Effects of alkyl groups on rates of SN2 reactions - ACS Publications

Aug 21, 1970 - 6.1 X 104 sec-1 and ft_2 = 8.0 X 109.1/ sec-1 ... 106 sec-1 at 25° and nearly zero ionic strength for aqueous ... (4) L. P. Holmes, D...
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where polvery slowly decreases, multilevel transitions (0 + 2, 0 -+ 3, etc.) would compete with the 0 1 transition, t,hus leadling to smaller values of pol. The result also sh xvs that for a given 1~ the probability normally decr3ases with increasing b. I n general the present calculratfon of the average transition probability

correctly reflects the physics of molecular collisions a t different values of b.I8 Acknowledgment. I wish t o thank Dr. Young 0. Koh of the Computer Center, University of Kevada, for assistingwith the programming*


(18) B. Widom and 8. H. Bauer, J . Chem. PhUs., 2 1 , 1670 (1953).

Kinetics af Hydrolysis of Ferric Ion in Dilute Aqueous Solution

by Paul Hemmes, Larry D. Rich, David L. Cole, and Edward M. Eyring* Department of Chemistry, University of Utah, Salt Lake City, Utah 8411!8 (Received August $1, 1970) Publication costs assisted b y the A i r Force Ofice of Scientific Research

Dilute aqueous solutioiis of ferric perchlorate have been studied by the electric field jump relaxation kinetic b2

technique. A t 25” and ionic strengths less than 3 x M the specific rates of the reactions FeOH2+(aq) Fe(QII),+(aq) H+(aq) were found to be k z = 6.1 x lo4sec-l and k-2 = 8.0 x 109 M - l see-’. A preceding hydrolysis step Fea+(aq) FeOH2+(aq) H-k(aq) was found to reach equilibrium too rapidly for rate measurements by this method.



Introduction The hydrolysis of metal ions in aqueous solution is an important process ’in many areas of pure and applied chemistry. In some cases, the normal solution chemistry of an element io a given oxidation state is not the chemistry cf the aquo ion at all but rather that of a hydrolyzed form of the ion. A classic example of such behavior is the vase of aqueous ferric ion.’ While for many years thermodynamic studies of aqueous metal ion hydrolysis have been made,2 especially in Scandinavia, the kinetics of hydrolysis have been susceptible to study only since the advent of relaxation techniques. Kinetic investigations of the hydrolysis of aqueous m d a l ions

Experimental Section The ferric perchlorate was reagent grade (G. F. Smith Co.). Stock solutions were analyzed volumetrically (1) F. A. Cotton and G. Wilkinson, “Advanced Inorganic Chemistry,” 2nd ed, Interscience, New York, N. Y . , 1366, p 859.

+ PlzO :z NOH2+ + H+ 1, 1


they do between -4 X loe and -1O’O M-l sec-’. A possible case in which jG1 could differ significantly from -1Oj sec-I would be aqueous iron(II1) since for this ion p”K1 is variously reportedg~’Oas 2.2 to 2.5 (at zero ionic strength) in contrast to 5.02 for aliamin~m(I1I)~ and 3.98 for chromium(III),6 for example. The electric field jump relaxation method3 kinetic study of dilute aqueous ferric perchlorate reported below confirms this expectation.

*K’ = k’/k-l



+ H 2 0z?M(OH)z++ H+






have revealed a surprising sameness of the hydrolysis rate constant k, g. 10j sec-’at 25” and nearly zero ionic strength for aqueous trivalent a l u m i n ~ r nchromium,s ,~ scandium,6 and indium ions.’ As would be expected from Debye’s equations for the specific rate of diffusioncontrolled ion recombinat>ion reactions, the values of k-1 also do not differ markedly for these metals lying as

(2) L. G. Sillen and A. E. Martell, “Stability Constants,” The Chemical Society, London, 1964, p 39 ff. (3) M. Eigen and L. DeMaeyer, “Technique of Organic Chemistry,” Vol. VIII, Part 11, S. L. Friess, E. S. Lewis, and A . Weissberger, Ed., Interscience, New York, N. Y . , 1963, Chapter 18. (4) L. P. Holmes, D. L. Cole, and E. M. Eyring, J . Phys. Chem., 72, 301 (1968). (5) L. D. Rich, D. L. Cole, and E. M . Eyring, i b i d . , 73, 713 (1969). (6) D. L. Cole, L. D. Rich, J. D. Owen, and E. R f . Cyring, Inorg. Chem., 8 , 682 (1969). (7) I?. Hemmes, L. D. Rich, D. L. Cole, and E. M Eyring, J. Phys. Chem., 74, 2859 (1970). (8) P.Debye, Trans. Electrochem. Soc., 82, 265 (1942). (9) A. B. Lamb and A. G. Jacques, J. Amer. Chem. Soc., 6 0 , 1215 (1938). (10) R. M. Milburn and W. C. Vosburgh, ibid,, 77, 1352 (1955). The Journal of Physical Chemistry, Vol. 76, N o . 7,1971



Table I : Calculated Molar Concentrations and Experimental Electric Field Jump Relaxation Times in Dilute Aqueous Ferric Perchlorate at 25" co,a 10-5 M


6.83 4.88 2.91 0 977 0.781

3.788 3 I972 4.1% 4 633 4.486

[H+Ipd 10-4 M



10-4 M

3.19 2.17 1.10 0.393 0.404

1.663 1.082 0.644 0.234 0.344

[Fe8+l,e 10-7 M

28.0 12.5 4.06 0.354 0.487

[FeOHs+l,e [Fe(OH)2Cl,E [Fez(OH)z4+l,B 10-5 M 10-6 M 10-9 IM

5.83 4.01 2.19 0.525 0.491

6.99 7.39 6.80 4.48 2.85

101.9 48.2 14.4 0.827 0.724

i,f fisec

0.68 i 0 . 1 6 1.02 0.10 1 . 7 2 ir 0.10 3 . 5 5 f 0.14 2.47 =t0.12 _+


6 6 6 3


a Total molar concentration of ferric perchlorate. Ionic strength calculated from eq 7 b Glass electrode pH of the sample solution. of the text. * Concentration of hydrogen ion calculated from eq 9 of the text. e Molar concentrations calculated from eq 3-6 of the text. Average experimental electric field jump relaxation time with standard deviation calculated from the range. Number of independent determinations of the relaxation time.


_ e

using stannous clnlciride and potassium dichromate.l1 Other experimental procedures and the conductometric electric field jump apparatus have been described before in considerable detai1.4-7 Solutions were all freshly prepared, dilute, low in pH, and never heated above room temperature, and thus were out of equilibrium insofar as the eventuttl formation of polymeric precipitates is concerned.

Results Table I con1,ains ihe values of total iron(II1) perchlorate concentratioiz, Coymeasured pH, and experimental relaxation tjimes. Also shown are calculated concentrations of the several types of ions present. On the basis of results of several equilibrium studies2 we have assumed the existence of dimer but no higher polymeric species in our dilute, freshly prepared sample solutions. (hicentrations were calculated from the following set, of equations











D M O H ) ~1~



TKzz CO= rill3+]




+ f;5'tQH2+]+ +

[M(OH)z+] 2[A!12(OH),4+] (6) p =

+ [lur(OH)a+]+

'/2(9[hi3+] 4- 4[MOH2+]

iG[;\/Iz(OH)24+]+ [E+]+ 3C0) (7) --log y*


iron(III), determined that p*K1 = 2.46 and p*Kz = 4.7 a t high dilutions, 25", and corrected to zero ionic strength. Hedstrom's12 p*Kl = 3.05, p*K2 = 3.26, and ptKzz = -3.19 for iron(II1) a t 2 5 O and p = 3.0 M are unsuited for use with electric field jump kinetic data that are obtainable only in solutions approaching aero ionic strength. The fairly pronounced ionic strength dependence of *K, and tKzz for aqueous iron(1II) found by hlilburn and Vosburghlo is ample warning against from Hedstrom's an extrapolation of *K1, *K2,and TK22 3.0 &I ionic strength constants.lz Milburn and VOSburghlo reported p*K1 = 2.17 and piK2z = -1.48 a t 25" and extrapolated to zero ionic strength. However, the neglect of equilibrium 2 (and the omission of "K?) by these authors explicitly contradicts the kinetic results described below. Thus we are obliged to use a composite set of equilibrium constants in our calculations of the concentrations given in ?'able I : *Kl = 10--2.46, *K2 = I , and tKzz = 30, As we \vi11 see later, the dominance of [H+] over [FeOH2+], [Fe(OH),+],and [Fe2(OH)z4++l under our experimental conditions malies a fairly reliable determination of ralle constants possible in spite of the uncertaiiities just noted in these equilibrium constants.



Relaxation method rate studies of the dimerization of aqueous ferric ion (in more concentrated solutions than we have considered here) have invariably been conducted on a much longer time scale (-1 see) than the microsecond relaxation time scale of the present w o r l ~ ~It~ is8 therefore ~ ~ reasonable to seek an explanation of our electric field jump relaxations in terms of hydrolysis rather than dimerization kiizetics. Since ferric ion reportedly undergoes two hydrolysis steps (11) D. A. Skoog and D. M. West, "Fundamentals of Analytical Chemistry," Holt, Rinehart and Winston, Kew York, K.Y . , 1963,

457. where brackets denote molar concentration, p denotes (12) B. 0. A. Hedstrom, A r k . K e m i , 6, 1 (1953). the ionic strength, m d -y& is the mean ionic activity (13) H. W-endt, 2. Elektrochem., 66, 235 (1962); Inorg. Chem., coefficient for monovalent ions. Lamb and J a c q ~ e s , ~ 1527 (1969). in a glass electrode potentiometric study Of aqueous (14) B. A. Sommer and D. W. Margerum, ibicl., 9, 2517 (1970).

The Journal of Phijaical Chemistry, Val. 76, No. 7 , 1971




(eq 1 and 2), we conceivably could by judicious choices of concentration observe two relaxations within the 0.3-10 psec time range accessible to our electric field jump relaxation me tlod apparatus. Experimentally, however, we have observed only one relaxation. The anticipated twu relaxations associated with the equilibria 1 and 2 %re given by 71,2-1


an t-a27L . . + 2

+ azz)2 - 4(allazz - a12a21)



where, omitting the charges of the ionic species for brevity all


k. I(*KI3- [HI

a22 = k-~(.'&

4- [HI

+ [MOH])



+ [NI(OH)z])= L 2 c p


C ~ ZE

ilG_1([H]- [MOH])


~ 2 = 1

d~z(*Kz- RII(0H)t)


I n cases where Pither all or u22is very much larger than the other, eq 413 reduces to 'Tfast-l



11 implies q-' > T ~ - ~ ) . The results of this sort of analysis can then be summarized as +/v

Iron (111) Gallium(lli1) Chromium (111) Thorium(lV) Scandium(EI1) Indium (III)

19-61 5.2-6.7 1.8-3.4 1.3-1.5 1.O-1.7 0.38-0.60

Slow process a22 a22

? all

assignment of specific rates based on a concordance of kinetic and thermodynamic equilibrium constants.5 On the other hand, our previous assignment of specific rates kl and k-l in the case of aqueous gallium(II1) hydrolysis was in error. We correctly determined that the slower of the two anticipated gallium(II1) hydrolysis reactions was the one we could observe. However, we mistakenly assumed all to be the slow p r o ~ e s s . ~I n the gallium(II1) case as with iron(II1) it is actually the second hydrolysis step (eq 2) that is slower, Thus the corrected specific rates for gallium(II1) are Jc-2 = 4.5 X l o 9 M-' sec-l and kz = 1.7 X 105 sec-' with = 10-4.4,in rough agreement with the potentiometric17 *K2 r= 10-3.5.

Acknowledgment. This research was supported by the Directorate of Chemical Sciences, Air Force Office of Scientific Research, Grant AF-AFOSR-69-1717-D.

a11 all

The chromiurxi(II1) case cannot be resolved by this argument although we see no reason to doubt our earlier

(17) R. Fricke and K. Meyring, Z . Anorg. Allg. Chem., 176, 325 (1928).

A Study of Nitrogen-15 Nuclear Magnetic Resonance Shifts in Pure

Methylamines and Pure CN,ClSNla y MIohammed Alei, Jr.,* Alan E. Florin, William M. Litchman,lb and James F. Univemity of California, Los Alamos Scient&

Laboratory, Los Alamos, N e w Mexico


(Received September $9, 1970)

Publicatwn costs assisted by the Los Alamos Scientific Laboratory

The I)Nliquid association shifts and temperature dependences of' the 15N chemical shifts of 15n'H3,CH3l5iYH2, (CE):3)2l5NH,(CHg)g16N,and CH3C16Nare presented and discussed. In the order given above, the vapor chemical shifts are 0, -14.5, -26.1, -28.7, and -273.4 ppm, respectively. The liquid association shifts at the melting point are -22.6, -9.4, -3.2, -6.9, and f11.3 ppm, respectively, and the temperature coefficienls are +4.3, f l . 6 , f0.5, f2.0, and -2.1 (all X ppm/'C), respectively. The difference in the sbifl data between the amines and acetonitrile is attributed to the dominance of the diamagnetic term in the case of the amines compared to the dominance of the paramagnetic term in acetonitrile.

Introduction I n recent publications2"Sbwe have demonstrated that the 170resonance in pure liquid water and the 15Nresonance in pure liquid ammonia are both considerably downfield OF the reeonances in their respective vaporphase molecules. 'The liquid-phase resonance also shifts, in each case, to lower field with decreasing temperature in linear fashion. Moreover, taking pure 16NH3 as an example the I5N shift between vapor and liquid and the temperature coefficient of the 15N shift in the liquid are botkl more than ten times as large as the corThe Journal o j Pir&cal

Chemistry, Vol. 76, No. 7, 1971

responding parameters for the KH3 proton resonance. It is thus possible for the I5Nresonance to be a sensitive probe for study of liquid-phase intermolecular interactions traditionally studied by proton reaonance measurements. We have, in fact, more recently shosvn3b4 (1) (a) Work supported by the U . S. Atomic Energy Commission; (b) AWU Faculty Research Participant at Los Alainos Scientific Laboratory. (2) (a) A. E. Florin and AM. Alei. Jr.. J. Chem. Phzis.. 47. 4268 (1967); (b) W. M. Litchman, M. Alei, Jr., and A. E.-Florin; ibid., 50, 1031 (1969).