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m (equiv.Ab00g.l Figure 3. Concentration dependence of (single-ion) activity of very low molecular weight cations: a,TP(HC1)6; d ,DT(HCl),; 9, KC1.
part of the macroions thermodynamically in spite of intermacroion repulsive force, so as to form an intermacroion “linkage.”g Thus, the (single-ion) activity of macroions decreaseswith increasing concentration, as was shown experimentally. On the other hand, there exists no strong interaction such as the coulombic one in solutions of neutral polymers. Therefore, the intermacroion linkage would give rise to greater polymer association than would be expected between neutral polymer molecules. Decreasing charge density or degree of polymerization clearly results in a decrease in the fraction of gegenions clustering around macroions and hence weakens the linkage. This would account for our third and fourth findings. Acknowledgments. The authors gratefully acknowledge the criticisms and encouragements received from Professor Ichiro Sakurada. Their sincere thanks are due to Professor Michio Kurata for his stimulating discussion. (9) This idea was earlier suggested (F. T. Wall and J. W. Drenan. J . Polynter Sci., 7 , 83 (1951)) and theoretically treated (J. A. V. Butler, B. E. Conway, and D. W. F. James, Trans. Faraday SOC: 50, 612 (1954)). It is interesting to note that, as originally found in the case of the simple electrolyte solutions (H. S. Frank and P. T. Thompson, J . Chem. Phys., 31, 1086 (1958)),the cube-root rule of the concentration dependence of logarithm of mean activity coefficient was found to hold also for polyelectrolyte solutions in ref 2, and the rule was qualitatively accounted for by the intermacroion “linkage.”
Absorption Spectrum of the Hydroxyl Radical’
by J. K. Thomas, J. Rabani, M. S. Matheson, E. J. Hart, and S. Gordon Chemistry Division, Argonne National L.iabmatory, Argonne, Illinois (Received Januury 80, 1966)
The discovery and identification of the absorption spectrum of the hydrated electron,2 eaq-, has made
possible the measurement by means of the technique of pulse radiolysis of some 200 or more absolute rate constants for this species.a It would also be advantageous to observe and identify the absorption spectra of the other primary transient species formed in the radiolysis of water. Reliable rate constants are known for the H atom;* however, one would not expect the H atom in aqueous solution to absorb in an accessible region of the spectrum. On the other hand, the! OH radical in the gas phase has groups of very narrow absorption lines belonging to a half-forbidden transition5 and, therefore, could exhibit a weak ultraviolet absorption in aqueous solution. In preliminary communications,B*’ we have suggested that there is indeed such a weak OH radical absorption below 3000 A. I n this paper this absorption is described and evidence for its identification presented.
Experimental Section The pulse-radiolysis apparatus incorporating two light passes in the 4-cm cell, the high-pressure Ha cell, and the dosimetry has already been described.* At wavelengths below 2500 A more than 10% of the photomultiplier signal was due to scattered light. However, by the use of interference filters (Baird Atomics Inc.) in conjunction with the Bausch and Lomb monochromator, the contribution of scattered light to the signal was reduced to less than 1%. I t was then possible to observe absorptions down to 2200 A precisely and probably to 2000 A. Dosimetry was carried out by the direct observation of Fe3+ in a modified Fricke dosimeter (10 mM Fez+, M Oa) where G(Fea+) = 15.6. Results Observation of the Spectrum. The points in Figure 1 are derived from initial optical densities, which were obtained by extrapolating optical density decay curves to the end of the 0.4- or 1.0-psec pulse. For any given solution in Figure 1 pulses of equal intensity were used (1) Based on work performed under the auspices of the U. S. Atomic Energy Commission. (2) (a) E. J. Hart and J. W. Boag, J . A m . Chem. Soc., 84, 4090 (1962); (b) J. W. Boag and E. J. Hart, Nature, 197, 45 (1963). (3) See L.M. Dorfman and M. S. Matheson, Prop. Reaction Kinetics, 3, 237 (1965),for a summary of work to May 1964. (4) J. P. Sweet and J. K. Thomas, J . Phys. Chem., 68, 1363 (1964). (5) 0. Oldenberg and F. F. Rieke, J . Chem. Phys., 6,439 (1938). (6) J. Rabani and M. 8. Matheson, J . Am. Chem. SOC.,86, 3175 (1964). (7) J. K. Thomas, Trans. Faraday SOC.,61, 702 (1965). ( 8 ) (a) L. M. Dorfman, I. A. Taub, and R. E. Btlhler, J. Chem. Phys., 36,3051 (1962); (b) S.Gordon, E. J. Hart, and J. K. Thomas, J . Phys. Chem., 68, 1262 (1964); (c) M.S. Matheson and J. Rabani, ibid., 69, 1324 (1965).
Volume 70, Number 7 July 1966
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Note in Figure 1 that the approximate doubling of the optical density of the band takes place in the 1.0 mM NzO and 0.2 mM HzOz solutions a t wavelengths between 2300 and 2800 A.
Decay of the OH Radical Absorption In the presence of high pressures of hydrogen, the OH radical absorption decays rapidly. In a typical experiment an initial optical density of 0.015 decays to a plateau level of 0.003. This residual absorption probably originates in the thick quarta window of the pressure cell. The rate of decay of the OH radical is first order and depends on the hydrogen gas pressure from 10 to 20 atm, giving k4 = (6.0 =t 2.0) X lo7 M-lsec-l. 1
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2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000
HFigure 1. The absorption spectrum of the OH radical (optical path length, 8 cm; 0.76 X lo-' M OH radicals/ pulse): 0, 1 m N HClOa, degassed; X, 1 m N HtSOd, degassed; 0 , 1 m M N20, neutral pH; A, 2 X lo-* M H202, neutral pH. I n these results the optical density was corrected for the loss of HZOZ[G( -Hz02) = 2.31 ; the extinction coefficients were taken from W. C. Schumb, C. N. Satterfield, and R. L. Wentworth in "Hydrogen Peroxide," A.C.S. Monograph Series No. 128, Reinhold Publishing Corp., New York, N. Y., 1955, p 287. The dashed line was obtained by multiplying the results in acid solution by 1.8. The molar extinction coefficient a t 2600 A is 370 M-' cm-l. h
on fresh solution at the various wavelengths indicated by the points. The molar extinction coefficient in M HC104 at 2600 A is E O H = ~ ~370 ~ M-l cm-l;' this is calculated from the dosimeter and using G(0H) = 2.40.
Identification of the Spectrum Evidence supporting our assignment of this transient absorption band to the OH radical is derived from the effect of increased OH yields and from the effect of OH scavengers on the half-life. Efect of Increased OH Radical Yields. Since GOHN Ge,,- = 2.6,9 the replacement of eaq- by OH radicals should double the OH radical yield. The following reactions are commonly used for enhancing OH radical reactions eaq-
+ N2O +N2O- +N2 + OH + OHeaq- + H2Oz +OH + OHHa0
(1) (2)
thereby doubling approximately G(0H) since eaq- H+ ---) H (3) is the normal mode of eaq- removal in an acid solution. In the absence of N20and HaOa,reaction 3 is important since it removes the appreciable eaq- absorption in the spectral region where the OH band is found.
+
The Journal of Physical Chenaistry
OH
+ Hz +H + HzO
(4) The agreement with the literature values of k4 = 4.5 X lo7 and 3.5 X lo7 (ref 10 and 7, respectively) is satisfactory. The decay of the OH radical absorption a t 2600 A via dimerization and via reaction with the H atoms is second order and has been reported.? The value for ~ ~ O H + O is H 1.05 X 1Olo M-l sec-l and agrees with the values in the literature, 8 X lO9.lo The value for kH+oH is 0.7 X 1Olo M-' sec-' and is lower than that reported by Fricke and Thomas." The above data support the assignment of the absorption spectrum in Figure 1 to the OH radical. At wavelengths below 2300 A, contrary to expectation, the spectrum in acid solution is larger than half that in the hydrogen peroxide and nitrous oxide solutions. This discrepancy from the predicted behavior might be attributed to another species, which is present only in the acidic solutions. (9) J. Rabani, W. A. Mulac, and M. S. Matheson, J . Phys. Chem., 69,53 (1965). (10) H.A. Schwarz, ibid., 66, 255 (1962). (11) H. Fricke and J. K. Thomas, Radiation Res. Suppl., 4, 25 (1964).
A New %Plot Treatment of Equilibrium Data and Its Application to the Vaporization of Bismuth Chloride' by Daniel Cubicciotti Stanford Research Institute, Menlo Park, California 94086 (Received January 6 , 1966)
The 2-plot treatment of equilibrium data as ordinarily used2requires that the heat capacities of the sub-
