PMRSTUDY OF H20-NH3 PROTON EXCHANGE sition. The first z-polarized transition (lAz”) is expected to be well separated from the first lE’. This is a reasonably good accounting of the expected electronic absorption spectrum of TcHg2-, its predicted onset at rather high energies correlating with the observed spectrum of ReHg2-.
857
Acknowledgments. The authors wish to thank Dr. David B. Neumann for many interesting and informative discussions on properties, Dr. Charles Hornback for the use of his atomic SCF program, and Dr. M. B. Robin for clarifying discussions on ligand field spectra.
Proton Magnetic Resonance Study of Water-Ammonia Proton Exchange in Water-Ammonia Solutions Containing Added Potassium Hydroxide 1 by Mohammed Alei, Jr., and Alan E. Florin University of California, Los Alamos Scientific Laboratory, Los Alamos, New Mesico
87544
(Received July 2 9 , 1 9 6 8 )
The exchange of protons between H20 and NH3 in solutions of BzOin liquid NH3 at 29.6 A 0.2’ is accelerated by addition of OH-. The overall kinetics for Hz0 concentrations from 1 to 12 M and added [OH-] from zero to -2 X loM3M is well represented by rate = kl[OH-]+ k2[0H-][Hz0]2 k3[NH41-][H20] k4[HzO]4 with kl = 7.4 X lo4 sec-l, kz = 0.84 X lo4 sec-l M-2, k3 = 3.48 X lo6 s e r l M-l, and kc = 0.058 set" A t the highest He0 concentrations, the effect of the third term in the above rate expression allows one to place Thus at 12.2 M HzO,K,,,,, = [NH*+][OH-]/ rather narrow limits on the ionization of Hz0 in liquid “3. and at 9.05 M H20, Kim = (1.1 ==I 0.1) X lo-”. The remaining terms in the [HzO] = (3.9 A 0.3) X rate expression suggest possible species in these systems.
+
Introduction I n a previous publication,Z we pointed out that welldefined, separate nmr peaks are observed for HzO and XHa protons at room temperature in HzO-NH~solutions containing roughly 30 mol % or less HzO. Thus the exchange of protons between HzO and XH3 is slow in the nmr sense under these conditions. We further demonstrated that this exchange could be markedly accelerated by addition of NH4+, and we reported on the results of a study of the kinetics of Hz0-NH3 proton exchange accelerated by N H 4 f . I n this paper we report results of a study of H20-NHa proton exchange accelerated by hydroxide. This process is slower than the process involving KH4+ and is dependent on HzO concentration in a way that suggests more than one HzO species in the Hz0-NH3 liquid system a t room temperature. Moreover, under certain experimental conditions, the NH4+ arising from the ionization of HzO can be detected and rather narrow limits can be placed on the ionization constant for H2O at certain concentrations in liquid KH3. Experimental Section Proton line width data were obtained using the Varian DA-60 instrument. All measurements were
+
made at the equilibrium temperature in the nmr probe which was found to be very stable at 29.6 =t0.2’. A given Hz0-NH3-KOH solution was prepared by mixing a measured amount of an appropriate dilute aqueous KOH solution with a measured quantity of anhydrous liquid KH3. The samples were prepared and examined in the special plastic-valve, glass nmr cell shown in Figure 1. Because of its small size, light weight, and axial symmetry, the cell can be spun and a resolution of 0.3 Hz at 60 MHz can be obtained. The glass section is standard 1-mm wall X 5-mm 0.d. Pyrex glass tubing, selected from several lengths of commercial stock for roundness and precise 0.d. A slightly enlarged section near the open end of the glass tube permits firm attachment of a plastic valve. The stem-inlet of this valve is machined to the standard-taper angle to fit a ground joint on a glass vacuum system. The stem was removed completely for introduction of the aqueous KOH solution with a calibrated micropipet. The reassembled cell was then placed on a vacuum system, and the glass tube was cooled in liquid and evacuated. NH3 was then added from a calibrated volume filled to a (1) Work done under the auspices of the U. S. Atomic Energy Commission. (2) M . Alei and A. E. Florin, J. P h y s . Chem., 72, 550 (1968).
Volume 7% Number 4 April 2069
MOHAMMED ALEI, JR., AND ALAN E. FLORIN
858
KEL-F STEM KEL-F BODY
VITON
O-RING POLYET‘HYLENE
INSERT
“0
5
10
ADDED [OH-], LUCITE CLAMP FOLLOWER
5mm 0,D. PYREX TUBE
Figure 1. Plastic-valve, glass nmr cell.
measured pressure with KHs gas. The cell was calibrated for volunie as a function of height of liquid in the cell so that final molarities could be calculated. The cell could easily withstand the -150 psi equilibrium pressure over pure liquid KH3 at room ternperature. In fact, it survived testing at pressures in excess of 300 psi. To obtain reproducible proton line widths in the KHB-H20-KOH solutions, it was necessary to rinse the cell two or three times with a given solution. These rinses were especially important for solutions low in Ha0 and KOH. It appeared that the glass tube was capable of consuming approximately the equivalent of a monolayer of KOH either by absorption or by neutralization of acidic constituents in the glass surface. The design of the cell made rinsing quite simple. After shaking a given liquid sample in the cell, simply inverting the cell and opening the valve allowed the KH3 pressure to force the liquid out of the cell. In an attempt to eliminate consumption of KOH by glass surfaces, two cells similar to the one shown in Figure 1 were constructed, one entirely of Teflon and one entirely of Kel-F (except for the Viton O-ring). The Journal of Physical Chemistry
15
20
M x IO4
Figure 2. HzO-NHa proton exchange accelerated by added [OH-]; 0,0.48 M HpO; 4,1.03 M HeO; 0, 2.21 M HpO; X, 4.25 M HsO; 0 , 6,20M HzO; A,9.06 M H20, Wj 12.2M HnO.
We found, however, that consumption of KOH was even more pronounced in these cells than it was in the glass-plastic cell. Whether this was due to leaching of acidic constituents from the plastic or diffusion of atmospheric COr through the thin plastic walls is not certain. In any case, the all-plastic cells were of little use in this work. They might, however, be extremely useful for nmr studies in media highly corrosive to glass, and they can be made to withstand up to an internal pressure of -10 atm.
Results The analysis of the proton-exchange kinetics was based upon measurement of the width at half-height of the separate resonance for the water protons in the system. The width is related to the residence time for a proton in the HzO environment3 by the relationship ~ / T H ~= O
(l/Tz’)- ( l / T z )
R A V H ~ O (1)
where r S s O is the average time which a proton spends in the HzO environment before returning to an NHa molecule and A m B o is the half-height broadening in Hertz due to exchange. Figure 2 is a plot of ~ / T H ~ ” vs. added [OH-] at several fixed concentrations of HzO in liquid XHa at room temperature. At low [H20], the highest added [OH-] which could be studied was generally limited by the point at which (3) We should emphasize that the term “H20 environment” implies nothing concerning the state of the water in these systems. The only justiflcation for using this term is the observation that the area under the nmr peak representing the protons in this environment corresponds to the number of protons introduced as H z O in making u p the solution. Thus the HzO environment could represent a single HzO species or any number of HzO species with rapid averaging of water protons among them. We also use the term “HzO proton” to refer to the average proton in the Ha0 environment.
859
PMRSTUDYOF H20-NH3 PROTON EXCHANQE further addition of KOH produced a solid residue and adding still more KOH produced more solid and no further increase in the width of the HzO-proton resonance. If we assume that this limit represents the saturation solubility of KOH in the final solution, we find this solubility increases linearly with HzO concentration in the region between 0 and 1.03 M HzO. Thus at 0.48 M HzO in liquid KH3, the solubility of $1, while at 1.03 M HzO, it is KOH is 6.3 X 12.8 x 10-4 M . At higher [HzO], the solubility of KOH increased much more rapidly with increasing [HzO]. Although KOH was used as the source of added [OH-] in all the data reported here, several experiments using KaOH or tetrapropylammonium hydroxide instead of KOH demonstrated that the broadening produced did not depend on the particular source of hydroxide. Addition of large amounts of KCI, on the other hand, produced no significant additional broadening in H20-XH3 solutions containing small amounts of KOH. We therefore conclude that the observed increased broadening of the HzO proton resonance with increasing addition of KOH is due to an exchange process involving a hydroxide ion species. We also observe that the width of the NH3 proton peak increases with increasing added [OH-] and, in HzO-NHa solutions with sufficient solubility for KOH, a single averaged peak for all protons can be produced by simply adding sufficient KOH at constant HzO. It seems to us that the only conclusion consistent with these observations is that H20-1L”s proton exchange is accelerated by a hydroxide ion species. The width of the HzO-proton resonance provides a convenient and sensitive quantitative measure of the rate of this exchange since no other processes contribute significantly to the width of this resonance. In principle, the width of the WH3 proton resonance should also reflect changes in the rate of NH,-H,O proton exchange and, with proper consideration of the relative abundances of the NH3 and HzO proton environments, one might expect to derive the same kinetic results from an analysis of the iYH3 proton line widths as from an analysis of the HzO proton line widths. I n practice, however, the KH1 proton line widths are much less amenable to quantitative study of Hz0-?;H3 proton exchange for two reasons. First, one can easily show that for a given change in the rate of exchange between protons in an HzO environment and protons in an NHI environment, the absolute change in hertz in the width of the HzO proton resonance is pNH8/pH20 times as great as the corresponding change in the width of the NH3 proton resonance, where P N H ~ and ~ H are ~ O the fractions of total protons in each environment. the ratio of ~ N H ~ / ~ isH -4 ~ o At 12 M HzO in ”3, and a t 1 M HzO in NH3 it is -30. Thus the HzO proton line width is a much more sensitive indicator of changes in the H20-NHs exchange rate under the
experimental conditions employed in this work. The second and more serious limitation in attempting to use the NH3 proton line width for quantitative study of H20-NH3 proton exchange is the fact that processes other than Hz0-NH3 proton exchange can make significant contributions to the NH, proton line width. In particular, since over nearly the entire compositional range of this study the SHs proton resonance is a triplet due to 14N-H spin-spin coupling, the KH3 proton spectrum can be influenced by changes in the rate of 14N quadrupolar relaxation and the rate of NH8-NH8 proton exchange. The latter process can become especially important at the higher HzO concentrations and low added COH-] where S H 4 + arising from the ionization of HzO in liquid NHs can accelerate NH3-NHs proton exchange to a much greater degree than it does NH3-Hz0 proton exchange. Thus Clutter and Swift4 have demonstrated that this process proceeds a t a rate of 6.9 X loe sec-1 which is at least two orders of magnitude faster than the rate of HZO-NHa proton exchange in the presence of NH4+. For these reasons and the fact that the primary purpose of this work was to examine the HzO-XHa proton-exchange process, we have not attempted to analyze the NH3 proton line widths in detail.
Discussion The data plotted in Figure 2 give direct insight into the form of the rate expression for H20-IC”s proton exchange in the presence of added [OH-]. If we define rate as being equal to the number of moles of HzO per liter which exchange a single proton with NH3 each second, then rHa0,the average residence time for a proton in the HzO environment, is related to to rate by the expression 1 / r ~ ~=orate/2[HzO]
where [HzO] is the molar concentration of HzO in the system. Thus from a knowledge of the dependence of l / r ~ on ~ ovarious parameters, one can readily deduce the dependence of rate upon these parameters. The most readily apparent feature of the data ploto ted in Figure 2 is the linear increase in I / - r ~ ~with increasing added [OH-], at constant [HzO], over nearly the entire range of the data. The only experimentally significant departure from this linear dependence occurs at 9.05 and 12.2 M H20 at very low values of added [OH-]. Under these conditions, we observe a minimum in the plot of 1/mSo vs. added [OH-] so that, at very low added [OH-], l / T H Z O increases rather sharply with decreasing added [OH-]. Moreover, a t 12.2 M HzO, even in the region where 1 / r ~ ~ 0 increases with increasing added [OH-], we have observed that the resonance for the NH3 protons becomes a better-resolved triplet as the HzO proton resonance (4) D.
R.Clutter and T.J. Swift, J.Amer. Chem. Soc., 9 0 , 601 (1968). Volume 73, Number 4
April 1080
860
MOHAMMED ALEI, JR.,
becomes broader. If we assume that NH4+ is considerably more effective than OH- in accelerating H20-EH3 proton exchange and that it accelerates KH3-KH3 proton exchange to an even greater degree, then the above observations are consistent with the presence of significant equilibrium concentrations of '4" arising from ionization of H2O at high concentrations of HzO in liquid NH,. Returning to the general features of the data in Figure 2, we note that the slopes of the straight lines decrease with increasing [HzO] at low CHd3-J and increase with increasing [HgO] at higher [HtO]. Moreover, a t constant [KOH-J, the dependence of 1 / m P o on [HzO] proceeds from an inverse dependence at low [HzO] to a direct dependence at high [HzO]. Finally, we note that at higher [HzO], the straight lines in Figure 2 extrapolate to positive values of l/rHzOat zero added [OH-] and the extrapolated value increases very markedly with increasing [HzO]. r'l l o interpret the above observations, we propose an expression of the form I/THzO
= k1[0H-]/[HeOl"
$. kJOH-l[H%O]fi
+ &["a+]
(3)
where the bracketed quantities are meant to denote equilibrium molar concentrations. Thus [OH-] is not strictly equal to added [OH-], the abscissa in Figure 2, but is essentially indistinguishable from it except at high [HzO] and low added [OH-] where the ionization of H20 contributes significantly to the equilibrium At the lowest HzO concentrations, dominance [OH-]. of the first term in eq 3 produces the direct dependence on [OH-] and inverse dependence on [H20] as observed. With increasing [HzO], the second and fourth terms become increasingly important so that, at HzO concentrations above -3 or 4 M , 1 / r W 2 0 becomes directly dependent on [HzO] as well as [OH-] and a significant and increasingly large intercept at zero [OH-] is produced. We tentatively assume that the dependence of this intercept on [HzO] is given by k4[Hz0]~, As mentioned earlier, the third term in eq 3 becomes experimentally apparent only at higher H20 concentrations. As added EOH-1 is reduced t o very low values, the equilibrium concentration of NH4+ produced by the ionization HzO NH3 KH4+ OHbecomes large enough t o make a very significant contribution to H20-NH8 proton exchange. As we have shown in a previous publication12 the acceleration of this exchange by NH4+ contributes 1.74 X 106[XH4+] to 1/mZ0. Thus k3 in eq 3 is 1.74 X lo6. To evaluate ICl, ICz, na, and n in eq 3 we note that the slope of a given plot of ~ / T . H ~us.o added [OH-] a t fixed [H,O] is determined by the first tmo terms and given by slope = kl/[H20]" The Journal of Physical Chemistry
*
+ kz[HzO]"
ALAN E. FLORIN
Thus [H2Olm.sIope = kl
+ ICZ[H~O-J~+~(5)
which requires that a plot of [HzOlm-slopeus. [HzO]m+@ be linear. Table I lists the slope of the 1 / US.~
Table I: Test of Parameters in Eq 5 [HzO] 10-4, [HzO]*, sec-1 M1
[HzOl, M
Slope X lo-', sec-1 M -
0.48
7.00
3.36
0.23
1.03
4.08
4.20
1.06
2.21
2.62
5.. 79
4.88
4.26
2.62
11.13
18.1
6.20
3.02
18.72
38.4
9.05
4.32
39.1
81.9
4.70
57.3
610~6X 1
IC,
ii
x
A([IIIO].slope) A ([HzOl? 10-4, scc-1
M-9
1.01
0.42 0.40
0.37
0.47 0.27
+ h[HzO]*
+
AND
+
(4)
12.2
149
added [OH-] plot for each H20 concentration studied (cf. Figure 2 ) . By trial and error we find that the best fit of the data is obtained by assuming ?:z = n = 1; i e , , the best line is obtained by plotting [H,OI-slope US. CH10]2. The pertinent calculated values for testing this best fit are also included in Table I, The quality of the fit is demonstrated by the constancy of lcz in the last column of the table. For HzO concentrations between 1.03 and 0.05 &!, the constancy of R2 is quite good. The average of the four values of kz in this region is 0.42 X lo4sec--l hf-2 with a standard deviation of k0.03 X lo4 sec-' M-2. Attempts to fit the data with other values of m and n demonstrate that deviations from linearity especially at higher H 2 0 concentrations become very large for values of n other than 1, For values of PI other than 1 a significant deviation occurs at lower H 2 0 concentrations (between 1.03 and 2.21 M [HiO]). Using 162 = 0.42 X lo4 and the expression (eq 5 above with 112 = n 1) kl = [H20].slope - k2[H20]2, me may calculate values of kl for H2O concentrations of 1.03 t o 9.05 M. The average of five values for kl is 3.7 X lo4 sec-I with a standard deviation of h 0 . 4 X lo4 sec-'. Significant deviations from the above fit occur at 0.48 and 12.2 M H20 where the slope of the 1 / w 2 0 us. added [OH-] plot is, in each case, somewhat less than required. The deviation at 0.48 M HzO is not understood but could be due to a systematic loss of KO11 to the glass walls of the nmr cell. The deviation at 12.2 M € 1 2 0 , on the other hand, is in the direction expected if the ionization of HzO produces concentrations of 013.-
~
~
861
Pam STUDY OF H20-NH3 PROTON EXCHANGE significant in comparison with the added [OH-]. With values for kl, kz, m, n, arid ka, we may utilize eq 3 and the data at 9.05 and 12.2 M HzO to place rather narrow limits on the extent of ionization of HzO at these concentrations in liquid NH, at room temperature. Thus, by substituting appropriate values, eq 3 becomes 1/7€120
= (3.7 X 1O4[0H-])/[H20]
X 1O6[NH4+]
+ 0.42 + k4[HzO]”
(6)
We now define Kion SO that
Substituting eq 7 in 6 and combining terms 1/7Hz0
+
= [OH-]
X C(3.7 X 104)/[Hz0]
With regard to the values of k4[H20]p we note that the value of 52.1 at 12.2 M HzO is somewhat smaller than the value (-58) which would have been obtained by extrapolation of the essentially linear portion of the experimental 1/m20 us. added [OH-] at 12.2 M HzO. This is consistent with the fact that a plot of I / 7 H 2 0 us. equilibrium [OH-] would have produced a steeper line with a smaller intercept. The value of IG4[HZO]p = 16.8 at 9.05 M IlzO is indistinguishable from the value obtained by extrapolation of the linear portion of the experimental data at 9.05 M HzO. At lower [HzO], therefore, one expects the value of k4[H20]P to be given quite accurately by extrapolating the experimental lines to zero added [OH-]. Values of k4[Hz0]p obtained by extrapolation at 6.20 and 4.25 M HzO are 7 and 2, respectively. As mentioned earlier, we have thus far only assumed the mathematical form, kd[HZO]p. If this assumption is valid, log ( k4[H20]p) = log k4 p log [H20] and a log-log plot of k4[H20]p vs. [HzO] should produce a straight line with slope = p . Such a plot is shown in Figure 3 where the data are fit very well by a line
+ 0.42 X 104[Hz0]]
+ C(1.74 X 10s[H~O].Kion)/COH-II
+ k4[H20]P
(8)
where [OH-], the equilibrium hydroxide ion concentration, is given by [OH-] = A
+X
- [ ( B - (B2- 4C)1’2)/2] (9)
where A = ([Hz0]-Ki0n)1’2JX = added [OH-], B = 2A $c = X.A. By combining eq 8 and 9 we may obtain an expression for 1/mZoas a function of added [OH-], [HzO], Kion,and IC4[Hz0]P. Thus, assuming arbitrary values for Kion and k4[H20]p we may calculate curves for l/wAous. added [OH-] a t a given [HzOj and compare these with the experimental data. Actually, a nonlinear least-squares program written for the CDC 6600 computer was used to find values for Kion and Ic4[HzO]n which gave the best agreement between calculated and experimental curves a t a given HzO concentration. For the 12.2 M data these values were Kion = (3.9 f 0.3) X lo-”, rC4[HzO]p = 52.1 =t: 0.7 sec-l and for the 9.05 M data, Kion= (1.1 f 0.1) X 10-l1, It,[HzOlp = 16.8 f Q.4 sec-’. lJTith regard to the values of Kion we note that they are increasing with increasing [HtO] and are both higher than the value of 3 X 10-l2 reported by Clutter and Swift3 for Kionin liquid NH3 containing up t o -0.5 M H20. In view of the expected increase in dielectric constant with increasing €LO in this system, one would certainly also expect Kion to increase. However, even with accurate knowledge of the dielectric constant as a function of composition it would be difficult to predict the exact variation in K,,, with any reliability.
x,
Figure 3. Ion-independent HrO-NHa proton exchange.
with slope = 3. Thus, the ion-independent contribution to ~ / T H ~ is O given by k4[H20l3. From any pair of values of Ic4[HzO]p and m z O ] we may then calculate kh = 0.029. We may now write the complete expression for 1 / w 2 o (cf. eq 3) in the following form 1 / ~ a z o= ki[OH-)/[I-IzO]
+ kz[OH-][HzO] Volume 79, Number 4 April 1969
MOHAMMED ALEI, JR.,
862 Combining eq 10 with eq 2 rate
=
kl’fOH-]
+ k2’[OH-][H20]2
+ ka’[”4+][HzO]
+ k4’[Hz0l4
(11)
where kl’ = 2kl = 7.4 X lo4 sec-’, k2’ = 2 k ~= 0.84 X lo4 sec-l il.I-2, ka’ = 3.48 X lo6 sec-I A P 1 , and k4’ = 0.058 sec-’ M-3. Equation 11 represents the simplest rate expression which adequately describes H20-3H3 proton exchange in the region from 1 to 12 M H2O in liquid NHa solutions with added hydroxide. As written, this expression implies no dependence upon the concentration of N& in any of t.he rate-determining steps. However, we should emphasize that the KHs concentration changes by only -15% (from -35 to -30 M ) over the entire range of this study. In view of the experimental uncertainties, it would therefore be difficult for this work to positively establish whether or not an [NHJ dependence is involved in kinetics. In spite of this shortcoming, however, the dependences upon [HzO], [OH-], and [NH4+] are quite clear and the terms in eq 11 can still provide valuable insight into possible species and mechanisms involved in the rate-determining processes. Thus the first term in eq 11 suggests exchange between a hydrated OH- ion and ”3. The existence of a hydrated OH- in this
The Journal of Physical Chemistry
AND
ALANE. FLORIN
solvated by “3. Because H2O is always in large excess relative to OH- in the systems studied here and because a t low [HzO] the change in NHa concentration with change in [HzO] is negligible, proton exchange between NH3 and a species (H2O)n.OHmight be well represented by the-first term in eq 11. The second and fourth terms in eq 11 suggest the possibility that a dimeric HzO species may exist in the H20-KH3 liquid system. Thus the second term could represent an exchange process involving a dimeric water species, whose equilibrium concentration would be proportional to @z0]2,and hydrated OH-. Whether or not a separate NH3 species were also involved would depend on the nature of the dimeric H 2 0 species. If the dimeric HzO species were also associated with NH3 (the species NH3.2Hz0, for example), then an encounter between the dimeric HzO species and hydrated OH- might suffice to produce NH3-H20 proton exchange whose kinetics could be expressed by the second term in eq 11. Likewise, the fourth term in eq 11 could represent an exchange process involving a collision between two HzO dimers or an exchange process involving a tetrameric HzO species. Thus, although other interpretations are possible, the kinetic data would be at least consistent with the existence of dimeric and monomeric forms of HzO in equilibrium in the H20-NH3 liquid system.
