270
NOTES
cm2/sec, while the data of Gosting and Morris extrapolate to D = 4.60 X cm2/sec. Since the sucrose used by Henrion was isotopically equivalent to that used by Gosting and Morris, the factor C becomes the ratio of the diffusion coefficients measured by the respective methods. This gives the same value of 1.020 for the correction factor C. This agreement provides additional support for the assumption that a systematic error exists when the diffusion of 0.5 &I KC1 is used to calibrate the diaphragm cell. Equation 2 will be used to calculate limiting intradiffusion coefficients from available mutual-diff usion coefficients for the systems studied by Mills, et al. I n order to obtain a valid comparison, the masses of the labeled molecules used by 92ills must be applied in eq 2. Specific activity datal3#l4 for the various tracer species used in these experiments indicate that the tracer species contained one 14C atom per molecule. This assumption provides a coherent correlation for the data from the urea, thiourea, mannitol, @-alanine, P-alanine, benzene, and cyclohexane experiments. The deviation of the corrected limiting iritradiffusion coefficient (D+= 0.515 X cm2/sec) of sucrose' from the value calculated from eq 2 ( D + c a ~ o d= 0.521 X cmZ/sec) with the assumption above and the limiting mutual-diffusion data of Gosting and l\lorris suggests that the sucrose 14C used in the experiments contained several 14C atoms per tracer molecule. Data obtained from the Radiochemical CentreI6 for the sucroseJ4C used by Mills and Ellerton indicate that this material contained not less than three 14C atoms per molecule. In Table I, the corrected limiting intradiff usion coefficients are compared with the values calculated from eq 2.
It is striking that agreement between the calculated and corrected D + is in all cases within the estimated experimental error of the measurements. Contrary to the suggestion of Mills and Ellerton,l this treatment suggests that "surface effects" probably do not increase the rate of diffusion of polar nonelectrolytes through the glass frit in the diaphragm cell. These results indicate the need for applying mass corrections as in eq 2 to the measured limiting intradiff usion coefficients in order to compare these coefficients with the limiting mutual-diffusion coefficients. It should be noted that radiochemical suppliers do not routinely supply any information concerning the molecular distribution of the l4C in their uniformly labeled compounds. Clearly future investigators in the tracer diffusion field should concisely describe the molecular distribution of I4C in their tracer species. Acknozoledgment. The author wishes to thank Dr.
J. G. Albright, Department of Chemistry, Texas Christian University for many helpful discussions and wishes to express his gratitude to Texas Christian University for a University Fellowship, 1967-1968. (13) R. Mills, Australian National University, personal communica-
tion.
(14) J. G. Albright, Texas Christian University, personal communica-
tion.
(15) Dr. J. R. Catch, Radiochemical Centre, Amersham, Bucltinghamshire, England, personal communication.
Shereshefsky's Equation and Binary-Solution Surface Tension
by Donald J. Cotton Table I : Calculated and Corrected Limiting Intradiff usion Coefficients
1 0 5 +&ad, ~ cmt//sec
Thiourea Mannitol Sucrose Benzene C-C~HI~ a-Alanine @-Alanine Urea
1.340a 0 .67Oalb 0 .52ja 1,890' 2.104' 0.92@ 0.944d 1.386k
106~0,
cms/sec
1.3310' 0,662' 0 .5226g 1.876h 2.101h 0.91Si O.93Qi 1.382'
iVa%alShip Research and Development Center, Annapolis, Maryland 81608 (Received *Wag 22, 1968)
1@D'calod D 'cor (Do/D' = ( = l O 6 D $ b s d / [ M + / ~ o ]lh), 1.020)~ oma/sec oma/seo
1.314 0,658 0,518"' 1.852 2.076 0.905 0.929 1.359
1.314 0.657 0.515 1.853 2.062 0.910 0.926 1.359
a See ref 5 . 'See ref 1. See ref 4. See ref 3. e D. B. Ludlum, R.. C. Wanner, and H. W. Smith, J . Phys. Chem., 66, 1.540 (1962). P. J. Dunlop, ibid., 69, 4276 (1965). 'See ref 12. H. S. Harned, Discussions Faraday SOC.,24, 7 (1947). F. J. Gutter and G. Kegeles, J . Amer. Chem. SOC.,75, 3893 (1953). H. C. Donoian and G. Kegeles, ibid., 83, 255 (1961). See ref 10. Calculated for three 14C atoms per See ref 2. sucrose-14C molecule.
~ _ _ _ _The Journal of Physical Chenzistrg
Equation 1, based on therodynamic considerations and on an assumed model of the surface region of a binary solution, has been derived by Shereshefsky'
- - --e
N21
AU
AUQ
-AFia/RT
Nzi + ---(I
- e-AF12/'T)
A go
(1)
where A U = u - ul; AUO = u2 - ul; AF12= (u1 us)Az,/t; Nzl is the solute mole fraction; u is thc surface tension of the solution; u1 is the surface tension of the solvent; 0 2 is the surface tension of the solute; Azs is the molecular surface area of the solute; t is the thickness of the adsorbed layer; T is the absolute temperature; R is the gas constant. Accordingly when Nzl/Au is plotted vs. Nzl a straight line should result and ( I ) J. L. Shereshefsky, J. Colloid Interfac. Sci., 24, 317 (1967).
NOTES
271
Table I : Surface Energy and Burface Area Constants for Several Binary Systems of Liquefied Gases System (solutesolvent)
Temp, OK
Calcd
Obsd
10-9AFta, ergs/m
Calcd
Density
(layers)
NrCO N~-CHI Ar-CH4 CO-CHd CH4-Kr
83.82 90.67 90.67 90.67 116.00
1.62 10.91 6.14 10.00 4.25
1.60 11.80 6.13 10.13 4.24
4.30 10.6 5.58 7.87 3.96
4.5 17.4 14.4 16.8 15.5
16.2 (78°K) 17.0 (90°K) 14.4 (90’K) 16.8 (90°K) 18.1 (133’K)
4
--Apso,
ergs/cm+
A29, 8
t
2
1 1 1 7
__
Table I1 : Surface Energy and Surface Area Constants for Molten Mixtures of Tin and Silver a t Various Temperatures Temp, OC
--Apso,
1000 1100 1200
400.0 393.0 383.0
Calcd
ergs/cml-Obsd
IO-ZOAF, ergs/m
14,93 15.56 14.48
399.0 396.0 386.0
Calcd
Age, AaIonic
Covalent
Ionic
6.20 6.56 6.28
6.33 6.33 6.33
25.1 25.1 25.1
1.02 0.96 1.00
r
-,t
(layers)Covalent
4.05 3.83 4.00
obtained for solidified-gas density datal4 and which implies that methane molecules in the surface region are packed as in a pure solid state. (intercept)
= a = -e-
A go
1 AUO = a+b
AFiz/RT
(3)
Binary Mixtures of Molten Metals
(4)
Consequently, if surface tension as a function of concentration is known for a particular binary system, Au0, AFlz, and Azs can be calculated. This note is to demonstrate the general applicability of the derived equation with surface tension data from a number of widely different types of binary systems.
Binary Solutions of Liquefied Gases Surface tension data for cryogenic binary solutions of carbon monoxide, and of methane in nitrogen,Z and solutions of argon, of carbon monoxide,2 and of krypton3 in methane were analyzed. A least-squares fit of mole fraction divided by Au us. mole fraction was made for each system, and Auo, AF12, and Ala were calculated by applying eq 1-3. Results are summarized in Table I, where Auo(ca1cd) and Auo(obsd) were calculated by using eq 4 and the actual data, respectively. Az8(calcd) was obtained by using eq 5 , and Azs(density) was calculated for the same molecule by Emmett4from density data. Auo(calcd) corresponds to Am,(obsd) to within 0.1 erg/cm2 for all systems, except N2-CH4, which was expected inasmuch as their difference is indicative of the degree of orientation of surface molecules. Azs (calcd) also corresponds closely to an integer multiple of Az,(density), except for the CH:-Kr system for which Azs(calcd) is approximately 15.0 A2, the molecular area
Data of the surface tension of molten mixtures of silver and tin at various temperatures measured by Lauermann, Rletzger, and Sauerwaldj were fitted by least squares to the derived equation. Results are summarized in Table 11, where ABs(ionic) and Ass (covalent) are the molecular surface areas Dcalculated using the Pauling ionic radius of tin,B 0371 and the Pauling covalent radius of tin,’ 1.412 A, respectively. Alls(calcd) closely approximates Az8(ionic) which implies that tin molecules in the surface region are in the ionic state. However, the ratio of Azs(covalent): Azs (calcd) indicates that the surface region is four layers thick with tin molecules. The latter interpretation is attractive inasmuch as normally covalent metallic bonds are expected to exist in a metal alloy, yet an adsorbed layer four molecules thick is unusually high. In both cases, the results predict that the surface of a liquid metal binary system is rich in the component of lower surface tension. Inasmuch as no large migration of atoms is expected upon solidification, the soli1 surface of the alloy is also expected to be rich in the same component. (2) F. B. Sprow and J. M. Prausnitz, Trans. Faraday Soc., 6 2 , 1105 (1966). (3) S. Fuks and A. Bellemanns, Physica, 32, 594 (1966). (4) P. H.Emmett, “Catalysis,” Vol. 1, Reinhold Publishing Corp., New York, N. Y., 1954,p 31. (5) I. Lauermann, L. G. Metzger, and F. Sauerwald, 2. Phys. Chem. (Leipzig), 216, 42 (1961). (6) L.Pauling, “The Nature of the Chemical Bond,” 2nd ed, Cornel1 University Press, Ithaca, N. Y., 1940. (7) L. Pauling, J . Amer. Chem. Sac., 69,542 (1947).
Volume 78, Number 1
January 1969
272
NOTES
Table 111: Surface Energy and Surface Area Constants for Molten Mixtures of Silver and Alkali Nitrates a t 350' --Am,
Solute
Calod
LiN08
30.12 24.56 29.32 35.42 43.78
NaNO,
KNOa RbN03 CSNO~
erps/em+ Obsd
29.95 24.00 29.15 35.35 44.40
A-
(layers)-
10-'OAF, ergs/m
Calcd
Density
Ionic
Density
Ionic
2.53 3.89 7.69 8.36 8.36
14.0 26.9 43.8 39.3 31.3
16.3 17.7 20.2 21.6 23.3
23.2 30.0 40.9 46.2 54.6
1.2 0.7 0.5 0.5 0.7
1.7 1.1 0.9 1.2 1.7
Ais,
---t
Table IV : Surface Energy and Surface Area Constants for Molten Mixtures of Alkali Nitrates at 350" -Am,
Solute
So1vent
Calcd
KNOs RbNOa CsNOa RbNO, CSN0a
NdOa KNOa KNOa NaKos KaNOa
5.64 6.25 12 94 12.53 20.47
Table V:
ergs/om+ Obsd
5.18 6.20 15.25 11.35 20 40
I
I
lO-lOAF, ergs/m
Calcd
A * ~A\, Density
Ionic
2.56 1.76 4.04 3.62 5.42
75.4 46.9 51.8 48.0 44.0
20.2 21.6 23.3 21.6 23.3
40.9 46.2 54.6 46.2 54.6
-t
(layers)Density Ionic
0.3 0.5 0.4 0.5 0.5
0.5 1.0 1.0 1.0 1.2
Surface Energy and Surface Area Constants for Molten Mixtures of Alkali Chloride and Alkali Sulfate a t 1200"
Solute
Solvent
Calcd
Obsd
lO-lOAF, ergs/m
Calod
Aas, A -Density
Ionic
Density
Ionic
NaCl
NasSOd &.SO1
83.5 64.0
83.4 58.3
3.14 6.66
6.7 20.4
17.0 20.8
41.2 41.2
2.5 1.0
6.1 2.0
-AvoD
xc1
ergs/om+
Binary Mixtures of Molten Salts Surface tension data for various molten mixtures of alkali metal nitrates, alkali metal nitrates and silver nitrate, and alkali metal chlorides and sulfates, obtained by Bertozzi and Sternheim* and Bertozzi and Soldani,p were analyzed. The results are ehown in Tables 111-V. In Tables IV and V, &(calcd) and Az,(density) refer to solute molecules. Azs(ionic) in Tables I11 and I V is the sum of the ionic surface areas of the cation and the anion comprising the solute molecule. Payling ionic radii were used for the cations, and 1.22 A was used as the radius of the nitrate ion,1° which was assumed to be symmetrical. I n Table V, &,(ionic) is the ionic surface area for a monovalent chloride ion. The surface layer thicknesses are labeled according to the molecular surface area employed in their calculation. I n Tables IV and V, t(density) is fractional, which is physically forbidden. This indicates, as expected for an ionic mixture, that the alkali nitrate molecules are not randomly oriented in the surface region. The surface layer thickness t(ionic), however, does closely approximate an integer, except for the KN03-NaN03 system. APl(ionic), used to calculate t(ionic), is based on a surface structure consisting of a cation lying adjacent to an anion as found in the solid state. Consequently, these results suggest that the surface structure The Journal of Physical Chemistry
y
t (layers)-
of the molten mixture is the same as for the solid state. I n Table V, t(density) for the NaCI-NazSO4 system, unlike that for the KCI-K2SO4 system, is noninteger. (ionic), however, is approximately an integer for both systems, which indicates that the surface region is comprised of a layer of chloride ions. Since the ionic surface area of a chloride ion is much larger than that of either cation, this result is unsurprising.
Conclusion It has been shown how the Shereshefsky equation can be used to obtain knowledge about the surface structure (molecular areas, orientations, and layer thickness) of a wide variety of binary solutions. However, for the results to be physically meaningful, it is necessary that the solutions conform to the assumptions used in the derivation of the equation. Inasmuch as it is impossible to establish independently from surface tension data that the requirements of the equation are satisfied, other confirmation may be desired. Other equations relating the surface tension of a binary solution to the concentrations and properties of its pure components have appeared in the litera(8) G. Bertozzi and G. Sternheim, J. P h y s . Chem., 68,2908 (1964). (9) G.Bertozzi and G. Soldani, ibid., 71, 1536 (1967). (10) N. Elliott, J. Amer. Chem. SOC.,59, 1380 (1937).
273
NOTES
time. l1-I5 Shereshefsky’s equation is similar in form to the latest of these equations, Eberhart’s,16 which Schmidt‘G has shown is a first-order approximation of all the earlier equations and which Ramalirishna and Suri” have extensively analyzed. Shereshefsky has utilized the same assumptions and approximations as Eberhart, but his equation generates more detailed information about surface region structure than Eberhart’s equation from the same surface tension data. (11) B. V. Srykowslti, 2’. Phys. C’hem. (Leiprig), 64, 385 (1908). (12) J. W. Belton and M. G. Evans, Trans. Faraday Soc., 41, 1 (1945). (13) E. A. Guggenheim, “Mixtures,” Oxford University Press, London, 1952. (14) 3. H. Hildebrand and R. L. Scott, “Solubility of Wonelectrolytes,” Dover Publications Inc., New York, N. Y., 1964. (15) J. G. Ebsrhart, J. Phw,a. Chem., 70, 1183 (1966). (16) R. L. Schmidt, ibzd., 71, 1152 (1967). (17) V. Ramaltrishna and S. K. Suri, Indian J . Cliem., 5, 310 (1967).
Calculation of the Wavelength Maxima for Some Triphenylmethane Dye Carbonium Ions by Edward 0. Holmes, Jr. Hughes Eesearch Laboratories, Ilrlalibu, California (RPceined J u n e 1’7, 1968)
90366
In a former publication* the author pointed out some interesting relations between the frequencies of the peak values ),,A,( of the absorption bands of the three triphenylmethane carbonium ions (crystal violet (CV+), malachite green (JIG+), and sunset orange (SO+)) as related to the structure of these ions. Since then the author has extended the investigation to include several more carbonium ions of this type and has found the ratios to be quite general and consistent, so much so that they are used as a guide in arriving at an empirical equation by which, , ,A can be calculated with a fair degree of accuracy for most of the bands. Table I shows the frequency ratios of the ions considered. The dyes are divided into three groups: (a) synimetrical, those in which all three nitrogens in the para position are bonded to hydrogen atoms or the same group : p-roseaniline2 (RO +), crystal violet (CV+), ethyl violet (EV+),and hexahydroxyethyl violet (HHEV+); (b) semisymmetrical, those having one phenyl group containing no amino group : Dobner’x violet (DV+), malachite green (MG +), brilliant green (BGf), and his [p-(diphenylamino) phenyl lphenylmethyl carbonium ion (2DPP+); and (c) unsymmetrical, sunset orangel (SO+). All solutions were in absolute ethyl alcohol. The ions were obtained from the leucocarbinols or ethers by adding a trace of acid or from the leucocyanides by photolysis with minimum exposure.
Table I : Frequency Ratios of the Absorption Maxima for the Carbonium Ion Dyes Ratios of
vmlLX--------
_ I ~ -
Ions
g:x
h:g
ET:+ HHEV+
1.89 1.93 1.92 1.93
1.21 1.21 1.21
DV + MG + BG + 2DPP +
RO +
cv
so
+
n:y
y:x
g:y
1.85 1.93 1.96 2.07
..* ...
...
1.27 1.26
1.81 1.82
...
1.41 1.45 1.45 1.44
1.31 1.35 1.36 1.42
...
1.31
1.81
, . .
1.35
+
...
A large number of expressions for the calculation of the Amax of the various bands were tried but none gave results as good as the relative!y simple formula stated below which we converted to a form that would yield results in wavelengths (in millimicrons) rather than frequencies. A,,
=
l.lN(A,
of the g band, in mp)
The g band is chosen for reference as it is common to all ions and can be measured with a fair degree of accuracy on a Gary spectrophotometer. N , the exponent of 1.1,is designated as the band number. The base 1.1 is used because when raised to the appropriate power it reproduces so many of the band ratios such as 1.21, 1.47, and 1.95, for example. Tables I1 and IT1 show our results.
Discussion The band number N is assigned the values of 7, 3, 0,
-2, and -3 for the bands x, y, g, h, and n, respectively.
For the symmetrical ions which have x, g, and h bands only 7, 0, and -2 are used. With one exception the agreement between the measured value and the calculated is fairly good. However, when the band numbers are applied to the semisymmetrical and unsymmetrical ions, the agreement is not as good. (By deviating from the above sequence of band numbers and using 6.5 instead of 7 for the x band of DV+, - 1in place of - 2 for the h band of HHEVf, etc., the agreement is very much closer.) At present we cannot explain the significance of the band numbers chosen. On calculating the ratios of the frequencies of the y :x bands of six other carbonium ions from the work of Tolbert and others4in which the phenyl group was substituted progressively for the methyl groups in malachite green, we find the ratios to be remarkably con(1) E. 0. Holmes, Jr., J. Phys. Chem., 70, 1037 (1966). (2) fIighly purified, supplied by Dr. John Vandenbelt of the Parke
Davis Co. (3) E. 0. Holmes, Jr., J . Phys. Chem., 62, 884 (1958). (4) B. M. Tolbert, G. E. K. Branch, and B. E. Berlenback, J . Amer. Chem. Soc., 67, 890 (1945). Volume ‘79, Number 1
January 1969
