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The rates of the electron exchange reactions between U(IV) and U(VI) ions in water and water-acetone solvents
J. lnorg. Nu¢l. Chem.. 1961, Vol. 17, pp. 325 to 333. Pergamon Pre8 Ltd. Printed In Northern Ireland
THE
RATES OF THE ELECTRON EXCHANGE REACTIONS BETWEEN U(IV) AND U(VI) IONS IN WATER AND WATER-ACETONE SOLVENTS S. L. MELTON, A. INDELLI a n d E. S. AMIS Chemistry Department, University of Arkansas, FayetteviUe, Arkansas (Received 13 June 1960; in revised form 4 August 1960)
Almraet--The rate of the electron exchange reaction between U(IV) and U(VI) ions was studied at 25 ° in water and water-acetone mixtures containing 30, 60, and 90 per cent by volume acetone, and at various concentrations of U(IV), U(VI), and hydrochloric acid. The order of the reaction with respect to each of these solutes was found to depend strongly upon the composition of the solvent. A departure in the trend of the rate dependence on hydrogen ion concentration was found for more dilute acid concentrations in sixty volume per cent acetone. Comparisons of the kinetics of the reaction in acetone-water and in ethanol-water are made. Mechanistic and kinetic discussions are included.
MATHEWS e t al. (1) studied the reaction between U(IV) and U(VI) ions in the presence of hydrochloric acid in water, ethanol, and water-ethanol solvents. These investigators found that the order of the reaction with respect to U(IV), U(VI), and hydrogen ions depended strongly upon the composition of the solvent in the water--ethanol system. INDELLIand AMIS(2) investigated the temperature coefficient of this reaction in this solvent system. The energy of activation was found to decrease with increasing weight per cent of alcohol in the solvent in general correspondence with an increase in reaction rate. No light or wall effects were found. RONA(3) studied the U(IV)U(VI) reaction in water and found no salt effects. It was felt by INDELLI and AMIS that the reaction should be studied in other solvent systems. The solvent system chosen in the present investigation was wateracetone since the dielectric constant range would be similar to that of the waterethanol solvent system and, at the same time, acetone would contrast with alcohol in that the former has a carbonyl rather than a hydroxyl group. EXPERIMENTAL Solid UCI, and UO~ClfH20 were prepared as described elsewhere. ~4' Experimental techniques, the preparation and analysis of stock solutions, and the tracer solution were as described by MATI-IEWS et aL ~1~. The runs were made, sampled, and analysed as described by these except that acetone w a s substituted for ethyl alcohol in the present experiments, and hydrofluoric acid was used as the precipitating agent. Aliquots of the U(VI) solution (50 2) were spotted on platinum disks, dried and counted. The U(IV) precipitate was dissolved in concentrated nitric acid, evaporated to dryness, taken up in 1 ml of dilute nitric acid, and a 50 A portion spotted, dried and counted. Triplicate samples for each valence type were spotted, counted, and the average of these were used to obtain a point on the rate plot. Fisher certified, A.C.S. grade acetone was used without further purification. ~l~ D, M. MA'rH1~WS,J. D. HEFLEYand E. S. Alms, J. Phys. Chem. 63, 1236 (1959). is~ A. INDELU a n d E. S. Alals, J. Amer. Chem. Soc. 81, 4180 (1959). ~a~E. Rosa, J. ,4mer. Chem. Soc. 72, 4339 (1950). ~4) D. M. MATHeWS,J. D. HEFLEVand E. S. A~ns. J. Inorg. NucL Chem. 12, 84 (1959). 325
326
S.L. MELTON,A. INDeLUand E. S. A~as TREATMENT
OF DATA
The electron exchange rates were calculated using the equation 0.693
t~
ab
(1)
a+b
where a and b are concentrations of U(IV) and U(VI) in the system. R is the total |0 9 e ?
• • •
S
ACID U(Vl) U(IV}
4
Iog (I-F)
9 e 7 6 5 4
175 Time in ~ t e n
Flo. 1.--Logarithm (1 -- F) vs. time in minutes when the solvent was 30 per cent acetone.
number of exchanges, labelled and unlabelled, per unit time in the concentration units used. The half-life, t~, was obtained and R calculated from ti, and a and b in the manner previously described. {1} The count-rate data was converted to 1-fraction (l-F) of complete exchange and a plot of such data for 30 weight per cent acetone is shown it. Fig. 1. In this figure the solid circles represent data taken when the concentration of acid was varied and the concentrations of U(VI) and of U(1V) were held constant. The triangles represent data taken when the concentration of U(VI) was varied and the concentrations of acid and U(IV) were held constant. The squares represent data taken when the concentration of U(IV) was varied and the concentrations of the other substances were held constant. Initial concentrations are referred to here. Figure 2 shows the plots of --log R corrected for constant concentrations and order
The rates of the electron exchange reactions
327
vs. --log C which were used to determine the order of the reaction with respect to U(IV); in Fig. 3 are given the plots of log R corrected for constant concentrations and orders versus --log C used to find the order of the reaction with respect to hydrogen ion. Each line has a slope which is the order of the reaction with respect to that reactant at the solvent composition specified. The line for pure water solvent from the data of RONA(3) was included in the drawings for reference purposes. The orders
6i/0 S
$.f
,f60~
7
4,o
3-(
31
2.%
~
~
,~
2!o
2:2
2~
z~
-,oo
F~o. 2.--Plots of --log ~R[H+]~ vs. --log [U(IV)] used in the determination of the order, r, of the reaction with respect to U(IV).
of the reaction with respect to U(VI) were determined in a similar manner and the data for these plots showed the same consistency as the data for U(IV) in Fig. 2. The data for Fig. 2 were obtained by making, for each solvent composition, several different runs with the same initial concentrations of U(VI) and of H + but different initial concentrations of U(IV). The initial rates were determined, and the logarithms of these rates plotted against the logarithms of the initial concentrations of U(IV). This gave the order of the reaction with respect to U(IV). In like manner the orders with respect to U(VI) and H + were found. Then to prove the reliabilities of the orders so determined, all pertinent data were included on the plots by introducing the concentrations of the reactants raised to the powers represented by their
S.L. MELTON,A. I~ELLI and E. S. A1vns
328
respective orders. This was likewise the procedure followed in arriving at Fig. 3. This procedure did not change the slopes of the lines and thus confirmed the orders. The intercepts o f the lines were changed of course.
@8
O'4
-0~
-I'2
-I~ 04
I 0"6
I 06
I l'O
I
I
1'2
I-4
I 1.6
-,0o [.@1 R
FIG. 3.--Plots of log [U(IV)],[U(VI)]~ vs. --log [H+] used in the determination of the order, q, of the reaction with respect to H+. TABLE 1.--ORDERS OF THE VARIOUS REACTANTS IN THE DIFFERENT SOLVENTS
Acetone
U(IV)
U(Vl)
Hydrogen ion
0 30 60 90
2.0 1.25 1.33 1.47
1.0 1-0 1.13 0.59
-3'0 --1"85 --2'85 (above 0.1 M concentration) --1.17
The orders of the reaction with respect to U(IV), U(VI) and hydrochloric acid are presented in Table 1 at various solvent compositions. The orders for pure water solvent are those of RON^. ta) The orders in the other solvents were determined in this investigation. F r o m Table 1 the orders are seen to have a marked dependence on the composition of the solvent. Between zero and ninety volume per cent acetone, the order of the reaction with reap ect to U(IV) first decrease with added acetone and reaches a minimum at about
The rates of the electron exchange reactions
329
40 volume per cent acetone of about 1.22, then with further addition of acetone, the order with respect to U(IV) again increases and becomes about 1-50 at 90 volume per cent acetone which was as far as the data extend. The general shape of the curve is similar to that found by MArrmws et al/1) for the order with respect to U(IV) for the same reaction in ethanol-water solvents. In the latter case the minimum was lower by about 0.40 and was reached at about 50 volume per cent ethanol. Also in
I'0
o tr
o
-I'0
/ -~-o
/
\
~o
/
¢o
• ~,c~)
,'o
VOLUHE % ACETONE
FIG. 4.--Orders of the various reactants vs. volume per cent ethanol.
the latter case the decrease in order was more gentle and the increase more abrupt with added alcohol, the value at 90 volume per cent alcohol being 2.89. Since the water-acetone data unfortunately extended only to 90 volume per cent, it was not possible to know whether there was the abrupt decrease in order with respect to U(IV) in pure acetone compared to the order in 90 volume per cent acetone as was found for pure ethanol compared to 90 volume per cent ethanol; (see Fig. 4.) In the case of the order with respect to U(VI) the shape of the curve out to 90 volume per cent acetone closely resembles the curve found for the U(VI) order out to 90 volume per cent alcohol. In both cases there is first a slight increase in the order out to about 60 volume per cent organic component of the solvent and then a more precipitous decrease of the order out to 90 per cent by volume o f the organic component. In the case of the water-acetone solvent the order dips to 0.59 at 90 volume per cent acetone while in the case of water-ethanol solvent the order drops to 0.10
330
S.L. ]~PLELTON,A. INDELLIand E. S. AMlS
at 90 volume per cent ethanol. In the case of acetone there is no way of knowing whether there is an abrupt rise of order beyond ninety volume per cent acetone as there was an abrupt rise of order beyond 90 volume per cent ethanol. It might be mentioned the runs in 100 per cent acetone were not made since pure acetone at the acidity used in the runs polymerized rather rapidly. It was thought that this change in the nature of the solvent might affect the electron exchange reaction rate in a manner different from the other solvent factors. In water-diluted acetone, the polymerization was slower and the exchange reaction rate could be determined before extensive polymerization occurred. It is the order of the reaction with respect to hydrogen ion in water-acetone which contrasts sharply with that in water--ethanol, especially at 60 volume per cent organic component of the solvent. In the case of water-ethanol the order with respect to hydrogen ion at first increases with increasing volume per cent ethanol, reaches a maximum at about 70 volume per cent and then decreases gradually out to 100 per cent ethanol. In the case of water-acetone solvent there is a maximum in the order with respect to hydrogen ion at about 30 volume per cent acetone, a minimum at about 60 volume per cent, and then an increase out to 90 volume per cent which is as far as the data go. In addition to the minimum in the order with respect to hydrogen ion at 60 volume per cent acetone, there is also the curious hook in the log R vs. --log C curve for hydrochloric acid (Fig. 3) in-this solvent. In Table 2 where half-lives, rates and specific velocity constants at various concentrations of reactants in various compositions of solvents are listed, it is to be noted that the specific velocity constants for these runs with the anomalous orders with respect to hydrogen ion are omitted. It will be noted that the hydrochloric acid concentrations in these anomalous runs were below 0"1 M in every case. At these low acid concentrations in 60 volume per cent acetone, the slope of the curve in Fig. 3 (right hand portion of 60 volume per cent curve) indicates a positive coefficient for the dependence of the rate upon hydrogen ion concentration. Since there was insufficient data in this region of acid concentration, the order with respect to hydrogen ion was not obtained and the specific velocity constants were therefore not calculated. Lower acid concentrations in this solvent would have been investigated except that the solutions proved unstable at lower acidities and hydrolysed complexes of uranium precipitated. As observed from Table 2 the order with respect to acid in each of the other solvents was consistently constant over the whole range of acid studied. The rate expressions proposed by MATHEWSet al. (1~ namely,
dx dt
[U(IV)]2[U(VO] LKIF[H+]+ 1]~F[H+]J k+~ 2T
1]
(2)
and dx
[U(IV)I[U(VI)]
dt
r[H +] 1] F[H+] 1 L K 1 + JLK~ +1
(3)
to explain the observed orders found in the water-ethanol solvent up to 60 volume per cent of ethanol can be used in the present investigation to explain the observed
The rates of the electron exchange reactions
TABLE 2 . - - R A T E S ,
331
CONCENTRATIONS OF EACH COMPONENT, HALF=LIVES AND SPECIFIC
VELOCITY CONSTANTS AT 25"OO°C FOR U(IV)-U(VI) EXCHANGE REACTION IN 30, 60 AND 9 0 PER CENT ACETONE i
U(IV)
U(VI)
[H ÷]
t.~ (rain)
R x 10~ (mole/l./min)
k'
× 102
I
30 % Acetone 0'0213 0"0213 0"0427 0'0213 0"0339 0"0242 0"0242 0'0145 0-0436 0'0145 0"0145 9'0145
0.0105 0-0105 0.0105 0"0105 0.00926 0.0185 0"0130 0.00926 0.00926 0-0130 0.00370 0.00370
0.1027 0.0912 0.0912 0.0797 0.0528 0-0574 0.0574 0.0528 0-0528 0.0528 0.0528 0.1090
57.75 45.0 23.0 37.0 11.25 13.75 17.5 23-4 8'4 23.5 31.5 120.0
8'44 10'83 25"39 13"17 44.80 52"85 33"49 16"74 63 '02 20.21 6"48 1.70
1.440 1.510 1.484 1-431 1.441 1.513 1.365 1.557 1"480 1.339 1.509 1.514 Ave. 1.465
60 Yo Acetone 0'01453 0"01453 0"01453 0'01453 0-01453 0"01453 0"01453 0"01453 0"01453 0"01453 0-02977 0"03970 0"O04945 0.009889 0.009924 0.009924
0.003704 0.003704 0.003704 0.003704 0.003704 0.003704 0.003704 0.003704 0.003704 0.003704 0.005434 0"005814 O.OO4484 0-004674 0"01376 0.008969
0"1099 0.1342 0"1136 0"2121 0'1434 0.07859 0.04733 0.04037 0.07457 0,07457 0"1443 0"1468 0"1474 0"1488 0"1492 0"1492
20"75 32.5 18"0 107'0 37-5 12.5 17"3 17.0 14"0 13"5 17-8 13-2 165"0 72"0 38-5 60.0
9"859 6.295 1t.37 1'912 5.456 16.36 11 "83 12-04 14'62 15"15 17"89 26.62 0"988 3.055 10"22 5.44
2"833 3.196 3.562 3'579 3"347
2"791 2'755 2.215 2"671 2"758 2"284 Ave. 2"908
90 % Acetone 0-002808 0.002808 0.002808 0.0O2808 0.002808 0.01127 0.005636
0.0007191 0.0007191 0.0007191 0.002549 0.001938 0.001046 0.000828
0.1185 0.2015 0"03962 0-03962 0"03962 0"03755 0"03892
492 885 128 150 143 21 "9 52"0
0-0806 0"0448 0-3099 0"6172 0'5556 3.029 0.9622
2"680 2"773 2"858 2"698 2.855 2.727 2"872 Ave. 2"780
332
S.L.
MELTON,A. INDELLI and E. S. AMIS
orders up to 30 volume per cent acetone. The equations, however, fail to show in 60 volume per cent acetone the order with respect to hydrogen ion is approximately negative three while the orders with respect to U(IV) and U(VI) remain nearly unity. If we consider the equilibrium: U a+ + 2H~O ~ U(OH)z2+ + 2H + the equilibrium constant, Ks, is
K3=
[U(OH)~Z+][H+]z
(4)
[U4+]
and the U(OH)~2+ concentration is given by the expression Ka[U(IV)]
[U(OH)~2+] = [ ~ ] ~ ([U(IV)] -- [U(OH)93+]) =
and we can explain the orders out to the 60 volume per cent acetone if we assume the kinetic expression for the rate is __dx= k[U(OH)2~+][UO~OH+ ] = k • dt
= k
K3[U(IV)]
K~[U(VI)]
[U(IV)][U(VI)]
+
+
where the expression for the concentrations of UO2OH + is taken from M A c a w s , et a l : 1) In the limit of [H+]~/K3 and [H+]/K~ each being much larger than unity the reaction would approach an inverse third order dependence on [H+] and at the same time would be first order with respect to both [U(IV)] and [U(VI)]. The reversal of slope in the 60 volume per cent alcohol solvent (Fig. 3) indicates that the rate is directly proportional to some power of the hydrogen ion concentration in this range of acidity. This is probably due to some complex formation involving hydrogen ion. As has been pointed out{l: ) the region of 60-70 weight per cent organic component of solvent composition has been found to exert marked influence with respect to chemical kinetic and other phenomena appertaining to ions in solution, and 60-70 volume per cent acetone solvent seems to verify these observations. While it is not justifiable to average the specific velocity constants given in Table 2 in a given solvent, when the concentrations of highly charged ions and acid vary so widely, and while it is not justifiable to compare the average of the constants in the different solvents since the orders change so drastically, yet a rough idea of the marked effect of the solvent upon the reaction rate constants can be observed by plotting the logarithms of the average of the constants in the different solvents against the Volume per cent of acetone in the solvents. Such a plot, assumed to be straight line segments, is given in Fig. 5. The maximum in the plot occurs at about 40--45 ts}
E. $. A~ns, J. Phya. Chem. 60, 428 (1956).
The rates of the electron exchange reactions
333
2"8
2"4
2"O "x
o .J 1'2
O'ff
"40
I 20
4I0
6I0
80
l I00
VOLUME % ACETONE
FIG.
5.--Logarithm of the specific velocity constant vs. the volume per cent acetone in the solvent.
volume per cent acetone which is a smaller volume per cent organic c o m p o n e n t o f the solvent than f o u n d by MATHEWS et al. C1) in the case o f the water-ethanol system. In the latter system the m a x i m u m occurred at 80--90 volume per cent ethanol. O u r precision in general caiculated to be between 5 and 7 per cent. O u r care in weighing, volume measurements, counting and analytical procedures were such that we feel that our accuracy was well within the limits o f our precision. Acknowledgements--The authors wish to thank the Atomic Energy Commission for a grant under Contract AT-(40-1)-2069 which made this research possible. Also one of us (S. L. M.) is indebted to the National Science Foundation for an Undergraduate Research Participation Grant.
THE
RATES OF THE ELECTRON EXCHANGE REACTIONS BETWEEN U(IV) AND U(VI) IONS IN WATER AND WATER-ACETONE SOLVENTS S. L. MELTON, A. INDELLI a n d E. S. AMIS Chemistry Department, University of Arkansas, FayetteviUe, Arkansas (Received 13 June 1960; in revised form 4 August 1960)
Almraet--The rate of the electron exchange reaction between U(IV) and U(VI) ions was studied at 25 ° in water and water-acetone mixtures containing 30, 60, and 90 per cent by volume acetone, and at various concentrations of U(IV), U(VI), and hydrochloric acid. The order of the reaction with respect to each of these solutes was found to depend strongly upon the composition of the solvent. A departure in the trend of the rate dependence on hydrogen ion concentration was found for more dilute acid concentrations in sixty volume per cent acetone. Comparisons of the kinetics of the reaction in acetone-water and in ethanol-water are made. Mechanistic and kinetic discussions are included.
MATHEWS e t al. (1) studied the reaction between U(IV) and U(VI) ions in the presence of hydrochloric acid in water, ethanol, and water-ethanol solvents. These investigators found that the order of the reaction with respect to U(IV), U(VI), and hydrogen ions depended strongly upon the composition of the solvent in the water--ethanol system. INDELLIand AMIS(2) investigated the temperature coefficient of this reaction in this solvent system. The energy of activation was found to decrease with increasing weight per cent of alcohol in the solvent in general correspondence with an increase in reaction rate. No light or wall effects were found. RONA(3) studied the U(IV)U(VI) reaction in water and found no salt effects. It was felt by INDELLI and AMIS that the reaction should be studied in other solvent systems. The solvent system chosen in the present investigation was wateracetone since the dielectric constant range would be similar to that of the waterethanol solvent system and, at the same time, acetone would contrast with alcohol in that the former has a carbonyl rather than a hydroxyl group. EXPERIMENTAL Solid UCI, and UO~ClfH20 were prepared as described elsewhere. ~4' Experimental techniques, the preparation and analysis of stock solutions, and the tracer solution were as described by MATI-IEWS et aL ~1~. The runs were made, sampled, and analysed as described by these except that acetone w a s substituted for ethyl alcohol in the present experiments, and hydrofluoric acid was used as the precipitating agent. Aliquots of the U(VI) solution (50 2) were spotted on platinum disks, dried and counted. The U(IV) precipitate was dissolved in concentrated nitric acid, evaporated to dryness, taken up in 1 ml of dilute nitric acid, and a 50 A portion spotted, dried and counted. Triplicate samples for each valence type were spotted, counted, and the average of these were used to obtain a point on the rate plot. Fisher certified, A.C.S. grade acetone was used without further purification. ~l~ D, M. MA'rH1~WS,J. D. HEFLEYand E. S. Alms, J. Phys. Chem. 63, 1236 (1959). is~ A. INDELU a n d E. S. Alals, J. Amer. Chem. Soc. 81, 4180 (1959). ~a~E. Rosa, J. ,4mer. Chem. Soc. 72, 4339 (1950). ~4) D. M. MATHeWS,J. D. HEFLEVand E. S. A~ns. J. Inorg. NucL Chem. 12, 84 (1959). 325
326
S.L. MELTON,A. INDeLUand E. S. A~as TREATMENT
OF DATA
The electron exchange rates were calculated using the equation 0.693
t~
ab
(1)
a+b
where a and b are concentrations of U(IV) and U(VI) in the system. R is the total |0 9 e ?
• • •
S
ACID U(Vl) U(IV}
4
Iog (I-F)
9 e 7 6 5 4
175 Time in ~ t e n
Flo. 1.--Logarithm (1 -- F) vs. time in minutes when the solvent was 30 per cent acetone.
number of exchanges, labelled and unlabelled, per unit time in the concentration units used. The half-life, t~, was obtained and R calculated from ti, and a and b in the manner previously described. {1} The count-rate data was converted to 1-fraction (l-F) of complete exchange and a plot of such data for 30 weight per cent acetone is shown it. Fig. 1. In this figure the solid circles represent data taken when the concentration of acid was varied and the concentrations of U(VI) and of U(1V) were held constant. The triangles represent data taken when the concentration of U(VI) was varied and the concentrations of acid and U(IV) were held constant. The squares represent data taken when the concentration of U(IV) was varied and the concentrations of the other substances were held constant. Initial concentrations are referred to here. Figure 2 shows the plots of --log R corrected for constant concentrations and order
The rates of the electron exchange reactions
327
vs. --log C which were used to determine the order of the reaction with respect to U(IV); in Fig. 3 are given the plots of log R corrected for constant concentrations and orders versus --log C used to find the order of the reaction with respect to hydrogen ion. Each line has a slope which is the order of the reaction with respect to that reactant at the solvent composition specified. The line for pure water solvent from the data of RONA(3) was included in the drawings for reference purposes. The orders
6i/0 S
$.f
,f60~
7
4,o
3-(
31
2.%
~
~
,~
2!o
2:2
2~
z~
-,oo
F~o. 2.--Plots of --log ~R[H+]~ vs. --log [U(IV)] used in the determination of the order, r, of the reaction with respect to U(IV).
of the reaction with respect to U(VI) were determined in a similar manner and the data for these plots showed the same consistency as the data for U(IV) in Fig. 2. The data for Fig. 2 were obtained by making, for each solvent composition, several different runs with the same initial concentrations of U(VI) and of H + but different initial concentrations of U(IV). The initial rates were determined, and the logarithms of these rates plotted against the logarithms of the initial concentrations of U(IV). This gave the order of the reaction with respect to U(IV). In like manner the orders with respect to U(VI) and H + were found. Then to prove the reliabilities of the orders so determined, all pertinent data were included on the plots by introducing the concentrations of the reactants raised to the powers represented by their
S.L. MELTON,A. I~ELLI and E. S. A1vns
328
respective orders. This was likewise the procedure followed in arriving at Fig. 3. This procedure did not change the slopes of the lines and thus confirmed the orders. The intercepts o f the lines were changed of course.
@8
O'4
-0~
-I'2
-I~ 04
I 0"6
I 06
I l'O
I
I
1'2
I-4
I 1.6
-,0o [.@1 R
FIG. 3.--Plots of log [U(IV)],[U(VI)]~ vs. --log [H+] used in the determination of the order, q, of the reaction with respect to H+. TABLE 1.--ORDERS OF THE VARIOUS REACTANTS IN THE DIFFERENT SOLVENTS
Acetone
U(IV)
U(Vl)
Hydrogen ion
0 30 60 90
2.0 1.25 1.33 1.47
1.0 1-0 1.13 0.59
-3'0 --1"85 --2'85 (above 0.1 M concentration) --1.17
The orders of the reaction with respect to U(IV), U(VI) and hydrochloric acid are presented in Table 1 at various solvent compositions. The orders for pure water solvent are those of RON^. ta) The orders in the other solvents were determined in this investigation. F r o m Table 1 the orders are seen to have a marked dependence on the composition of the solvent. Between zero and ninety volume per cent acetone, the order of the reaction with reap ect to U(IV) first decrease with added acetone and reaches a minimum at about
The rates of the electron exchange reactions
329
40 volume per cent acetone of about 1.22, then with further addition of acetone, the order with respect to U(IV) again increases and becomes about 1-50 at 90 volume per cent acetone which was as far as the data extend. The general shape of the curve is similar to that found by MArrmws et al/1) for the order with respect to U(IV) for the same reaction in ethanol-water solvents. In the latter case the minimum was lower by about 0.40 and was reached at about 50 volume per cent ethanol. Also in
I'0
o tr
o
-I'0
/ -~-o
/
\
~o
/
¢o
• ~,c~)
,'o
VOLUHE % ACETONE
FIG. 4.--Orders of the various reactants vs. volume per cent ethanol.
the latter case the decrease in order was more gentle and the increase more abrupt with added alcohol, the value at 90 volume per cent alcohol being 2.89. Since the water-acetone data unfortunately extended only to 90 volume per cent, it was not possible to know whether there was the abrupt decrease in order with respect to U(IV) in pure acetone compared to the order in 90 volume per cent acetone as was found for pure ethanol compared to 90 volume per cent ethanol; (see Fig. 4.) In the case of the order with respect to U(VI) the shape of the curve out to 90 volume per cent acetone closely resembles the curve found for the U(VI) order out to 90 volume per cent alcohol. In both cases there is first a slight increase in the order out to about 60 volume per cent organic component of the solvent and then a more precipitous decrease of the order out to 90 per cent by volume o f the organic component. In the case of the water-acetone solvent the order dips to 0.59 at 90 volume per cent acetone while in the case of water-ethanol solvent the order drops to 0.10
330
S.L. ]~PLELTON,A. INDELLIand E. S. AMlS
at 90 volume per cent ethanol. In the case of acetone there is no way of knowing whether there is an abrupt rise of order beyond ninety volume per cent acetone as there was an abrupt rise of order beyond 90 volume per cent ethanol. It might be mentioned the runs in 100 per cent acetone were not made since pure acetone at the acidity used in the runs polymerized rather rapidly. It was thought that this change in the nature of the solvent might affect the electron exchange reaction rate in a manner different from the other solvent factors. In water-diluted acetone, the polymerization was slower and the exchange reaction rate could be determined before extensive polymerization occurred. It is the order of the reaction with respect to hydrogen ion in water-acetone which contrasts sharply with that in water--ethanol, especially at 60 volume per cent organic component of the solvent. In the case of water-ethanol the order with respect to hydrogen ion at first increases with increasing volume per cent ethanol, reaches a maximum at about 70 volume per cent and then decreases gradually out to 100 per cent ethanol. In the case of water-acetone solvent there is a maximum in the order with respect to hydrogen ion at about 30 volume per cent acetone, a minimum at about 60 volume per cent, and then an increase out to 90 volume per cent which is as far as the data go. In addition to the minimum in the order with respect to hydrogen ion at 60 volume per cent acetone, there is also the curious hook in the log R vs. --log C curve for hydrochloric acid (Fig. 3) in-this solvent. In Table 2 where half-lives, rates and specific velocity constants at various concentrations of reactants in various compositions of solvents are listed, it is to be noted that the specific velocity constants for these runs with the anomalous orders with respect to hydrogen ion are omitted. It will be noted that the hydrochloric acid concentrations in these anomalous runs were below 0"1 M in every case. At these low acid concentrations in 60 volume per cent acetone, the slope of the curve in Fig. 3 (right hand portion of 60 volume per cent curve) indicates a positive coefficient for the dependence of the rate upon hydrogen ion concentration. Since there was insufficient data in this region of acid concentration, the order with respect to hydrogen ion was not obtained and the specific velocity constants were therefore not calculated. Lower acid concentrations in this solvent would have been investigated except that the solutions proved unstable at lower acidities and hydrolysed complexes of uranium precipitated. As observed from Table 2 the order with respect to acid in each of the other solvents was consistently constant over the whole range of acid studied. The rate expressions proposed by MATHEWSet al. (1~ namely,
dx dt
[U(IV)]2[U(VO] LKIF[H+]+ 1]~F[H+]J k+~ 2T
1]
(2)
and dx
[U(IV)I[U(VI)]
dt
r[H +] 1] F[H+] 1 L K 1 + JLK~ +1
(3)
to explain the observed orders found in the water-ethanol solvent up to 60 volume per cent of ethanol can be used in the present investigation to explain the observed
The rates of the electron exchange reactions
TABLE 2 . - - R A T E S ,
331
CONCENTRATIONS OF EACH COMPONENT, HALF=LIVES AND SPECIFIC
VELOCITY CONSTANTS AT 25"OO°C FOR U(IV)-U(VI) EXCHANGE REACTION IN 30, 60 AND 9 0 PER CENT ACETONE i
U(IV)
U(VI)
[H ÷]
t.~ (rain)
R x 10~ (mole/l./min)
k'
× 102
I
30 % Acetone 0'0213 0"0213 0"0427 0'0213 0"0339 0"0242 0"0242 0'0145 0-0436 0'0145 0"0145 9'0145
0.0105 0-0105 0.0105 0"0105 0.00926 0.0185 0"0130 0.00926 0.00926 0-0130 0.00370 0.00370
0.1027 0.0912 0.0912 0.0797 0.0528 0-0574 0.0574 0.0528 0-0528 0.0528 0.0528 0.1090
57.75 45.0 23.0 37.0 11.25 13.75 17.5 23-4 8'4 23.5 31.5 120.0
8'44 10'83 25"39 13"17 44.80 52"85 33"49 16"74 63 '02 20.21 6"48 1.70
1.440 1.510 1.484 1-431 1.441 1.513 1.365 1.557 1"480 1.339 1.509 1.514 Ave. 1.465
60 Yo Acetone 0'01453 0"01453 0"01453 0'01453 0-01453 0"01453 0"01453 0"01453 0"01453 0"01453 0-02977 0"03970 0"O04945 0.009889 0.009924 0.009924
0.003704 0.003704 0.003704 0.003704 0.003704 0.003704 0.003704 0.003704 0.003704 0.003704 0.005434 0"005814 O.OO4484 0-004674 0"01376 0.008969
0"1099 0.1342 0"1136 0"2121 0'1434 0.07859 0.04733 0.04037 0.07457 0,07457 0"1443 0"1468 0"1474 0"1488 0"1492 0"1492
20"75 32.5 18"0 107'0 37-5 12.5 17"3 17.0 14"0 13"5 17-8 13-2 165"0 72"0 38-5 60.0
9"859 6.295 1t.37 1'912 5.456 16.36 11 "83 12-04 14'62 15"15 17"89 26.62 0"988 3.055 10"22 5.44
2"833 3.196 3.562 3'579 3"347
2"791 2'755 2.215 2"671 2"758 2"284 Ave. 2"908
90 % Acetone 0-002808 0.002808 0.002808 0.0O2808 0.002808 0.01127 0.005636
0.0007191 0.0007191 0.0007191 0.002549 0.001938 0.001046 0.000828
0.1185 0.2015 0"03962 0-03962 0"03962 0"03755 0"03892
492 885 128 150 143 21 "9 52"0
0-0806 0"0448 0-3099 0"6172 0'5556 3.029 0.9622
2"680 2"773 2"858 2"698 2.855 2.727 2"872 Ave. 2"780
332
S.L.
MELTON,A. INDELLI and E. S. AMIS
orders up to 30 volume per cent acetone. The equations, however, fail to show in 60 volume per cent acetone the order with respect to hydrogen ion is approximately negative three while the orders with respect to U(IV) and U(VI) remain nearly unity. If we consider the equilibrium: U a+ + 2H~O ~ U(OH)z2+ + 2H + the equilibrium constant, Ks, is
K3=
[U(OH)~Z+][H+]z
(4)
[U4+]
and the U(OH)~2+ concentration is given by the expression Ka[U(IV)]
[U(OH)~2+] = [ ~ ] ~ ([U(IV)] -- [U(OH)93+]) =
and we can explain the orders out to the 60 volume per cent acetone if we assume the kinetic expression for the rate is __dx= k[U(OH)2~+][UO~OH+ ] = k • dt
= k
K3[U(IV)]
K~[U(VI)]
[U(IV)][U(VI)]
+
+
where the expression for the concentrations of UO2OH + is taken from M A c a w s , et a l : 1) In the limit of [H+]~/K3 and [H+]/K~ each being much larger than unity the reaction would approach an inverse third order dependence on [H+] and at the same time would be first order with respect to both [U(IV)] and [U(VI)]. The reversal of slope in the 60 volume per cent alcohol solvent (Fig. 3) indicates that the rate is directly proportional to some power of the hydrogen ion concentration in this range of acidity. This is probably due to some complex formation involving hydrogen ion. As has been pointed out{l: ) the region of 60-70 weight per cent organic component of solvent composition has been found to exert marked influence with respect to chemical kinetic and other phenomena appertaining to ions in solution, and 60-70 volume per cent acetone solvent seems to verify these observations. While it is not justifiable to average the specific velocity constants given in Table 2 in a given solvent, when the concentrations of highly charged ions and acid vary so widely, and while it is not justifiable to compare the average of the constants in the different solvents since the orders change so drastically, yet a rough idea of the marked effect of the solvent upon the reaction rate constants can be observed by plotting the logarithms of the average of the constants in the different solvents against the Volume per cent of acetone in the solvents. Such a plot, assumed to be straight line segments, is given in Fig. 5. The maximum in the plot occurs at about 40--45 ts}
E. $. A~ns, J. Phya. Chem. 60, 428 (1956).
The rates of the electron exchange reactions
333
2"8
2"4
2"O "x
o .J 1'2
O'ff
"40
I 20
4I0
6I0
80
l I00
VOLUME % ACETONE
FIG.
5.--Logarithm of the specific velocity constant vs. the volume per cent acetone in the solvent.
volume per cent acetone which is a smaller volume per cent organic c o m p o n e n t o f the solvent than f o u n d by MATHEWS et al. C1) in the case o f the water-ethanol system. In the latter system the m a x i m u m occurred at 80--90 volume per cent ethanol. O u r precision in general caiculated to be between 5 and 7 per cent. O u r care in weighing, volume measurements, counting and analytical procedures were such that we feel that our accuracy was well within the limits o f our precision. Acknowledgements--The authors wish to thank the Atomic Energy Commission for a grant under Contract AT-(40-1)-2069 which made this research possible. Also one of us (S. L. M.) is indebted to the National Science Foundation for an Undergraduate Research Participation Grant.