M. M. KREEVOY,R. A. LANDHOLM, AND R. ELIASON
1088
The Distribution of Hydrogen Isotopes between H2P04-and Water in Partially Deuterated Solutions1. by Maurice M. Kreevoy, Richard A. Landholm,lband Robert Eliasonlo SchooE of Chemistry of the University of Minnesota, Minneapolis, Minnesota
55455
(Received June 3 , 1 9 6 8 )
Using nmr, the distribution of hydrogen isotopes between water and diacid phosphate in partially deuterated aqueous solution has been determined. When coupled with the known isotopic ratios of acid dissociation constants of phosphoric acid and diacid phosphate, and certain assumptions, this permits the distribution to be evaluated for phosphoric acid and monoacid phosphate as well. The first two are reasonable and permit a reasonable approximation of the acid dissociation constant of phosphoric acid in isotopically mixed solvent. That for monoacid phosphate is unreasonable, and it is concluded that AFo of transfer of this species from HzO to D20 is probably not zero.
An essential prerequisite to the use of solvent hydrogen isotope effects for quantitative mechanistic studies is knowledge of the isotopic composition of reagents as a function of the isotopic composition of the solvent. Phosphoric acid is particularly interesting in this respect because it is a convenient acid for study in many acid-catalyzed reactions, and also because of its analogy with the acids related to water. That is, Hap04 is analogous with H30+, H2P04- with HzO, HP02- with OH-, and P O P with 02-. To avoid complications arising from symmetry, it is convenient to consider these compositions in terms of fractionation factors,2 symbolized by &,x, where MnX is a molecule containing n exchangeable hydrogen atoms. (The symbol M is used throughout this paper to designate one of the isotopes of hydrogen, without specifying which; Mx is used for one H, D, or T in the , molecule X.) The fractionation factor, + A ( ~ xis defined as the equilibrium constant for the redistribution reaction shown in eq 1.
+
4X"A
+
D M ~ OHM,AeD M ~ AH Y ~ O
(1)
The fractionation factor for M80+is L2 The fractionation factor for a monobasic acid, C$MA, is given by KHA13/KDA,2 where K M Ais the acid dissociation constant of MA in MzO, if the solvated M A has only one site of exchangeable protons with a n isotopic content different from that of the solvent and A - has none. This caveat is equivalent to the assumption that AFO of transfer of A-, HA, or DA from H 2 0 to DzO would be zero in the absence of exchange in the latter two cases. However, for a polyprotic acid the equivalent assumption still does not permit the evaluation of +M,A, because KH.AP/KD,Athen gives + M , A ~ / C $ M , - ~ A ~ - ~ . ~ If all the ratios of dissociation constants in the series M,A, M,-IA, etc., were available it would be possible to deduce all the +'s, at each step making the assumption described above. For phosphoric acid the ratios are The Journal of Phyeical Chemistry
available, with high reliability, for the first and second dissociation, but not the third.2J Instead + M * P O ~ and +MzP04- have been inferred from K Y ~ Pas Oa ~function of the deuterium content of the solvent.2 Since K M ~ Pis O ~ a relatively insensitive function of the +'s, this technique does not limit them very closely. An nmr technique has now been used to determine + M n p 0 4 - d i r e ~ t l y . ~ , ~ The resulting 4's are numerically somewhat different from the earlier values, but they are reasonably compatible with the isotopic variation of KMvrPOa.The derived value for C$Mpo:- seems anomalous, and an explanation is offered.
Experimental Section Nmr shifts were measured with a Varian Model A-60 spectrometer. A Hewlett-Packard Model 3300A function generator was used to generate side bands. Their frequency was determined with a Hewlett-Packard Model 373A electronic counter. The temperature of the probe was measured with an iron-constantan thermocouple during each series of measurements and was always 28 lo. The position of the combined H20-H2P04- peak was measured relative to 0.05 M tetramethylammonium chloride (Eastman White Label) as an internal reference by plotting A (the chart position of the H20-HzPOhside band less the chart position of the reference resonance) against the side-band frequency. When A (1) (a) Bupported, in part, by the National Science Foundation through GP-7915. (b) National Aeronautics and Space Administration Graduate Trainee, 1965-1968. National Science Foundation Summer Fellow (Graduate Teaching Assistant), 1965. (c) Hercules Corporation Summer Fellow, 1965; d u Pont Company Summer Fellow, 1966; Ethyl Corporation Fellow, 1966-1967. (2) P. Salomaa. L. L. Schaleger, and F. A.-Long, J. Amer. Chem. Soc., 86, 1 (1964). (3) R. Gary, R. G. Bates, and R. A. Robinson, J . Phys. Chem., 68, 3806 (1964). (4) A. J. Kresge and A. L. Allred, J . Amer. Chem. Soc., 85, 1541 (1963). (6) V. Gold, Proc. Chem. Soc., 141 (1963).
DISTRIBUTION OF HYDROGEN ISOTOPES
1089
is zero the side-band frequency is the separation between the reference and the parent Hz0-HzP04- resonance. The position of the HzO resonance in undeuterated water, 6TMACH2', was measured on two separate occasions and values of 1.602 and 1.605 ppm were obtained. The average of these, 1.603, was adopted for B T M A C ~ ~ ' , and all obeerved resonance positions, &MAC, were assumed to be uncertain by -0.002. The plots of A vs. the side-band frequency were accurately linear, and the apparent uncertainty of BTMAC was much less than this. Most of the scatter is thought to be due to small temperature changes. A change of 1' corresponds to a change of 0.005 ppm in &MAC.' Solutions were made up from demineralized water, D20 (Bio-Rad Laboratories, 99.8 atom % ' D) and NaH2PO4.H20 (Mallinkrodt, Analytical Reagent) by weight. After each solution was made up and a sample removed for the nmr study the water was removed from the remainder by distillation and its H content determined from its near-ir spectrum.'
Results Values of
&MAC
for various solutions of NaMzP04 in
M20 are shown in Table I. Table I:
~ T M A Cin Isotopically Mixed Aqueous Diacid Phosphate Solutions at 28'
(N~MzPO~ M) ,
Atom % H
~ T M A C ,ppm
0.0 1.5
100.0 100.0 100.0 100.0 100 0 100.0 59.3 54.8 53.1 28.1 28.0 23.2 1.0
1.603 1.747 1.815 1.940 2.082 2.323 1.818 2.118 2.378 2.413 1.823 2.145 1.574
2.0 3.0 4.0 5.5 2.0 4.0 5.5
I
5.5 2.0 4.0 0.0
+PM*PO*-
... ... ... 0.85 0.74 0.82 0.81 0.84 0.76
If the shifts characteristic of HzP04- and HzO, and B T M A C H ~ O are independent of the NaM2P04 concentration, &MAC, in the absence of deuterium, is governed by eq 2, where XH.A is the fraction of hydrogen atoms present as H,A. Figure 1 shows that eq 2 is accurately obeyed, within the 6TMACH2'O4-j
STMAC
=
XH20aTMACH20
+
(2)
I
u
2 4 0.00
0.02
0.04
0.06
0.08
0.10
O.lL
XNhHr,POI
Figure 1. A test of eq 2 for HaO-NaH2POa mixtures a t 28 2~ 1". When ~ T M A C H ~isO that measured in pure water the plot (open circles, solid line) shows no visible curvature, and the least-squares intercept is zero, as required by eq 2. The least-squares slope, When ~ T M A c H ~ O is that 7.19 f 0.03 ppm, is 6TMACH2"". measured in NaN03 solutions whose concentration equals that of the NaH2P04the plot (closed circles, dashed curve) is systematically nonlinear and the best straight line forced through the points would not go through the origin. The origin is an experimental point in both series.
magnitude of which depend on the nature and concentration of the salt.? In 2, 4: and 5.5 M NaNOa B T M A C ~ ~ ' has been remeasured, and the salt-induced shifts are in very good agreement with those previously r e p ~ r t e d . ~They are in the opposite direction from those induced by NaHzP04, and smaller by about a factor of 2. Similar results have been reported for NaC1O4,g If it is assumed that NaH2P04 has a salt effect on b ~ M A c ~ 2of 0 ,approximately the same magnitude as n'aNO8, in addition to the effect caused by its exchangeable hydrogens, the the ~ T M A C ~ to ~ ' be used in eq 2 should be that measured in the presence of an appropriate concentration of NaN03, rather than that measured in pure water. Figure 1 also shows a test of eq 2 using such values of B T M A C ~ ~ ' . From this comparison it is clear that eq 2 fits the data far better with ~ T M A C ~ measured ~ ' in water, and this has been used throughout the rest of this work. A small change in the position of the water resonance occurs when H is partially replaced with D. Equation 3 has been suggested for the corrected water resonance position, ~ ' T M A c H ~ ' . ~ ~
-
+ 0.017T)
~ ' T M A C ~= ~ ' ~ T M A C ~ ~ '0.019~(1
(3)
(The atom fraction D is x; T is the centigrade temperature). A check of eq 1 with x, 0.99, and T, 28' yielded a ~ ' T M A C of 1.574 ppm while eq 3 requires 1.575 ppm.
X € I I P O ~ - ~ T M A C ~ ~ ~ ~ ~ -
uncertainty of the present measurements, and permits the evaluation of C ? T M A C ~ ~ ~ ' ~7.19 -, f 0.03 ppm (50% confidence limits, evaluated by the method of least squares.s) Previous work on salts without exchangeable hydrogens has shown that they induce changes in FO, the
(6) G. V. D.Tiers, J. Chem. Phys., 6 2 , 1151 (1958). (7) M. M.Kreevoy and T. 9. Straub, Anal. Chem., 41, 214 (1969). ( 8 ) C. A. Bennett and N. L. Franklin, "Statistical Analysis in
Chemistry and the Chemical Industry," John Wiley and Sons, Inc., New York. N. Y., 1954,pp 36-40. (9) J. A. Pople, W. G. Schneider, and H. J. Bernstein, "High Resolution Nuclear NIagnetic Resonance," McGraw-Hill Book Co., New York, N. Y., 1959, p 449. (10) A. Merbach, J. Chem. Phys., 46, 3450 (1907). Volume 75,Number 4 April 1969
M. M. KREEVOY, R. A. LANDHOLM, AND R. ELIASON
1090 By definition tpM2p04- is given by eq 4. (The parentheses indicate atom fractions or mole fractions.) In isotopically mixed solvents ~ T M A C ( D M ZPO 4- ) ( H M 2 0 ) M aP0 4- ) (D M 20)
=
cbMZP04-
(4)
is given by eq 5. It, together with the conservation conditions, eq 6-8, is sufficient to determine all the ~ T M A C=
+ (HMZPO)
(HM20)~’TMAC”’ (Hb120)
+
~
4-
(HM2P04-)
T
M
A
4- C
~
~
1
is similar in structure and acidity to HsP04, gives a 4 ~ ~ of0 0.72. ~ - Values of MA for carboxylic acids of about the strength of HaP04 are similar to, though somewhat higher than 4~ a~~ p13 Many authors18-17 have anticipated that, within a series of related acids, + M A (or KHAIKDA, which is proportional to MA for monoprotic acids) should increase with decreasing KHA, but that various series of acids should show quantitatively different behavior.l3J5J6 Using eq KH~PO~/ K ~ M~ aPO can be calculated for various H20-D20 mixtures from 4~ 8 ~4, 04M ZPO 4- , and 1.
(5)
atom fractions required in eq 4. Values of 4M2P04obtained using eq 4-8 are shown in Table I. The only 2(1 - X)
2(M20)
=
+ ( H M ~ o+) ( D M ~ o ) (7) ( H M ~ P o+ ~ -()D M ~ P O ~ - )(8)
( H M ~ o ) ( H M ~ P o ~ - ) (6)
=
2(MzP04-) =
additional assumption involved in these calculations is that 6TMACHZPo4- is independent of x. Table 1 shows no apparent trend in + M a p 0 4 - as a function of x, supporting this assumption, which also seems intuitively attractive. Cursory inspection of the calculations shows that most of the scatter in t$Map04- originates in error in the nmr measurements, rather than in (M2O) and (M2P04~). That being so, standard theory for the propogation of . errorll gives eq 9 for the uncertainty in ~ M ~ P O ~ -(The uncertainty in x is indicated by A (x); C is a collection of constants). Since
Figure 2 compares the calculated curve with the experimental values of Salomaa, Schaleger, and Longs2 The fit is reasonable, about as good as the fit originally shown (Figure 1 of ref 2) and better than that produced with the original (b values and the present value of 1.
tb
-
I
I
8
I
t
A ( ~ M ~ P o= ~ -~) A ( ~ T M -A~ T ~M A ~C ) ~ ~ ~ ~ -
x A(
(1 - x)
(9)
- &MAC)is also approximately Constant,
~ T M A c ~ 4-~ ”
the inverse of
+
[ ~ / ( H M ~-I-o ~) / ( D M z o )
1/(HM2P04-)
+ ~ / ( D M z P o I(1 ~ - ) - $1 was used as a weighting factor to get a weighted 0 ~is 0.80 - with a probable average value of 4 ~ ~.I1 ~ This
error of &0.01. The same values are obtained if an unweighted average is taken instead.
Figure
with
2.
Comparison of theoretical curve produced by eq 10 and 1, 0.69 (solid line) with the experimental Salomaa, Schaleger, and Long (circles). The dashed
@ H ) P O ~ 0.80; ,
values
of
curve is that and 1, 0.69.
produced
with h ) p 0 4 , 0 . 7 7 ; @ H ~ P O ~ -0.98; ,
(11) J. Topping, ‘‘Errors of Observation and Their Treatment.” 3rd ed, Chapman and Hall, Ltd., London, England, 1962, pp 82, 88, 89. (12) M. H. Lietzke and R. W. Stoughton, J . Phys. Chem., 67, 652 Discussion (1963), report 2.27; a recent redetermination by Mr. John Melquist i n this laboratory gave 2.18. From ~ M ~ P O ~ ~- ,M Q P Oand ~ +MPO(~are readilty (13) R. P. Bell and A. T. Kuhn, Trans. Faraday SOC.,59, 1789 evaluated. The already mentioned assumption that (1963). AFO of transfer is zero was made, 1.603 was taken for (14) C. K . Rule and V. K . La Mer, J . Amer. Chem. Soc., 6 0 , 1974 (1938). K H Q P O ~ K D and Q P O3.79 ~ for K H ~ P O ~ - / K D ~ The PO~-.~ (15) E. Hdgfeldt and J. Bigeleisen, ibid.. 82, 15 (1960). P 0.70 ~ ~ and that for 4 ~ ~ 0 4 is 2 -0.51. value of + M ~ is (16) N. 0. Li, P. Tang, and R. Mathur, J . Phys. Chem., 6 5 , 1074 The 4M2p04- value is entirely reasonable, as is Cpna3po4. (1961). Based on a KHso4-/KDSo4of 2.2,12bisulfate ion, which (17) References to much earlier work are given in ref 13-16. The Journal of Physical Chemiatru
REDUCTIONOF Co(II1) COMPLEXES
1091
which is a fairly strong base, hydrogen bonds to a On the other hand, the value of 4 ~ ~ 0 4is2 -unreasonable both in magnitude and its relation to + M ~ P O ~ - . number of solvent molecules more strongly than they hydrogen bond to each other. This would be likely to Acids as weak as HP042- generally have 4 values well above l.O.’a The values of K H ~ P O ~ - / K Dwith ~PO an~ 1- , lead to a positive AFO of transfer from H 2 0 to DzO,l9 and could account for the observed effect. Direct, of 0.69, and the assumption that AFO of transfer is zero, experimental determination of KHPO ,~-/KDPO p 2 - , and requires that ~ M P O(2 - be substantially smaller than also + a f p o 4 2 - might help to clarify this situation. 4 ~ ~ regardless ~ 0 ~ -of the value assigned to the latter. The assumption of a zero AFo of transfer is the likely culprit. It has long been known and recently re(18) D. M. Goodall and F. A. Long, J . Amer. Chem. SOC.,90, 238 emphasized that this is an inexact approximation.18 (1968). Structurally an attractive hypothesis is that H P O P , (19) M.M . Kreevoy, J . Chem. Educ., 41, 636 (1964).
Reduction of Cobalt(II1) Complexes by Monovalent Zinc, Cadmium, and Nickel Ions in Aqueous Solutions1
by D. Meyerstein2 and W. A. Mulac Chemistry Division, Argonne National Laboratory, Argonne, Illinois, (Received June 26, 1 9 6 8 )
and the Nuclear Research Centre, Negev, Israel
The specific rates of reaction of Zn+, Cd+) Ni+, and e,, with a series of Co(II1) complexes have been determined. The mechanisms of reduction and their dependence on the electronic structure of the monovalent cations are discussed.
The specific rates of reduction of a series of cobalt (111) complexes by different cations3-* and by hydrogen atoms,9-11 have been recently measured. The results have been used as guides for the elucidation of the reaction mechanism. Several criteria based on the kinetic evidence have been suggested in order to differentiate between “outer-sphere” and “innersphere” reducing agent^.^-^,'^ Recent studies have shown that monovalent zinc, cadmium, and nickel ions, formed by the reduction of the corresponding bivalent ions by the hydrated electrons, are powerful reducing agents.13J4 Many reactions of these cations have been measured.lk17 It has been of interest therefore to measure their rates of reaction with a series of cobalt (111) complexes in order to obtain a better understanding of the mechanism of reduction by these cations. The specific rates of reaction of Zn+, Cdf, and Ni+ with a series of Co (111)(“3) &Xand Co (111)(En) 2XY complexes have been determined. The results suggest that Zn+ is mainly an outer-sphere reducing agent, Ni+ is mainly an inner-sphere reducing agent, and Cd+ reacts via both mechanisms.
Experimental Section iWateriuls. The water has been triply distilled. ZnS04,CdSOr, NiSOp, and CH30Hwere Baker Analyzed (1) Based on work performed under the auspices of the U. S. Atomic Energy Commission. ( 2 ) Reprint requests to be sent to D. Meyerstein, Nuclear Research Centre, Negev, Israel. (3) J. F. Endicott and H. Taube, J . Amer. Chem. Soc., 86, 1686 (1964). (4) A. Zwickel and H. Taube, ibid., 83, 793 (1961). (5) J. P. Candlin, J. Halpern, and D. L. Trimm. ibid., 86, 1019 (1964). (6) J. P.Candlin and J. Halpern, Inofg. Chem., 4, 766 (1965). (7) J. H.Espenson. ibid., 4, 121 (1965). (8) J. P. Candlin, J. Halpern, and S. Nakamura, J . Amer. Chem Soc., 8 5 , 2517 (1965). (9) G. Navon and G. Stein, J . Phys. Chem., 69, 1391 (1065). (10) M.Anbar and D. Meyerstein, Nature, 206, 818 (1965). (11) J. Halpern and J. Rabani, J . Amer. Chem. Soc., 88, 699 (1966). (12) H. Diebler, P. H. Dodel, and H. Taube, Inorg. Chem., 5 , 1688 (1966). (13) J. H.Baxendale and R . 8 . Dixon, 2. Physik. Chem. (Frankfurt am Main), 43, 161 (1964). (14) D.iMeyerstein and W. A. Mulac, J.Phys. Chem., 72, 784 (1968). (15) J. H.Baxendale, J. P. Keene, and D. A. Stott in “Pulse Radiolysis,” Academic Press, London, 1965. p 107. (16) J. H. Baxendale, J. P. Keene, and D. A. Stott, Chem. Commun., 715 (1966). (17) G. V. Buxton, F. 9. Dainton, and G. Thielens, (bid., 201 (1967). Volume 7S,Number 4 April 1969
