NOTES
3212
(7) where L = 2.3026. Since the terms of eq. 7 are functions of Tb, To,and Po only, vapor pressures can be predicted from just these input data. Detailed comparisons of RPME with experiment and with the better reduced predictors, namely, RPML (low pressure), RPMH (high pressure), R, and FK, are given in Table I, including the number of compounds whose vapor pressures are not predicted to within lo%, the average maximum Toerror,l0and Sfor various classes of compounds6 where
Here n is the number of experimental vapor pressure points and 6 is the per cent residual in P divided by 100. Table I shows that RPME is equivalent or superior to all the others in the 1CLl500-mm. range in t e r n of over-all S, average maximum per cent error, and the number within 10%. In the Tb-To region, it is slightly better than R, is only slightly poorer than FK or RPMH, and is an excellent predictor. Therefore it compares favorably over-all with the pair of RPM equations as well as with R and FK. Moreover, it has the important advantage of being much simpler for hand calculations than R or FK, since no log terms or iteration are required. As with RPM, a value of log Pr is obtained with one pass on a hand cahlator once G and k are calculated. In common with other reduced predictors, RPME is not too good at low pressures with pathological liquids such as alcohols, carboxylic acids, and associated or dissociating ones if G is estimated by eq. 6. However, the predictions are substantially improved if G is calculated from a low pressure point, should one be available in addition to the regular input data. The expression for C\H/AZ derived from the Clapeyron equation is also rather simple; namely AH
(1
+ Tr') + 3k(l - Tr')']
(9)
Unpublished calculations show that the heat of vaporization at the boiling Doint. Ut-,,.can be estimated with an average error Of Only 1*2% (l*'%if the patholo@cal liquids are included) using eq. 6, 9, and Thonuon's estimate" Of dzb ~~
I-
M b
Because RPME is over-all as good or better a uredictor than other single reduced equations and because it is substantially simpler for calculations, it is recommended for rapid estimation of vapor pressures over the whole liquid range using only the normal boiling and critical points as input data.12-14 (10) This quantity is the maximum per cent error for each compound averaged over all the compounds. It is a more stringent measure of good fit than the average per cent error; the latter is about half the former. Ordinarily, the maximum error occur8 a t the lowest temperature when below Tb, and in the middle of the range when bc+ tween Tb and To. (11) G. W. Thomson, C h . Rev., 38, 1 (1946). (12) However, if an experimental value of AHb should be available aa well aa Po,substantially better eatimates of P in the 10-1600-mm. region are given by the semireduced predictor MRA.196 (13) Othmer and Huang have shown (privata communication) that slightly better reduced predictions in the 10-1600-mm. region can be made using Othmer's reference liquid method.'' However, the method requires an extensive table of data for the reference liquid in addition to the RPME input data. (14) D. F. Othmer, Ind. Eng. Chena., 34, 1072 (1942).
Proton Magnetic Resonance Line Widths, Ligand Exchange, and Electronic Relaxation Times for Some Arylphosphine Complexes of Cobalt(I1) and Nickel(II)la
by Gerd N. La Marlb Frick Chsnticol Laboratory,Princston University,Princeton, New Jerssy (Received M a y $1, lQ86)
The careful analysis of proton magnetic resonance (p.m.r.) line widths for paramagnetic complexes can result in a variety of useful information.2t8 The observed line width in excess of that for the pure dit+ magnetic ligand can arise from two main sourcesligand exchange and paramagnetic relaxation due to the unpaired electron(s) on the metal. From a temperature study, the contribution from chemical exchange may be estimated,* and the remaining excw line width can then be attributed to paramagnetic relaxation effects.2ap8 The systems of interest here are the bis(triary1phosphine) dihalides of Co(I1) and Ni(11).4
I
0.97 1 -P J r b
(10)
research hw been supported by a grant from the N(1) (a) tional Institutes of Health; (b) Chemical Laboratory IV, H. C. 0rsted Institute, University of Copenhagen, Copenhagen, Denmark. (2) (a) N. Bloembergen and L. 0. Morgan, J. C h . Phya., 34,842 (1961); (b) E. A. LaLancette and D. R. Eaton, J. Am. C h . SOC., 86,6146 (1964). (3) 8. Lue and 8. Meiboom, J. C h . Phys., 40, 1068, 1066 (1964).
NOTES
It has been observed2b that for these Ni complexes, ligand exchange is quite important in determining the line widths (AHt/,). LaLancette and Eaton concluded that the rate of ligand exchange for the iodide complex was slow by the n.m.r. criterion, with the rates increasing in the order I < Br < C1.2b Upon addition of excess ligand to solutions of the Co complexes, we observed the same phenomenon as for the Ni complexes2b: that the ligand exchange rate increases in the order I < Br < C1, with the rate for the iodide also very slow as measured by n.m.r. The observed4p.m.r. lines for the ortho protons for both the pure Co and Ni complexes exhibit increasing widths, I < Br < C1, indicating increasing contributions to the line widths due to ligand exchange. In order to determine the relative importance of ligand exchange for the various halides, we obtained AH1/, for the two complexes, ( p - t ~ l ~ P ) ~ Cand o I ~(p-t0laP)~NiI2,in CDCls over the temperature range -60 to 60°, using a Varian DP-60 spectrometer in conjunction with a variable temperature probe. The results are illustrated in Figure 1. The curves of line width vs. temperature exhibit two distinct regionsa; at low T, AHl/, decreases with T, and at high T ; AHl/, increases with T. The former region gives the variation of AHl/, in the absence of ligand exchange, while the latter region indicates increasing contributions to the width from ligand exchange. The data exhibit too much scatter to make any quantitative estimates to the rate of exchange; however, two conclusions may be drawn from inspection of Figure 1. The first is that the contribudue to ligand exchange appears to set in tion to AHl/, at lower temperature for the Co than for the Ni complex, indicating, at least for the iodides, that the Ni complex is more stable than the Co complex.zb Similar measurements on the bromides and chlorides were inconclusive since the data were quite unreproducible and there was evidence for some decomposition or precipitation of ligand. Since ligand exchange contributed significantly to the observed line widths for the bromides and chlorides to much lower tempera tures than for the iodides, it could not be definitely established whether there exists significant differences in AH1/, for the three halides in the absence of ligand exchange. Since the order of ligand labilities for the Co and Ni2b complexes is identical, the explanation offered by LaLancette and Eaton2b appears to be applicable also to the Co system^.^ Their reasoningzbis that the donation of an electron to the phosphine ligand wia d?rdn bonding is partially compensated by a-bonding with the halide, and the order of halogen a-bonding abilities is I > Br > C1. The fact that for the iodide
3213
1000
I
]700
loo 70
d
500 V 400 300
8 4
*3
2
.9
- 150
15 RT
complexes the Ni appears to be more stable than the Co bears out this postulatezblS16that dn-dn bonding is very significant in determining the stabilities of these complexes. From p.m.r. contact shifts, it has been e~tablished~~~4' that the unpaired spin densities on the phosphine ligands for the Ni complexes are comistantly 50% greater than in the Co complexes, indicating that d d s delocalization is more extensive in the Ni systems, hence their greater stabilities. The second conclusion indicated by Figure 1 is that the contributions to the observed line widths at room temperature are essentially negligible for both the Ni and Co complexes. These AH1/, values must thus result from paramagnetic relaxation effects since the width for the pure ligand is only -2-3 c.p.s.* The p.m.r. line widths due to the presence of unpaired electrons have been related to the electron correlation times by Solomon* and Bloembergen: The combined equa tion2a can be expressed as
+
+
Here B = S(S l)y1~g~,f3~/(15@), C = S(S l)AB/ 3h2, r0 and re are the electron dipolar and exchange correlation times, respectively, WI and wg are the proton and electron Larmor frequencies, and the other symbols have their conventional meanings.2b,a Since the ortho (4)
G. N. La Mar, W. D. Horrooks, Jr., and L. C. Allen, J. C h .
Phya., 41, 2126 (1964). ( 5 ) M. C.Browning, J. R. Mellor, D. J. Morgan, S.A. J. Pratt, L. E. Button, and L. M. Venanzi, J. C h . SOC.,693 (1962). (6) A. D.Allen and C. D. Cook, Can. J . C k . ,41, 1235 (1953). (7) G.N.La Mar, J . C k . Phys., 41, 2992 (1964). (8) I. Solomon, Phys. Rev., 99, 559 (1955). (9) N.Bloembergen, J . C h m . Phys., 27, 592 (1955).
Volum 69,Number 9 September 1966
NOTES
3214
proton peaks are considerably broader than the other peaks,' the main relaxation is via the dipolar part of eq. 1, rather than the term depending on the hyperfme interaction. This is due to the r+ dependence of the first term in eq. 1 and the nearness of the ortho position to the metal. Using only the fist term, with (r")Bv = 6.8 X cm.B (structural parameters taken from ref. 4), g = 2.39, S = 3//z for Co,loand g = 2.32, S = 1 for Ni,I1 an upper limit to the dipolar correlation time, rc, is ~alculated.~ We obtain ro = 2 X and 6 X 10-13 sec. for the Ni and Co complexes, respectively. These r0 values are too short to be associated with the molecular tumbling time in solution, which the sec., so that Debye equation estimates to be -lo-" rC may be identified3 with the electronic relaxation time, T1. For the related complex anions,' [(phew P)Co13]- and [(phen3P)NiIS]-, similar calculations using the observed line widths' yield Tl values of about the same magnitude as for the complexes discussed above. Only very rough estimates to the ortho proton line widths are available for the anionic complexes, due to considerable overlapping of lines? It is of interest that for these complexes r > T I , where 7 is the molecular tumbling time in solution, the opposite to what has been previously assumed in the analysis of the isotropic s h i f t ~ . ~ J * ' ~ Acknowledgments. The author wishes to acknowledge the hospitality of the Bell Telephone Laboratories, Murray Hill, N. J., and thanks Mr. E. W. Anderson for obtaining the p.m.r. spectra. Valuable discussions with Profs. L. C. Allen and W. D. Horrocks, Jr., are gratefully acknowledged. (10) F.A. Cotton, 0. D. Faut, D. M. L. Goodgame, and R. H. Holm, J . Am. Chem. doc., 83, 1780 (1961). (11) F. A. Cotton, 0. D. Faut, and D. M. L. Goodgame, ibid., 83, 344 (1961). (12) H. M. McConnell and R. E. Robertson, J . Chem. Phys., 29, 1361 (1958).
The Abnormal Relation between the Velocity of Sound and the Temperature in Sodium Sulfate Solution
by Tatsuya Yasunaga, Mitsuyasu Tanoura, and Masaji Miura Departmsnt of Chembtry, F d t y of Science, Hirosh&ta Univerdy, Hiroshima, Japan (Received January $6,1066)
Since the first report by one of the authors1 on the abnormality in the velocity of sound in sodium sulfate The Journal
of
Physical Chemistry
and sodium carbonate aqueous solutions near the crystal transition point of the salts, a similar abnormality has been discovered in the electric conductivity for sodium sulfate by Hirano2 and in the viscosity of sodium carbonate by F ~ j i t a . This ~ communication is to report more detail on the abnormal relation between the temperature and the velocity of sound in sodium sulfate aqueous solution. The velocity of sound was measured by an ultrasonic interferometer described in detail elsewhere. The electrical oscillations controlled by quartz crystals having each fundamental frequency 2.5, 3.5, 4.5 Mc./sec. in a thermostat were derived to the X-cut quartz crystal having its fundamental frequency 0.5 Mc. Special circuits were added to detect precisely only the change in the interference. The frequency of oscillation was measured carefully within +50 C.P.S. during each series of runs by a frequency meter. The vertical double glass tubes were sealed through a Teflon 0 ring to a holed stainless steel plate, below which was attached a gold-plated 0.5-Mc. crystal. A plane reflector made of stainless steel was connected to a micrometer and balanced for the crystal by controlling a spring. It could be moved vertically without any rotation, and its position was determined within *0.001 mm. with the micrometer having a traveling range of 6 cm. I n order to protect the sample solution from contamination during measurement, a glass tube was fixed to the shaft of the micrometer. The ultrasonic interferometer was immersed in a water bath and maintained at a constant temperature to *0.002". The velocity of sound at 3.5 Mc. for various concentrations of sodium sulfate solution at different temperatures (0.1963-1.849 M) is given in Table I and shown in Figure 1. From these results, it is clearly seen that the change in the velocity of sound with temperature below 32.4" is not the same as that for greater temperatures, even for solutions as dilute as 0.1963 M. In particular, a discrepancy in the velocity of sound waa observed for the concentrated solution at 32.4'. A similar measurement was also done for a 1.144 M solution at various frequencies. The results obtained in the process of increasing the temperature are shown in Table I1 and show no dispersion in the velocity of sound by frequency. This suggests that the abnormality is not caused by a relaxation phenom(1) T. Sa& and T. Y-aga, Kagaku To Kogyo (Tokyo), 7 , 146 (1964). (2) K.Hirrtno, Nippon Kagaku Zasshd, 79, 648 (1958). (3) K.Fhjita, Bull. C h . SOC.Japan, 32, 1005 (1959). (4) T. Yasunaga, M. Tanoura, and M. Miura, in preparation.
