Ultraviolet and ultrasonic absorption spectral studies of the association


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3986

PAULHEMMES AND SERCIO PETRUCCI

Ultraviolet and Ultrasonic Absorption Spectral Studies of the Association of CuSO, and Cu(en),S,O, in Water at 2501 by Paul Hemmesa and Sergio Petrucci Department of Chemistry, Polytechnic Institute of Brooklyn, Brooklyn, N e w York 11,901 (Received February 7, 1Q68)

Spectrophotometric absorbance measurements of aqueous solutions of CuSOd and Cu(en)zSzOsat constant ionic strength in the ultraviolet region are reported. Analysis of the data together with existing literature values leads to the conclusion that the association constant of the two electrolytes is the same within experimental errors, ?l = 220-230 M F 1 , Ultrasonic absorption measurements on the same systems show the same relaxation frequency, f r = 170 i 10 Mcps. After analysis of the data, the results are interpreted by a mechanism in which the same process is observed for both electrolytes, namely, the eliminationof an axial water molecule from the distorted octahedron of Cu2+(aq) or Cu2+(en)z(aq), this process being coupled to a faster diffusion approach between solvated ions.

Introduction The extent of ionic association of Cu2+and Sod2- has been studied by Owen and Gurry3 and by Atkinson, et OZ.,~ by means of electrical conductance. The same system has been studied spectrophotometrically by Monk, et u Z . , ~ Prue, et U Z . , ~ and more recently by MathesonU7 In a succeeding paper,s the latter author studied the association of aqueous solutions of C ~ ( e n ) ~ S ~ (en 03 is ethylenediamine) by means of spectrophotometric methods. Matheson's c0nclusion7~~ was that a range of values of the association constant, K (170-250 M-' for the case of CuSO4 and 170-300 M-' for the case of Cu(en)zS203), were consistent with optical density data. The ambiguity arose from the use of calculated values of the activity coefficients. The theoretical equations used for this purpose all introduce arbitrary parameters such as the minimum approach distance of free ions, a (d in the original papers'J). Since no good reason exists for preferring one value of this parameter over any other, an apparently insoluble dilemma arose. I n addition, structural and kinetic data on these and similar systems have become available in recent years. For example, studies using nmr spectroscopy have indicated that a planar configuration of nitrogen atoms about the central copper exists in the C ~ ( e n ) ~ ~ + It has also been shown'O (in the case of ligand exchange reaction of Cu-polyamine complexes with EDTA) that the rate constant (IC = 2 X 105 sec-') is comparable with the rate of water exchange about Co2+. Yet the axial water of hexaaquocopper(I1) is substituted at a rate several orders of magnitude faster" because of the Jahn-Teller effect. I n view of the ambiguity of the calculated values of the spectrophotometric association constant and in view of the above structural and kinetic data, our interest was focused on a reinvestigation of the association of The Journal of Physical Chemistry

CuSO4 and Cu(en)zSzOa. It was decided to use the spectrophotometric method again and the more modern tool, ultrasonic relaxation, in the hope of gaining both a definite value of the association constant as well as a more intimate insight into the association mechanism of these systems.

I. Spectrophotometry The method used7s8consists of measuring the difference in optical density between two solutions, a reference containing Cu(C104)2 and NaC104 and a solution of Cu(C104)2,NazS04, and enough NaC104 to maintain constant ionic strength. If a is the concentration of Cu(c104)2,b is the concentration of Na2S04, e is the concentration of NaC104, and z is the concentration of the CUSOPcomplex and/or ion pair, the following two equations apply

(1) This work is part of the thesis of P. Hemmes in partial fulfillment for the requirements for the Degree of Doctor of Philosophy, Polytechnic Institute of Brooklyn, Brooklyn, N. Y. (2) Kirk Research Fellow 1966-1969, sponsored by the National Science Foundation through the Science Development Program of the Polytechnic Institute of Brooklyn. (3) B. B. Owen and R. W. Gurry, J . Amer. Chem. SOC.,60, 3074 (1938). (4) G. Atkinson, M. Yokoi, and C. J. Hallada, ibid., 83, 1570 (1961). (5) W. D. Dale, E. W. Davis, and C . B. Monk, Trans. Faraday SOC., 52, 816 (1956). (6) C. W. Davies, R. J. Otter, and J. E. Prue, Discussions Faraday Soc., 24, 103 (1957). (7) R. A. Matheson, J . Phys. Chem., 69, 1637 (1965). (8) R. A. Matheson, ibid., 71, 1302 (1967). (9) W. B. Lewis, M. Alei, and L. 0. Morgan, J . Chem. Phys., 45, 4003 (1966); M. Alei, W. B. Lewis, A. B. Dennison, and L. 0. Morgan, ibid., 47, 1062 (1967); W. B. Lewis, M. Alei, and L. 0. Morgan, ibid., 44, 2409 (1966). (10) D. B. Rorabacher and D. W. Margerum, Inorg. Chem., 3, 382 (1964). (11) M. Eigen and K. Tamm, 2. Elektrochem., 66, 93, 107 (1962).

3987

ULTRAVIOLET AND ULTRASONIC ABSORPTION SPECTRAL STUDIES and

D - D’ = XlAe

(2)

I n eq 1, K1 is the stoichiometric association constant of CuSO4. The thermodynamic association constant will then be

K’ K = , Y*

where y+ is the mean activity coefficient of Cuz+ and S042-, the activity coefficient of the pair CuSO4, being taken equal to unity. I n eq 2, D - D’is the difference in optical density of the solutions measured in a cell of length 1 cm. If eo is the molar absorbtivity of Cu2+ and €1 is the molar absorptivity of the complex CuSO4, then Ae = €1 - EO. Equations 2 and 3 assume that the formation of CuSOr is the only reaction present and that Cu2+ and CuS04 are the only absorbing species. Further, from eq 1 and 2 one can derive the equation

- -ab -a+b-x D - D’ lA e

1 +-ZAeK‘

(4)

+

barely valid at any finite concentration. The data of Mathesons unfortunately cover only three ionic strengths for Cu(en)&03. For CuS04’ only two ionic strengths were studied, making impossible any graphical interpretation of the data. It was therefore necessary to confirm and extend the above results by collecting additional data in the same range of ionic strengths. It was of interest to establish whether the completely theoretical Debye-Huckel equation (6) l4 or the well-established Davies equation (7)‘6 (which describes the experimental ionic activity coefficients up to I = 0.5) would be suitable for the calculations of y&in the present case -log y*2 =

2Srdi

1

+Aadl (7)

I n eq 7 B = 0.20,16while the use of Aa = 1 in the denominator of the first right-hand term in eq 7 is equivalent to choosing a = 4.3 A. The purpose of the present work was to establish whether eq 6 (using various values of a) or eq 7 could give consistent values for the expression

Therefore, a plot of a b / ( D - D’) vs. a b - 2 (or a b as a first approximation, if a b >> x) will give log K’ - log y+’ log K a straight line with slope l/lAe and intercept l/lAeK1, assuming that Ae and K’ are constants and that K’ when the left-hand side of the above equation is plotted depends only on the total ionic strength I = 3a 3b us. the ionic strength. More important, it was of interc - 42. The same equation applies to C ~ ( e n ) ~ S ~est 0 ~to see whether convergent values of the extrapolated if one reads a as the concentration of Cu(en)z2+, b as figures at I = 0 (where y+ = 1 and K1 = K) were obthe concentration of S2032-(or NazSz03, neglecting the tained giving a value of K insensitive to the choice of a small association between Na+ and S Z O ~ ~ -x) ,as the and to the theory used for Y ~ . concentration of the complex C ~ ( e n ) ~ S ~ 0EO3 as , the Experimental Section molar absorbtivity of Cu(en)zZ+,and €1 as the molar Optical densities were determined at 25 f: 0.5” with absorptivity of the Cu(en)zSzO, complex. Also in a Beckman DU spectrophotometer and 1-em length this latter case c is the concentration of NaC104. quartz cells. For the CuSO4 solution, the wavelength The above equations were applied7tsto aqueous soluused was X 250 mp, while for Cu(en)zSzO3 solutions the tions of CuSOe and Cu(en)zSz03 by first taking x = 0, wavelength used was X 310 mp. calculating a K1 and Ae, then finding x from eq 2, and The slit width was kept at 0.4 mm. A hydrogen recycling until convergence was achieved. lamp was used as the light source. NazS04 (Baker reThe final aim of this work is to calculate K , the theragent), NaC1O4 (Fisher reagent), and NazSz03 (Fisher modynamic association constant. I n order to do this, reagent) were used. C U ( C ~ Owas ~ ) ~prepared by disit is necessary to obtain estimates of y+. solving CuC03 (Baker reagent) in HC104solution. The Matheson7J applied semiempirical relations of Gugsolution was boiled to eliminate COZ, and the salt was genheimlZ for mixed electrolytes. The conclusion, as recrystallized from water. C ~ ( e n ) z ( C l O ~was ) ~ prealready mentioned above, was that a large range of pared as suggested by Matheson.8 All the solutions values were consistent with the data, depending on the were prepared by dilution of stock solutions of the activity coefficients used and on the values of the minivarious components. For the case of CuSO4, small addimum approach distance between free ions.l3 Examination by the present authors of the results for Cu(en)zSz0S8 gave roughly linear plots of log K 1 us. (12) E. A. Guggenheim, “Thermodynamics,” North-Holland Pub4 7 . Since the limiting law of Debye-Huckel is lishing Co., Amsterdam, The Netherlands, 1957.

+

+

+ +

-log y*z

=

2 s 4

(5)

a plot of log K’ vs. dj should be linear in a first approximation. Equation 5, however, is a limiting law

(13) This distance for a mixed electrolyte solution is the average among all the possible pairs of ions. (14) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” Butterworth and Co. Ltd., London, 1958. (16) C. W. Davies, J. Chem. Soe., 2093 (1938). Volume 79, Number 12 November 1068

PAUL HEMMES AND SERQIO PETRUCCI

3988 tions of HC104 to repress hydrolysis of Cu2+ were necessary. For the case of Cu(en)22+solution, addition of ethylenediamine at a concentration of l.lO-a M was enough to give reproducible and stable values of optical in density (by repressing any formation of solution). It should be noticed that MathesonTr8used 2- and 4-cm length cells, therefore having twice and four times, respectively, our values of D - D'. I n an attempt to overcome this drawback, measurements were repeated 10-20 times after unbalancing the spectrophotometer with respect to dark current, sensitivity, and absorbance readings, and the results were averaged. Generally the reproducibility of the measurements of D - D' was within *0.001 unit (therefore, the maximum error in precision in individual readings of D D' was within A 2% for the most dilute solutions).

Results I n Tables I and I1 the results for D - D' at the various ionic strengths, I , are reported for CuSO4 and Cu(en)2S 2 0 3 solutions, respectively. I n the same tables the values of a-c and the calculated x are reported. Table I : Results of Ultraviolet Absorption of the Cut + f SOa2- Ion in HzO at 25' ( A 250 mp)" lOBa, M

IOab, M

D

- D'

loa,, M

loax, M

0.143 0.206 0.260 0.312 0.352 0.389

0.103

I

Table 11: Results of Ultraviolet Absorption of Cua+(en)z St0sz- Ions in Water a t 25" ( X 310 mp)(l

?

10' Cen

0.058 0.083 0.104 0.122 0.137

0.0355

1.00

0.44 0.67 0.83 0.97 1.11 1.23

0.067 0.101 0.126 0.147 0.168 0.186

0.0465

1.00

40.69 30.55 20.41 10.24 0.00

0.64 0.87 1.02 1.20 1.35

0.098 0.134 0.157 0.185 0.208

0.0664

1.00

4.00 8.00 12.0 16.0 20.0 24.0 28.0

68.7 57.2 45.8 34.3 22.9 11.4 0.0

0.26 0.46 0.64 0.78 0.90 1.04 1.13

0.048 0.084 0.118 0.144 0.166 0.191 0.207

0.0875

1.00

7.50 11.25 15.00 18.75 22.50 26.25

75.0 63.7 52.5 41.2 30.0 18.7

1.10 1.56 2.00 2.36 2.69 3.01

0.177 0.251 0.320 0.379 0.432 0.481

0.109

1.00

10% M

10*b, M

lo%,M

2.50 2.50 2.50 2.50 2.50

3.33 5.00 6.67 8.34 10.0

18.00 13.25 8.50 3.75 0.00

0.34 0.49 0.61 0.72 0.81

2.98 2.98 2.98 2.98 2.98 2.98

4.00 6.00 8.00 10.0 12.0 14.0

27.3 21.8 16.4 10.9 5.5 0.0

3.00 3.00 3.00 3.00 3.00

6.77 10.2 13.5 16.9 20.3

2.63 2.63 2.63 2.63 2.63 2.63 2.63 7.50 7.50 7.50 7.50 7.50 7.50

loa,, M D

- D'

4.05 4.05 4.05 4.05 4.05 4.05

8.00 12.0 16.0 20.0 24.0 28.0

56.5 45.2 33.9 22.6 11.3 0.0

0.52 0.75 0.95 1.13 1.28 1.42

5.00 5.00 5.00 5.00 5.00

4.74 7.10 9.46 11.83 14.21

42.6 36.4 29.3 22.7 17.3

0.48 0.68 0.90 1.06 1.23

0.134 0.187 0.247 0.293 0.340

0.070

tures of electrolytes.

5.00 5.00 5.00 5.00 5.00

1.66 3.34 6.66 8.34 10.00

41.1 26.9 28.5 24.2 20.0

0.22 0.43 0.78 0.94 1.10

0.046 0.087 0.160 0.193 0.226

0.0615

Table I11 : Results for the Stoichiometric Association Constants and Molar Absorbtivity at X 250 mp

a

The cell length (1) equals 1 cm.

The cell length ( I ) equals 1 cm.

Excluding the points at I > 0.1, straight lines can be drawn through the data. The extrapolated values at

for Aqueous Cut+

+ SO2-

i

K', M - 1

0.061 0.070 0.103

31.5 28.4 18.9

10a/A,, M om

4.84 4.00 3.70

Discussion In Tables I11 and IV the results for K' and 103/Ae are reported for CuSO4 and Cu(en)zSzOa, respectively. In Figures 1 and 2, the plots of log K' - log VS. I are reported. The values of -log y*2 were calcu; lated by eq 6 and 7. I n eq 6 the values a, = 0 and 5 A were used for CuS04and a = 0, 5, and 10 A for Cu(en)2S20a.o Only the values of a 'v 2.5 8 for CuSOd and a 5 A for Cu(en)&,Oagive horizontal lines. The present authors, however, do not attach any physical significance or preference to these values of a in these mixThe Journal of Physical Chemistry

+

Table IV : Results for the Stoichiometric Association Constants and Molar Absorbtivity a t X 310 mp for Aqueous Cu(en)P+ Sz02-

+

I

K1, M-1

0.0355 0.0465 0.0664 0.0875 0.109

54.5 50.8 43.7 35.7 26.4

lOa/Ae, M o m

6.00 6.33 6.53 6.39 6.23

ULTRAVIOLET AND ULTRASONIC ABSORPTION SPECTRAL STUDIES

unambiguous (although not) very precise) values of the association constant. Because of the equality of K for both electrolytes, one might suspect some similarity in the association processes. I n order to investigate the validity of the above hypothesis, measurements of association rates by ultrasonic relaxation have been performed and will be described in the following section.

2.70

2.20

2,10

3989

t-

"-0U

K=225?20 M-'

I

I

I

I

It

It

It

I

t

.

I t

Figure 1. CuSOa in water a t 2 5 " : 0 , literature values; 0, this work; 6, conductance result.

11. Ultrasonics Relaxation kinetics has been applied rather extensively to 2 : 2 electrolytes in water," to mixed solv e n t ~ , and ' ~ ~to~ ~1: 1 electrolytes in nonaqueous solvents.21 For 2 :2 electrolytes in water, the generally accepted mechanism of ionic association is multistep, beginning with a diff usion-controlled approach between solvated ions to form an outer-sphere complex or ion pair, followed by one (or two steps) which corresponds to the collapse of the outer-sphere complex (by eliminating a solvent molecule(s)) and to the forming of a contact species (inner-sphere complex). The simplest scheme for the above is the two-step mechanism Me2+(aq)

+ L2-(aq) 3Me2+(H20),L2kZL k2a

J_ MeL k0l

+ H20

(8)

Eigenl' has also shown that for a two-step mechanism of type 8 we can write TI,II-' 2.00 0.00

I 0.01

I 0.02

t I 0.03

t

t I

I 0.04

I

0.05

t I

0.06

0.07

I 0.06

f I 0.09

I

t

0.10

I

Figure 2. Cu(en)&08 in water at 25': 0, literature values; 0, this work.

=

*

(9)

where T is the relaxation time related t o the experimentally determined relaxation frequency fr by T-' = 27rfr. The positive sign before the radical in eq 9 corresponds to .r(fast). Further

+ + + p = k1Z08(C)(k23+ + 8 = klZo8(c)

I = 0 give K = 225 20 M-' for CuSO4 and K = 220 k 20 M-' for C~(en)&~Oa.For CuSO4 the conductance result is K ( A ) = 233 From above it is

d S 2 - 4P)

I/*(#,

k2l

k23

k32)

IC32

(10)

k21h

(1 1)

Gi

concluded that even if the calculated values of fail to give the exact numerical value$f the activity coefficicnt (except by setting a Z 2.5 A for CuSO4 and a 5 A for Cu(en)zSzOain eq S), still the extrapolated values at I = 0 converge to a band which defines an association constant within i10%. There is a positive agreement for CuSO4 with the conductance value3 of K and a drastic reduction of scattering with respect to the previous values7** of K for both electrolytes. A similar graphical method has been used successfully by Taube and PoseylB and Nancollas17 and also has been suggested by Davies.'* The convergence of the data and the agreement with the conductance value K(A) = 233 M-13 for CuSO4 lead to confidence in the ability of the uv spectrophotometric method to give

where u is the degree of dissociation related to the

(16) F. A. Posey and H. Taube, J. Amer. Chem. Soc., 7 8 , 15 (1958). (17) G. H. Nancollas, "Interactions in Electrolyte Solutions," Elsevier Publishing Co., Amsterdam, The Netherlands, 1966. (18) C. W.Davies, "Ionic Association," Butterworth and Co. Ltd., London, 1962. (19) K. Tamm and G. Kurtne, Acustica, 4, 380 (1964); D.A. Bies, J. Chem. Phys., 2 3 , 428 (1956); J. R. Smithson and T. A. Litovitn, J. Acoust. SOC.Amer., 28, 462 (1956); €3. K. Kor and G. S. Verma, J. Chem. Phys., 29, 9 (1958). (20) €3. Petrucci, J. Phys. Chem., 71, 1174 (1967),F. Fittipaldi and €3. Petrucci, ibid., 71, 3414 (1967). (21) 8. Petrucci and M. Battistini, ibid., 71, 1181 (1967). Volume 78, Number 18 November 1968

3990 over-all association constant (determined by independent methods like conductance or spectrophotometry) by

PAULHEMMESAND SERGIO PETRUCCI Results I n Table V and VI the results of the absorption coeficient (nepers cm-l) a t the frequency (Mcps) investigated and of the excess sound absorption per wavelength (pexc = [a - a(solvent)] (u/f)) are reported for CuSO4 and C~(en)i3~Os solutions. u is the sound velocity, taken equal to the velocity of the solvent u = 1500 m/sec. The ratio a(solvent)/f2 was taken as 23 X 1O-l’ cm-’ sec2,

Experimental Section Equipment and Procedures. The equipment and procedures have been discussed elsewhere.20v21 Minor changes to improve the precision were introduced, such as providing the twin-crystal interferometric cell with Table V: Ultrasonic Absorption Data of Aqueous Gus04 Solutions at 25.0’ 1-in. micrometers for more precise leveling of the two crystals, using a 1/432C Kay attenuator which reads f, a, down to 0.1-db attenuation. Some of the measureMops nepers om -1 ments were taken on a Matec 560 pulser-receiver by c = 0.20M comparing the signal from the cell with the one from a 0.504 30 149 608D Hewlett-Packard standard signal generator; 1.502 50 278 other measurements were recorded by inserting the 2.740 70 346 1/432C attenuator between the cell and receiver. This 4.428 90 428 110 426 5.904 arrangement allows for changing the attenuation (and 130 8.223 500 thus the displayed signal amplitude) by amounts from 150 553 10.70 0.1 up to 10 db. The signal amplitude is then restored 13.22 170 580 to its initial value by changing the acoustical path 190 15.23 547 499 210 17.13 length. 230 19.03 480 I n order to check the reliability of the data, some measurements were taken with another assembly conC = 0.15M sisting of a Chesapeake U-100 pulse generator, an 0.443 30 118 190 1.209 50 APR-4 receiver, and a 608A Hewlett-Packard standard 269 2.383 70 signal generator. 304 90 3.684 Materials. CuSO4.5HzO (Baker reagent) was used 5.411 359 110 without further purification; C~(en)~Sz03 was prepared 400 130 7.354 as follows. CuS04 was dissolved in water. Ethylene429 11.51 170 420 13.63 190 diamine (Fisher reagent) and then solid BaSz03(Amend Drug Go.) were added. The mixture containing solid c = 0.10M BaS20a, which is slightly soluble, was stirred overnight. 80.7 30 0.368 After this a sample of the solution was tested with 1.122 164 50 255 90 3.396 Ba(N0a)2to check the absence of Sod2- in solution. 300 4.979 110 The solution containing C ~ ( e n ) ~and ~ +SzOa2- (any 342 130 6.853 C ~ ( e n ) forms ~ ~ + insoluble precipitates with both Sod2350 10.62 170 and S 9 0 3 2 - ) was treated with a large excess of ethylene336 12.56 190 diamine to precipitate Cu(en)3S203. The salt was redissolved in water (Cu(en)2S20g going in solution from the dissociation of C ~ ( e n ) to ~ ~form + Cu(en)P), Blank experiments of sound absorption of Cu(C104)2 then reprecipitated with ethylenediamine, and re(0.2 M ) and Cu(en)z(C104)2 (0.2 M ) gave values equal dissolved with water. to the pure solvent in the same frequency range as above This last solution was checked for Ba2+and found to for CuSO4 and Cu(en)zSzO3, indicating the absence of be free of it. The salt was recrystallized twice from a relaxation processes. 1:2 water-methanol solution and finally dried in a In Figures 3 and 4,pevais plotted os. f i n a log-log plot desiccator over Mg(C104)t. for the two electrolytes at the concentrations investiAnalysis of the salt was performed by dissolving a gated. The solid lines are calculated from the funcweighed sample in about 75 ml of water. A direct tions for a single relaxation process1’ titration of the Sz032- was performed using standard 1 2 with a few milliliters of CC1, as an indicator. Blank corrections were made by titrating Cu(en)z(GlOa)a under identical conditions. The solid Cu(en)2S~03 where w = Z r f , (pexo),,,axis the experimental value read was found to be anhydrous. ~

The Journal of Physical Chemistry

3991

ULTRAVIOLET AND ULTRASONIC ABSORPTION SPECTRAL STUDIES

Table VI: Ultrasonic Absorption Data of Aqueous Cu(en)&Os Solutions at 25'

f, Mcps

1000

-

500

-

a,

nepers om-'

l0'pexo

C = 0.25 M 0.512 1.128 2.199 3.377 4.835 8.404 10.59 12.20

33 50 70 90 110 150 170 190

C 30 50 70 90 110 150 170 190 210

0.20 M 0.415 1.082 2.015 3.223 4.663 8.059 9.671 11.66 13.56

30 50 70 110 150 190

C = 0.15 M 0.345 1.036 1.813 4.260 7.368 11.03

129 166 230 252 280 323 348 308

j

200-

2 0

3.

100-

20

=

114 152 190 227 256 288 267 265 244 69.0 138 147 201 219 215

on the plots themselves, and 7 is the relaxation time (7-l = 2 rfr,where f r is the relaxation frequency). The solid lines in Figures 3 and 4 were calculated by assuming fr = 170 Mcps in all the concentrations studied. The actual possible scatter in f r is f r = 170 f 10 Mcps. No definite trend of the relaxation frequency with concentration is visible within the precision of the data.

-

50

- 01

I

10

20

50

100 f (Mc/s)

200

500

200

500

Figure 3. CuSO4 in water at 25': 0 , 0.20 M ; 0, 0.15 M; a, 0.10 M

IOoo

t

lo10

20

50

100 f(Mc/s)

Figure 4. Cu(en)tSSOa in water at 25' : 0 , 0.25 M; 0, 0.20 M; c),0.15 M.

Discussion I n view of the known structure of both hexaaquo Cu(HzO)e2+and of Cu(en)Z2+(aq),it is postulated that water in the same position, namely, the axial one, is substituted during the association process. The simplest scheme consistent with the above corresponds to process 8. I n order to apply eq 9 and following, calculations of k d , k21, and B(c) and estimates of IC23 and kaz are necessary. (The same numerical values have been assumed for both the electrolytes in the following.) I n calculating the quantity ICI~", the Debye-SmoulchowskyZ2equation has been assumed. The diffusion approach distance has been taken to be Y D = 5 X lo-* cm, corresponding to a model of Cu2+ and separated by one molecule of water.2a This value is also close to the minimum approach distance of free ions as obtained through conductance.

Thus, we have the equation

where N is Avogadro's number, IC is the Boltzmann constant, T is the absolute temperature, 7 is the solvent viscosity, and b is the Bjerrum parameter (b = I&Zz[eo2/TDDkT,where eo = 4.80 X 10-lo esu, 2, and 2- are the ionic charges, and D is the solvent dielectric constant). The problem of calculating kzl has been approached by equating (22) M. von Smoluchowsky, Z . Phys. Chem. (Frankfurt am Main), 92, 129 (1917); P. Debye, Trans. Electrochem. Soc., 82, 265 (1942). (23) M. Eigen and L. DeMaeyer, "Investigation of Rates and Mechanisms of Reaction," A. Weissberger, Ed., John Wiley & Sons, Inc., New York, N. Y.,1963,Part 11. Volume 72, Number id

November 1088

3992

PAUL HEMMES AND SERGIO PETRUCCI

Table VII: Results of Calculations on Ultrasonic Spectra of Aqueous CuSOl and Cu(en)&Oa Solutions at 25' f n Mops-

I--

0,M

Exptl (f10)

Calcd

0.20 0.15 0.10

170 170 170

172.3 172.1 172.0

0.25 0.20 0.15

170 170 170

172.5 172.3 172.1

K Z -1,

Kiz-1,

10-'Qk1*0,

K(exptDa (*20), M -1

M -1

Kea

M

167

4

209

225

Cu (en)ZSZOS 4.2 167

4

209

220

M-1

880-1

-1

CuSOa

a

4.2

Value determined in the first part of this work.

where K ~ j - lis the Bjerrum function.24 The function O(c) has been calculated by combining eq 13 for the association constant and eq 7 for the activity coefficient. The numerical value of K(uv) has been retained from part I. The over-all association constant can be related to the rate constants in scheme 8, since l1yZ4

where KZ3= k32/k23. Values of the rate constants k23 and k32 have been chosen so as to give the best agreement with the experimental relaxation frequency (eq 9) and to satisfy simultaneously the equilibrium constant (eq 17). I n Table VI1 the results of these calculations are reported for both CuSO4 and C ~ ( e n ) ~ S ~It0 can ~ . be seen that the agreement between fr(calcd) and fr(exptl) is excellent. One should also note the effect of varying the parameters kt3 and kaz upon fr(calcd) and K(ca1cd) (Table VIII). From these results, the conclusion is drawn that the same mechanism is probably responsible for the associTable VIII: Effect of Varying the Parameters uponf,(calcd) and K(ca1cd) (C = 0.2 M , K(uv)= (220-225) i 20 M - ' ) lO-nkza, seo -1

1 2 3 2 2 3 1

IO-nkaz, sec-1

8 8 8 9 7 7 9

Mops----

k23

Exptl

K(oalod), M -1

152 173 192 187 159 178 166

170 170 170 170 170 170 170

189 209 231 205 216 240 186

The Journal of Phusical Chemistry

K23 =

k32/k23

= [Me(HzO), L]/[MeL] = 4

(18)

concentration of outer-sphere complexes and contact species for the two electrolytes. The fact that these ratios are the same in both cases indicates that there exists no apparent steric hindrance to association by the two bulky ethylenediamine molecules. The only real difference observable between the two processes is the magnitude of excess sound absorption. This can be calculated2a for a two-step relaxation by assuming that the volume change due to step one in scheme 8 equals zero, AVlz S 0, and

and kS2

Calod

---fr,

ation of the two electrolytes in water. A diffusioncontrolled approach between the solvated ions is followed by the slower removal of an axial water from the distorted octahedron of the hexaaquocopper(I1) by the ligand S0k2-. Since the relaxation frequency and the association constants are the same for both CuSOl and C ~ ( e n ) ~ S ~we 0 3 believe , analogous reactions take place in both cases. This implies that the two ethylenediamine molecules must lie in a planee blocking four of the six octahedral sites but leaving the axial water molecules (which are loosely bound because of the Jahn-Teller effect) unaffected. The constancy of k23 in the two systems also implies a ligand-independent rate and probably an SN1 mechanism. This is further substantiated by an exploratory run on Cu(en)zSOawhich gives precisely the same results as C ~ ( e n ) ~ S ~ 0 ~ . The value of K23 expresses the ratio between the

where ps is the solvent compressibility and AV is the volume change due to the process. Since (T is essentially the same for the two electrolytes, the only source of difference is AV. Indeed AV expresses the difference in partial molar volume of products and reagents assuming an isothermal sound compression in aqueous solutions. (24)

N. Bjerrum, Kgl. Danske Videnskab. Selskab.,

9, 7 (1926).

3993

MECHANISM OF GASEOUS SILOXANE REACTION WITH SILICA

Acknowledgment. The authors wish to acknowledge the National Science Foundation for research sup-

port through the Science Development Program of the Polytechnic Institute of Brooklyn.

Mechanism of Gaseous Siloxane Reaction with Silica. I1 by William Hertl Research and Development Laboratories, Corning Glass Works, Corning, New York 14830 (Receised March 11, 1968)

The reactions of monomethoxy trimethyl silane (I) and dimethoxy dimethyl silane (11) with the surface of silica were studied spectroscopicallyby the same methods described in part I. These silanes react only with nonhydrogen-bonded hydroxyl groups; the rate-determining step is the reaction of a physically adsorbed siloxane molecule to form an Si-0-Si bond. The reaction parameters are: (I) m = 1.6, n = 1.7, and E = 22 kcal, and (11) m = 2.2, n = 2.2, and E = 32 kcal. m, the order of the reaction with respect to the surface sites, is the number of surface sites on average consumed per silane molecule; n is the number of surface sites occupied on average by one physically adsorbed silane molecule; and E is the experimental activation energy. About 60% of 11reacts monofunctionally, and about 40% reacts difunctionally. The reactivity of the silica toward these silanes increases with increasing pretreatment temperature of the silica. An inverse trend was noted between the reactivity and the concentration of nonreactive hydrogen-bonded surface hydroxyl groups. These bonded groups can be largely removed by heating the silica to 800". The isosteric heats of physical adsorption of the silanes on free hydroxyl groups on the silica and the heats of vaporization were also measured. The heat of adsorption is proportional to the amount of perturbation of the free hydroxyl group.

Introduction I n part I1 the mechanism of the reaction of trimethoxy methyl silane with the nonhydrogen-bonded (free) hydroxyl groups on silica was described. When the silica is in the presence of gaseous siloxane, a certain fraction (at any given temperature and pressure) of the free hydroxyl groups are covered with physically adsorbed siloxane molecules. The rate-determining step of the reaction with the hydroxyl group is the reaction of a physically adsorbed siloxane molecule to form an Si-O-Si bond (R8SiOR),d,

+ HOSif

----t

RsSOSif

+ ROH

The ROH produced reacts, in part, also ROH

+ HOSif

---t

ROSif

+ HOH

This paper describes the reactions of dimethoxy dimethyl and monomethoxy trimethyl silanes with the silica surface, the effect of silica heat treatments on the rate of the reaction, and the thermodynamics of physical adsorption of siloxanes on silica.

Experimental Section The apparatus and experimental procedure were the same as previously described.' Briefly, a silica disk, mounted in a furnace connected to a vacuum rack, was placed in an infrared spectrophotometer. The gaseous reagent was admitted to the furnace and was allowed to

react for a given time; the furnace then was evacuated. A spectrum was taken and the procedure was repeated. Spectra were taken at intervals of a few per cent reaction so that the gas-phase composition was essentially constant during the course of the reaction. A gas chromatographic analysis of the dimethoxy trimethyl silane (Dow Corning Corp., 2-6072) and the monomethoxy trimethyl silane (Peninsular Chemresearch Inc.) gave only one peak. It was estimated that the siloxanes used contained less than 0.5% of impurities. The latent heats of vaporization were determined in a boiling point apparatus connected to a vacuum rack. Various pressures of helium, measured to the nearest 0.01 torr, where admitted to the initially evacuated system and the siloxane boiling point was observed for each pressure. The thermometer measured the vapor pressure to the nearest 0.1" a t the bottom of the reflux condenser.

Results and Discussion The measurement of the peak intensity of the band due to the free hydroxyl group (3745 cm-l) at various times during the course of the reaction gives the reaction curve. These curves are in good agreement with those obtained by following the buildup in peak in(1) Part I: W. Hertl, J. Phgs. Chem., 7 2 , 1248 (1968).

Volume YR, Number 13 November 1968