1074
VALUESOF
p
]'OR
Temp., OC.
-5.0 5 0 15 0 25 0 35 0 40 0 45 0 50 0 55 0 60 0
TABLE VI some of these organic acids have also been deterWe CARBOSTETRACHLORIDE AND METHAXOLmined in DzO by a polarographic method. have demonstrated experimentally for the first p x 109 Carbon tetrachloride
Methanol
1 86
1 40 1 43 1 42 1 47 1 45 1 46 1 55
1 99 1 87
1 53 2 00
of p would lend to be low since no correction was applied to the molar volume to account for association effects However, since association effects decrease as the temperature increases, the p values should iiicrease with temperature as shown in Tables V and VI. The data for benzene in Table V and carbon tetrachloride in Table VI indicate a slight temperature effect, but the average value of p for each liquid is within lOy0of the theoretical value. The data for carbon tetrachloride in Table VI were not reported for temperatures below 25'. At lower temperatures, dispersion of heavy tracer molecules leaving the capillary is not obtained; and as a result, the measured self-diffusivities are abnormally low. This effect could be corrected by stirring the bulk solution. DEUTE:RIUJI ISOTOPE EFFECTS O S DISSOCIATIOS CONSTAKTS AXD FORJI1TIOS CONSTAKTS1 BY
Vol. 65
NOTES
NORNAS
Department
0.7"
c. LI, PHILOlilENA TANGAND RAJL l A T H U R Chemistry, Duquesne Cniversity, Pittsburgh, Penna. Receized December 9 , 1960
-\ survey. of the recent literature shows that kinetic deuterium isotope effect's have been extensively studied ; however, relat.ively little has been published on the effects in solution equilibria. This situation is not surprising because isotope effects on reaction velocit'ies are much more pronounced t8hanon equilibrium constants. Several p,apershave appeared recently on the use of ordinary calomel-glass electrode couple for measurement of acidity in D20 solutions.2 These authors have studied the relat'ion between true and apparent p H of solutions in DzO and found the correction for DC1 solutions and DC10, solutions in D20 to he +0.4 pH unit'. In t'his paper we report the use of this method for the determination of acid dissociation constants of a number of organic acids containing different functional groups. The formation constants of metal complexes of (1) This investigation was supported b y the U. S. Atomic Energy Commission through Contract No. AT(30-1)-1922 and b y Research Grant N 8 F G7447 from the National Science Foundation. (2) (a) K. Mikkelsen and S. 0. Nielsen, J . Phys. Chem., 64, 632 (1960); (b) H. H. Hyman, A. Kaganove and J. J. Kata, .4bstracts, Am. Chem. Soc., Btlantic City Meeting, Sept.. 1959; ( c ) P. K. Glasoe and F. A. Lone:, Abstracts. 4111.Cheni. Soc., Atlantic City Meeting, Sept., 1969.
time that the deuterium isotope effect on acid dissociation constant can be attributed to the specific bond affected.
Experimental Materials.-Deuterium oxide, 99 3% DzO, . was purchased from Bio-Rad Laboratories and used uithout further purification. Fully deuterated acetic acid was prepared from malonic acid and D20 according to the method of Halford and Anderson.3 Histidylhistidine, obtained from Kutritional Biochemicals Corp., was found to be 80% pure,4 the impwities being water of hydration and inert salt. All other chemicals were of C .P. grade. Procedure.-pH measurements were made at 25' using a conventional calomel-glass electrode couple with a Beckman Model G pH meter, in both HrO and DzO systems. The pH meter was standardized in the usual way with buffers in water solution. In D2O systems, glass electrodes were conditioned by immersing for several days in DzO buffer solutions with no change in the observed pH readings on standing. The deuterium solutions were made by dissolving the anhydrous hydrogen compounds in deuterium oxide, except for hydrochloric acid, in which case the concentrated aqueous solutions 11-ere diluted with DzO. For the low concentrations investigated this did not alter the deuterium content by a significant amount. All the solutions used for pH measurements contained 0.02 X organic acid in 0.1 AT sodium chloride and neutralized to different extents with acid or alkali. The total ionic strength of the solutions waq krnt at u = 0.11. _. The pH oi a 6.1 M'XaCl, 0.01 31 HC1 solution in H90 IS 2.10 and the apparent pH of a 0.1 AI hTaC1, 0.01 JI DCl solution in D 2 0is 1.70. The apparent pH of a DC1 solution in DqO is 0.40 unit less than a similar solution in H,O. and this -has aleo been observed by previous workers.% In solutions containing only dilute acid and sodium chloride, the concentration of HaO+ in H20 solutions cannot differ appreciably from the concentration of D 3 0 +in D20, since in both cases there is essentially complete hydrogen ion transfer from the hydrochloric acid to the solvent. In order to calculate the acid dissociation constant in DJO, therefore, the pD of a solution in DzO can be determined by use of the equation pD = "pH" 0.40 (1) where "pH" is the apparent pH meter reading in DzO medium. Equation 1 has been obtained previously by Hyman, et a1.,2b using perchloric acid, and by Glasoe and Long,2cwing hydrochloric acid. In aqueous systems, pH is defined as - log CR,o+ - log f + where f* is the activity coefficient. At a total ionic strength of 0.11 we have assumed - log f = to be 0.10,j and this value is used for all Eolutions studied in the present investigation. Polarographic current-voltage curves were made with a Fisher Elecdropodr. ill1 potentials were measured at 25" against a saturated calomel electrode' (S.C.E.) in the manner described by Li, et aZ.6.'
+
Results and Discussion (A) pH Measurements.-Table I lists the results obtained on the acid dissociation constants of organic acids containing t v o or more polar groups, and the deuterium isotope effect, measured by ~ K D ~ K H The . equilibrium constants refer t o the equilibria HA"' DA"+
+ HzO = A("-')+ + H30+ + DzO = A("-')+ + D30+
KH KD
(3) J. 0. Halford and L. C. dnderson, J . Am. Chem. Soc., 58, 736 (1936). (4) R. B. Martin and J. T. Edsall, i b i d . , 82, 1107 (1960). ( 5 ) Symposium on pH Measurement, ASTM Special Technical Publication N o . 190 (1956). (6) N. C. Li and R. A. Manning, J . Am. Chem. Soc., I T , 5225 (1955). (7) N. C. Li and 31. C . Chen, ibad., 80,5678 (1958).
NOTES
June, 1961 Examination of Table I shows that ~ K D ~ K isHa linear function of ~ K for H acid dissociation from specific groups. Linear plots of ~ K D ~ K us. H ~ K are H obtained and the equations of the straight-lines are
+
1075
and 5.15, respectively. This difference, although small, may be ascribed to secondary isotope effect." (B) Polarographic Measurement of Cadmium Complexes.-For a reversible mercury dropping electrode reaction, the polarographic equation is
for -COO: ~ K D~ K = H 0.086 0.124pK~ (2) (El/& - ( E I / %=) ~-0.0296 log K p - p X 0.0296 log ( A ) for -KH3+ and -1mH': ~ K -D~ K =H0.243 0.0417pK~ (4) (3) where (E1/Jcand (EI,& are the half-wave poten-
+
The fifth and sixth columns of Table I give comparison between the observed values of ~ K D ~ K and H the values calculated from equation 2 or 3. The agreement between the observed and calculated values is excellent.
tials of Cd++ in the presence and absence of a complexing agent A, respectively, and K is the formation constant of the cadmium complex
Glycolic acid -COOH 3.74 0.53 0 . 5 6 Malonic acid -COOH 2.86 .44 .44" Citric acid .45" 2.95 ( p K 1 ) .49 -COOH -COOH 4.38 (pKz) .64 .63 5.80(pK3) .75 .80 -COOH Tricarballylic -COOH 3.50 ( p K , ) .53 .52" acid -COOH 4.60 (pKz) .68 .66 -COOH 5.75(pK3) .80 .SO Glycine -COOH 2.47 .39 .39" -NH3 9.65 .63 .64b Glycylglycine -?;Ha + 8.18 .58 .58' Glycylglycyl- -COOH 3.28 .47 .49" glycine -NH3 + 8.00 .58 .58* Imidazole -1mH + 7.09 .56 .54* Histidine -COOH 1.81 .33 .31" -1mH 6.11 .54 .50b -KH3 9.20 .63 .63* D-LeucY-1-L- -COOH 2.87 .41 .44" tyrosine -XH3 8.36 .GO .59' -OH (tyrosine) 10.28 .79 Histidyl-1mH + 5.54 .51 .47* histidine -1mH 6.80 .50 .53* -IYH3 7.82 .57 .57b Calcd. from equation 2 . Calcd. from equation 3.
TABLE I1 POLAROGRAPHIC MEASUREMENT OF CADMIUM COMPLEX OF IMIDAZOLE IN D10, p = 0.15, 25"
Cd++
+ pA = CdA,
KP
Table I1 summarizes the polarographic result obTABLE I tained with DzO solutions containing 5 x M ACID DISSOCIATION CONSTANTS OF ORGAXIC ACIDS CON- Cd(KOJa, 0.15 M KN03 and varying concentraTAISING Two OR MOREPOLAR GROUPS,p = 0.11, 0, 25" tions of imidazole. A plot of El/, us. - log (Im) ~ K D yields a straight line with slope of 0.119, so that Organic ~ ~ KKDH %k p = 4.0. The electrode reaction is reversible. acid Acid group PKH
+
+
+
(14
-El/*
log K4
0 0 087 193 594 894 1.005 1.273
0.576 672 ,713 .768 .792 ,798 ,810
7.49 7 49 7.39 7 49 7 49 7.49
The formation constant of the cadmium-imidaBole complex in HzO,p = 0.15, 2 5 O , has previously been determined polarographically by Li, et al. l 2 : log K* = 7.48. Experimentally, there is no deuterium isotope effect on the formation constant of the cadmium-imidazole complex. This is as expected because the complexing agent is taken to be the uncharged imidazole. If the complexation reaction is written Cd++
+ 4ImH+ = CdIml + 4 H C
K'
A
then K' = K 4 K ~ ,where 4 K H is the acid dissociation constant of ImH+. The deuterium isotope effect on K' would then correspond to the fourth Previous t v o r k e r ~ have ~ ~ * ~shown ~ that the ratio power of the isotope effect on the acid dissociation of K H I K D should increase with decreasing acid constant of imidazole, 10-2.24(see Table 11). strength. Hogfeldt' and RigeleisenlO conclude that The formation constants of the 1:2 cadmium t,he type of acid is more important than the acid complexes of histidine , glycylglycinate and glycylH glycylglycinate in DzO, p = 0.15, 2 5 O , were deterstrength in so far as t'he difference between ~ K and ~ K is D concerned. We have demonstrated ex- mined polarographically in precisely the manner perimentally for the first time that the deuterium described by Li, et dJ6' for the same complexes in isotope effect does indeed depend on the specific HzO. The dropping mercury electrode reaction is bond affected (-COOH or -NHz+ and -ImH+ reversible in every case. The ~ K D 'ofs histidine, bonds), but that wit,hin a series of similar bonds, glycylglycine and glycylglycylglycine were taken from Table I. The formation constants in DzO, ~ K -D~ K isHa linear function of ~ K H . The ~ K for H acetic acid is 4.64 a t p = 0.11, and log Kz, were calculated to be 11.3, 5.6 and 5.4, ~ K D~ K = H 0.49. The isotope effect for this respectively. These values are about 0.2 log unit acid is not given by equation 2, since acet'ic acid higher than the corresponding values in HzO. contains only one polar group, whereas equations The formation constant of the 1:2 cadmium com2 and 3 apply to organic acids which contain two plex of histidylhistidine has not hitherto been deteror more polar groups. The pK's for CD3COOD mined. We have studied this complex polaroand CHsCOOD in DzO a t p = 0.11, 2 5 O , are 5.19 graphically, CL = 0.15, 25': in H20, log K z = 8.1; +
( 8 ) G.
(1934).
h ' . Lewis and P. W. Schultz, J . Am. Chem. Soc., 16, 1913
(9) C. K. Rule and V. K. LaMer, i b i d . , 60, 1974 (1938). (10) E. Hogfeldt and J. Bigeleisen, ibid., 62, 15 (1960).
(11) A. E. Halevi, Tetrahedron, 1, 174 (1957): A. E. Halevi and M. Nuasrm, BUZZ. Res. Council Israel, EA, 263 (1956). (12) N. C LI, J . M. White and E. Doody, J A m Chem Soc , 7 6 ,
6219
(1954).
NOTES
1076
in D20, log K , = 8.5. The acid dissociation constants of histidylhistidine in H20 and DzO were those of Table I. In the complexation of histidine and the peptides to Cd++, the amino group probably is involved in binding. Since the amino hydrogens are easily exchanged in DzO medium, we would expect a slight deuterium isotope effect on the formation constants, as has been found to be the case. Acknowledgment.-We wish to thank Mr. E. Tucci for preparing the fully deuterated acetic acid. KINETICS OF BOROHYDRIDE
HYDROLYSIS BY 171. H. STOCKMAYER, ROYR. MILLERAND ROBERT J. ZETO Deportment
0.i
Chemistry, Massachusetts Instatute of Technology, Cambridge 69, Mossachusetts Recewed December 0, 1060
Recently Davis and Swain' observed that the hydrolysis of borohydride ion EiHI-
+ 4Hn
+ 3H20
was subject to general acid catalysis, according to the expression
- d In (BHI-)/dt
kl = Cki(HAi) i
From measurements of the rate over a wide range of pH with several buffer systems at 25", they determined an accurate value of kHao+and reported approximate values for kHaBos,kHco, - and
-.
kHaP04
Our earlier studies2J of the rate of this reaction supplement the results of Davis and Swain. Confining our experiments to the neighborhood of pH 9, but employing a range of buffer concentrations, we determined kHsO + and kHaBosat 0.0 and 25.0' at an ionic strength of 0.16, and we also evaluated k",+ at 25". Our value for kHaO+ at 25' is in good agreement with that of Davis and Swain, but our value for ~ H ~ BisOconsiderably ~ higher than theirs. Experimental Research grade potassium borohydride (Metal Hydrides, Inc., Beverly, Mass., over 96% KBH,) was used a t an initial concentration of approximately 0.01 M in most runs. The iodate method4J was used to determine borohydride concentrations. The buffers were prepared from HaBO3NaOH or NI-14C1-NaOH,. with addition of NaCl where necessary to bring the ionic strength to 0.16 M . All measurements of pH were made on a Reckman Model G meter a t 25.0'. The values of pH in the borate solutions a t 0" were evaluated from those measured a t 25" from the known change in the ionization constant of boric acid6 (5.79 X 10-10at250to3.09 X 10-laatOo).
-___
(1) R. E. Davis and C. G. Swain, J. Am. Chem. SOC., 82,5949 (1960) ; earlier literature is quoted there. (2) R. R. Miller, S.B.Thesis, M.I.T., May. 1958. (3) R. J. Zeta. S.M. Thesis, M.I.T.. January, 1959. (4) D. A. Lyttle, E. H. Jensen and W. A. Struck, Anal. Chem., 24, 1843 (19.5.2). (5) E. H. Jensen, "A Study on Sodium Borohydride," N y t Nordisk Forlag, Arnold 13usch, Copenhagen, 1954. (6) H. S. Hsrned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions," Reinhold Publ. Carp., New York, N. Y., Third Edition, 1958, p. 755.
Vol. 65
7 t 0
0.05
0.10 0.15 (HzBOa), M . Fig. 1.-Pseudo-first-order rate constant kt, for hydrolysis of borohydride at O", ionic strength 0.16 M and H 9.27 f 0.02, as a function of the molar concentration ofundissociated boric acid.
Results and Discussion Results for the borate buffer system a t 0.0" and pH 9.27 f 0.02 are shown in Fig. 1, where the pseudo-first-order rate constant kl is plotted against the molar concentration of un-ionized boric acid. The slope of the line gives directly the value of kHsBOa, while that of kHaO+ is found from the intercept and the pH with an assumed value of 0.72 for the activity coefEcient of any univalent ion in the solution. These constants and those found in similar fashion a t 25" are collected in Table I. The energies of activation calculated from these results are 9 f 1 kcal. mole-' for the reaction with H 3 0 +and 14 f 2 kcal. mole-' for that with Hac),. Our value for kHsO+ at 25" compares well with that of Davis and Swain, (10.0 f 0.4) X lo5 M-' set.-' a t p = 0.10 M ; with a reasonable estimate of the difference in salt effect, their figure and ours agree to better than 10%. However, their estimate of ICH~BO, was (1 f 5 ) X M-' see.-', and even their upper limit is well below any figure that could accommodate our results (Table I). TABLE I REACTIONS OF BOROHYDRIDE IONWITH ACIDS ki
Reaction
BH4-
+ HaO+, 0"
H30+, 25" &Boa, 0' H3B03, 25' "a+, 25" a All a t ionic strength 0.16 M .
(2
(M-1
sec.-V
o f0.2) x
105
(8 f 1) X lo6 (2 3 0.2) f 10-4 ( 2 o f o 3) x 10-3 (1 5 f 0.4) x 10-3
*
From the rates for H 3 0 +and NH,+, we estimate an exponent of well over 0.9 in the Bronsted catalysis law for acids of this charge type. Clearly the H-A bond of the attacking acid is very largely broken in the transition state. This conclusion is also supported by the magnitude of the observed difference in activation energy for the H30+ and H3B03 reactions, which within the experimental error equals the enthalpy of ionization of H3B03. Since the enthalpy of ionization of NH4+ is about 12 kca1.-1 mole-', we might expect the activation energy for the NH4+ reaction with BH4- to lie near 20 kcal. mole-', as is in fact borne out by very rough results2 for this reaction a t 0".
