46
ROBERT W. TAFT, JR.,
which may be transformed to log
(70ortho -
1.5) =
B t - __ 2.303
+ log 98.5
A plot of log (% ortho - 1.5) against t should therefore yield a straight line. The fact that in Fig. 2 it does not, demonstrates the presence of a time dependent concentration or activity other than that of the cymenes in the absolute rate expressions. The fact that there is no extremely rapid initial rate in exp. 4 is most likely due to the mesitylene present, since mesitylene was absent in the other two experiments. This hypothesis suggests that the dramatic deviation from linearity in expt. 1 and 2 was due to the formation of some strongly basic side-product. Experimental The experimental procedures may be illustrated by the procedure for exp. 4.
[CONTRIBUTION FROM
THE
AND
E. H. COOK
VOl. 81
To a 2-I., %necked creased flask, equipped with a gas inlet tube, thermometer, stirrer and a water trap connected to the flask through a CaCIz drying tube, was added 869.4 g. (9.45 moles) of toluene, 12.6 g. (0.105 mole) of mesitylene and 14 g. (0.105 mole) of AlCls. Through the stirred reactants HCl was passed for five minutes while they were being cooled to 0'. To this solution a t 0' was added 140.7 g. (1.05 moles) of o-cymene. At specific times, 50-ml. portions of the reaction mixture were withdrawn, quenched, washed and dried. The toluene was distilled off of each sample in a Piros-Glover spinning band micro still. The residue then was analyzed by infrared spectroscopy. The results given in Table I are normalized for the cymenes. Experiments 5, 6 and 7 were carried out on a one-tenth scale in a 200-ml. beaker. To quench the reaction, water was added directly to the stirred reaction mixture. The aluminum chloride was Baker and Adams powdered anhydrous reagent grade.
Acknowledgments.-The authors are indebted to D. S. Erley and H. J. Sloane of the Dow Spectroscopy Department for the infrared data. MIDLAND, MICHIGAN
COLLEGE O F CHEMISTRY A N D
PHYSICS, THE P E N N S Y L V A K I A
STATE UNIVERSITY]
Rate and Equilibrium in First Complex Formation between Thenoyltrifluoroacetone (TTA) and Aqueous Metal Ions BY ROBERT W.TAFT,JR., AND E. H. COOK' RECEIVED AUGUST1, 1958
A kinetic study has been made of the reaction of a series of aqueous metal ions with TTA. Under the reaction conditions the rate-determining step for the formation of the first (one-one) complex with Sc"', Cu", ZnlI and MglI is the rate of enolization of TTA. With FelI1 the kiretics are consistent with the rate-determining reaction of the metal ion with the enolate ion. The rate constants for the reaction of Cu +2 and Sct3ions with the enolate ion exceed 106 1. rnole-'-min.-', while those Fe+3, Be+2,Al+a and Cr+*are less than this figure. These results indicate qualitatively that the free energy of activation in first complex foimation increases with increasing Born charging energy of the central ion, However, the equilibrium constants for the first complex formation show, in addition, a dependence on the availability of open d orbitals. The results are taken as an indication that the interaction between the central ion and its immediate shell of water molecules parallels that expected of ion-dipole interaction.
Although equilibrium studies of the formation of coordination complexes of metal ions with organic ligands (;.e., displacements in the aquo complexes of metal ions) have been systematically investigated,2 few kinetic studies of these systems have been made. The latter are of interest from the standpoint of the mechanism of chelate formation. Further, the comparison of rate and equilibrium of this reaction offers insight into the nature of the interaction between water molecules and polyvalent ions in aqueous solution. In this paper are reported results of studies by spectrophotometric means of the kinetics of first (one-one) complex formation for a series of aqueous metal ions with a common P-diketone, thenoyltrifluoroacetone (TTA), in dilute nitric acid solution. TTA was selected as the common ligand in this work because of its importance in solvent extractions of metal ionsa and the convenient absorption maxi(1) Taken from the Ph.D. Thesis of E. H. Cook, Pennsylvania State University, June, 1953. (2) (a) Cf. A. E. Martell and M . Calvin, "Chemistry of the Metal Chelate Compounds," PrenticeHall, New York, N. Y., 1952, Chap. 3; (b) L. G. Van Uitert and C. G. Haas, THIS JOURNAL, 75, 451 (1953); ( c ) L. G. Van Uitert, W, C. Fernelius and R. E. Douglas, i b i d , 7 6 , 457, 2736 (1953); (d) L. G. Van Uitert and W. C. Fernelius, ibid., 76, 3862 (1953); 7 6 , 375 (1954). (3) (a) E. H. Huffman and L. J. Beaufait, ibid., 71, 3179 (19491; (b) R. A. Bolomey and L. Wish, ibid., 72, 4483 (1950); ( c ) E. M. Larsen and G.Terry, ibid., 76, 1560 (1953); (d) R. A. James and W. P.
mum (approx. 350 inp) exhibited by the first coniplexes. The aquo complexes of ScIII, FeIII, AlIII, CrIII, CuII, ZnII, Mg" and Be11 have been investigated. The results provide evidence that studies of this kind may be used to determine the rates of 0 0 nC--CH2--CCF,
4-
MY&
S
H
the very fast reactions ( K E lo7 1. mole-1 min.-') between enolate and aqueous metal ions. The method is the same in principle as that used by Bell and studentsse to determine the rate constants for the reaction of enolate ions with halogens. Procedure and Results (1) Ionization of Aqueous TTA.-This &-diketone exists in acidified aqueous solution largely as the hydrate4 Ryran, ;bid,, 76, 1982 (1954); (e) R. P. Bell and P. Engel, J. Chenr. SOL.,247 (1057), and earlier references cited there. (1) ( a ) E. Zebroski, A. F,. C. Report BC-63 (1947); P h . D Thesis, University of California; (b) E. L. King and W. H. Reas, THIS JOURNAL, 73, 1806 (1951); (c) E. H. Cook and R . W. Tart. Jr., i b i d . . 74, 6103 (1952).
MU+
0-H I
0 j!!--CH2--C--CF3 S
M(u
I
0-H
The apparent pKa cannot be determined by titration with strong base because of interfering cleavage of the hydrate to acetylthiophene and triAn~ unambiguous , ~ apparent fluoroacetate i ~ n . ~ pKa has been obtained by the titration of TTA enolate ion solution with a strong acid. The value obtained is 6.4 a t 25’ ,4c The rate of ionization of aqueous TTA has been studied by Reid and Calvinb using a bromine titration method. Their method gives results pertaining t o a solution very dilute in ethanol. Reid and Calvin obtained first-order rates which are independent of the acid concentration in the approximate region pH 1 to 4. The need for the ionization rate in completely aqueous solution for purposes of the present work prompted us to redetermine the rate under these conditions. A spectrophotometric procedure was employed to analyze for the rate of consumption of bromine. To determine the rate of ionization k - H by a decrease in optical density of the bromine solution, the following expression was developed a
= initial concn. of ketone
b
= concn. of diketone at time 1 = initial concn. of bromine = amount of Br2 and diketone reacted at time t
K 1:
D
mine at 400 mp molar extinction coefficient at 400 mp x = a
(b
- (K)
- x)
(Bra) = (b
= (Br2)
(1) (2)
D - a + (K))= eBr
(3)
+u -b
(4)
D (K)= -
+ HA
+ HA
-
+ H+
MA(V -I)+ MAI(v
-
+
+ H+, etc.
so that higher complexes are favored by high pH. Previous work has indicated that the formation constants for the first complex (the product of the first step) of &diketones generally exceed those for the second complex (the product of the second step) by factors of about ten.l It is thus possible to regulate the point of equilibrium so as t o stop the reaction a t thc first step, a t least to a reasonable approximation. 1.4 I
0
= optical density at time t due to absorption by bro-
E B ~ =
47
COMPLEX FORMATION BETWEEN TTA AND METAL IONS
Jan. 5, 1959
1.0 2.0 3.0 4.0 Time, minutes. Fig. 1.-Bromination of TTA in aqueous solution at 25’. Typical plot of log
;[
centration 2.00 X tion 5.34 X M.
+ a - b ] vs. time.
Initial TTA con-
M and initial bromine conceatra-
I n the present work, the pH was kept low and other concentrations were adjusted so that usually only 5 to 30% of the TTA or the metal ion, whichSince the rate equation6 is ever was present in the smaller amount, was con--d(K) = k-H(K) verted to first complex. The rate of formation of (5) dt first complexes has been found to be appreciably then faster than that for the higher complexes, a further In ( K ) = k-a t c (6) factor permitting the study of only the first step. or ScIII, (21111, MgII, ZnI1.-With these metal ions In - + a - b =K-=t+c (7) the first complex with TTA has an absorption maxiPlots of log (D/~B, o - b) 11s.time give linear re- mum in the region around 350 rnp. Experiments sults (Fig. 1 is a typical example). It was also de- were carried out in the 1-cm. absorption cells. The termined that one equivalent of TTA absorbs one aqueous TTA solutions were rapidly injected into equivalent of bromine. An average value of k - H = the metal ion solutions using a hypodermic syringe. 0.59 min.-‘ was obtained from the rate of bromina- In each experiment the acid and metal ions were in sufficient excess so that their concentrations retion a t 25.0’. Extrapolation to zero time of the plot of log (D/ mained constant. The ratio of the metal ion to e~~ a - b) versus time, indicates that approxi- acid concentration was varied by factors of five to mately 2% of the TTA brominated instantly, thus one hundred in separate experiments. In each exgiving a measure of the enol content of aqueous periment plots of log (De - D) were linear with reTTA. The present results are in close agreement spect to time (D= optical density a t time, f; D e = with those of Reid and Calvin who obtained k - H = equilibrium optical density) over the range of reaction studied (generally 70% of the total change in 0.61 n k - ’ and 1.5% for the enol content.6 (2) First Complex Formation.-Complex for- optical density). Increasing the acid concentramation takes place in a series of reversible steps,e tion in a given experiment increases the slope of the plot, whereas increasing the metal ion concentration e.g. decreases the slope. The intercepts of the log (De CBr
+
(€tr+
)
+
( 5 ) J. C. Reid and M. Calvin, THISJOURNAL,71,2948 (19601. (6) I. Bjerrum, “Metal Ammine Formation in Aqueous Solution,”
P. Haase and Son, Copenhagen, 1941.
(7) W. C. Fernelius, B. E. Bryant and L. G. Van Uitert, unpublished compilation of formation constants.
48
ROBERT W. TAFT,JR.,
AND
E. H. COOK
- D) vs. time plots fall below the intercepts expected on the basis of no reaction a t zero time. Several typical plots are shown in Fig. 2.
1.0
0
1.4
0.8
9 +
+
1.2
0
Vol. 81
0.6
1.c
2 + 60.8
W M
0.2
I u
3 0.6 0
??
Cl
0.4
Fig. 3 -Rates
40 80 120 160 200 Time, minutes. of first complex formation for aluminum-
(111) with TTA a t 25':
0.2
typical plots of log
0.1 0.2 0.4 0.6 0.8 Time, minutes. Fig. 2.-Rate of first complex formation for scandium(II1) and copper(I1) with TTA. Typical plots of log (De- D) (1) 2.00 X 10-2 M Cu", 1.00 X M us, time a t 25': HNOa, initial TTA, 5.0 X lO-'M; (2) 2.80 X loF3M Sc"', 1.00 X M HN08, initial TTA, 5.0 X lO-'hf; (3) 2.26 X 10-a MSc"', 1.00 X MHNOI, initial TTA, 5.0 x 10-4 M . 0
FeW-In the work with FeIII, the TTA and acid concentrations were held constant in a given experiment. Rates were observed by the increase in optical density a t 520 mp accompanying complex formation. Contrary t o the previous cases, the slope of the linear plots of log (De - D)/Devs. time are virtually independent of the hydrogen ion concentration. The results are summarized in Table I.
['" D. D)l
(1) 1.35 X M Al"', 0 100 M HN03, initial M Al"', 0.100 M TTA, 5 0 X lO-'M; (2) 4 00 X " 0 8 , initial TTA, 5 0 X l o w 4M .
e's. time:
CrIII and BeII.--Only qualitative observations were made with these ions. CrIII ion reacted so slowly with TTA that a satisfactory equilibrium value for optical density could not be obtained. Under equivalent conditions the rate of first complex formation with CrIII ion must be a t least an order of magnitude slower than with AIIII. The qualitative results with Be11 indicate that the ratedetermining step also involves the metal ion. Interpretation of Kinetics ScIII, CUI$ MgII and ZnI1.-The lower-thantheoretical intercepts obtained in the first-order plots indicate that the ScIII, Cu", SIgII and Zn'I aquo complexes react instantaneously with the enol form of TTA. The following two-step sequence is thus suggested for the formation of the first complex of these metal ions, with step (a) rate determining.
TABLE I SUMMARY OF RESULTSFOR KINETICSOF FIRSTCOMPLEX (a) Ionization of the 8-diketone: FORMATION OF Fe"' WITH TTA k-a Initial (Fea+) X 104 (HKOR) l o 3 X (TTA) r a n g e Slope, m h - 1 HA H+ xResults at 24.86' k+H 3 . 0 to 7.0 0.153 =k 0.007 (b) Cotnplexing of the enolate ion: 4.09 0.100 7.0 to 13.0 .158 == ! .006 4.09 .200 k+ 11 Mu+ + AMX(Y - I ) + Results a t 15.170' k- hi 4.09 0.100 6.0 0.054
+
Jr
4.09
Results a t 34.51' 0.100 6.0
(8)
(9)
In terms of this sequence, the over-all equilibrium is given by
0.390
AW.-Experiments were carried out so that the metal ion and acid concentrations remained constant. The AlIII chelate has a maximum absorption near 350 mp. A typical half-life of the first complex formation under the conditions employed was 100 min. This is appreciably slower than that for the other chelations. Increasing both the acid and the metal ion concentrations increases the slope of the linear plots of log (De - 0)vs. time. Figure 3 illustrates some typical plots.
From the earlier work (cf. section on bromination of TTA) we have K , = 4.2 X lo-'; k - H = 0.59 min.-'; k + = ~ 1.43 X lo6 1. mole-' min.-'. Applying the steady state approximation to the enolate ion, the following equations may be derived for the conditions that k + > ~ ( M y + ) > ~ + H ( H + )
ddM = 0 t
= kUH (a
- x) -
k-a ( H + ) ( . \ - , - k + w (A-i(MY+/ 4- k - \ l i x )
(11
Jan 5, 19.59
COMPLEX
FORMATION BETWEEN TTA
where a = initial TTA concentration and x complex concentration a t time, t
.'. ( A - ) [ k + y
(Mu+)
+
W+)1
k+H
k-H
(a
.4ND METAL
49
IONS
1st- aqueous TT4 has been calculated. The results (illustrated in Table IV) are in very reasonable accord with those obtained in bromination experiments. (12)
=
- X) f k - y ( X )
but !E- - k + M (A-) (MU+) - k - M (x) dt
(13)
IONIZATION
Substituting (12) in (13) and collecting terms 2.26 2.26 2.80 2.80 1.81 1.81 1.81 3.50 4.96 4.96
but if k + ~ ( M y > ) K+H (H+)
therefore a t equilibrium and
theref ore
(17)
substituting (10) in (17)
ie., k - H = slope X fraction of HA converted to first complex or
TABLE I1 RATEk - H FROM RATEO F FORMATION O F FIRST Sc"' COMPLEX, 25.0"
100 200 200 100 5 0 5.0 5.0 5.0 5.0 5.0
5.0 5.0 5.0 5.0 1.0 1.0
1.0 1.0 1.0 1.0
1.40 0.710 0.890 1.76 1.52 1.52 1.51 1.60 1.63 1.65
3.82 7.79 5.50 2.42 0.60 .61 .63 .5T .56 .55
8.91 4.52 5.66 12.2 9.3 9.3 9.3 9.8 10.0 10.0
0.66 .68 .60 52 56
--
DI
.59 36 .56
.55
The low formation constants of CuII, MgII and ZnII prevent complete conversion to first complex a t desirable ratios of hydrogen-ion to metal-ion concentration. Equation 19 was tested for these metal ions by solving for the molar extinction coefficient E using the observed rate data (slopes) and the rate of ionization k - H of TTA. The rate equation is confirmed by the fact that the values of E calculated are constant within the precision of the measurements, cf. Table III. The extinction coefTABLE I11 MOLAREXTINCTION COEFFICIENTS FROM RATESOF FIRST COMPLEXFORMATION BY EQ. 19 Copper
For first complex formation with Sc"1 ion, eq. 18 and 19 have been confirmed in the following manner. I n a series of experiments with a given initial TTA concentration, the ratio of metal-ion t G hydrogen-ion concentration was increased from about 0.1 to 10. The equilibrium optical density increased regularly with this ratio and approached a limiting value for ratios of about 10. The latter result indicates that nearly complete conversion to first complex has been achieved. Under these conditions the average value of the slope of the log (De- 0) vs. time plots is 0.56 & 0.02 min.-l, which, in accord with eq. 18 for complete conversion to first complex, is the rate of ionization of T T A (see first section). No attempt has been made here or later to consider the effect of varying ionic strength on rates because the values obtained are not highly precise. There is, indeed, no indication that the effect of the ionic strength for the range used exceeds the experimental error of the rate measurement. Further confirmation of the indicated kinetics is obtained using the limiting value of equilibrium optical density to obtain the molar extinction coefficient for tbe first complex (average value E = 16,200). With this value i t is found that the rate data for experiments with incomplete conversion follow equation 19--see Table 11. From the difference in the theoretical and experimental intercepts of plots (see Fig. 2) and the extinction coefficient obtained above, the equilibrium per cent. of enol in
initial TTA X 10'
5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5 0 5 .0
D.
0.860 1.50 1.55 2.45 1.50 2.36 1.36 0.740 2.36 1.25 3.16 3.70
Molar (calcc! eq. 19
Slope, min.-'
4.65 2.97 3.52 1.85 3.14 2.12 4.11 5.94 2 06 3.44 1.38 1.20
)
Av.
13 ,300 14,800 18,200 15,100 15,700 16,700 18,500 14,600 16,200 14,400 14,500 14,800 14,800* 1100
Av.
l5,T00 16,200 13,300 13,400 14,600 i 1300
Magnesium"
5 0 5 0 5 0 5.0
0.790 ,380 ,530 ,900
5 96 12.89 7.54 4 45
Zinc11
5.0 5.0 5 0
2.36 1.40 1.13
3.36 5.09 5.50
26,400 93,800 21,000 Av. 23,700 i 1800
ficients also lead to values for enol content (see Table IV) concordant with the bromination results. Minimum values for k+ M may be estimated from the present data. I n order that the observed kinetics be followed, it is necessary that the term ( k + l f )
ROBERTW.
50
T A F T , JR., AND
TABLE IV
ENOLCONTENT FROM INTERCEPT DIFFERENCES Metal ion SCT"
ADi
Initial (TTA)IO'
Enol, %
0.17
5.0 5.0 5.0 5.0 5.0 5.0 5.0
2.1
.14 .1G
.15
hlg"
.I1 cu"
.I8
. 06
Min. k f M 1. mole-l min.-1
Ion
> I . O x io7 >3.0 X IO6
curI
In the case of Mg" and ZnII the minimum (My+)/(H+) ratio necessitated by the instability of the complexes is too large t o lead to minimum K+M values of utility (>IO4 1. mole-' min.-I). It is probable (although not required by the data) that k + M exceeds Io6 1. mole-' min.-' for these metal ions. FeW-The kinetic data are consistent with the reaction sequence of eq. S and 9 but with step b rate determining. Zebroski previously made this interpretation.& The equations derived to interpret the kinetic results are due to Zebroski. With conditions such that the TTA and acid concentrations are essentially unchanged throughout the reaction, the following equations apply: A = (metal)o, B = (enolate ion)o, x = amount of complex formed a t time t . The subscript 0 refers to initial concentrations. dx _ dt
k+u (a -
X)
(B)
Vol. S l
The reaction of iron(II1) with TTA could take place in the following reaction sequence which is kinetically indistinguishable from the enolate ion mechanism.
1.8
2.0 2.0 1.5 2.4 0.8 Av. 1.8
(MY+)/(K+H)(H+) be greater than unity. The minimum value of the (MY+)/(H+)ratio employed, and the experimental value of k+ H, thus lead t o the following minimum values of K+M. SC"'
E. H. COOK
fast
M"-t
+ HA.Hz0 I_MA.HzO(Y - + H +
r.d. MA.HzO(Y- 1 ) + Jr MA(Y - 1) +
However, we favor the enolate ion mechanism, largely on the basis of the kinetics shown in the reaction with SC"', MgI*, Cu" and ZnII, as well as some general observations (see Discussion) on the rate of dehydration of TTA hydrate. The molar extinction coefficient of the first complex of iron(II1) with TTA also was obtained by the method used by Zebro~ki.~"The symbols used below are the same as those previously in eq. 20-27 withx = D / E . or AbKeq
- b(De/e)Keq - A(De/e)Keq
(X)
According to equation 29 plots of A b / D e versus (A b) give a slope of l / e and intercept of H+/ (de,). The results are listed (Table V) and shown graphically in Fig. 4. The average slope gives a
+
TABLE V EVALUATION OF THE MOLAREXTINCTION COEFFICIENT FOR THE FIRST COMPLEXES O F Fe"' AND THE EQUILIBRIUM CONSTANT, K,, ( A b / & ) 10-6 (av. values)
dt
(20)
((1
- xe)(B) - It-M - x)
dx - x = k+M
+ k-M
(B)
+ k-M
(x,
(3%)
(21)
- x)
(22)
dt
5.40 6.40
2.41 6.40 Intercept = 2 . 0 0 X 10-8 4.34 7.40 4.49 10.40 4.53 12.40 4.62 13.40 Intercept = 4 . 0 3 X 10-8 Av. slope = 0.0567 X 10-2
0 , 2 0 Af IISOa
(23)
value of 1950 for the molar extinction coefficient of the first complex FeT" a t 520 mp. The rate constants derived from eq. 27 and the equilibrium constants from eq. 29 are summarized below. Values of Ke, a t 15.70' and 34.51' were calculated by eq. 29 from equilibrium optical densities of several experiments carried out a t these temperatures.
or
Temp.,
where B
3.40
2.38
= k + M (B)(x.
x.
10'(A f b)
2.20 2.26
a t equilibrium dx -- = 0 = k + M dt
= (De/e)(H+)
the term ( D / E being ) ~ negligible. Rearranging gives
0.10 Af H S O I
- k-M
+ HzO
=
( b ) (Ka)/(H+) and b = (TTA)o
In accord with eq. 26 the data indicate (cf. Table I) that the slope is not charged with increasing acid since both B and Xe show essentially the same dependence on acid concentration.
Acid 0.1 M "01 . I M HNO. , I M "01 . 2 M HNO,
OC.
15.70 24.86 34 51 24 86
10 - b k + M , mple-1 k+MK. min. -1 0.073 1.74 . 3 3 (0.288)* 7 . 9 (6.9)' .94 22.4 .34
8.1
R, 1.49 2 . 5 6 (2.04)s
2.83 2.54
(8) The values which are given in parentheses were obtained in a second determination (using a second stock solution of TTA) at the time the temperature coefficients of rate and equilibrium were investigated. The discrepancy in the two sets of values is serious, certainly
COMPLEX FORMATION RETWEEN TTA
Jan. 5, 1959
The temperature coefficients of rate and equilibrium (which follow the Arrhenius and Van? Hoff equation to reasonable precision) lead to the following thermodynamic quantities For the reaction Fea+ H A J_ FeAZ+
+
+ H-
For the over-all rate process Fea+ HA +(FeA)*f
+
AH0 = $6 kcal.
ASo = 4-22 e.u. A P 2 9 8 = -0.55 kcal.
+H+
AH$ = 23 kcal. AS% = $4 e.u.
Further, by virtue of the relationship
__ Ka_--K,,
k+31
k- m
and the corresponding thermodynamic equalities, these quantities also have been obtained for the rate process (FeA)*++(FeA4f)2+ k - M (at 25') = 0.130 min.-l AH%= 17 kcal. ASf = -17 e.u.
AND
METALIONS
51
Initial (AIT, M
2.70 x 4.00 X 4.00 X 1.35 x 2.00 x 4.00 X 4.00 X 2.00 x 2.00 x 3.00 X 0.10 0.100
10-3
(HNO:), M
0.00
0.100
.00 .00 .00 .00
.loo lo-' 10-3
.loo
10-2
.200
lo-'
.loo .loo
lo-* 10-4
10-4 lo-*
(KNOs), M
.200
.10 10 5.00 X 10-1 .OO 0.200 1.00 0.100 1.00 1.00 0.00 0.500 0.50 *
(%?M
De
Sl,ope mm. - 1 25.0'
5 . 0 0 310 0,00705 5 . 0 .485 ,00742 ,214 .0128 5.0 5.0 ,156 .00594 5.0 .lo9 .0115 .00;99 5.0 .440 5.0 .440 ,00852 5.0 ,520 ,00440 5.0 .086 .0163 5.0 5.0 5.0
,255 .480 .845
,00965 .0235 .0204
Discussion Ionization of TTA.Schwarzenbach and Felder have determined the enol content of aqueous acetylacetone t o be 15'% a t 2Oo.l1 The value of
Uncertainties of 1 or 2 kcal. or 4 t o 8 e.u. are estimated for these thermodynamic quantities. The entropy of activation of - 17 e.u. for the latter process is reasonable since it involves the dissociation of a bivalent ion to a tervalent and univalent ion. More solvent molecules are tied down by the latter than the former0 and a part of the accompanying entropy decrease may be expected in the reaction transition state. The temperature coefficient for the ionization of TTA has not been determined quantitatively, but it probably is quite small. Assuming the standard enthalpy of ionization of aqueous TTA t o be +1 t o + 3 kcal. gives these values for the thermodynamic rate quantities for the process Fe*+
+ A - -+-
(FeA$)z+
A H $ = +20 to 22 kcal. A S S = $24 t o +31 e.u.
The estimated entropy of activation of $24 to f 3 1 e.u. for the ion-combination process agrees well with the value predicted by equation (30) derived from electrostatic considerations and the transition state rate theory1° (for H20, 25') ASf = -1OZ,Zb = -10(3)(-1)
= +30 e.u.
(30)
AP.--A satisfactory kinetic law which describes the results with AllI1 ion has not been found, The rate-determining step must, however, involve the A1111 ion. Experiments a t the higher acid concentration (0.5 and 1.0 M " 0 3 ) gave results similar to those for FerT1,i.e., with slope nearly independent of hydrogen-ion concentration. The data are summarized below sufficiently so that the temperature coefficients would he virtually valueless if the data at each of the three temperatures contain random uncertainties of the magnitude of the difference in these values. However, since the same stock solutions were used in obtaining the results at the three temperatures the relative values (which determine the enthalpy changes) may be considerably more reliable than the absolute value at any single temperature. The precision with which the results follow the Van't HOE and Arrhenius equations supports this conclusion. (9) Cf., for example, E. Rabinowitch and W. H. Stockmayer, TEIS JOURNAL, 64, 335 (1942). (10) (a) A . A. Frost and R . G. Pearson, "Kinetics and Mechanism," John Wiley and Sons, Inc., New York, N. Y., 1953, p. 133; (b) W. F. R. WynneJones and H. Eyring, 1.Ckem. Phyr., 3, 492 (1935).
(A + b) x IO3, Fig. 4.-Plots for determining the molar extinction coefficient for the first complex of Fe"' and TTA. and the equilibrium constant K e q . Plots of A b / D , X 1 0 vs. ( A b) X lo8 at 25': (1) 0,100 M "01; (2) 0.200 M HNOI.
+
only 2% enol content for aqueous TTA is therefore abnormally low. A reasonable explanation of this result may be made on the basis that hydrate formation shifts these equilibria toward the right OH
I
CFp-C=CH-C-R
0
I1
0 Ke
I1
1_ CFa-C-CHz-C-R
0
11
Kb
J_
OH
I1 (11) G. Schwarzenbach and E. Pelder, Helr. Ckim. Acta, 27, 1044 (1944).
52
ROBERTW. TAFT, JR.,
AND
E. H. COOK
1-01, h l
if one assumes that the equilibrium constant Ke have been estimated using ionic radii in crystals':' has a value on the order of that for acetylacetone, and are summarized below the relative enol contents may be taken t o indicate (Ze)s/v, fithl, (in accord with other evidence)4 that most of the electronic I . mole-) 1011 Radius, A . rlnitsQ/.k. m i n . - l . 2.5" TTA is present as the keto hydrate (11). NeverZn+2, Cu'? 0 74 5.4 theless, the keto form I is probably a necessary --, I I)" Mg+* .70 0. intermediate in both the bromination and the .89 1 1 . o s c +a first complex formation, i.e., enolate ion is formed directly from I instead of 11, with the forward Be + 2 3" 12.5 and reverse rates of the equilibrium Kh being relaCr +3 .64 14.1 < 106 tively fast. This interpretation is consistent with Fe+3 .60 15.0 the following facts: (1) the rate of bromination and A1 +3 .50 18.0 the rate of first complex formation with ScI" (and others) are the same, indicating the presence Ion Structure and Chelate Formation Constants. of only an unsaturated (and conjugated) enolate ----The concentration equilibrium constants Keq ion; ( 2 ) the rate of ionization of the keto hydrate obtained in this work are listed in Table VI. The I1 is probably slow since it more closely resembles a values given apply a t the ionic strengths listed in mono- than a p-diketone. This conclusion is sup- the adjacent column. The thermodynamic conported by the fact that hexafluoroacetylacetone stants listed for FeIII, ScI", CuII and A1111 have been estimated by extrapolation of plots of log which exists in solution as the dihydrate Keq vs. p, using the limiting slope expected from the OH OH Debye-Huckel theory (see Fig. 5). I
CF~-C-CH~-C-CF~
I
OH
I
OH
although a relatively strong acid (pKa = 4.35), ionizes a t a relatively very slow rate. Thus, in a titration of 2 X l o p 3 mole of this substance with 1 M NaOH, Van Uitert reported that over 3 hr. are required for neutralization12; (3) the equilibrium between acetaldehyde and its hydrate (not too distant malogs of I and 11) in aqueous acid solutions is fast and rever~ible'~;(4) the rate of ionization of TTA is slower than predicted on the basis of its PK, and the rate vs. equilibrium correlation of Pearson and Dil10n'~but is more reasonably in line if one corrects the observed rate by an estimate for the equilibrium wiistzii, ICh, Le., rate ionization (I) = (observed rate, k - ~ , ) ( K h ) . Ion Structure and Rate of Complex Formation.A comparison of rate constants, k + M , [for the rate process: M%'+ + (^1I2~'"-~~+] with the metal ion structure is both interesting and instructive. The present work permits these constants to be separated into two groups. The first group has a minimum value of lo6 1. mole-1 min.-'. The second group has a maximum of a value of lo6 1. mole-' min.-' and a minimum value less than 1 O 3 1. mole-' min.-l
+
Ion
Cu2+,Sc3+, (Zn?', Mg2+1 Fe3+ &2', A ] 3 + , Cra+
k - \ I 1. mole-' min.-l, water, 25O
10*or greater less than 1G6
The order of rate constants neither correlates with charge type nor the availability of stable d orbitals in the metal ions involved. Examples of both these types are to be found among the more or the least reactive aquo complexes. There is, however, a clear parallel between the rate constants of first complex formation and the Born charging energy of the central ion, as measured by (Ze)2/r, (where Y is the radius of the bare ion). The latter ( I ? ) L . C > , V a n U i t r r t , .\I S. The-is, T h e Pennsylvania S t a t e College, 19.il. (13) K . 1'. Hell a n d H. H . D a r w r n t , Truns. Pa2vndny Soc., 46, 34 (1950). (14) ( a ) K .
