1540
JOHN
[CONTRIBUTION FROM
THE
0. EDWARDS
Vol. 76
METCALFCHEMICAL LABORATORIES OF BROWSUNIVERSITY ]
Correlation of Relative Rates and Equilibria with a Double Basicity Scale BY JOHN 0. EDWARDS RECEIVED OCTOBER 29, 1953
A new equation, which is a combination of a nucleophilic scale and a basicity scale, is presented for the correlation of the reactions of electron donors. A new nucleophilic scale for donors, based on electrode potentials, is devised. Data used to test the equation and the scale include rates of displacement reactions of carbon, oxygen, hydrogen and sulfur, and equilibrium constants for complex ion associations, solubility products and iodine and sulfur displacements. The results are good for most of the correlations, and are especially encouraging for those cases, such as complex ion constants, which have been treated heretofore only qualitatively. Advantages and consequences of a double basicity scale for electron donors are discussed briefly.
It has been known for some time that rates of nucleophilic displacements on alkyl carbon atoms do not follow the normal basicities (to protons) of the entering electron d0nors.l Recently, a linear free energy relationship, based on the displacement rates of methyl bromide as standard substrate, was employed by Swain and Scott? (hereafter S.S.) to correlate many rate data. The rates of nucleophilic displacements in aromatic compounds follow similar patterns as those in aliphatic compounds but there appears to be a greater dependence on the basicity of the entering donor.3 Similar difficulties involving lack of correlation of basicity to protons with basicity to Lewis acids (such as aqueous cations4z5)and to formally positive sulfur c o r n p o ~ n d are s ~ ~also ~ well established. Although there has been no quantitative treatment of these data to date, Foss6f7pointed out that there appears to be a relationship between nucleophilic character and electrode potentials. I n this study, the correlation of many rate data (of the nucleophilic displacement type) and equilibrium data (involving some degree of covalent bond f ormation) has been attempted. The equation
where K/'& is a relative (to water) rate or equilib-. rium constant,s En is a nucleophilic constant characteristic of an electron donor, H i s the relative basicity of the donor to protons? and CY and fl are substrate constants, has been used for these correlations. The calculations have been made by using a least squares analysis of the observed data to determine a and p. In many cases, K Ois known, but in others it is necessary to treat K Oas an additional parameter. The H Scale.-For one standard reaction of donors, the basicity to protons is used. The normal $Ka values of the conjugate acids in aqueous solution are employed; they are changed, however, (1) (a) P. D. Bartlett and G. Small, THIS J O U R N A L , 72, 4867 (1950); (b) C . K. Ingold. "Structure and llechanism in Organic Chemistry," Cornell Univ. Press, Ithaca, S. T., 1953, Chapter V I I , pp. 306-418; (c) E. D. Hughes, O u n ~ t Revs., . 6 , 245 (1951). (2) C. G. Swain and C. B. Scott, THIS J O U R N A L , 76, 141 (1953). (3) (a) J. F. Bunnett and R. E. Zahler, Chem. Revs., 49, 273 (19j1); ( b ) Ref. l h , Chapter X V , pp. 797-815. (4) E. C . Lingafelter, THISJOVRSAI., 63, lORO (1941). ( 5 ) J . Bjerrum, C h e m Revs., 46, 381 (1950). ( G ) 0. Foss, Kgl. S o i s k e V i d . Selsk. Skuij%r, 2 (1945). (7) (a) 0. Foss, A c t a Chem. Scand., 1 , 8 (1947); (b) 1 , 307 (1947); (c) 3, 1383 (1840). (8) Wherever possible, d a t a for room temperature (1s 2'cic) and aqueous solution will be used.
by the addition of the constant 1.74which is the correction for the pKa of H 3 0 + . By definition H = pKa + 1.74 Many of the needed pKa values are either unknown or poorly known. This is true for HCl, HBr, HI, HSCN and others; estimated values are employed in these cases. In Table1,Hvaluesfor the donors (for which the symbol N is used) are presented; those values which are estimates are placed in parentheses. TABLE I ELECTRODE I'OTEBTIALS ABD DONORC O N S T A S T S
Data from ref. 9, except nhere indicated otherwlse. Ref. 7. e P LV Preisler and L Berger, THISJOURNAL 69, 422 (1917) dAssuming the free energy change for the reaction C21\T2(g) C,N,(aq) is negligible. e Calculated from Hg(XOl), complex; ref 5 . f Calculated from Ag(C1CH2C00)2- complex. Calculated from epichlorohydrin rate. Calculated from mustard cation rate. Calculatcd from ICH2COO- rate 3 Calculatcd from methyl bromide rate.
h
+
The En Scale.-A search was made for zt standard state for the nucleophilic character of a donor which would be more fundamental than rates of reaction with an arbitrary substrate. While nucleophilic character is strongly linked to electron polarizability, i t is difficult to relate the measured
1541
RELATIVE RATESAND EQUILIBRIA WITH DOUBLE BASICITY SCALE
Mar. 20, 1954
polarizability of a donor particle to the nucleophilic strength of a specific part of this donor. Inspection of electrode potentials given by Latimer9 for oxidative dimerizations of the type 21-
19
+ 2e-
showed that these potentials become more positive in the same order as the n values of S.S. become larger. That the relationship is a linear one may be seen in Fig. 1; in this figure the data for the six donors for which there are reliable data are presented. As all of the rate and equilibrium constants correlated in this study are values relative to the water values, the potential for the couple 2H20
HaOzf2 f 2e-
is needed. However, i t is not reported9 and there does not appear to be any way to calculate it from the present thermodynamic data. I t was, therefore, necessary to calculate a value for this couple by means of a least squares correlation of the data shown in Fig. 1. From this calculaticn the potential value -2.60 is obtained for the above couple.1° From the value of the potential of the couple and the values of the oxidation potentials of the donors, a nucleophilic scale defined by the equation E, = E”
6
+ 2.60
I
0
-06 -0.9 -1.2 Electrode potential Fig. 1.-The linear relation between the nucleophilic constant of Swain and Scott and the electrode potential. -0.3
are low for OH-, CH3COO-, CoHbNH2 and S203=, are high for Br- and I-, and are close to the observed values for SCK- and C1-. Only in one case (Cl- with mustard cation) is the deviation significantly inverted to the direction one would expect because of the lack of a PH term. TABLE I1 CORRELATIONS OF Two DISPLACEMENTS ON CARBOX 6-Propiolactone
htustard cation
0bsd.a Ca1cd.b S.S.C 0 b s d . d C a l c d . e S.S.c N is set up. In Table I, Envalues for all of the donors 2.49 2 . 3 5 2 . 1 0 2.72 2.80 2.58 CH3COOto be correlated are presented. In the absence 2.26 2.27 2.34 3.04 2 . 8 1 2.89 c1of electrode potential data, En values were obtained Br. .. . . 2.77 2 . 6 0 3.00 by secondary standardizations; for example, the 6.08’ . , . 5.62 5,3:3 3 . 9 9 OHEn value for CICH2COO- was obtained using the CeHbSH2 .. .. . . 4 . 6 0 4.82 4 . 2 6 known formation constant for the complex Ag3 . 5 8 3.74 3.67 4.54 4.54 4.53 SCN(ClCHzCOO)?-, the known H value for CICH23 . 4 8 3 . 5 1 3.87 4 . 5 4 4.37 4.79 1COO- and the values of a and /? found for other 5.28 5 . 3 0 4.90 6.15 6 . 4 3 6 . 0 4 SZO3complexes containing a silver ion a,id two donors. Calculated using N = 2.00 and p = Displacement Rates on Carbon.-S.S. correlated Data of ref. l a . the rates of nucleophilic displacements on carbon 0.069. Calculated by S.S. Data of ref. 11 and 2 . This rate is Calculated using N = 2.49 and fi = 0.074. with eight substrates. For six of these substrates, enot comparable with the others since OH- reacts with 8the experimental data can be reasonably well corre- lactones in a tnatmer different from that of other donors. lated using only the al?, term. For mustard There are other pieces of data from the studies cation and P-propiolactone, however, the results show a skewness which can best be interpreted as on mustard cation’l which can be correlated by the need for the PI1 term. For example, with equation 1. These are presented in Table 111. OH- attacking the mustard cation, the former cal- The results are poorer, especially for thiourea. culated rate2 was over forty-fold lower than the Since thiourea is about twenty times more nucleophilic to alkyl bromides than is pyridine,’? it is observed rate. For comparison of the present correlation with difficult to understand why the two donors should that of S.S., log ( K / K J data are presented in Table show qiiite similar reactivities to mustard cation. TI. The deviations of the calculated from the obTABLE I11 served values using equation 1 are all less than 0.30, i.e., a factor of 2 , and the average deviation OTHERDISPLACEMENTS O N MUSTARD CATION for the 13 pieces of data calculated using equation N Obda Calcd. L 1 is 0.14. Concerning the need for the BH term sod” 2.41 1.72 in these correlations, it is pertinent to point out that 3 . 45c . . CbHsS the calculated values using the equation of S.S. SC(N H z ) ~ 3.90 5.39 ,
,
J
(9) W. Latimer. “Oxidation Potentials,” 2nd E d . , Prentice-Hall, Inc., New York, N. Y.,1982. (10) This value is quite reasonable for it is more negative t h a n - 1.77 which is t h e potential for t h e couple
2H20
+ 2 H + + 2eHzO? + 2H+
H202
and t h e equilibrium constant for t h e reaction
H40?+’
is overwhelmingly in favor of the right side.
CH~C~HISO~S4.43 4.73 5.34 5.36 (CzH60)gPOSRef. 11. Calculated using CY = 2.446 and p 0.0741. Used as secondary standard.
=
(11) A. G. Ogston, E. R. Holiday, J. S t . L. Philpot and L. A . Stocken, Trans. Faraday SOC., 4 4 , 4 5 (1948). (12) R . G. Pearson, S. H. Langer, F. V. Williams and W. J . RIcGuire, THISJ O U R N A L , 74, 2130 (1992).
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JOHN
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Vol. 76
I n Table IV, the results for ten series of displacements on carbon are presented. Of the 59 pieces of data, four were used for secondary standards and for only two did the calculated rate differ from the observed rate by more than an order of magnitude. One of these two cases is shown in Table 111; the other is with CN- replacing Iin ICHzCOO- with the calculated rate being high by almost two orders of magnitude.
calculation gives excellent results (average deviation = 0.08). Although the data on the enolization of acetone do not include as many donors, i t is important to note that the deviations from Bronsted's equation are in the opposite direction to those for the mutarotation of glucose. Acetate ion is high relative to H20 and OH- l 4 which indicates the need for a positive value of a. For this reason, poor results are obtained if the acetone and glucose data are TABLE IV plotted in accordance with the ideas of Pfluger.15 FOR DISPLACEMENT O N CARBON SUBSTRATE CONSTANTS Further, the fact that deviations are in both direcSubstrate Ala a 8 tions from the proton basicity scale indicates that Ethyl tosylate* 5 1.68 0.014 statistical factors, and perhaps steric factors, are Benzyl chloride' 3 3.53 - .128 secondary in comparison to some more fundamental B-Propiolactoned 7 2.00 .069 cause of deviation with these two substrates.
Epichlorohydrine 6 2.46 ,036 Glycidole 6 2.52 ,000 Mustard cation' 12 2.45 .074 Methyl bromideg 6 2.50 .006 Benzoyl chlorideh 4 3.56 .008 Diazoacetone' 4 2.37 .191 Iodoacetate anioni 6k 2.59 .052 Number of bases correlated including HtO. The relative rates are given along with experimental conditions in Table I of ref. 2, except for diazoacetone and iodoacetate ion. H. R . McCleary and L. P. Hammett, THISJOURNAL, 63, 2254 (1941). G. W. Beste and L. P. Hammett, ibid., 6 2 , 2481 (1940). Ref. la. e J. N. Bronsted, M. Kilpatrick and M. Kilpatrick, ibid., 51, 428 (1929). f Ref. 2 and 11. 0 Ref. 2; E. A. Moelwyn-Hughes, Trans. Faraday Sa., 45, 167 (1949); A . Slator and D. F. Twiss, J . Ref. 2. ' C. E. McCauley Chem. Soc., 95, 93 (1909). 74, 6221 (1952), in water and C. V: King, THISJOURNAL, a t 25'. 7 H. J. Backer and W. H. van Mels, Rec. trav. chim., 49, 177, 363, 457 (1930); C. Wag;er, 2. physik. Chem., A115, 121 (1925); in water a t 25 . kSince the K O value is not known, it was necessary to calculate it in the least squares analysis. The calculated log KOvalue is -6.25. The rate with C S - was not used in the least squares as it is inconsistent with the other data.
TABLE IVA RELATIVE RATESI N MUTAROTATION OF GLUCOSE N
SO,' ClCHoC00CHsC00CsHsN
-
I n their review, Bunnett and Zahler3a point out that there have been no experiments designed to elucidate the order of nucleophilic strength of donors toward aromatic carbon displacements. They do, however, give preliminary data in their Tables 31 and 32 which indicate that the basicity to protons is important in the nucleophilic character of the entering group. The approximate order of strength found (with l-chloro-2,4-dinitrobenzene as substrate under a variety of conditions; see ref. 3 ) is SOi"
-
013-
ma
OH-
(13) J. N. Brdnsted, Chcm. Reus., 6 , 231 (1928).
Calcd. (1)b
1.61 1.74 2.43 2.92 4.47 7.60
1.52 1.75 2.60 2.82 4.53 7.56
BronstedC
1.56 1 .BO 2.70 2.94 4.69 7.31
J. N. Bronsted and E. A. Guggenheim, THISJOURNAL,49, 2554 (1927); and G. Kilde and W. F. K. WynneJopes, Tmns. Faraday SOC.,49, 243 (1953). * Calculated Calculated using P using a = -0.407 and B = 0.4705. = 0.418.
Displacement Rates on Oxygen.-Reactions of hydrogen peroxide with electron donors have rate laws which indicate that the mechanism involves displacement on oxygen.lB In Table IVB, the correlations for two groups of rate constants of HzOz reactions are presented. The agreement of calculated and observed values is satisfactory for the average deviation is 0.26 and the maximum deviation is 0.46. It is apparent, moreover, that these rates would be poorly correlated by either the E , scale or the H scale alone. TABLE IVB HYDROGEN PEROXIDE5
OXIDATIOXS BY
Base
C1Br-
I-
> C6HSO- > CeH6NH2 > NH3 > I- > Br-
The halogens are much less reactive than are the donors which have higher H values. It is apparent that displacements on aromatic carbons cannot be correlated with displacements on aliphatic carbons by means of a single scale of base strength; rather a double scale such as equation 1 will be required. Displacement Rates on Hydrogen.-In only one case, the mutarotation of glucose, is there an adequate amount of data to test equation 1. These data are presented in Table IVA; the observed relative rates are compared with calculated values from equation 1 in column three and with values calculated by the Bronsted equation13 (modified to give relative rates) in the last column. The new
0bsd.o
e
&Os-' CN-'
Rate law I Obsd. Ca1cd.b
-6.96 -4.64 -0.16 -1.61 -3.00
-7.33 -4.43 0.22 -1.84 -3.01
Rate law I1 Obsd. Calcd.e
-4.30 -1.8; 1.02 0.22
-2.31 1.40 0.27
....
....
For details concerning the mechanisms, etc., see ref. 10. b Calculated using cy = 6.31, @ = -0.394 and log K O = -16..?.?. CCalculaterl using a = 5.20, B = -0.279 and Mohammed and H . A . Liebhafsky, e H . A . Liebhafskv and a
Since the data available for the reactions of HzOz with donors do not include the water rate, it is necessary to employ equation 1 in the long form (14) (a) 11. X I . Dawson and E. Spivey, J. Chem. Soc., 2180 (1930); (b) C. G. Swain, T H IJ~ O U K N A L , 72, 4578 (1050); ( c ) R . P. Bell and P. Jones, J . Chcm. .Soc., 88 (1958). (15) H . L. Pfluger, THISJ O U R N A L , 60, 1513 (1932). (16) 1. 0. Edwards, J . P h y s . C h o n . , 56, 279 (1952).
RELATIVE RATESAND EQUILIBRIA WITH DOUBLE BASICITY SCALE
Mar. 20, 1954
and t o solve this equation using KOas a n additional parameter. There is another test which can be used to check the validity of these correlations. This test concerns the reaction of HzO2 with either H2O or OHto give oxygen atom exchange. Using the correlation for rate law I , i t is calculated that the secondorder rate constant for the reaction
1543
OH- follows bimolecular kinetics is in agreement
with a displacement mechanism in the rate-determining step. In order to correlate these data, both aEn and PH terms probably are necessary. Bases which react with polythionates and related compounds but do not appear to cause decomposiH, tion are CN-, SOa', S=, C ~ H ~ O Nmercaptide ions, xanthate ions and dithiocarbamate ions ; the products of these reactions indicate that disHOOH 6 ~ - H O ~ H OHplacements on sulfur have o c c ~ r r e d . ~The . ~ reshould be about 2 X 10-13 liter/mole/sec. Using actions of S406' and s506- with CN- and so3' the correlation for rate law 11, i t is calculated that have been subjected to kinetic study20-2z;all four reactions are bimolecular, all are rapid and in each the first-order rate constant for the reaction case s 5 0 6 - reacts faster than S406=. I n the case of the SOS- reactions, tracer studiesz3hare proved HOOH + H ~ JJ H H O ~ H HOH that these reactions are indeed displacements. is about 1 x 10-lo per sec. in normal acid. These The recent tracer studies of the reaction of Scalculations predict that the rate of oxygen iso- with 24 are also in agreement with a displacetope exchange of H202 with HzO is extremely slow ment mechanism. in aqueous solution a t room temperature. It is One can conclude from the data available for reassuring to find that the exchange of labeled displacements on chalcogens that the donors which oxygen atoms between H202 and H2O has never are most active usually are both strongly nucleobeen observed. l 7 philic and strongly basic to protons. AlternaAlthough the lack of observed isotope exchange is not a quantitative test for the validity of log K O tively, any correlations of chalcogen reactions will (the "calculated water rate") the predictions based probably require positive values for both a and P. Complex Ion Equilibria.-Using equation 1 and on the calculated rate constants are certainly borne the values of En and H from Table I, the correlaout qualitatively. Ross'* found that HZOZoxidized (HOCZH~)ZStion of equilibrium, as well as rate, data has been to the corresponding sulfoxide with the same type attempted. The results of fourteen correlations of rate behavior as had been found for the oxida- of complex ion formation constants are presented tions of S ~ 0 3 - and the halide ions.Is Unfortu- in Table V; in Table VI, the values of CY and 0 nately, neither En nor H is known for this compound (obtained by least squares analysis of the observed but i t certainly should be strongly nucleophilic constants) used to calculate the formation conwhile being a weak base to protons. The nature of stants are given. As both of the standard states the product also indicates that displacement on employed in this study are systems which involve covalent bonding to a fair degree, only those comoxygen in H20z has transpired. plex ions for which there is quite a bit of covalent Displacement Rates on Chalcogens.-Although there are few quantitative data available, i t seems character can be correlated by equation I. Since these formation constants are really relaprobable that the rates of displacements on the tive constants to water (the cations are undoubtchalcogens can be correlated using equation 1. It was found2 that the rates of displacement of edly hydrated), the value of log KO for equation 1 C1- from benzenesulfonyl chloride in 50% water- used for these correlations was 1.74 times the coordinated number of the cation for the particular ser50% acetone a t 0.5' decrease in the order ies being investigated. For example, in the correOH- > CsHbNHz > HzO lation of Hg+2complexes, the values 1.74, 3.48 and Using equation 1 and the observed rates, the values 6.96 were used for HgN+z,HgNz+zand HgN4+?,recalculated for a and B are 2.56 and 0.094, respec- spectively. It is assumed that each entering donor replaces a water molecule; this is very likely a tively. Foss7C has found that catalysis of the decomposi- valid assumption. The observed values in Table V for AgN2+, tion of monotelluropentathionate ion by bases HgN2+2, CdN4+2, ZnN4+z, CuN2+ and C U N ~ + ~ decreases in the order come, with a few exceptions, from the review by OH- > SzO3' > I- > Hz0 Bjerrum.6 A larger number of other values have and that CHaCOO- probably is a catalyst while C1- been taken from this review5 and from the book by does not appear t o be one. I n the decompositions LatimerSg Listings of Hg+z complexes with the of SaOe' and SeS406-, OH- is a better catalyst than halides are given by Sillen,26of so4- complexes by SZOS-. Evidence that the decomposition is ini- Whiteker and Davidson,26of Fe+3 complexes by tiated by a displacement reaction is discussed b y (20) F. Ishikawa, 2. p h y s i k . Chem., 130, 73 (1930). (21) F. Foerster and K . Centner, 2. anoig. Chem., 167, 45 (1926). FOSS?~; the factlg that the reaction of SSOS' and
+
+
+
(17) (a) E. R. S. Winter and H. V. A. Briscoe. THISJOURNAL, 79, 496 (1951); (b) P. Baertschi, Ex#cricn:ia, 7, 215 (1951); (c) J. Halperin and H. Taube, THIS JOURNAL, 74, 380 (1952); (d) M. Dole, G. Muchow. DeF. P. Rudd and C. Comtc, J . Chcm. Phyr., 30. 961 (1952). (18) S. D. Ross, T H I S JOURNAL, 68, 1484 (1946). (19) J . A. Christiansen, W. Droit-Hanaen and A. E. Niolien, Acta Chcm. Scand., 6, 333 (1952).
(22) B. Foresti, Z . ano7g. allgem. Chcm., 217,33 (1934). (23) J. A. Christiansen and W. Drost-Hansen, N a f u r c , 164, 759 (1949). (24) (a) H.B. v. d. Heijde and A. H. W. Aten. Jr., THISJOWRNAL, 74, 3706 (1952); (b) H. B. V. d. Heijde, Rcc. ftau. chim., 73, 510 (1953). (25) L. G . Sillen, A c f a Chcm. Scand., 8, 539 (1949). (26) R. A. Whiteku and N. Davidson, THIEJOURNAL, 76, 3081 (1953).
1544
JOHN
Vol. 76
0. EDWARDS
TABLE V COMPLEX Iox FORMATION CONSTAXTS (LOGK f ) AgN + Obsd. Calcd.
N
NOa -
sor-
CICHzC00 CHaCOOCsH6Ii
c1-
-
..
...
0.2 .6a .7a 2.0 3.1*
-0.2 .1 .7 1.4 2.3
..
BrOH CsHsNH? SCN -
2.3 1.4
"1
3.4
Is203-
soa-
...
2.0 3.2
...
..
3.1
.. ..
,.. ... ...
..
AgS2 Obsd. Calcd. (-3.9) -1.5 0.2 -0.1 .64 .6' 1.8 4.2 3.5 5.1* 6.0 (9.0) 8.7 3.6 4.3 3.2 7.8 7.6 9.4 7.2 7.1 (14.0) 13.3 13.0 13.7 8.5 12.8 18.7 14.0 +
*
HgNz+* CdNi +2 Obsd. Calcd. Obsd. Calcd. 0.0 * (-5.4) -4.8 2.3 3.8 (2.2) -1.9
..
..
..... 1.8 1.8 2.2 2.7c 9.8
13.2 17.3 22.7
11.3 12.9 16.6 16.1
..
....
(16.9) 17.5 23.8
20.0 19.2 24.0
2.6 7.4 5.6' 7.4
.... ...
..
....
t .
.....
CN -
..
NO3 -
..
...
.....
...
....
..
0.8
-0.2
(2.2) 3.4 5.8 -4.6 (-6.6) 16.2
-0.6 3.6
,,,.
.. ..
.....
..
.....
... CdN+Z
so
