Lours S. KASSEL
1838
SZOS" and Ag + to Cr207- and then testing with hydrogen peroxide or diphenylcarbazide. The solution containing M n + + is treated with sodium hydroxide and sodium peroxide to precipitate
[CONTRIBUTION FROM
THE
Vol. 56
manganese dioxide, which is then identified by the sodium carbonate-potassium chlorate bead test or with sodium bismuthate in nitric acid. NEWYORK
RECEIVED MARCH1, 1934
CITY
PITTSBURGH EXPERIMENT STATXON OF THE U. S. BUREAU OF MINES]
Thermodynamic Functions of Nitrous Oxide and Carbon Dioxide' BY Lours S. KASSEL~ Spectroscopic data have been used to calculate The vibrational levels are given by accurate values for the free energies, and in some E 1288.7Ui 593.0~~2 2237.9s - 3.3Wi2 3.1(Vz2 -Z2/3) - 13.8$ - 9.8~1b- 26.7viQ cases the entropies, heat contents, and specific 13.3vza8c m - 1 heats, of nearly all the common diatomic gases. Approximate values have also been obtained for where v1 and v3 are the quantum numbers of the several polyatomic gases, with the neglect of all two single valence vibrations, and v2 and I are the anharmonic and interaction terms. The the total and azimuthal quantum numbers of infra-red spectrum of carbon dioxide has now the double deformation vibration; the allowed been rather well mapped, and the results have values of I are f v2, * (v2 - 2 ) , etc. Using the been analyzed quite completely; it should notation therefore be possible to calculate thermodynamic y = 6-1288.7F s = e-68a.OF t = e-ZZ37.9F b = 3.1F c = 13.8F functions for carbon dioxide with high accuracy. a = 3,3F e = 26.7F f = 13.3F d = 9.8F The spectrum of nitrous oxide has received much g = 3.1F/3 F = hc/kT less attention, but the data amply justify calculation, since the free energy is quite unknown. the vibrational factor of the Q-sum becomes The simpler case of nitrous oxide will be treated Qvxb. = Z, 2, Z, Zl rvlsYztYa exp. (avlz bvla cvg2 dv1vz ev1v3 fvzvs - g P ) first. We now expand the exponential term into a Nitrous Oxide power series and perform the indicated summaPlyler and Barker3 studied the infra-red spections. In addition to formulas previously given,6 trum of nitrous oxide; their work identifies we require the first of the following two formulas, the three fundamental vibration frequencies which will be useful for other linear molecules also. and determines roughly the anharmonic and = (v/3)(w l)(v 2) coupling constants. The molecule is definitely Z1' = ( ~ / 1 6 ) + ( ~ l ) ( u + 2)(3oP + 6~ - 4) linear and unsymmetrical. As was pointed out by Badger and WOO,^ Plyler and Barker made an where the sums run over alternate integral error in calculating the moment of inertia, the values of 1 from -v to f v . The significant correct value being 66.1 X g. cm.2. Since terms in the result are the rotational stretching terms and the rotation- Q")b. = RS2T( [l + ar(1 r)R2 2bs(I 2 3 ) s ct(1 + t)T2 + ZdrRsS + erRtT + 2fsStT vibration interactions are not known, the Q-sum 2gsS2] + [b2s(l + 18s 339 8s3)S4+ for each electronic level factors into one term abdrRs(1 + 7s + 4s2)SS 2bfs(1 7s + s2) due to a rigid rotator and one to a group of S3tT - 2bgs(l + 10s + 93')s' + d2r(l + 7 ) R%(l + 2s)Sz] f [(b3/3)s(l 88s 71W coupled oscillators. We assume that the lowest 1 2 0 8 ~+~ 473s4 + 32.+)SB1) electronic state is ' 2 and that no others need be considered. The only problem then is to calcu- where late the vibrational factor of the Q-sum. T = 1/(1 - t ) S = 1 / ( 1 - 3) R = 1/(1 - 7) ( 1 ) Publisbed by permission of the Director, U. S. Bureau of In this expression the first bracket contains all Mines. (Not subject to copyright ) the terms from the linear term of the exponential (2) Associate physical chemist, Pittsburgh Experiment Station, U. 9. Bureau of Mines, Pittsburgh, Pa. expansion, the second bracket the five largest
+
+
+ + + +
+
+
+
+
( 3 ) Plyler and Barker, Phys. R e v , 38, 1827 (1931) (4) Badger and Woo, THISJOURNAL, 64, 3623 (1932).
+ + + + + + + + + +
( 5 ) Kassel, Phrs. Rev., 43, 384 (1933).
Sept ., 1934
THERMODYNAMIC FUNCTIONS OF NzO AND COZ
quadratic terms and the third bracket the single largest cubic term; this cubic term is not actually used in the calculations, since it is quite small. The factor RS2T is just the harmonic contribution to the Q-sum, and we have therefore isolated within the braces the exact correction factor due to anharmonic and coupling terms. It is a simple matter to differentiate this factor twice with respect to ( l / T ) ; the factor and its deriva.tives may then be evaluated at several temperatures and the anharmonic contributions to the various functions obtained. Table I gives F/T, H and C, up to 1500°K. at intervals of 50", vihich permit interpolation by second differences. It has not seemed worth while to tabulate the = 56.941 including a spin entropies; &,.I entropy of R In 9 = 4.366. TABLE I THERMODYNAMIC FUNCTIONS FOR Ng0 NUCLEAR SIN T , OK.
250 298.1 300 350 400 450 500 550 600 650 700 750
800 850 900 950 1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500
-(Fo
- EPo)/T
47.927 49.257 49.306 50.513 51.592 52.574 53.479 54.319 55.107 55.847 56.547 57.212 57.845 58.451 59.032 59.590 60.127 60.644 61.145 61.627 62.096 62.549 62.990 63.418 63.834 64.239 64.634
H 1859.0 2290.6 2308.2 2785.1 3286 3809 4351 4911 5488 6079 6683 7300 7928 8568 9216 9873 10539 11213 11893 12579 13272 13969 14672 15381 16093 16810 17530
INCLUDING CS
8.687 9.251 9.272 9.790 10.246 10,6519 11.029 11.363 11 .67:3 11.961 12.221 12.45!3 12.678 12.87!3 13.064 13.23:3 13.38!) 13.534 13.661 13.790 13.904 14.01 1 14.110 14.203 14.290 14.373 14.44!)
1839
TABLEI1 SPECIFIC HEATOF NITROUS OXIDE T,
OK.
271.6 287.4 389.5
Cp, obs.
C p , calcd.
8.910 9.149 10.034
8.948 9.131 10.154
The heat of formation of nitrous oxide a t 20" has been reported as -19,500 ~ a l by . ~Awbery ~ and Griffiths17and as -19,740 cal.ls by Fenning and Cotton.* These determinations almost certainly supersede all earlier measurements ; we shall adopt the average value, -19,620 caL15. Combining the results of Table I with the values previously calculated for nitrogen by Giauque and ClaytonlB and by Johnston and Davis,1° and with values for oxygen calculated = by Johnston and Walker,l' we obtain Goo 20,429 cal. for the formation of 1 mole of gaseous nitrous oxide. Table I11 gives a few values for the equilibrium constant of this reaction, and shows the equilibrium concentrations of nitrous and nitric oxides in air, assumed to contain 78.03% nitrogen and 20.99% oxygen. It is clear that no appreciable amount of nitrous oxide would be formed at any temperature. TABLEI11 FORMATION OF NITROUS OXIDE IN AIR AT ATMOSPHERIC PRESSURE T , O K . [NIO~/[N~][~I'/~ Nz0, % NO, % 300 6.87 X 2 . 5 X lo-*' 3.70 X 10-14 1000 6.87 x 10-9 2 . 5 x 10-7 3 - 5 9 x 10-8 1500 1.98 X lo-' 5.1 X 0.134
Although nitrous oxide is very unstable with regard to the elements, it is very stable compared to ammonium nitrate. Using data in Lewis and Randall, we estimate NzO(g)
+ 2B0(1)
=
AF0tg8 =
NHbNOdaq) 43,000 cal.
Thus 100,000 atm. NzO would be in equilibrium with lo-'* M NH4N03.
Carbon Dioxide The infra-red and Raman spectra of carbon dioxide have been studied with considerable p r e c i ~ i o n .Following ~ ~ ~ ~ a~ suggestion ~ ~ ~ ~ ~ of~ ~ (7) Awbery and Griffiths, Proc. Roy. Soc. (London), A141, 1
The most reliable specific heat measurements (1933). (8) Fenningaud Cotton, {bid., Al41,17 (1933). on nitrous oxide are those of Eucken and Liide.6 (9) Qiauque and elayton, T ~ JOURNAL, s S6, 4875 (1933). As Table I1 shows, the agreement with the (10) Johnston and Davis, ibid., 66, 271 (1934). (11) Johnston and Walker, ibid., 66, 172 (1933). calculated values is quite good, although at. the (12) Barker, Asfrophys. J . , 66, 391 (1922). highest temperature it is beyond Eucken's esti(13) Martin and Barker, Phys. Reo., 41, 281 (1932). (14) Adams and Dunham, Pub. A . S. P., 44, 243 (1832). mated error of 0.5%. (15) Dickinson, Dillon and Rasdti, Phys. Rev., S4, 682 (1928). (6) Eucken and Lade, 2. physik. Chcm., 6 8 , 413 (1929).
(16) Langseth and Nielsen, 2. physik. Chcm., lSB, 427 (1932).
LOUISS. KASSEL
1840
Fermill' Dennison18 and Adel and Dennisonlg have given a detailed theoretical interpretation of the unusual characteristics of these spectra. The molecule is linear and symmetrical; it would be expected to have one symmetrical valence vibration, vl, and one unsymmetrical one, v3; in addition, there would be a double bending vibration vz, with a subsidiary quantum number I measuring the angular momentum about the figure axis. The frequencies vz and v3 would appear in the infra-red spectrum; v1 would occur in the infra-red only in combination bands, but would be the strongest line in the Raman spectra. It IS found, however, that the Raman spectra contains a strong doublet, and that the infra-red also will not fit such a simple scheme. Fermi showed that the experimental results were those to be expected for the case that vl ~ V Z and , the complete working out of the theory by Adel and Dennison gave a highly satisfactory agreement with every detail of the observations. It turns out that each set of levels with the same values of I and of V = 2V1 Vz goes over into an equal number of levels which are, in the first approximation, linear combinations of the simple levels. There are thus two levels which are partly (0200) and partly (1000) ; both levels are excited in the Raman effect, due to their (1000) nature; both are excited in the infra-red spectrum by absorption from (OlOO), because both are to some extent (0200). This interaction thus gives a richer spectrum than would otherwise be found. It also produces large shifts in position for the levels; thus the two levels formed from (0200) and (1000) have a separation of 102.6 ern.-', although v1 - 2vz is only 14.1 cm.-l. Since the molecule is symmetrical, alternate rotational levels are missing when I = 0. When 121 > 0 all values of J 2 121 are allowed, but for each J only +I or - E has the correct symmetry.21 The first approximation to the rotational energy is (h2/8?r21)(J2 J - P ) . The corresponding Q-sum is less than that for a simple rigid rotator with the same moment of inertia. At the lower temperatures this effect outweighs the anharmonic corrections; the specific heat is below the harmonic oscillator-rigid rotator approximation
+
+
(17) Fermi, 2. Physik, 71, 250 (1931). (18) Dennison, Phys. Reo., 41, 304 (1932). (19) Adel and Dennison, r b d , 48, 718 (1933); 44, 99 (1933) (20) The quantum state is designated by (ViVJVa). (21) Dennison, Reo. Modern Physics, 9, 334 (1931).
Vol. 56
up to 700'K., and the heat content up to 1000"K., while the free energy is still below at 1500°K. As a result of the resonance degeneracy, the calculations are more than usually complicated. It is necessary to treat each value of V - 111 as a separate problem, setting up new series and summing independently. It proves convenient also to treat each value of V3 separately, since v3 is so large that term by term summation is easier than use of the series. For V - 111 = 0 there is no degeneracy, the first order perturbation energy is (1/2)hA,18 and the stabilized wave f u n c t i ~ n 'is~ entirely Vl = 0, VZ = 1. For V - 111 = 2 the two states with first order perturbation energies h [* d( V 1)/2 Ab A . . . ] have the composition
-
+ + (1/2)[1 (1/2)[1
( A / P ) / d F 2 ] VI = 1, vr = T'- 2 A / @ ) / d m VI = 0, Vz = V
=i=
*(
The second order perturbation energies for the vibration, and the rotational perturbation energies are functions of V1 and VZ, so that it is necessary to know the composition of the various actual states. For larger values of V - (21 the levels become more complex and the results will not be given here. The square root terms would be awkward to sum, but fortunately they disappear when we combine the two states which the =t sign indicates. It would require too much space to give the details of the various special devices used in the calculations. The results are given in Table IV. Accurate values have been computed only to TABLEIV THERMODYNAMIC FUNCTIONS FOR CARBON DIOXIDE T,OR.
300 400 500 600 700 800
900 lo00 1100 1200 1250 1300 1400 1500 1750 2000 2500 3000 3500
-(Po
- E0")fT
43.620 45.848 47.681 49.261 50.660 51.921 53.074 54.137 55.125 56.049 56.490 56.917 57.737 58.513 60.29 61.88 64.64 67.15 69.02
H
CP
2256.1 3197.5 4226.8 5327.9 6488.0 7697.4 8948.1 10233 11548 12886 13564 14246 15624 17017 20557 24159 31500 38970 46540
8.908 9.885 10.676 11.324 11.862 12.312 12.689 13.005 13.27 13.50 13.60 13.69 13.86 14.00 14.3 14.5 14.8 15.0 15.2
THERMODYNAMIC FUNCTIONS OF NzO AND
Sept., 1934
1500°K. for FIT, and to 1000OK. for H and C,. At higher temperatures estimated anharmonic corrections have been added to values calculated from the simple Einstein functions, and the results are progressively less reliable as the temperature increases. The exact values of - (F' Eo")/T differ from the earlier approximate calculations of Gordon22by a maximum of 0.033, which is within that author's intended accuracy. The heat content and specific heat have not been calculated previously. Table V gives the equilibrium constants for the dissociation of carbon dioxide and the important producer-gas and water-gas reactions. The free energy table of Clayton and GiauqueZ3is used for graphite, and the revised table of the same authors for carbon monoxide.24 The heat content of carbon monoxide, needed in calculating A€&", is taken from Johnston and Davis.25 Values for oxygen are those of Johnston and Walker." The free energy of hydrogen up to 2000°K. is from Giauque;26 the correct free energy above that temperature, and the heat content, are given by Davis and John~ton.~' The values used for water are those given by the recent exact calculations of Gordonz8up to 150OoK.,and somewhat less accurate estimatesz9at higher temperatures. Rossini has found the heats of combustion of hydrogen30 and carbon monoxide31to be 68,313 and 67,623 cal., respectively, at 25". The heat of vaporization of water at that temperature is 10,500 cal./mole.a2 The heat content of saturated water vapor at 25' is only 0.4 cal./mole less than that for the ideal gas, according to a calculation based on the van der Waals equati.on with u = 5.47 X lo6 C C . ~atm. and b = 30.55 cc. It is thus unnecessary to make a correction to Ai%". The heat of combustion of graphite is taken as 94,240 ~ a land . ~the ~ heat content used is the "I. C. T." value. Hence we have Reaction 2c0, = 2 c o 0 co, c = 2 c o COz Hz = CO
+ +
+
2
+ HzO
AHa,, cal. 135,252 41,006 9808
AEoO, ail.
133,51d 39,526 963'3
Gordon, J . Chcm. Phys., I, 308 (1933). CIayton and Giauque, TRISJOURNAL, 64, 2610 (1932). Clayton and Giauque, ibid., 66, 5071 (1933). Johnston and Davis, ibid.. 66, 271 (1934). Giauque, ibid., 61,4818 (1930). Davis and Johnston, ibid., 66, 1045 (1934). Gordon, J . Chem. Phys., 4, 85 (1934). Gordon, private communication. Rossini, Bureau of Standards Journal oj Research, 6, 1 (3931). Rossini, ibid., 6, 37 (1931). &home, Stimson and Fiock, i b i d , 6, 479 (1930).
coz
1841
TABLEV EQUILIBRIUM CONSTANTS INVOLVING CARBONDIOXIDE T, O K Ka Ki If; 300 3.36 x 10-90 1.63 X 1.15 X 1.53 X 400 5.40 x 10-14 6.90 x 10-4 1.82 x 10-9 9 . 9 x 10-61 7.71 X 10-8 500 3.71 x 10-2 7 . 4 x 10-41 1.90 x 10-6 600 0.111 2 . 7 1 x 10-4 700 8 . 4 x 10-34 0.247 1.63 X 1.11 x 10-2 800 0.195 0.451 2.08 x 10-24 900 1.91 0.719 4.00 X 1000 1.23 X 10' 1.04 1100 1.92 X 1.41 1200 3.27 X 1O-lB 5.73 x 10' 1.60 3.13 x 10-15 1.12 x 102 1250 1.80 2.09 X IO2 2 . 5 2 x 10-14 1300 2.21 6.28 X IO2 1400 1.03 X 2.63 2.57 X 1.63 x 103 1500 3.65 1.56 X IO-* 1.06 x 104 1750 4.59 4 . 2 1 x 104 1.87 x 2000 6.08 2.72 x 105 1.42 x 10-3 2500 7.08 0.112 3000 8 . 8 X lo5 2.43 .......,.. 3500
in presence of graphite
The calculated values for the water-gas equilibrium are in excellent agreement with the direct measurements of Neumann and kohl^^^ and the indirect determinations of Emmett and Schultz.3 4 The constants for the producer-gas reaction agree well with the earlier values of Rhead and Wheeler,35 but other work, as pointed out by Gordon,22 indicates a "zero-point" entropy of 0.5 cal./deg. for graphite. The calculated specific heats agree well with the results of Eucken and Liide,eand up to 2500°K. they fall within 1 cal. of the best experimental values deduced by E a ~ t m a n . ~ There ~ is little doubt that the calculated values are more nearly correct.
Carbon Monoxide Thermodynamic functions for carbon monoxide previously given by the author3' and by Clayton and Giauque23 are in error due to a confusion of signs of certain spectroscopic constants. Revised values of the free energy have been published by Clayton and Giauque,24and of the other functions by Johnston and Davis.l0 Dr. C. W. Montgomery has kindly repeated the calculations at 5000°K., using the author's analytic methods (33) Neumann and Kahler, 2. Elektrochcm., 34, 227 (1928). (34) Emmett and Schultz, THISJOURNAL, 65, 1390 (1933). (35) Rhead and Wheeler, J. Chem. Soc., 97, 2178 (1910). (38) Eastman, Bureau of Mines, Technical Paper 445 (1927). (37) Kassel. J . Chem. Phys., 1, 576 (1933).
1842
MAURICE L. ERNSBERGER AND WALLACE R. BRODE
of summation; his results check the specific heat of Johnston and Davis to 0.002 cal./deg. and the other functions to 0.001 or better. Ackmw1edgment.-The author is very grateful to both Professor D. M. Dennison and Dr. 0, K. Rice, each of whom independently corrected an error in the quantum weights for carbon dioxide.
Summary 1. The free energy, heat content and specific
[CONTRIBUTION FROM
THE
VOl. 56
heat of nitrous oxide have been calculated up to 1500°K. 2. The heat content and specific heat of carbon dioxide have been computed to 1000°K. and the free energy to 1500°K.; less accurate estimates have been made up to 3500'K. The equilibrium constants for the water-gas and producer-gas reactions have been tabulated from 300 to 3000°K., and that for the dissociation of carbon dioxide to 3500°K. PITTSBURGH, PA.
RECEIVED APRIL4, 1934
DEPARTMENT OF CHEMISTRY, OHIO STATE UNIVERSITY ]
The Absorption Spectra of Cobalt Compounds. V. The Cobalt-EthylenediamineHalogen Complexes BY MAURICE L. ERNSBERGER AND WALLACE R. BRODE TABLE I In a continuation and extension of previously O F THE ABSORPTION SPECTRA reported work' on compounds of the type (Co- RESULTSO F BANDANALYSES OF SALTS O F THE TYPE ( CoEn2X2)X En&)X, this paper presents the absorption specMultra of a series of halogen substituted derivatives and Mean tiple Bands frequency numOb- CalcuDifferthe effect on the absorption caused by a change in Compound difference her served lated ence the halogen substituent. Some of these compounds 1,6-(COEn2F2)NOi 51.4 10 515 514 - 1 13 660 668 i-8 described have not been previously prepared or had - 12 16 835 823 their absorption spectra recorded, and in the case of - 1 485 48.5 10 484 some of the compounds with recorded absorption - 4 13 635 631 spectra, the data available were not satisfactory. 16 775 776 + 1 The compounds were prepared according to 1,6-(CoEn2ClBr)NOa 47.0 10 470 470 0 the methods used by Werner.2 They react slowly 13 620 611 - 9 with water and this vitiates to some extent the (Fig. 1) 16 752 (18) 825 822 ( -3Ib accuracy of the absorption spectra measurements. 19 894 By dissolving the compounds in the least possible 45.6 10 456 456 0 amount of water and diluting to the desired con- 1,6-(CoEnzBr2)Br - 7 13 600 593 centrations with alcohol, solutions were obtained - 10 16 740 730 in which the reaction with water was retarded suffi(18) 820 (821) + 1 ciently to make reliable measurements possible. 19 860 867 $ 7 22 1010 1003 - 7 The spectra were measured in the visible region 44.8 10 448 448 0 by means of a Bausch and Lomb spectropho- 1&( CoEngI2)I 13 583 tometer. In the ultraviolet region measurements (Fig. 2) 16 720 717 - 3 were made with a Bausch and Lomb quartz 19 850 852 + 2 spectrograph using as a light source an under- 4 22 990 986 water spark between tungsten electrode^.^ The I$-( CoEn2FI)F0 84.7 7 605 593 - 12 Hilger rotating sectorphotometer system was used. 10 $35 847 12 The compound 1,6-(CoEnzIz)I was prepared 1,2-(CoEn2C12)Cl 79.7 7 858 558 0 10 800 797 - 3 from (CoSnzC03)I. Solid (CoEn2C03)I was 7 551 551 treated with concentrated hydriodic acid (44%) 1,2-(CoEn2C1Br)Br 78.7 .o
+
(1) (a) selbt, D h e r h t i o n , Zurich, 1813, p. 63; Gmclin's "Handbuch def anorganlschan Chemie," Berlin, 1930, Vol. SB-B, p. 228; (b) Lifschb, Z.phpsik. Chem., 106, 33 (1923). (2) Werner, Ann.. 816, 1-272 (1912). (3) Brode, Bur. Slandar$$ J . Research, 4'7, 604-507 (1928).
1,2-(CoEn2Brz)Br
77.9
10 7
790 545
10
780
Values taken from Gordienko.'"
787 545 779
- 3 0 - 1
' Approximate,
