1072
NOTES
Vol. 65
SELF-DIFFUSION I N LIQUIDS. 111. of the group in the native and denatured forms will differ. This will give rise to a pHdependence of TEMPERATURE DEPENDENCE I N PURE the standard free energy of denaturation. While LIQUIDS such a pH-dependence has heretofore been atBY R. E. RATHBUN AND A. L. BABB tributed to side-chain hydrogen bonding18which has been shown to be involved in several protein de- Department of Chemical Engineering, Unioersity of Wushington, Seattle, Washtngton naturations,lOJ1it appears that a contribution from Received December 0, 1960 hydrophobic blonding is also involved in the case of Self-diffusion coefficients were measured in benribonuclease. l1 In the latter case, a preliminary attempt already has been made to obtain a quanti- zene, carbon tetrachloride, methanol and ethanol over a wide range of temperatures using a capillary ta tive treatment . cell technique with carbon-14 labeled tracers. Kinetics of Protein Denaturation-If a native The apparatus and procedure have been fully deprotein contains hydrophobic bonds which are rup- scribed e l s e ~ h e r e . ~ . ~ tured in the formation of activated complexes, Thg ethanol-l-CE4was purchased from the Volk Radiothen these bonds will contribute to the standard chemical Company. The uniformly labeled benzene waa free energy of activation. If, in addition, the purchased from the Nuclear Chicago Corporation and the tetrachloride-C14 and methanol-C14 were obtained production of activated complexes from native carbon from the Nuclear Instrument and Chemical Corporation. protein requires that ionizable groups emerge from The chemicals used in diluting the tracers to the desired and in preparing the non-radioactive bulk solutions a hydrophobic to an aqueous environment, then the activity were of the highest grade commercially available. The rate will be pHdependent. This pH-dependence benzene, carbon tetrachloride and methanol were reagent can be deduced from the model previously used12 g a d e chemicals aa obtained from Merck and Comand the ethanol was pure anhydrous ethyl alcohol to account for denaturation kinetics in terms of the pany, produced by the U.S. Industrial Chemical Company. involvement of side-chain hydrogen bonds. Results and Discussion Ultraviolet IDiff erence Spectra.-If a chromophoric group is embedded among non-polar sideIn Tables I, 11,I11 and IV, the measured self difchains in a native protein and becomes accessible fusion coefficients are tabulated and compared to water during a limited or extensive configura- with data available in the literature ( b e n ~ e n e , ~ > ~ * ~ e t h a n 0 1 , ~ * ~and - ~ * ~methtional change of the protein, there will be a pertur- carbon tetrachl~ride,’*~ The new experimental values reprebation of the spectrum of the ~ h r o m o p h o r e . ~ ~ - ~ ~ sent, averages of three determinations (except where Deuterium-Hydrogen Exchange.-LinderstrZmand are reported with the maximum deviaLang has interpreted the slow exchange of deu- noted) tions from the average values. terium and hydrogen in terms of hydrogen bondThe recommended average values reported in ing.36 It is worthwhile devising experiments to Tables I-IV were obtained from the reported difdetermine whether the embedding of a group (hav- fusivities by weighting them in inverse proportion ing exchangeable hydrogens) among non-polar side- to their variances. The method of Davies and Pearson’O was used to convert the ranges of the chains will lead to slow exchange. The examples cited above illustrate the possible reported diffusivities shown into unbiased estiprofound influence which hydrophobic bonds can mates of the population standard deviations from have on protein reactions. An attempt is now which the variances were determined. The recommended average values are reported together with being made to treat these effects quantitatively, as the best values of their standard deviations. was done previously for side-chain hydrogen The self-diffusion coefficient (D = cm.2/sec.) bonds.2-’3 Presumably both hydrophobic and has been related to the viscosity (7 = g./(cm.) hydrogen bonds exist between the side-chains of (sec.)), molar volume (V = ~m.~/rnole), and absonative proteins; if so, they may cooperate in pro- lute temperature ( T = OK.) by the relationl1Pl2 viding stabilization of the native structure, as was D?V‘/3/T = p (1) suggested in the case of ribonuclease.” This work was supported by the Office of Ordnance Research, ADDEDIN PR,ooF.-Some of these problems also U.(1) S. Army. have been discussed by Tanford3’ in a recent paper. (2) P. A. Johnson and A. L. Babb, J. Phys. Chem., 60, 14 (1956). (3) A. P. Hardt, D. K. Anderson, R. Rathbun, B. W. M a r and A. L. Acknowledgment.-I should like to thank George Babb, ibid., 65, 2059 (1959). (4) K. Graupner and E. R. S. Winter, J . Chem. Soc., 1, 1145 (1952). N6methy for helpful discussions of these problems. (5) H. Hiraoka, J. Osugi and W. Jono, Ren. Phys. Chem., Japan, 28, (30) D. B. Wetlaufer, J. T. Edsall and B. R. Hollingworth, J . B i d . 52 (1958). Chem., 233, 1421 (1958). (6) J. R. Partington, R. F. Hudson and K. W . Bagnall, J. chim. (31) E. J. Williams and J. F. Foster, J. A m . Chem. Soc., 81, 865 phys., 66, 77 (1958). (1959). (7) H. Watts, B. J. Alder and J. H. Hildebrand. J. Chsm. Phys., 23, (32) C. C. Bigelow and I. I. Geschwind, Compt. rend. trav. lab. Carla659 (1955). berg, 31, 283 (1960). ( 8 ) H. Hiraoka, Y. Izui, J. Osugi and W. Jono, Rev. Phys. Chem., (33) T . T . Herskovits and M. Laskowski. Jr., J . B i d . Chem., 235. Jupan, 28, 61 (1958). PC56 (1960). (9) A. P. Hardt, Ph.D. Thesis, University of Washington, 1957. S. Yaiiari and F. A. Bovey, ibid., 235,2818 (1960). S. J. Leach and H. A. Soheraga, ibid., 235, 2827 (1960). K. Linderstrgm-Lang, “Symposium on Peptide Chemiatry,” SOC.(London). Spec. Pub. No. 2, 1 (1955). (37) C. Tanford, J . Am. Chem. SOC..8 5 , 1628 (1961).
(34) (35) (36) Chem.
(10) 0. L. Davies and E. 9. Pearson, Suppl. J. Roy. Sfatiaticol SOC. 1, 76 (1934). (11) E. N. d a C. Andrade, Phil. Mog., 11,496, 698 (1934). (12) S. Glaastone, K. J. Laidler and H. Eyring, “The Theory of
Rate Processes,“ McGraw-Hill Book Co., New York. N. Y., 1941.
NOTES
June, 1961
1073
TABLE I SELF-DIFFUSION COEFFICIENTS OF BENZENE, D x lo6 C Y . ~ / S E C . Temp., ‘C.
Ref. 4
Ref. 5
1.88 f 0.01 2.15 f .05 2.40 f .03 2.67 f .06
1.83 f 0.06 2.13 f .06 2.44 f .02 2.86 f .03
This work
6.8 1.42 f 0.08 15.0 1.70 f .06 25.0 2.21 f .21 35.0 2.51 f .12 45.0 2.815 f . I 6 55.0 3.565 f .OB 65.0 4.07 f . I 6 Based on six determinations.
Recommended a v . values
Ref. 2
2.18“ f 0.13
1.87 f 0.006 2.16 f .02 2.44 f .01 2.84 f .02
original Eyring equation by including a parameter, TABLE I1 (, which accounts for the average number of viscous SELF-DIFFUSION COEFFICIENTS OF CARBON TETRACHLORIDE, shears of the neighboring molecules which causes D X los CM.~/SEC. Temp., OC.
This work
Ref. 7
Ref. 9
Recommended av. values
25.0 40.0 50.0 60.0
1.30 f 0.02 1.41 1.37 f 0.06 1.32 f 0 . 0 0 9 1.78 It .04 1.87b 1.82 1 0 . 0 2 2.00“ f .07 2.44 f .06 * Based on six determinations. * Interpolated value.
one lattice position advancement by the diffusing molecule. If their proposed value of 5.6 for 5 is used, the constant p in equation 1 would have a value of 2.08 X Values of DqV’/a/T = p calculated from the recommended average diff usivities when available, or from the new experimental values, are presented
TABLE I11 SELF-DIFFUSION COEFFICIENTS OF ETHANOL, D X lo6 CM.~/SEC. Temp.,
OC.
This work
6.8 15.0 25.0 35.0 45.0 55.0 65.0
0.618 f 0.016 0.810 f .014 1.02 f .03 1.28 f .01 1.65 f .04 2.06 ?c .04 2.61 f .03
Ref. 4
Ref. 6
Ref. 9
Ref. 2
0.80 f 0.01 1.05 f .03 1.31 f .07 1.70 f .03
0.768 1.010 1.300
1.00 f 0.05
1.02 f 0.02
Recommended a v . values
0.770 1.01 1.30 1.66
f 0.001 f ,001 f .002 f .02
TABLE IV SELF-DIFFUSION COEFFICIENTS OF METHANOL, D X 106 CM.=/SEC. Temp., OC.
This work
-5.0 1.26 f O . 0 5 1.55 f .04 5.0 1.91 f .01 15.0 2.34 f .01 25.0 2.74 f .20 35.0 40.0 3.37” f .37 45.0 3.88 -I .13 55.0 a Based on six determinations.
VALUESOF p
FOR
Ref. 8
Ref. 6
Ref. 2
1.84 f 0.01 2.21 f .02
1.933 2.32 2.71
2.37 i 0.06
3.01 f .08
TABLE V BENZENE AND ETHANOL, p X
Temp., OC.
Benzene
Ethanol
6.8 15.0 25.0 35.0 45.0 55 0 65.0
1.BO 2.02 1.85 1.89 1.80 2.05 2.04
1.32 1.37 1.44 1.49 1.55 1.59 1.67
lo9
where is a constant. Recently, Ottar,13 using a random walk approach for molecules diffusing as for p. monomers, obtained a value of 2.06 X In addition, Ree, Ree and Eyring14 modified the (13) B. Ottar, “Self-Diffusion and Fluidity in Liquids,” Oslo University Press, Oslo, Norway, 1958. (14) F. H. Ree, T. Ree and H. Eyring, l n d . En#. Chem., 60, 1036 (1958).
Ref. 9
Recommended a v . values
2.83 f 0.08
1.91 & 0.003 2.32 f .006 2.71 f .03 2.80 f .03
in Tables V and VI. Density and viscosity data were obtained from the literature. 15-17 The p values were not constant with temperature as expected. The maximum deviations from the average values for benzene, carbon tetrachloride, ethanol and methanol were 6.7, 3.6, 12.1 and 6.27,, respectively. Moreover, the deviations were, in general, not random; and the values of P tended to increase with temperature. For ethanol and methanol, where association is known to occur, the molar volumes should not properly be based on the monomeric species. Consequently, the values (15) American Petroleum Institute Research Project 44, “Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds,” Carnegie Press, Pittsburgh, 1953. (16) “Handbook of Chemistry and Physics,” 33rd Edition, Chemical Rubber Publishing Co., Cleveland, Ohio, 1951. (17) J. Timmermans, “Physico-Chemical Constants of Pure Organic Compounds,” Elsevier Publishing Go., Inc., New York, N . Y.,
1Q60.
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).
