentally determined 4diffusion coefficient. Figure 2. Variation of the mutual diffusion coefficient (as repreAs p1 0 in the ternary system, with p2 constant, sented by 3 ~of )choline chloride at various concentrations in (Dll)" approaches the tracer diffusion coefficient, ( D I ) ~ , water at 25". Circles represent experimental data. The solid line in the very dilute region represents values of the mutual diffuof choline ion for concentration pz of KC1 in water
-
[(Dll)~lpl -o
(p2 constant
f
f
0 ) (14)
These data iin the ( D I ~-) p ~ z 1 I 2 plane were not available, but the limiting tracer diffusion coefficient
[(DJl,
--to
-
(Dl%
(15)
was calculated from the relation39
(Df)t
=
( R T / F 2 ) h i 0X lo-'
(16)
The resulting value, 1.017 X 10-5 cm2 sec-l, is shown in Figure 1. A description of the graph of (D22)" in Figure 1, showing how it includes the mutual diffusion coefficient, ( D Z ) ~of, H:;O-KCl and the tracer diffusion coefficient, of potassium ion (or KCl) as limiting cases, is readily obtained from the preceding discussion of (Dll)" by changing the word choline to potassium and replacing subscripts 1 by 2 and 2 by 1 (except where numerical values are given). With the additional value Azo (potassium ion)33 = 73.50 cm2 ohm-1 equiv-1 one may calculate the limiting mutual and tracer diffusion coefficients ( 0 ~= 1.994 ~ ) X ~10-5 and ( D z O ) = ~ 1.956 X 10-5, respectively, which ,are shown on the graph. In the limits p1 0 or p2 0 the cross-term diffusion ~ ( D z l ) ~shown , in Figure 1, do not coefficients ( D l z ) and reduce to diffusion coefficients which have been commonly measured before. As pointed out previouslys ( D l 2 ) ~ 0 as p1 0 with p2 constant and nonzero, and ( D z l ) ~ 0 as p 0 with p 1 constant and nonzero. However, in the opposite limiting case for (D12)V or (D21)v each cross-term diffusion coefficient approaches a nonzero value (when 0 both solutes are electrolytes). For example, if first p z and then p l -- 0 in approaching infinite dilution, (DIP)" for this system approaches the relatively small value40
-
-
--
--
-
-
= 0.047 X
However, if first p1 0 and then es the much larger value40
p
= 0.246 X
cm2 sec-l (17) 0, (D21)\7 approach-
cm2 sec-'
These limiting values are included in Figure 1.
(18)
sion coefficient predicted by the Onsager-Fuoss theory (eq 610-6 of ref 29). Units DA, c m 2 s e c - ' ; p i , g c c - ' . The dotted line represents the mutual diffusion coefficient predicted by 610-15 of ref 29, and the dashed line by eq 6-10-3.
The present study was undertaken as part of a series of physical-chemical measurements on solutions containing choline chloride.42.43 This compound can be prepared in high purity, and it forms stable solutions suitable for accurate measurements. The results in this paper show that the HZO-choline chloride-KC1 system exhibits marked deviations from Fick's first law. For the compositions studied, the relatively large values of (D& indicate that a concentration gradient of choline chloride is 1525% as effective as a gradient of KC1 in producing a flow of KC1. Therefore a suitable concentration gradient of choline chloride can cause KC1 to flow from a region of lower KC1 concentration to a region of higher KC1 concentration against an appreciable concentration gradient of KC1. It should be noted that the values of the cross-term diffusion coefficients reported in Table I1 are for solute flows and concentration gradients expressed in grams in eq 1 and 2. If these quantities were expressed in moles the values of (D& would be nearly twice as large, because then they must be multiplied by the molecular weight ratio M 1 / M z = 1.8728; the values of ( D I z )would ~ be about half as large because then they must be divided by l . 8 7 2 ~ . ~ The O addition of other solute components, such as those commonly found in nerve cells, to the present system would cause some change in the values of the diffusion coefficients reported in Table 11; also, additional diffusion coefficients3 would be required to describe completely diffusion in the more complicated systems. The present data represented by the three-dimensional graphs in Figure 1 would then represent parts of the graphs for these four diffusion coefficients in more complicated systems. s5
Supplementary Material Available. Listings of the calculated values of J, D A , Q, the refractive index increments, and Table 111 will appear following these pages in the microfilm edition of this volume of the journal. Photocopies of the supplementary material from this paper only or microfiche (105 X 148 mm, 2 0 X reduction, negatives) containing all of the supplementary material for the papers in this issue may be obtained from the Journals Department, American Chemical Society, 1155 16th St., N.W., Washington, D. C. 20036. Remit check or money order for $3.00 The Journal of Physical Chemistry, Vol. 77, No. 20, 1973
2376
for photocopy of $2.00 for microfiche, referring to code number JPC-73-2371.
References and Notes (1) One of us (R. F.) is indebted to the Wellcome Trust (London) for
(2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
(12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22)
the award of a Travel Grant. This investigation was supported in part by the National Science Foundation (U. S.) Research Grant No. G-179 and by the National Institute of Arthritis and Metabolic Diseases (USPHS) Research Grant No. AM-05177 and career award AM-K6-16,715 (to L. J. G.) Present address, School of Pharmacy, University of London, London, England. R. L. Baldwin, P. J. Dunlop, and L. J. Gosting, J. Amer. Chem. SOC.. 77. 5235 (19551. P. J: Dunlop and L.' J. Gosting. J. Amer. Chem. SOC., 77, 5238 ica, 19, 1095 (1953). G. J. Hooyman, Physica, 22, 751 (1956). G . J. Hooyman, H. Holtan, Jr., P. Mazur, and S. R. de Groot, Physica. 19, 1095 (1 953). J. G. Kirkwood, R. L. Baldwin, P. J. Dunlop, L. J. Gosting, and G. Kegeles, J. Chern. Phys., 33, 1505 (1960). I. J. O'Donnell and L. J. Gosting in "The Structure of Electrolytic Solutions," W. J. Hamer, Ed., Wiley, New York, N. Y., 1959, Chapter 11. H, 0 , Spivey and F. M. Snell, J , Phys. Chem., 68, 2126 (1964). L. A. Woolf, D. G. Miller, and L. J. Gosting, J. Amer. Chem. SOC., 84, 317 (1962), Estimated from data given in the "Handbook of Chemistry and Physics," 41st ed, Chemical Rubber Publishing Co., Cleveland, Ohio, 1959, and Heilbron's Dictionary of Organic Compounds, Oxford University Press, New York, N. y., 1943. L. J. Gosting, E. M. Hanson, G. Kegeles, and M. S. Morris, Rev. Sci. lnstr., 20, 209 (1949). P. J. Dunlop and L. J. Gosting, J. Amer. Chem. SOC.,75, 5073 (1953). Footnote 27 of ref 15. D. F. Akeley and L. J. Gosting, J. Amer. Chem. SOC.,75, 5685 (1953). R. P. Wendt, Ph.D. Thesis, University of Wisconsin, Madison, Wisconsin, 1961 (Microfilm No. 61-680). J. Albright, Ph.D. Thesis, University of Wisconsin, Madison, Wisconsin, 1963 (Microfilm No. 63-2878). L. J. Gosting and H. Fujita, J. Amer. Chem. SOC.,79, 1359 (1957). H. Fujita and L.J. Gosting,J. Phys. Chem., 64, 1256 (1960). L. G. Longsworth, J. Arner. Chem. SOC., 69, 2510 (1947). H.Fujita, J. Phys. SOC.Jap., 11, 1018 (1956). Equations 8 and 9 of ref 17 or eq A-5 and A-8 of ref 21.
The Journal of Physical Chemistry, Vol. 77, No. 20, 1973
Robert Fleming and Louis J. Gosting (23) Method of least squares-Mercury Autocode program P 1000, used on Atlas Computer, University of London. 83, 2862 (1961). (24) H. Fujita, J. Amer. Chem. SOC., (25) See p 173 of ref 8. (26) See paragraph at end of paper regarding supplementary material. (27) P. J. Dunlop and L.J. Gosting, J. Phys. Chem., 63, 86 (1959). (28) L. J. Gosting, J. Amer. Chem. SOC.,72, 4418 (1950). (29) H. S. Harned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions," 3rd ed, Reinhold, New York, N. Y., 1958. (30) The mutual diffusion coefficient for a binary liquid system is defined to correspond to a volume-fixed frame of reference so, for any given composition of the system, it will have the same value in Fick's first law written for either the solute or solvent (see ref 31). Because this choice of reference frame is not arbitrary the subscript v is omitted in the symbol (D,)m; the subscript number after D is included to designate the system considered (1 for HzO-choline chloride or 2 for H20-KCI). (31) R. P. Wendt and L. G. Gosting, J. Phys. Chern., 63, 1287 (1959). (32) For this limiting case where first ( p 2 / p 1 ) 0 and then p1 0 see, for example, eq 11.4 of ref 33. (33) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," 2nd ed, Butterworths, London, 1968. (34) L. Onsager and R. M. Fuoss, J . Phys. Chem., 36,2689 (1932). (35) This limiting slope was computed from eq 6-10-6 of ref 29 with the values 0.008903 P and 76.30 for the viscosity and dielectric constant, respectively, of water at 25". (36) G. E. Boyd, A. Schwartz, and S. Lindenbaum, J. Phys. Chem., 70, 821 (1966). (37) Equation 4-4-24 of ref 29. (38) Equation 6-1 0-5 of ref 29. 0 see, for (39) For this case where first ( p j ! p 2 ) + 0 and then p~ example, 18 and 23 of ref 8 or the first term on the right of eq 610-13 of ref 29. (40) Relations 17 and 18 were obtained by taking the appropriate limits of eq 19 and 20 of ref 8, after first multiplying the latter equations by ratios of the solute molecular weights so they will give diffusion coefficients corresponding to grams instead of moles (see ref 41). When the equations of ref 8 were derived, only the requirements of electroneutrality and zero net electric current were considered; hence the electrophoretic effect, the time of relaxation effect, and the effects of changes of activity coefficients with concentrations were neglected. These effects should not influence relations 17 and 18 for infinite dilution, but they may contribute substantially to values of the (Di,)" as the solute concentrations are increased. Because the electrolyte concentrations used in this investigation are relatively high, no comparison is included of the (Dlj)\r reported in Table II with values predicted from the equations of ref 8. (41) See the footnote to Table 3 of ref 8. (42) R. Fleming, J . Chern. SOC.,946 (1966). (43) R . Fleming, J. Chern. SOC.,3100 (1961).
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