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CLARKEC. MINTER
Thermal Conductivity of Binary Mixtures of Gases. I. Hydrogen-Helium Mixtures by Clarke C. Minter Department of Chemistry, The American University, Washington, D. C. 2001 6 (Received January 8, 1968)
The thermal conductivity of mixtures of hydrogen and helium has been determined in a conventional thermal conductivity bridge. The previously reported minimum in thermal conductivity at 8 mol % is confirmed experimentally. It is found that the thermal conductivity of hydrogen-helium mixtures over the entire range of concentrations can be expressed by K , = 41.8(1 0.0796 In p ) p 34.4[1 0.048 In (1 - p ) ] ( 1 - p ) , in which p is the mole per cent of hydrogen.
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Introduction About ten years ago it was reported by Madison1 that the quantitative determination of hydrogen in a conventional gas Chromatograph employing helium as the carrier gas was difficult because of the anomalous thermal conductivity of hydrogen-helium mixtures a t low concentrations of hydrogen. Madison observed that when hydrogen is first added to helium the response of the chromatograph is in the same direction as that observed for hydrocarbons. This suggests that for low concentrations of hydrogen in helium, the thermal conductivity of the mixture is actually lower than for pure helium, even though the thermal conductivity of hydrogen is 21% greater than that of helium. The question of low conductivities at low concentrations of hydrogen was discussed by Smauch and Dinerstein,2who concluded that the anomalous result was due to a minimum in the thermal conductivity hydrogenhelium mixtures. Their measurements showed that a minimum occurred at about 8 mol yo hydrogen, the mixture having 17% hydrogen showing the same conductivity as pure helium. The thermal conductivity of hydrogen-helium mixtures over the entire range has been measured by CottonJ3who found that all mixtures containing less than 17% hydrogen had a conductivity lower than that of pure helium. A later experimental investigation by Hansen, Frost, and RSurphy4 found the minimum hydrogen concentration at 13% hydrogen and the mixture containing about 26% hydrogen had the same conductivity as pure helium. Although the minimum in the conductivity of hydrogen-helium mixtures had been definitely established by the three articles just cited, there was some disagreement among the three as to which concentration had the minimum conductivity and which concentration had the same conductivity as pure helium. The first object of the present paper was to determine the concentration of hydrogen at minimum conductivity and also to find the mixture having the same conductivity as pure helium. The experimental results of The Journal of Physical Chemietry
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the present investigation show that the minimum conductivity is at about 8% hydrogen and that the mixture containing 17% hydrogen has the same conductivity as pure helium. These results appear to be a good check on those of Smauch and Dinerstein. The principal object of the present work, however, was to obtain experimental confirmation of some calculations made by the present writer several years ago, I n an article published some time ago, AIinter and Schuldiner5 developed an equation for the thermal conductivity of binary mixtures of hydrogen and deuterium which appeared to agree quite well with their experimental observations. Some time later the same equation, assuming appropriate values for the constants, was used to calculate the thermal conductivity of hydrogen-helium mixtures, and it was found that the thermal-conductivity curve showed a minimum. It was not possible to obtain experimental confirmation at that time, and the present work is the attempt to obtain experimental results so that the proper values of the coefficients in the equation for binary mixtures could be obtained from experimental results and not by manipulation of kinetic-theory models. The generalized rule-of-mixtures expression, which Minter and Schuldiner found to agree very well experimentally in the case of mixtures of hydrogen and deuterium, is I&
=
1&(1
+ N1 In p > p + 1&[1 + N21n (1 - P)IU - P)
(1)
where 1K1 and lKz are the thermal conductivities of the two gases at one atmosphere, p is the mole per cent of (1) J. J. Madison, Anal. Chem., 30, 1861 (1958). (2) L. J. Smauch and R. A. Dinerstein, ibid., 32, 343 (1960). (3) J. E. Cotton, Ph.D. Dissertation, University of Oregon, Eugene, Ore., 1962; University Microfilms, Inc., Ann Arbor, Mich., 1963. (4) R. S. Hansen, R. R. Frost, and J. A. Murphy, J . Phys. Chem., 68, 2028 (1964). (5) C. C. Minter and S. Schuldiner, J . Chem. Eng. Data, 4, 223 (1959).
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THERMAL CONDUCTIVITY OF BINARY MIXTURES OF GASES 4 ,op
.L_
THERMAL
T O CONSTANT CURRENT
CONDUCTIVITY
BRIDGE
BURET
Figure 1.
the first gas, and N1 and N z are the mixing coefficients of the two gases. The values of N1 and N z are not based on kinetic-theory assumptions; the values have to be calculated from the experimental observations. It is now planned t o obtain these coefficients experimentally for binary mixtures of the principal gases and t o determine if the simple equation developed in the earlier paper can be applied to all combinations of gases. It is well known that kinetic-theory calculations of the thermal conductivity of binary mixtures of gases are not only complicated and difficulte but also yield results which agree only approximately with experimental observations. See, for example, Lindsay and Bromley,’ as well as Hansen, Frost, and Murphy.* It is hoped that the experimentally determined coefficients for various binary combinations will lead to a greatly simplified treatment of gas mixtures.
Experimental Section All measurements of thermal conductivity were carried out at atmospheric pressure and room temperature, using the apparatus shown schematically in Figure 1. With this setup, the thermal conductivity of the mixture, K,, in one side of the bridge block can be compared with that of hydrogen or helium by exposing the mixture and the other gas t o two similar filaments of the four-filament bridge. The millivolt output of the bridge, EH or E H e , can be interpreted in terms of absolute thermal conductivity a t 0” by means of either of the two equations I -
which involve measuring the bridge output, E , when two pure gases of known absolute thermal conductivity are passed through the two sides of a bridge block, the two gases in this case being hydrogen and helium. It should be pointed out that the bridge output when the mixture is compared with pure hydrogen, &-I, will differ from the output when the mixture is compared with helium, E H ~ .However, the sum of the two outputs, EH E H ~will , be equal to the bridge output, E, obtained when hydrogen is compared with helium. The reason for expressing the thermal conductivity in terms of 0” should be explained. The bridge operates at room temperatdre, and the small tungsten filaments positioned in cells, 0.18 in. in diameter and 0.5 in. deep, operate at about 50” above room temperature when carrying a current of 100 mA in hydrogen, Since more than 98% of the gas in these cells is only a little above room temperature, the thermal conductivity of the gas is naturally slightly greater than it would be at 0”. Because the temperature differences are not great and the temperature coefficient of thermal conductivity is practically the same for hydrogen and helium, the errors resulting from such a procedure are expected to be negligible. Ibbs and Hirstg used a similar method for obtaining the absolute thermal conductivities of several mixtures and found the results obtained at the higher temperature were relatively in the same proportion as those obtained at 0”, because the value of the bridge constant
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41 e.
kf a
4o
“
i
39
I
8 38
w
3 i37
2F 36 35 34 0.1 0.2
0.3
0.4 0.5 P, mol %.
0.6
0.7
0.8
0.9
1.0
Figure 2. Plot of thermal conductivity of mixture us. mole per cent of hydrogen: -, calculated; A, observed.
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in which OKH and JCH~ are absolute thermal conductivities of hydrogen and helium at 0”, and B is the “bridge constant,” determined by well-known methods,8
(6) J. 0. Hirschfelder, C. F. Curtiss, and R. B. Bird, “Molecular Theory of Gases and Liquids,’’John Wiley and Sons, Inc., New York, N. Y . , 1964,pp 534,535. (7) A. L. Lindsay and L. A. Bromley, Ind. Eng. Chem., 42, 1508 (1950). (8) H. A. Daynes, “Gas Analysis by Measurement of Thermal Conductivity,” Cambridge University Press, London, 1933, pp 11, 12. (9) T . L. Ibbs and A. A. Hirst, Proc. Roy. Soc., A123, 134 (1929).
Volume 72, Number 6 June 1968
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H. TANIGUCH~, E(. FUKUI, S. OHNISHI,H. HATANO, H. HASEGAWA, AND T. MARUYAMA
B is based on the thermal conductivity at 0" for the gases involved. Mixtures of hydrogen and helium were made by measuring definite volumes of the two gases into the calibrated buret, taking into account the 4.8 ml included between points A and B of Figure 1, which was determined by PV measurements. Experience showed that the thermal conductivity of the mixture became constant (the bridge output did not change) after raising and lowering the mercury levelling bulb about 75 times, which indicated that the mixture was uniform. The bridge output for a given mixture was measured first with hydrogen as reference, E H ,and then , constant value of the with helium as reference, E H ~the sum, E H EHe, serving as a check on the accuracy of the observations. Approximately 200 observations were made over the entire range of concentrations, and the thermal conductivity of the mixture, K,, calculated by means of eq 1, was plotted against the measured per cent of
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hydrogen. A smooth curve drawn between the points of the graph established average values of conductivity against the per cent of hydrogen, by means of which it was possible to calculate the values of constants NH and in eq 1. Taking &H = 41.8 X lo6 cal sec-l cm-l deg-l and O K ~=e 34.4 X lo5 cal sec-l cm-I deg-l1 it is found that N H = 0.0796 and NHe = 0.048. When these values are inserted into eq 1, calculated values of K,, which are plotted in Figure 2, can be obtained from the relation
K , = 41.8(1
+ 0.0796 In p ) p + 34.4[1 + 0.048 In (1 - p)](l - p )
(3) A few of the observations are plotted in Figure 2 in order to show the precision of the measurements. It can be stated, however, that the greatest deviation of any observation from the calculated graph was less than =4=0.5%, with the majority of the observations lying between 0.1 and 0.2% from the calculated average.
Free-Radical Intermediates in the Reaction of the Hydroxyl Radical with Amino Acids by Hitoshi Taniguchi, Katsuji Fukui, Shun-ichi Ohnishi, Hiroyuki Hatano, Department of Chemistry, Faculty of rScience, Kyoto University, Kyoto, Japan
Hideo Hasegawa, and Tetsuo Maruyama Japan Electron Optics Laboratory Company, Akishima, Tokyo, Japan
(Received January 3,1968)
Intermediate radicals formed in the reaction of the hydroxyl radical with some carboxylic acids, amines, and amino acids have been studied by esr spectroscopy using a continuous-flow method. A titanous chloridehydrogen peroxide system is employed as a source of the hydroxyl radical in most experiments and Fenton's reagent is also used in the case of alanine. Some good esr spectra are obtained for glycine, a-alanine, 0alanine, serine, threonine, valine, leucine, and isoleucine. The structures of the radicals deduced from analysis of the spectra and the hyperfine coupling constants are tabulated. It is found that the hydroxyl radical abstracts hydrogen atom preferentially from the CH bonds distant from the protonated amino group, those adjacent to the methyl group, and those distant from the carboxyl group. This is consistent with the electrophilic character of the hydroxyl radical. Hyperfine coupling data of various protons and 14N nuclei give information concerning steric conformations of the radicals and freedom in the internal rotations.
Introduction The flow method in esr studies first developed by Dixon and Norman' has been successfully used to study unstable intermediate free radicals in many organic redox reactions, and much knowledge on the nature and structure of these free radicals has been accumulated. With this technique, we have investigated the interThe Journal of Physical Chemistry
mediates in the reaction of the hydroxyl radical with amino acids and also with some related carboxylic acids and amines. Such knowledge might be basically important in understanding radiation-biochemical reactions in aqueous solutions, since the OH radical formed (1) W. T. Dixon and R. 0. C. Norman, J . Chem. Soc., 3119 (1963).
