NOTES
2569
observed experimentally and the protons at positions 1,4,5,8 are predicted to have a significant positive temperature coefficient. The magnitude is, however, predicted to be +l.06 mG/deg against an experimental value of $0.44 mG/deg. The above calculations indicate that our initial as= at sumption regarding the cos2 0 dependence of p ~ is least substantiated for the DMN system where good agreement can be obtained for the temperature dependence of the proton splitting constants. The agreement for DMA is not as good and together with the low value of the calculated temperature coefficient for the
methoxyl group suggests that further modifications may be necessary for this molecule. Acknowledgments. I would like to express my appreciation to Dr. J. R. Bolton, in whose laboratory the experimental measurements were carried out, for all his help and encouragement during the course of this work. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. The research was also supported in part under Grant No. NSF-GP-8416 from the National Science Foundation.
NOTES
Analysis of Sound Velocities in Aqueous Mixtures in Terms of Excess Isentropic Compressibilities
This quantity is defined in eq 3 and 4 below. If represents a complex isentropic compressibility
K,~. K~
Department of Chemistry, The University, Leicester, L E 1 Y R H , England (Received October 0 , 1969)
Many studies of sound velocities as a function of mixture composition have established that at constant temperature and pressure, the velocity, c, generally increases when alcohol is added to water.’ (A similar trend is observed when methyl cyanide,2 t-butyl alC O ~ O and ~ , ~n-propyl , ~ alcohol,6 are added.) When more alcohol is added the velocity goes through a maximum and then decreases. Measurements of sound absorption have been less extensive.6 First indications were that the absorption (a/f2--where CY is the amplitude absorption coefficient and, f , the frequency) also passed through a maximum, the PSAC’ (peak sound absorption concentration). However, it is now known that over the composition range where c rapidly increases, a/f2 remains relatively constant. We wish to examine these two trends. The analysis described here was used in an examination of the properties of methyl cyanide water mixtures,2 but it may have a wider application. Certainly this analysis shows how the link between the absorption and the velocity can be made more readily than by a direct comparison of the plots of c and a/f2against composition. The key to our approach is in an analysis of velocity data in terms of an excess isentropic compressibility,
+
=
- jK.“
(1) where K,’ is the real part and K,“ is the imaginary part; these two quantities are the two axes of an Argand diagram where j is the root of - 1. The quantity K,” can be linked with sound absorption* (out of phase component), while K ~ ’ can be related to the phase velocity, the in-phase component with respect to the pressure variation of the travelling sound wave. Since the frequency dependence of the velocity is generally small compared with that of the absorption, K ~ ’ can be calculated from the measured sound velocity at low frequencies by the equation of Newton and Laplace Ks*
by M. J. Blandamer and D. Waddington
K ~ ’=
where
p
K,‘
( b In V / b P ) , = l/pc2
(2)
is the density.
(1) F.Franks and D. J. G. Ives, Quart. Rev., 20, 1 (1966). (2) M. J. Blandamer and D. Waddington, Trans. Faraday SOC., in press. (3) J. Kenttamaa, E. Tommila, and M. Martti, Ann. Acad. Sci. Fenn., Ser. A$, 93, 3 (1959). (4) C. J. Burton, J. Acoz~st.SOC.Amer., 20, 186 (1948). (6) B. Jacobson, A r k . Kemi, 2 (ll), 177 (1951);data are from J. Timmermans, “Physico-chemical Constants of Binary Systems in Concentrated Solutions,” Vol. 4, Interscience, New York, N. Y., 1960. (6) See for example, G. W. Willard, J. Acoust. Soc. Amer., 12, 1941 (1941). (7) M.J. Blandamer and D. Waddington in Advan. Mol. Relaxation Processes, in press. (8) See for example, K. Herafeld and T. A. Litovita, “Absorption and Dispersion of Ultrasonic Waves,” Academic Press, Inc., Ltd., London, 1959. The Journal of Physical Chemistry, Vol. 74, No. 12, 1970
NOTEB
2570 k:
k,“
+
cyanide water,2 the maximum in a / f 2occurs quite ) ~ zero. In terms close to the composition where ( K ~ ‘ is of the Argand diagram approach outlined above, this means that where the velocity changes rapidly and a / f z remains unaffected, the vector K ~ *is directed along ‘ At the maximum in a / f 2 the , projection on the K ~ axis. the K ~ ” axis has correspondingly reached it maximum value. Here all the nonideal properties of the binary liquid mixture contribute towards the imaginary (outof-phase component) isentropic compressibility.
(total)
I
‘
k,*(ideal)
Figure 1. Relationships between the various isentropic compressibilities.
+’1
Acknowledgments. We thank Professor M. C. R. Symons and Dr. N. J. Hidden for valuable discussion. We acknowledge the award of a maintenance grant to D. W. from S. R. C.
I*
6
’,
?h
0.6 0.7 0.0 0.9 1.0 mole fraction x p
.-N E ( b ) O .w*
0! .
2 0.3 0.4 0.5 0.6 0.7
(9) M. J. Blandamer, D. E. Clarke, N. J. Hidden, and M. C. R. Symons, T m n s . Faraday Soc., 64, 2691 (1968).
0.0 0:9 1!0
The Reaction of Silica Surfaces with Hydrogen Sequestering Agents -1
1-
mole fraction x2
0.4
by J. A. Hockey Chemistry Department, University of Manchester Institute of Science and Technology, Manchester, England (Received December 8, 1968)
0.5 0.6 0.7 0.8 0.9 1.0 mole froction x;!
Figure 2. Variation of excess isentropic compressibility with mixture composition for: (a) ethanol water; (b) n-propyl alcohol water; (c) t-butyl alcohol water; (d) methyl cyanide water, all at 298’ K. T h e asterisk indicates the position of the maximum in the ultrasonic absorption (the PSAC, see text). (“,)E
+ +
+
+
The real (in-phase) component of the isentropic compressibility of an ideal binary mixture, id, can be calculated from the mole fraction of water, xl, and of the cosolvent, x2, by (Ks’)id
=
X1(Ks’)lo
+
Z~(KS’);~~
(3)
where ( K ~ ’ ) ~ Oand ( K ~ ’ ) ~ Oare the isentropic compressibilities of the two pure liquids. The excess isentropic Compressibility is given by (Ks’)‘
=
Ks’
-
(4)
(Ks’)id
The relationship between the various isentropic compressibilities is summarized in Figure 1. Plots of ( K ~ ’ ) ~as, a function of liquid composition, are given in Figure 2 for a number of binary aqueous mixtures. For each system there is a given composition where ( K ~ ’ )is~ zero; in this context these are ideal mixtures, however, on other grounds they are not ideal. Thus they correspond to systems having excess absorptions. A stiking feature, and one which we wish to draw attention to, is that for those mixtures with large excess absorptions, e.g., t-butyl alcohol waterJ9methyl
+
The Journal of Physical Chemistry, Vol. 74,No. I f , 1970
It is possible to obtain information on the concentration and coordination of the surface hydroxyls present on silicas by studying the reactions of these surface groups with hydrogen sequestering a g e n t ~ . l - ~I n a recently published study,* the reactions of alkyl chlorosilanes with the surface hydroxyls of a Cabosil silica have been followed in an elegant manner by a combination of analytical and spectroscopic techniques. The infrared spectrum shown in this paper’ illustrates that with high spectral resolution the absorption band a t about 3750 cm-’, which previous authors6have assigned as corresponding to isolated or single surface hydroxyls, may be resolved into three adjacent sharp peaks at 3751,3747, and 3743 cm-l. Similar results to this have been obtained in the author’s own laboratory. HOWever, it has always been felt that this splitting is artefactual rather than real. The spectra in Figure 1 illustrate this point. Spectrum a corresponds to the absorption spectrum of the residual water vapor in the optical path of a “dry air” flushed PE 125 spectrophotometer on “single (1) M . L. Hair and W. Hertl, J . Phys. Chem., 73,2372 (1969). (2) C. G . Armistead, A. J. Tyler, F. H . Hambleton, 9. A. Mitchell, and J. A. Hockey, ibid., 73, 3947 (1969). (3) J. B. Peri, ibid.,70, 3168 (1966). (4) H. P. Boehm, M. Schneider, and F. Arendt, 2.Anorg. Chem., 66, 800 (1962).
(5) L. H. Little, “Infrared Spectra of Adsorbed Species,” Academic Press, Inc., New York, N.Y., 1966.
