A GENERALIZED RELATION BETWEEN REDUCED DENSITY AND

P. J. MCGOXIQAL

1686

gen evolution in KOH solution at the potential used in this work (Table I) is much smaller than the current density for metal deposition. Calculations were based on the data of Kaptsan and Iofa781sfor the Tafel’line. (b) Polarograms for dilute solutions of MOH (Fig. 3) exhibit a well defined plateau except for LiOH, and it is concluded that reduction of HzO a t current densities of the order of those used for metal deposition in generation in situ requires appreciably more negative potentials than the potentials prevailing in faradaic rectification measurement^.'^ Evidence for lithium is not con-

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(18) 0. L. Kaptsan and 2. A. Iofa, Zh.

Fir. Khim.,Z6,193, 201 (1952).

1-01. 66

elusive, and the data in Tables I to I11 for this metal should be regarded as tentative. There was some evidence of H, evolution for Rb, and this is why the method used in the calculation of the concentration CRb a t the electrode was devised (see Experimental). It should be noted that the k0’s for Li and Rb are not out of line with respect to the other metals. Acknowledgment.-This investigation was supported by the National Science Foundation. (19) It must be noted that the solution composition was not the same in the polarographic and faradaic rectification measurements. Further, the OfI- concentration a t the electrode increases with the current for Hz evolution in the polarographic experiments.

A GENERALIZED RELATION BETWEEN REDUCED DENSITY AND TEMPERATURE FOR LIQUIDS 1 5 7 1 ~ SPECIAL ~ REFERENCE TO LIQUID METALS’ BY P. J. MCGONIGAL~ Research8Institute of Temple University, Philadelphia 44, Pennsylvania Received March 19, 1083

A correlation exists among various liquids in regard to their reduced density us. temperature behavior. The dimensionless quantity A is defined. When the reduced variable &ed is plotted against reduced temperature, a series of quite similar curves is obtained. The correlation is shown for fifteen liquid metals and seven other liquids. A method for estimating critical densities is described.

The density us. temperature behavior of liquid metals has recently been the subject of extensive investigation a t this Institute. A consideration of the results obtained from these investigations as well as those reported by other workers shows that there is a broad spread in the densities of different liquid metals as well as in the values of the temperature coefficient of density. To date there has been no general correlation among the density data for different metals. In an attempt to produce such a correlation, use was made of the reduced properties of metals. It has been shown by Grosse3 that reasonable estimates of the critical temperatures of metals can be made by application of the law of corresponding states to the entropies of vaporization. Critical densities may be estimated if reliable liquid density data are available by evaluation of the equation of the rectilinear diameter a t the critical temperature. In many cases the density us. temperature behavior of a metal between its melting point and normal boiling point can be represented by a straight line well within the limit of experimental error. The equation of the rectilinear diameter is then one-half of the density us. temperature equation. I n cases where the density us. temperature behavior is best represented by a curve, the rectilinear diameter may (I) (a) This work was supported b y the National Science Foundation under grant 18829; (b) presented before the Division of Physical Chemistry, 142nd National Meeting of the American Chemical Society, Atlantic City, N J , September, 1962. (2) A report of this work will constitute a portion of a dissertation t o be submitted by the author to the Graduate Council of Temple University in partial fulfillment of the requirements for the degree of Dootor of Philosophy. (3) A. V. Grosse, J . Inorp. N z d . Chem., 32, 23 (1961).

be constructed by using one-half the sum of the liquid and vapor densities at various temperatures. Critical densities then may be obtained by evaluating the rectilinear diameter equation a t the critical temperature. If reliable estimates of the critical temperatures and critical densities are available, the density us. temperature behavior of liquids may be compared on the basis of reduced variables. Such a comparison is most conveniently made by utilizing the reduced rectilinear diameters, since these are straight lines which all begin at the point (D8 ) r e d = 1, T r e d = 1, where (D~ ) is ~ the reduced ~ d rectilinear diameter and T r e d is the reduced temperature. The variation in the slopes of these lines for different liquid metals is considerable. In a previous publication4 the density of magnesium a t the normal boiling point and the density a t the critical point, as well as the slope of the density vs. temperature line between the melting point and the normal boiling point, were predicted with a fair degree of accuracy (relative to the values of these quantities as determined by experiment and extrapolation of experimental data) by using an average reduced rectilinear diameter based on data for six metals. The use of such a method is, of course, justifiable only in the absence of experimental data or, as in the case of magnesium, in cases where available experimental data disagree to a very large extent. The concept of the reduced rectilinear diameter, as such, does not indicate the general relation be( 4 ) P. J. MoGonigal, A. D. Kirshenbaurn, and A , V. Grosse, J . Ph?/a. Chem., 6 6 , 737 (1962).


Sept., 1962

RELATION BETWEEK REDUCED DENSITY AND TEMPERATURE FOR LIQUIDS

1687

9 i0 Fig.

l.-Ared~

T r e d - P US. Fred. for liquid metals.

tween reduced density and temperature that exists for liquids. This relation was arrived a t by use of the dimenrjionlessvariable (dD 8 /dT) ( T / D 8 ) which TABLEI SUMMARY OF PERTINENT DATAFOR LIQUIDMETALS Metal

Ag Na ~i

K Au In

Mg Pb U Hg Cd Zn Li Sn Ga

a, g.,’cm.a

5.232 0.5810 6.~14 0.454 9.44 3.658 0.917 5.734 9.678 7.19 4.33 3.78 0.273 3.642 3.12

- b X 104, g./cni.SOK.

4.534 1.234 7.67 ‘1.194 6.00 3.400 1.324 6.587 5.164 14.38 5.37 4.61 0.4125 3.00 2.88

Dc g./cm.a 2

To,O K . 7460 2780 4830 2440 9460 6680 3850 5400 12500 1733 2970 3430 4110 8720 7620

1.85 0.17 2.39 1.63 3.76 1.39 0.41 2.18 3.22 4.70 2.75 2.20 0.10 1.03 0.93

-Ac

1.83 2.05 1.55 1.79 1.51 1.63 1.24 1.63 2.00 0.53 0.58 0.72 1.64 2.55 2.36

Ref.

6 7 8 7 9 10 4 11 12 13,14 7 15 7 16 17

is termed A (by analogy to the ?r of Codegone,s who proposed a dimensionless expression relating the temperature and pressure of saturated vapors). The use of the rectilinear diameter permits the eval( 5 ) C. Codegone, Allgem. Waermetech., 9, 58 (1959). (6) A. D. Kirshenbaum, J. A. Cahill, and A. V. Grosse, 1.Inorg. Nucl. Chem., 22, 33 (I96l). (7) “Liquid Metals Handbook,” 2nd Ed., R. N. Lyon, Editor-inchief, sponsored by the Committee on the Basic Properties of Liquid Metals, Office of Naval Research, Department of the Navy, in COIlahoration with the Atomic Energy Commission and the Bureau of Ships, Department of the Navy, Washington, D. C., June, 1952, NAVEXOS P-733 (Rev.). (8) A. Schneider and G. Heymer, 2.anoig. allgem. Chsm., 286, 111 (1958). (9) W.Krause and F. Sauerwald, ibid., 181, 347 (1929). ( I O ) P. J. McGonigal, J. A. Cahill. and A. D. Kirshenbaum, J . Inorg. Nucl. Chem., in press, 1962. (11) A. D. Kirshenbaum, J. A. Cahill, and A. V. Grosse, {bid., in press, 1962. (12) A. V. Grosse, J. A. Cahill, and A. D. Kirshenbaum, J . Am. Chem. Soe., 83, 4665 (1961). (13) J. Bender, Phyailc. Z., 16, 246 (1915). (14) J. Bender, ibid., 19, 440 (1918). (15) P. Pascal and A. Jouniaux, Compt. rend., 168, 414 (1914). (16) A. L. Day, R. B. Sosman, and J. C. Hostetter, Am. J . Sci., 87, 1 (1914). (17) W. H. Hoather, Proc. Phys. SOC.(London), 48, 699 (1938).

P. J. MCGONIGAL


1688

Tred. Fig. 2.-A,,d.

TABLE I1 -5

x

Liquid

so2 n-Butane

co2

Hz0

g./cm.3

104, g./cm.aO K .

T,, OK.

1.059 12.45 430.4 0.408 4.30 426 .815 11.40 304.3 .632 4 . 7 5 647.4 .546 5.23 516.2

CzH50H Perfluoro-2-nbutyltetrahydrofuran 1.358 15.4

500.21

DO. g./cm.3

-Ac

Ref.

0.523 1.025 18 ,225 0.814 18 ,468 ,740 18 .324 .276

.588

18 .978 18

.949

1.309 19

uation of A a t the critical point, whereas the actual density us. temperature curve would have an infinite slope a t the critical point. In order to compare the behavior of different liquids, the quantity Ared is plotted against Tred. Ared is simply A/Ac (18) “Handbook of Chemistry and Physics,” 35th Ed., Chemical Rubber Publishing Co., Cleveland, 0. (19) R. M. Yarrington and W. B. Kay, J . Chem. Eng. Data, 5, 24 (1960).

-

vs. Tred. for other liquids.

SU~XVARY OF P E R T I N ~ DATA N T FOR OTHERLIQUIDS

a,

Vol. 66

where7Ac is the value of A a t the critical point. Figure 1 shows Ared us. T r e d plots for liquid metals and Fig. 2 shows the plots for several other liquids. Table I is a collection of numerical values pertinent to this work for liquid metals and Table I1 gives similar information for several other liquids. The a and b refer to the constants in equations of the form

D 8 (gJcm.3)

= a

- bT(O1C)

The literature references are for density data. Critical temperatures for the metals were estimated according to the method described by Grosse with the exception of that for mercury, which was experimentally determined.20 Rectilinear diameter equations for the metals were calculated as necessary from the original data. The data for argon are omitted from Table I1 since A and Ared were calculated from the reduced density equation of Guggenheim.21 The references in Table I1 are for tables of thermodynamic func(20) F. Birch, Phys. Reb., 41, 641 (1932). (21) E. A. Guggenheim, J . Chem. Phys., 13, 253 (1945).


Sept., 1962

KINETICSOF THIG REVERSIBLE HYDRATION OF 2-HYDROXYPTERIDINE

tions or density data from which the rectilinear diameter equations were calculated. The agreement shown in Fig. 1 among the liquid metals is considered good since, with the single exception of mercury, the critica,l temperatures are estimated and evaluation of the critical densities involves extrapolations which are large compared with the temperature range over which experimental measurements were made. Two curves are shown in Fig. 1 since the behavior of the group I I B metals, although internally consistent, appears to he rather different from that of the other metals. The agreement in Fig. 2 is better since the critical temperatures and critical densities for these liquids have been experimentally determined. The correlation illustrated in Fig. 1 and 2 may be presumed valid for other metals and liquids in general, a t least in the absence of experimental evidence to the contrary. The Ared vs. Tred curve may be used to estimate critical densities for those metals and other substances for which adequate experimental data are not available. Since the curve for the group I I B metals is so distinct, it is considered reasonable not to refer to it in making the estimates. If the density of a liquid is known a t only a single point between its melting point and normal boiling point, its critical density may be determined to a first approximation from the average value of Ared a t T r e d corresponding to the temperature a t which the density is known. Knowledge of the two density values permits estimation of the slope of the rectilinear diameter and hence that of the density us. temperature line between the. melting point and the normal boiling point. As an example of the application of the method described herein, the critical densities, densities a t the normal boiling points, and slopes of the density us. temperature lines have been calculated for rubi-

1689

dium and cesium, two metals for which reliable density data are available only a t the melting points.' Results of experimental measurcments on the densities of liquid rubidium and cesium will be reported in a subsequent publication from this Institute. The calculated values, which agree rather closely with those predicted by GrosseZ2 on the basis of an average ratio of density a t the normal boiling point to critical density for several metalsJ3are shown in Table 111. The recent values of WeatherfordZ3in Table I11 mere taken from a density vs. temperature plot for the alkali metals, apparently constructed with the assumption that the slopes for rubidium and cesium would be quite similar to the slopes for sodium and potassium. The true situation is more complicated, however, since even in the case of elements in the same group of the periodic table, comparisons should be made only on the basis of reduced properties. TABLE I11 RUBIDIUM AND

1)ENSITY D A T A FOR

CESIUM

-dD/dT

x DB.P., g./c~n.~ K p . , Dx,p., B.p., This Weather- To, Do, Metal a K . g./cm.3 "K. work ford CK. g./eni.a

Rb Cs

104, g./

crn.3. OK.

312 1.475 974 1.16 1 . 3 3 2190 0.29 4 . 8 301 1.84 958 1.44 1.68 2150 0.36 6.0

Acknowledgment.-The aut,hor gratefully acknowledges the encouragement and guidance of Dr. A. V. Grosse. (22) A. V. Grosse, "The Liquid Range of Metals and Some of Their Physical Properties at High Temperatures," Paper No. 2159, A.R.S., Space Flight Report to the Nation, New York, N. Y., Oot. 9-15,

1961.

(23) W. D.Weatherford, Jr., paper presented a t the Symposium on High Temperature Properties and Applications of Liquid Metals, Fifty-fourth Annual Meeting, b.I.Ch.E., New York, N. Y., Dee. 2-7 1961.

KINETICS OF THE REVERSIBLE HYDRATION OF 2-I-IYDROXYPTERIDINE BY Y. INOUE' AND D. D. PERRIN Department of Afedical Chemistry, Institute of Advanced Studies, Australian Y'cctional University, Canberra, Australia Received Narch $0, 1068

Rapid-reaxtion methods have been used to study the kinetics of reversible hydration of 2-hydroxypteridine across the C(4), Nc3)double bond. The reaction is acid-base catalyzed and, over the pH range 4.55 to 12.4, times of half-completion a t 20' range from 0.5 to 375 see. A possible reaction mechanism is suggested.

Introduction Althoug,h reversible hydration across C=O bonds, for example in aldehydes and some ketones, is well known, similar reactions involving C-N bonds have been much less investigated. Known examples where such hydration occurs include pteridine (cation and neutral molecule), 2-hydroxyand 6-hydroxypterjdine (neutral molecule and anion),3-6 2-mercaptopteridine (neutral molecule (1) Australian National University Scholar. D.D. Perrin, J. Chem. Soc., 645 (196%). (3) A. Albert, i b i d . , 2690 (1955). (4) D. J. Brown a n d S. F. Mason, ibid., 3443 (1956). ( 5 ) D. D. Perrin a n d Y . Inoue, Proe. Chem. Soc., 342 (1960).

(2)

and anion),G 1,4,6-triazanaphthalene (cation and neutral m ~ l e c u l e ) ,and ~ ~ ~quinazoline (1,3-diazanaphthalene) (cation and newtral rnole~ule),*~V as well as some of their methyl and other derivatives. I n each case, the first of the forms given in parentheses exists mainly as the hydrate while the second form is mainly anhydrous. Covalent hydration and dehydration of 6-hydroxypteridine (across positions 7 and 8) proceeds (6) Y . Inoue a n d D. D.Perrin, J . Chem. Soc., 2600 (1962). (7) A. Albert and 0. Pedersen, i6id., 4683 (1956). (8) A. R. Osborn, K. Schofield, and L. N. Short, ibid., 4191 (1956). (9) A. Albert, W. L. F. Armarego, and E. Spinner, abid., 5267 (1961).

A GENERALIZED RELATION BETWEEN REDUCED DENSITY AND

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