state value 1046 cm.-l.13 The observed transitions fit the following formula, derived by a least squares fit. at
= 80,995
6lSl
HEATSOF FORMATION OF CHROhlATES 4 N D DICHROMATES
Dec. 5, 19%
+ 1278z'? - 1 9 . 0 ~ 2+~ 975~s+ 3.803~- 21.2212113 %'2
=
1. . 5 , 213 = 1. .3
;inalysis of the vibrational structure of the corresponding (sal) state of CF3H, shown in Table 111, utilizes v 2 = 1191 cm.-' and Y S = 446 cm.-l. The (13) F. Andersen, B. Bak and S. Brodersen, J . Chenz. Phys., 24, 989 (1956).
former is interpreted as a symmetrical C-F stretching mode with normal state value of 1209 cm.-l, while v 3 is interpreted as a CF3 symmetrical deformation mode with normal state value 699 cm.-1.14 The frequencies of Table I11 fit a formula, derived by least squares fit v
83.015
+ 1191~~2+ 3.4212' + 446~3- 1 8 . 2 ~ 3-~ 2'2
=
1. . 5 , 213
=
9.81'22'3
1,2
(14) H. D. Rix, ibid., 21, 1077 (1953).
ROCHESTER, XEWYORK
[CONTRIBUTION FROM THE CoBB CHEMICAL LABORATORY, UNIVERSITY
OF
YIRCISIA]
Thermodynamics of Aqueous Hydrogen Chromate and Dichromate Ions. Heats of Formation of Chromates and Dichromates BY LORENG. HEPLER' RECEIVED JULY 11, 195s S e w thermodynamic calculations based on results of earlier calorimetric investigations have been carried out and heats of CrOd-(aq) and Cr?O;=(aq) H20 = 2HCr04-(aq) have been obtained from these calculations. These reaction heats have been combined with entropies and free energies from the literature t o obtain new values for the entropies of Cr20i=(aq)and HCr04-(aq). Also, from the heats of the above reactions, the heat of solution of (?;H4)2Cr20;(c)and the heat of reaction of CrOl(c) with OH-(aq), it has been shown that the heats of formation of Cr03(c) and (NH4)pCr207(c) are consistent. Heats of formation of HCrOl-(aq), CraO;'(aq), CrOl=(aq), K2CrZ07(c)and K2CrO4(!) and free energies of formation of HCr04-(aq), Cr20;'(aq) and CrOl"(aq) have been calculated. The relation between calorimetric and equilibrium investigations of various Cr (IY) species in aqueous solution has been discussed. t h e reactions HCr04-(aq) = H + ( a q )
+
+
As a result of calculations made to determine the optimum conditions for a reasonably direct calorimetric investigation of the aqueous hydrogen chromate ion, HCrOd-, i t became apparent that results of heat of solution and reaction experiments already reported2 from this Laboratory were sufficient to give the desired information about HCr04-(aq). Some of the calculations of heats of formation and entropies given in the earlier paper2 are incorrect because of the unjustified neglect of HCr04-(aq). Results of correct and more complete calculations, reported in this paper, yield directly the desired information about HCrOd-(aq) and also bring the heats of formation of CrO3(c) and (NH4)2Cr207 into accord, thus making possible reliable calculations of a number of heats and free energies of formation. The important species in a weakly acidic aqueous solution of Cr(V1) can be deduced from the equilibrium constants4-6 for equilibria 1, 2, 3 and 3, all a t 25'
+
HCrO,-(aq) = CrOl'(aq) H+(aq) H2CrOl(aq) = H-(aq) HCrO.i-(aq) Cr?O,'(aq) H?O = 2HCr04-(aq) HCrzOi-(aq) = H + ( a q ) Cr,O;=(aq)
+
+
+
(1) (2)
(3) (4)
In solutions in which the total Cr(V1) concentration is between about lop3and 5 X and the PH is about 3, the important Cr(V1) species are HCrOa-(aq) and CrlOi=(aq). These conditions of (1) Alfred P. Sloan Research Fellow. (2) C . K.Muldrow, Jr., and 1.. G. HeplPr, IS J O U R N A L , 79, 404: (1957). (3) C. A . h'engehauer and J. I.. RIargrave, .T, P h y s . Chrm., 61, 142!l (19.57). (4) J. D. Neuss and W. Rieman, T H I S J O U R N A L , 66, 2'2338 (1934). ( 5 ) J. Y. Tong and E. L. King, i b i d . , 76, 0180 (1953). (0) LV. G. Davies and J. E. Prue, T i n i i s . Fnrntfny Sac., 51, 104; ( 19.53,
Cr(V1) and H + concentration are pertinent to the calculations that follow. The heat of solution of K2Cr207(c)in dilute HC104 has been measured a t a number of total Cr(V1) concentrations2 denoted by 2(Cr). The two important reactions that occur in this process are given by equations respectively. From the equilibrium constant (at zero ionic strength) for reaction 3 given by Tong and King5 and a known value of Z(Cr), a first approximation was made to the concentrations of HCr04-(aq) and Cr207=(aq). These calculations were based on relations 10 and 11. The ( H e r o 4 ) and (Cr207=)
+ (HCrOd-)
Z(Cr) = 2(Cr20;=) Z(Cr) = Z(HCrO,-)/Kt
+ (HCrOc)
(10)
(11)
so obtained were used to calculate to a first approximation the ionic strength of the solution under con-
LORENG. HEPLEK
(il82
sideration. Tong and King's5 equation for the dependence of K3 on ionic strength then was used to obtain a value for Ka applicable a t the approsimate ionic strength of the solution. This value for IC3 now was used with equations 10 and 11 to obtain better values for (HCr04-) and (Cr207=j and these calculations were repeated until consistent values of (HCr04-) and (Cr207=) were obtained which then were used to evaluate X and >-. From the intercept and slope of the straight line in a plot of XlAIi!, US. Y l A I I 7 , AH5 and AH6 have been found to be 2 0 . i and 15.S kcal. 'mole of &CrL07, respectively. Heats of solution of (NH4)2Cr20;(c)analogous to the heats of solution of K2CrzOi(c)represented by equations 3 and 6 may be denoted by AH5' and AIJG'. Similar treatment of the experimentally determined heats2leads to AH5' = 16.7 and A H 6 ' = 12.4 kcal./mole (NHq)2Cr20i(c). Calculations based on observed heats of reaction of K2Cr04(c) with excess dilute acid must also take proper account of the presence of both HCr04(xi) aiid CrzO;.-(aq) in the final calorimetric solutions. The two important reactions that occur are given by equations 12 and 13 and equation 14gives KzCr04(c)
+ H'(,iq)
K!cl04(C)
f Ixc(dq) = 2K'(Jq)
(
=
2Ki(dq)
+ HCrOl-(dq) A H L (12) + ('/j)Cr&;-(dq) +
1701.
SO
Davies and PrueGhave determined K 3 at 20 and 25' and we have calculated from their results that AH3' = 4.6 kcal.;'mole CrzOi=. The present values for AJIj' and AII6" have been combined to give 2&" = -1.9 kcal. 'rnole Cr?O;= from the relation AI13O = AIIjfl - AI16n. Similarly, AI$;" and AI160' and AI€I?O and AI113fl have been combined to give AII3" = AIIj'' = 4.tj kcal./mole Cr207= - AH13') = 5.2 kcal.,/mole and AII;," = Crs07=. On the basis of all four of these somewhat interdependent values we may take AI130 = l.i f0.3 kcal.l'mole Cr20;= as the "best" value. The satisfactory agreement of the calorimetric heats with the heat calculated from the temperature confirms the reliability of the eyuicoefficient of librium studies and of the present interpretation of the calorimetric data. The previously reported3 heat of solution of K2Cr04(c)as in equation li, AE11;' = 4.2 kcal.;' mole, has beell combined with A1llsfl to obtain K;.Cr04(c) = 2K+iaq)
--
Cr04=!aq)
AH170
(17)
AHl0 to be -0.8 kcal./inole from the relation AHI' = AII17' - AII1ao. Similarly, the previously reported2 heat of reaction of K2Cr20j(c) with OH-(ay) as in equation 18 KE;zCrzO;(c)
(13)
+
20H-!aq) = 2K-(aq) 2CrOa'(aq)
+
+ HzO
AH1P
(18)
AIIIJJ = -7.3 kcal./niole K2Cr0,, has been combined with AfIbfl and the heat of ionization of water AZI,O, as calculated from Bureau of Standards' heats of formation, to obtain U I l o to be -0.(i (14) the total calorimetric reaction where p and q kcal. ,'n-iolefrom the relation AITlo = ( I ,'?j (AIII8OAIIWo. The "best" value for AIIlo is represent the number of moles of K2Cr04 that give AIIbfl) HCr04-(aq) and Cr207=(aq), respectively. AII14 taken to be -0.7 =t 0.4 kcal./moIe. Heat content changes of reactions 1 and 3 have represents the calorimetrically determined heat content change per mole of K2Cr04(c)and AH12 and been combined with free energy changes of reacA H l 3 represent the heat content changes of reac- tions (l)? arid (3)4-6 to give AS," = -32.1 and tions 12 and 13 per mole of KZCr04(c). Equation AS30 = 8.7 cal./mole deg., respectively. These 15 gives AII14 in terms of $, q , AI512 arid AHl3. This entropies of reaction combined with Bureau of Standards7 entropies of Cr04=(aq) and HzO give PAIII? qAH13 = ip (1)AHIr (15) the standard partial molal entropies of HCr04-(aq) equation has been rearranged to equation 16 where and Cr207=(aq)to be 41.3 and 57.2 cal./deg. mole, (P/AIIi4) = - ( ~ / A H , , ) ( ~ ~ , ~ / ~ Iifl ,lAHi?) ~) (16) respectively. Heats of formation of Cr04=(ay),HCr04-(aq) I-' arid Q represent $/($ q ) and q/ (p q ) , reand Cr20;=(aq) can be calculated from several spectively. Equations 10 and 11 and Tong and King's5 heats of solution and reaction. One value for the equilibrium data were used t o obtain p a n a q heat of formation of Cr04=(aq) (-207.6 kcal./ and hence P and Q as before. From the intercept mole), based on the heat of reaction of CrOa(c)with and slope of the straight line in a plot of (P/AHI4) OH--(aq) and the heat of formation of CrOs(c), has already been reported.2 The heat of reaction 5' 21s. (Q,'AIJ14), AI112 and AJIIJhave been found to be with the heats of formation of (NH~),C~,OT(C),~ 5.0 and 2.4 kcal./mole K$304, respectively. For all these calculations based on calorirnetri- NHe+(aq)' and H20' leads to -205.6 kcal./rriole calli- measured heats of solution and reaction,2heats for the heat of formation of HCr04-(aq) which of dilution have been neglected and all calculated gives with AIIlothe heat of formation of CrO*=(acl) heats (AI15, AII6, A n , ' , AH6', AIIE and AI$,,) are to be -209.3 kcal., 'mole. Similarly, the heat taken equal to the standard heats of the appropriate of reaction ti' with heats of formation of NH4+and (NH.,)2Cr20i(~)3 leads to -338.1 kcal.1 reactions. The calorinietric experiments were carried out in very dilute solution so all of the neg- mole for the heat o f formation of Cr?O,=(acl). lected heats of dilution are small. Furtherinore, in This heat of fuririatiori combined with AfIl" and the reaction of K2Cr04(c) with H*(aq), heats of AII:]' gives the heats of formation of HCrOl--(aq) dilution tend to cancel. The best estimate that and CrO4=(aq) to be -20'3.3 and -2209.0 kcal. 1 intlican be made is that the total uncertainties in AJI5', mole. 'These heats oi forination of CrO4-.::(:iq) AI&', AIIGn', AHSO', AH1zo and AI~X,Oare about one- cate that the heats of forinatiori of Cr03(c)2anti half kcal. 'mole and are surely less than one kcal. i i i "Sdccted I.alues i(gr i'hctnic;ii I'hermod) namic I'ru]>eriic,s,'' mole. Circular 500, S a t i u n a l Bureau o f S t a n r l u d s , 15152. AH13
€120
+ g)KXrOdc) + (p + y)H+(dq) = 2(@f (])K+('lS) f PHCrOl-(dq) (q/2)CrD7-(aq) + (y/a)HzO (P + Y ) A H l l
(p
+
+
+
+
+
+
'
Dec. 5, 1958
IONIZATION AND DISSOCIATION OF OXYGEN BY ELECTRON IMPACT
(NH4)2Crz07(c)are consistent to within about one and one-half kcal./mole. The “best” value for the standard heat of formation of CrOc‘(aq) is taken to be the average of the values based on CrO2 and (NH4)~Cr207~ namely, - 208.6 kcal./mole. From the “best” heat of formation of Cr04-(aq) and heats of reactions 1 and 3, the “best” heats of formation of HCrOr-(aq) and Cr207-(aq) have been calculated to be -207.9 and -352.2 kcal./ mole, respectively. These heats of formation have been combined with heats of solution and reaction from this and the earlier paper2 to calculate “best” heats of formation of KzCrO4(c) and KK!r207(c) to be - 332.8 and -488.3 kcal./mole, respectively. From heats of formation and entropies given in this paper and others tabulated by the Bureau of Standards,?free energies of formation of Cr04-(aq), HCrOl-(aq) and C r 2 0 ~ ( a q )have been calculated t o be -171.1, -1180.0 and -305.9 kcal./mole, respectively.
[CONTRIBUTION FROM THE
6183
Conclusions News and Rieman,‘ Tong and King“ and Davies and Pmee are in fair agreement as t o the value of K 3 a t 25’. Their concordant results give us confidence in the reported values for K3 that is substantiated by the satisfactory agreement between our calorimetric A H 3 O and the A H 3 O calculated from the temperature dependence of K3. It also seems very likely that the reported values for KP and K4 are a t least approximately correct. The equilibrium constant for reaction 1 has been less adequately investigated than has K3. It is planned to reinvestigate in this Laboratory this equilibrium a t 25’ with the aim of checking the results of Neuss and Rieman.4 It is also intended to investigate this equilibrium a t several temperatures in order that an independent value of AHlo may be obtained to be compared with the calorimetric AHl0 reported in this paper. CHARLOTTESVILLE, VIRGINIA
DEPARTMENT OF CHEMISTRY,
UNIVERSITY OF
BRITISHCOLUMBIA]
The Ionization and Dissociation of Oxygen by Electron Impact’ BY D. C. FROST AND C. A. MCDOWELL RECEIVED JUNE 30, 1958 The ionization and dissociation of molecular oxygen has been studied using the retarding potential difference (r.p,d.) method of obtaining essentially mono-energetic electrons. All the spectroscopically known excited states of molecular *If,, *nu, 42g-,and one additional state, have been observed. The vertical ionization potentials here deteroxygen, ;.e., mined are in very good agreement with those calculated from available spectroscopic data. Six different dissociation processes leading to the production of O+ ions have been observed. These ions arise from either of these two types of processes: 0 2 f e = O f f 0 f 2e (a), 0 2 f e = O + f 0- f e (b). Each particular process has been identified by a careful study of the negative and positive ions formed. Ambiguities in earlier work, which arose largely from the difficulty of calibrating the negative ion energy scale, have been overcome by using sulfur hexafluoride as a calibrating gas.
Oxygen has been the object of many fairly detailed electron impact studies. The most detailed work is perhaps reported by Hagstrum.2 Besides studying the various ionization and dissociation processes, Hagstrum measured the appearance potentials of the positive and negative oxygen ions. Hagstrum also determined the kinetic energies with which the various ions are formed in the different dissociation processes observed. Later work by ThorburnShas, however, shown that some of Hagstrum’s observations are perhaps not quite as well founded as they formerly appeared. Examination of Thorburn’s results indicates that these more recent observations are still not quite satisfactory. The main difficulties in all the earlier work arise from the fact that the various workers used electron beams which had quite a large spread in their energy distribution. These experimental methods thus precluded the observation of fine details which are to be expected if the known spectroscopic data on oxygen are studied (see McDowel14). (1) This work was supported in part by the Geophysical Research Directorate of the U. S. Air Force Cambridge Research Centre, Air Research and Development Command, under Contract No. AF19(604)-2275, and by grants from the National Research Council of Canada. (2) H. D. Hagstrum, Rev. Mod. Phys., 23, 185 (1951). (3) R. Thorburn, “Report of Conference on Applied Mass Spectrometry,” Institute of Petroleum, London, 1955, p. 185. (4) C. A. McDowell, “Applied Mass Spectrometry,” Institute of Petroleum, London, 1954, p. 129.
Furthermore] in studying negative ion efficiency curves, these workers were unable to observe the true shape of the electron resonance capture peaks, and also they were unable to calibrate accurately the negative ion energy scale. Both these major difficulties recently have been shown to be resolved if one uses essentially mono-energetic electrons.6-7 It is now possible to calibrate the negative ion energy scale accurately by using the near-zero appearance potential of the SFs- ion from sulfur hexafluoride as a standard.6 Our own previous work68819 has shown that the retarding potential difference method of obtaining essentially mono-energetic electrons developed by Fox, et aL17yields accurate values for the excited states of molecular and atomic ions. It thus seems that the application of this method to oxygen would resolve many of the discrepancies noted in earlier electron impact studies of this molecule.
Experimental The mass spectrometer used was that described in our earlier publications.810 Krypton served as a calibrating gas for the measurements on the positive ions. Sulfur (5) D. C. Frost and C. A. McDowell, Proc. Roy. SOC.(London), 8282, 227 (1955). (6) W.M.Hickam and R. E. Fox, J . Chem. Phys., 26, 642 (1956). (7) R. E. Fox, W. M. Hicknm, T. Kjeldaas. Jr., and D. J. Grove, Phys. Rev., 84, 859 (1951). (8) D. C. Frost and C. A. McDowell, Proc. Ray. SOC.(London), A236, 278 (1956). (9) D. C.Frost and C. A. McDowell, C a n . J . Chem., 3 6 , 39 (1958).
