784
F. J.
The Journal of Physical Chemistry, Vol. 82, No. 7, 1978
(10) T. Sakurai and A. Takahashi, unpublished results. (11) T. Sakurai, A. Takahashi, and Y. Komaki, J . Nucl. Sci. Techno/., 11, 74 (1974). (12) U. Merten, J . Phys. Chem., 63, 443 (1959). (13) (a) W. E. Bell, U. Merten, and M. Tagami, J. Phys. Chem., 65, 510 (1961); (b) W. E. Bell and M. Tagami, bid., 87, 2432 (1963). (14) R. C. Rea and T. K. Sherwood, "The Properties of Liquids and Gases", McGraw-Hill, New York, N.Y., 1966, p 520. (15) 0. Kubaschewski and E. L. Evans, "Metallurgical Thermochemistry", Pergamon Press, New York, N.Y., 1958, p 151. (16) (a) N. G. Schmahl and P. Sieben, "National Physical Laboratory Symposium No. 9, The Physical Chemistry of Metallic Solutions and Intermetallic Compounds", Vol. 1, Her Majesty's Stationary Office, London, 1959, p 2k; (b) T. Kikuchi, T. Kurosawa, and T. Yanahashi,
Millero, A. Lo Surdo, and C. Shin
J . Jpn Inst. Met., 28, 497 (1964). (17) T. Sakurai and A. Takahashi, unpublished results. (18) E. Cartmell and G. W. A. Fowles, "Valence and Molecular Structures", Butterworths, London, 1961, p 49. (19) H. H. Claassen, H. Selig, J. G. Malm, C. L. Chernick, and E. Weinstock, J . Amer. Chem. Soc., 83, 2390 (1961). (20) A. J. Edwards and E. R. Steventon, J . Chem. Soc. A, 2503 (1968). (21) A. J . Edwards and G. R. Jones, J . Chem. SOC. A , 2074 (1968). (22) C. G. Barraclough, J. Lewis, and R. S. Nyholm, J . Chem. Soc. A, 3552 (1959). (23) A. M. Mathieson, D. P.Mellor, and N. C. Stephenson, Acta Crystalbgr., 5. 185 (19521 .(24) Reference 18, p 192. (25) G. Manevy et al., French Report CEA-N-1479, 243 (1971). \
The Apparent Molal Volumes and Adiabatic Compressibilities of Aqueous Amino Acids at 25 OC Frank J. Millero,*+ Antonio Lo Surdo,+ and Charles Shin$ Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida 33 149 (Received October 21, 1977) Publication costs assisted by the National Science Foundation
The apparent molal volumes and adiabatic compressibilities of 15 amino acids in water have been determined at 25 "C from precise density and sound measurements. The electrostriction partial molal volume and compressibility of the amino acids were determined from p(meas) - P(int) and I?'(meas) - I?'(int). The values of P ( i n t ) have been estimated from P of the uncharged amide isomers and PCryst, the crystal molal volume. Both P(e1ect) and P(e1ect) yield values of 4.1 f 0.4 for the number of water molecules hydrated to the amino acids. Group contributions for the partial molal volume and adiabatic compressibilitieshave been determined from the amino acids. The volume results are in good agreement with the values calculated by other workers on soluble organic solutes.
Introduction Recently there has been an increased interest in the state of water in the living cell. Since most biological macromolecules are physiologically active in aqueous solutions, a knowledge of water-protein interaction is necessary to understand the role of water solvated to soluble organics in the living cells. A better understanding of this type of interaction may be obtained from dipolar ions. Since amino acids are zwitterions in aqueous their volume and compressibility properties should reflect structural interactions with water molecules as in the case of electrolytes. Many experiments4on the properties of protein solutions indicate that ca. 0.3 g of water per gram of dry protein are bound or hydrated in aqueous solutions. Work on the volume properties of proteins and some amino acids have shown that they undergo a decrease in volume upon dissolving in ~ a t e r . ~ -This l ~ decrease in volume upon dissolution is similar to what occurs for electrolyte~l~ and can be attributed to electrostriction due to water-protein, and water-amino acid interactions. The number of water molecules determined from the electrostriction of proteins16 and amino a c i d ~ (using ~ ~ J ~methods that have been applied to electrolytes)lg agree very well with the values determined by other Although these results might indicate that proteins behave as electrolytes, the effect of pressure on the specific volumes12 indicate that the so-called "bound water" behaves more like water solvated to soluble organic solutes.16 To better
understand the hydration of proteins and amino acids, basic physico-chemical properties are needed. In this communication, we report on the volume and compressibility measurements made on amino acids in water at 25 "C. Experimental Section The amino acids used in these studies were obtained from ICN Pharmaceuticals, Inc., and were used without further purification. All solutions were made by weight with ion-exchanged (Millipore Super Q) water. All weights were vacuum corrected. The densities were measured a t 25 "C to f 3 X g cm-3 with a vibrating flow densimeter (Sodev, Inc.). The values of Ad = d - do, where d and do are the densities of the solution and water are listed in Table I.2oThe system was calibrated with N2gas and ion-exchanged water using the densities of Ke11.21 The accuracy ( f 3 ppm) of the system has been determined by measuring the densities of standard seawater solutions.22 The sound velocities were measured a t 2 MHz to a precision of f0.02 m s-l using a "sing around" sound velocimeter (Nusonic, Inc.). The system was calibrated with pure water using the sound velocities of Del Grosso and made^-.^^ The accuracy ( f 0 . 1 m s-l) has been determined by measuring the speed of sound in seawater solutions.24 The relative sound velocities (Au)of the aqueous solutions at 25 "C are listed in Table 120 and were determined from the frequency measurements using
TRosenstiel School of Marine and Atmospheric Science, M i a m i Fla.
33149.
* Chemistry Department, University of Miami, Coral Gables, Fla.
33100.
0022-3654/78/2082-0784$01 .OO/O
0 1978 American Chemical Society
The Journal of Physical Chemistry, Vol. 82, No. 7, 1978 785
Molal Volumes and Compressibilities of Aqueous Amino Acids
TABLE 11: Limiting Values of Apparent Molal Volumes, Aqueous Amino Acids at 25 C a
@v', Adiabatic Compressibilities,
@VO,
Compound
cm3 mol"
@K(Q',
SV,and SK(S)for
1O4@K(S)'9
SV
ub
cm3 mol-' bar-'
104sK(S)
u( 104)c
0.28 0.60 I- Alanine 0.13 dl-Alanine 2- Arginine 0.20 0.07 dl-Aspartic acid 0.26 1-Cysteine 0.38 Glutamic acid 0.44 Glycine 0.29 Histidine 0.56 2-Leucine 0.25 d2-Methionine 1.48 Phenylalanine 0.11 1-Proline 0.23 d-Tryptophan 0.23 1-Valine a The least-squares program used to obtain these coefficients had a weighting factor related to the errors in $JV and Standard error in @K(s), cm3 mol-' bar-'. Standard error in @v,cm3 mol-'. d -Alanine
60.43 60.47 60.50 127.34 73.83 73.44 85.88 43.19 98.79 107.74 105.35 121.48 82.83 143.91 90.78
0.778 0.661 0.618 1.623 9.588 1.376 6.652 0.864 3.295 -0.059 1.072 11.731 0.466 0.233 0.250
where u and uoare the speed of sound in the solution and in water, f and f O are the pulse repetition frequencies in solution and water, and 7 is the electronic delay time. The value of r was determined by calibration with (Millipore Super Q) ion-exchanged water at various temperatures. The temperature of the various thermostated bath systems regulating the densimeter and sound velocimeter was set to f0.002 "C using a platinum resistance thermometer (calibrated by the National Bureau of Standards), and a G-2 Mueller Bridge.
Results The apparent molal volumes, $", and the adiabatic apparent molal compressibilities, $K(S), of the amino acids solutions were determined, respectively, from the density, d , and adiabatic compressibility, fist of the solution using the equations M (do- d)103 $v += ; mddo and
(3) where do is the density of water, m is the molality, M is the molecular weight of the solute, and fiso = 44.773, X lo4 bar-I is the adiabatic compressibility for water. The adiabatic compressibilities ( P S ) of the aqueous solutions a t 25 "C were calculated from the sound speeds (u) using
Ps
(4)
= l/u2d
The densities and sound velocities were determined from the relative densities and sound speeds given in Table I by using do = 0.997 045 g 21 and uo = 1496.69 m s-1.23 The values of and $K(S) are listed in Table I,2oand are plotted, respectively, vs. m in Figures 1 and 2. The curves represent the least-squares best fit. The values of 4" and &(s) were least-squares fitted t o the equations $v = $ v o + S v m
(5)
and @K(S) = $K(S)
0
+ SK(S)m
(6)
where $Vo = F'and $K(S)O = Ro are, respectively, the infinite dilution partial molal volumes and adiabatic partial
0.09 0.02 0.07 0.12 0.08 0.03 0.01 0.02 0.04 0.05 0.02 0.08 0.08 0.14 0.01
-25.53 -25.56 -25.03 -26.62 -33.12 -32.82 -36.17 -27.00 -31.84 -31.78 -31.18 -34.54 -23.25 -30.24 -30.62
5.01 4.75 4.08 12.06 47.78 7.92 16.06 4.56 -13.91 13.61 14.28 36.26 5.79 -41.10 8.43
@K(s).
TABLE 111: A Comparison of the Infinite Dilution Partial Molal Volumes for Amino Acids Obtained in This Study with Literature Values
@vo,cm3 mol-' Compound
This work
Literature values
Alanine Glycine
60.47 60.61,a60.6,a60.6,b61,c60.47d 43.19 43.3,a43.22,e43.29,f43.20,g 43.5,b 44c Histidine 98.79 99.3h 107.74 107.5,a 107.7 5d Leucine Phenylalanine 121.48 121.2,a121.3C 82.83 81.0,a81.0,b81c Proline 143.91 144.1b Tryptophan Valine 90.78 91.3,a90.78,g91,C91.05b a Reference 14. Reference 1. Reference 2. RefReference 28. Reference erence 29. e Reference 25. 27. Reference 26.
molal compressibilities, and SVand SK(S) are the experimental slopes. The values of @vo,$Kcsf, SV,and SK(S) for the amino acids studied at 25 "C are listed in Table I1 along with the standard deviations (~7). The infinite dilution partial molal volumes of the amino acids reported in the literature1~2~5~8~14~18~2~2g are compared with our results in Table 111. Our results are in good agreement with the literature values. There is little compressibility data for the amino acids in the literature. The infinite dilution apparent molal compressibilities of Gucker and Haagl' for alanine and glycine (respectively, 104$K = -24.56 and -26.84) are in good agreement with our $K(S)O values (Table 11). Shown in Figure 1 are plots of $V vs. m for the amino acids at 25 "C. The of the amino acids is a linear function of the molal concentration. With the exception of leucine, all amino acids have positive slopes. Large positive slopes are found for amino acids having aromatic rings and terminal -(O=)C-OH and H,N-(HN=)C-NHgroups (Table 11). Amino acids with aliphatic and sulfur groups, and cyclic groups have smaller slopes. Leucine has a small negative slope. Histidine with two nitrogens on a ring has a large positive slope, while tryptophan with one nitrogen on a aromatic ring has a smaller positive slope (Table 11). Shown in Figure 2 are plots of @K(S) vs. m for the amino acids at 25 "C. The $K(s) of the amino acids are linear functions of the molal concentration. The slopes for the compressibility data behave similarly to the slopes of the volume data, i.e., positive SK(s,slopes are observed for all
786
'
The Journal of Physical Chemistry, Vol. 82, No. 7, 1978 128 2
F. J. Millero, A. Lo Surdo, and C. Shin
I
128.0
--
I27 8
I44 2
I27 6
1440
1274
-- 143 8
0
0
E 1272
1436
-6 121 8
"E
le;
910
''
121 6
90.8
121 4 74 0
826
73 8
'
73 6
0
04
0.2
0.6
0
001
m
002 rn
003
Q,04
1 -8 6 6
742
864 862 -
- 734
/
'-
DL- Alanine
"
2 988
"E
2 604
66 0 6 60 4
60 2
606
:46
1 - D-Alanine
vL
.
98 6 IO8 0
.0.04.
008
00;
~-ieucine
Glycine
430
105.2
'
0
02
' 08
06
04
IO
m
4
0.0;
107 8
43 2
Flgure 1. Plot of
1.
vs. m for amino acids in water at 25
105.0
0
0.05
0.10
0.15
t !O
m OC.
amino acids studied with the exception of histidine and tryptophan which have large negative slopes. Amino acids with complex functional groups have greater positive slopes when compared with the slopes of the amino acids having aliphatic and sulfur groups.
Discussion The partial molal volumes of the amino acids at infinite dilution, as shown in Figure 3, are a linear function of the molecular weight. These results indicate that the volume contribution of the hydrocarbon portion of the amino acids is proportional to the molecular weight (similar to other organic solutes) and the volume contribution due to NH3+CHC(=O)O- is not strongly affected by the hydrocarbon groups. A similar correlation of the partial molal compressibilities does not exist. This is expected since the compressibilities (which vary from -23 to -36 X are more closely related to solute-water interactions. These results led us to examine the additivity properties for the hydrocarbon portion of the amino acids. The first investigation of the additivity properties of group partial molal volumes in homologous series of or-
ganic solutes in water was made by T r a ~ b e . ~ ORecent studies of partial molal volumes of tetraalkylammonium halides,31azoniaspiroalkane bromides,32 a l ~ o h o l s ,al~~,~~ kylamines hydro bromide^,^^^^^ cyclic amines hydrobromides,37 aliphatic acids,38dicarboxylic a c i d ~ , and ~~J~ sodium salts of aliphatic and dicarboxylic a ~ i d shave ~ ~ , ~ ~ been utilized to calculate the group partial molal volumes, P(group). Values for P of -CH3, -CH2-, and -CH groups are given in Table IV. For methylene groups on carbon atoms, P(-CH2-) = 15.9 cm3 mol-l which is in excellent agreement with p(-CH2-) = 16.1 cm3 mol-1 found by T r a ~ b e .The ~ ~ values of -CH2- on nitrogen are smaller than those on carbon. For methyl groups P(-CH3) = 18.1 cm3 m01-1,31,32 Also listed in Table IV are the various groups contributing to the of aqueous amino acids solutions_at 25 "C obtained from the literature data. The values of V" for H2N+NH; I
-N+-
26.3 17.8 14.0 18.4
From CH,(CH,),COONaa From [CH,]n(COONa),a~ From CH,(CH,),NHIC From cyclic aminesd
11.7 From R,NX and azoniaspiroalkane halidese
i
-CH, -CH,-
18.1 On carbon atoms from R,NXeif 16.1 From Traubeg 15.9 On carbon atoms from R,NXepf and RNH,Xh 14.8 On H,N+-CH-C( =O)-0-, from I a ,w -aminocarboxylic acidsz
14.1 On cyclic aminesd 13.8 From azoniaspiroalkane halidese I
-CH
17.8, and P(-CH2-) = 15.9 cm3 mol-', we obtain
-
Vo(glycine),ld
-
= vO(-NH,')
+ Vo(-CH,-) +
Vo(-C(=O)-O-) = 47.7 cm3 mol-'
6
110
n' E 90 0
I
12.0 From alcohols'
I
12.4 Estimated by additivity from -CH, and -CH,- groups on R,NX I
-c-
9.1 Estimated by additivity from -CH,, -CH,, +CH and -H 9.9 Estimated by Traube at 16 "Cg -H 3.0 Estimated from -CH,, -CH,- from R,NX, and -CH from alcohols 3.1 Estimated by Traubeg -S15.5 Estimated by Traube at 1 6 "Cg -OH 12.0 From mono and dialkylamino alcoholsh 11 From alcoholsj a Reference 38. References 38 and 39. References 35 and 36. Reference 37. e Reference 32. f Reference 31. References 1, 2, and 30. Reference 34. Reference 14. Reference 33. I
J
obtained from these data are in good agreement with our group values. It should be noted that these group values contain contributions due to the intrinsic size of the group, P(int), as well as hydration and hydrophobic effects which are especially important with aliphatic side chains and side chains that can hydrogen bond with water. The group V's can be used to estimate the VO of glycine. From the groups P(-NH3+) = 14.0, P(-C(=O)-O-) =
(7)
For p(-C(=O)-O-) = 26.3 cm3 mol-l, ~(glycine),,l,d = 56.2 cm3 mol-'. These estimates are in poor agreement with the measured value of 43.2 cm3 mol-'. The measured value is 4.5-13.0 cm3 mol-' lower than predicted. These results indicate that the decrease in volume due to -NH3+ and -C(=O)-0- on glycine are greater than on aliphatic compounds. This is presumably due to the inductive effect of the two charged groups increasing the hydration. Similar effects are found for dicarboxylic acids and their Na salts. In Table V we list the various groups contributing to the P of the amino acids. These values are determined from the experimental data and are compared with the group values calculated from first principles using the literature values given in Table IV. While most of these calculated results are in excellent agreement, the last two entries are in poor agreement (Table V), even when using the lower value for -COOH (Table IV). At 25 "C, the isoelectric points of aspartic and glutamic acids are about pH 2.8 and 3.2, re~pectively.~~ At this pH, the amino group carries a positive charge and the two carboxyl groups carry one equivalent of negative charge between them, most of it on the a-carboxyl group, which has the lower pK value.42 Thus, the -COOH group on the side chains of these acids is expected to be ionized and, therefore, it could account for the poor agreement in the last two entries in Table V. If we assume that the -COOH group is ionized and use the P(-COO-) values (Table IV), a better agreement between observed and calculated values is obtained for the last two entries listed in Table V. Similarly, the isoelectric point of arginine is close to pH ll.42 At this pH, ionization of the HzNC(NH)z- group can occur and the value of P for HzNC(NH)2(CH2),-is for some ionized form of this group (Table V). Although the values of for the amino acids are not linear functions of the molecular weight, it is possible to estimate group contributions for Ets! from the data. Literature data are available for the Kso for alcohols,43 amines, and the tetraalkylammonium salts.44 From these results, it is possible to estimate KSovalues for -CH2- and -CH3. These values are given in Table VI along with the values estimated from the amino acids. Further studies on a large number of organic solutes in water are needed before the reliability of these group contributions can be asserted. The partial molal volumes of the amino acids can be examined by a simple model
-
Vo(amino acid) = Vo(int)
+ vo(elect)
(8) where p ( i n t ) is the intrinsic partial molal volume of the amino acid and P(e1ect) is the electrostriction partial molal volume due to the hydration of the amino acid. The P ( i n t ) is made up of two terms, the van der Waals volume ( and the volume due to packing effects ( Vpo)
vwo)
-
Vo(int) =
Vwo+ Vpo
(9) The V(e1ect) can be estimated from the experimentally measured P s providing a reasonable estimate can be made for P ( i n t )
-
Vo(elect) = p o ( a m i n o acid) - v o ( i n t ) (10) Earlier ~ ~ r k e r have ~ ~estimated ~ , ~ values ~ , of ~ P~( i n*t ) ~ ~ ~ ~ for amino acids by assuming they are equal to the partial molal volume of the equivalent amide. Since experimental
Molal Volumes and Compressibilities of Aqueous Amino Acids
The Journal of Physical Chemistry, Vol. 82, No. 7, 1978 789
TABLE V: Partial Molal Volume of Various Functional Groups Calculated from Amino Acids at Infinite Dilution in Water at 25 'C Vo, cm3 molp1 From amino acids
Group -CH,-CH, -CH(CH3), -CH,CH(CH3), -CH,SH -SH
16.9 17.3 47.6 64.5 30.3 62.2 14.4
e m 2 -
78.3
-(CH%)2SCH3
H-N
H
8 \
Calcda 15.4 18.4 49.2 64.6 29.9 60.7
Method
A
1.5 -1.1 -1.6
From leucine-valine From alanine-glycine From valine-glycine From leucine-glycine From cysteine-glycine From methionine-glycine Estimated by additivity from -CH,SH and -CH,- from R,NX
-0.1 0.4 1.5
From phenylalanine-glycine
100.6
CH2-
I
From tryptophan-glycine
55.7
From histidine-glycine
84.2
From arginine-glycine
@H2-
NH I1
H,N-C-NH(CH,),0 II
HO-C-CH,-
30.6
41.2b 49.7'
-10.6 -19.1
From aspartic acid-glycine
42.7
56.6b 65.1'
-13.9 -22.4
From glutamic acid-glycine
0 /I
HO-C-(CH,),-
a Calculated using p ( - C + ) = 9.4 (average value), v o ( ~ H=) 3.0, vo(-S-) = 11.4, and vo(-COOH) = 25.8 and 34.3 em3 Vo(-COOH) = 34.3 cm3 mol-!. mol-' (Table IV). b Vo(-COOH) = 25.8 cm3 mol-'.
'
P(e1ect) = V'- P(isomer). The values of P(e1ect) range data are not available for all the necessary amides, we have from -11.6 to -39.0 (av -22.3) cm3 mol-' for p = 0.6, and estimated the various amides by using the group contributions discussed earlier and the P of g l y c ~ l a m i d e . ~ ~-8.7 ~ ~ ~to -29.2 (av -16.3) cm3mol-' for p = 0.634. In contrast, the values of P(e1ect) estimated from the isomer method The values of P(e1ect) calculated in this manner are given range from -10.8 to -15.1 (av -13.1) cm3 mol-l. in Table VII. The values of P(e1ect) vary from -10.8 to -15.1 cm3 mol-l (av -13.1 cm3 mol-') and are in good The values of V'(e1ect) estimated by these methods are agreement with earlier estimate^.'^^^' Since amides are in reasonable agreement. For amino acids with only hydrocarbon side chains P(e1ect) is --12 to -24 cm3mol-l hydrated, one might expect the magnitude of the values of P(e1ect) calculated in this manner to be too low. for p = 0.6 and --a to -16 cm3 mol-' for p = 0.634 (Table Another approach that can be used to estimate V'(int) is VII). Since the packing densities of the amino acids could from crystal molar volumes, Pcryst = (mol wt)/dcryst, vary as much as 14%, the values of P(e1ect) estimated making the appropriate corrections for packing densities. from P(cryst) have larger errors (5 cm3 molw1)than those estimated from the isomer amides. The values of P(e1ect) The packing density ( p ) is defined by estimated from the isomer amides is --13 cm3 mol-'. For p = VwO/VOcryst = Vw"( VWO VPO) (11) the amino acids, P(e1ect) is much larger in magnitude than predicted from theoretical models of F u o ~ sand ~~ where Vwo is the van der Waals volume and Vpo is the Kirk~ood~~ packing volume in the crystal. The packing density for molecules in organic cyrstals is about 0.7.51 This gives Vwo 3p2N aD = 0.7Pcryst. The packing densities of organic solutes in Vo(elect) = water have values of 0.57-0.59 for hydrocarbons, alcohols, 4b3D2 (aP)T and carboxylic acids52and 0.61 for amines.53 The packing where y is the dipole moment, N is Avogadro's number, density for random packing spheres is 0.634.54 If we use b is the radius of a sphere containing the dipole, D is the the values of 0.60 and 0.634, the P(int) for the amino acids dielectric constant, and P the pressure. For glycine Pin solution is given by (elect) = -4 cm3 mol-' (Yayanos13) compared with the Vo(int) = (0.7/0.6)~0cry,t (12) calculated value of -13 cm3 mol-'. The decrease in volume due to electrostriction can be and related to the number of water molecules (nH)hydrated Vo(int) = (0.7/O. 634) to the amino acid byI9 (13) The values of P ( i n t ) for the amino acids have been esdetermined from timated from eq 12 and 13 using Pcryst the work of Berlin and PallanshS7The values of P(e1ect) where pEo is the molar volume of electrostricted water and calculated from the values of P ( i n t ) using eq 10 are given VBois the molar volume of bulk water (18.069 cm3 mol-' in Table VI1 and are compared with those calculated from at 25 "C). This model assumes that for every water
+
~
vocryst
790
The Journal of Physical Chemistry, Vol. 82, No. 7, 1978
TABLE VI: Apparent Molal Adiabatic Compressibilities of Various Functional Groups Calculated from Amino Acids at Infinite Dilution in Water at 25 " C
F. J. Millero, A. Lo Surdo, and C. Shin
TABLE VII: Values of Vo(elect)for Amino Acids Estimated by Various Methods
-
-Vo(elect), cm3 mol-'
104@K(S)0;
Group
cm3 molbar-' (from amino acids)
Method
0 il
H,N+-CH-C-0I
-CH,-
-CH,
-CH(CH3)2
-CH,CH(CH,), -CH,SH -(CHZ)ZSCH3
Assumed value from glycine -1.16 CH, next to H,N+CHC(=O)O- from leucine-valine CH, next to terminal -3.05 -COOH from glutamic acid-aspartic acid -1.6 t 0.6 From alcoholsa -1.2 * 0.8 Average value from R,NXb 1.63 From alanine-glycine 2.0 * 0.2 From methylaminesb From alcoholsa 0.8 -3.62 From valine-glycine From leucine-glycine -4.78 From cysteine-glycine -5.82 From methionine-glycine -4.18 -27.00
Amino acid
a
b
Alanine Arginine Aspartic acid Cysteine Glutamic acid Glycine Histidine Leucine Methionine Phenylalanine Proline Serine Tryptophan Valine Average
15.34 26.05 21.09 21.10 23.74 11.62 29.40 23.39 27.44 25.09 14.77 17.20 88.95 17.10 22.31
11.26 17.83 16.00 16.33 17.86 8.68 22.53 16.36 20.32 17.23 9.54 13.05 29.15 11.32 16.25
a Vo(ele_ct)=
C _______
7'- x 0 ( i n t ) , whgre VJint)
13.0d 13.0 13.0 13.0 13.0 13.1d 10.Bd 13.0 13.0 13.7d 13.'Bd 12.gd 15.1d 13.0 13.10 =
(0.7/O.6)Voc,,t. VO(dect)= VoL Vo(int),,kwhere Vo(int),,l = (0.7/0.634)V0c,st. Vo(elect)= Vo Vo(int),where Vo(int)= V0(isomer) and vo(isomer)= Vo(glycolamide) + To( amino acid) - To( glycine). Reference 18; ref 1,p 159.
0 /I
HO-C-CH,0
-6.12
From aspartic acid-glycine
-9.17
From glutamic acidglycine
-7.54
From phenylalanineglycine
-4.84
From histidine-glycine
-3.24
From tryptophanglycine
il
HO-C-( CH,),-
H-%H2-
EO(elect)= E o ( a m i n o acid) - E o ( i n t )
II
Reference 39.
From arginine-glycine
Reference 43.
molecule taken from the bulk phase to the region near the amino acid, the volume is decreased by ( VEo- VBo). For Using electrolyte solutions EO - VBo) = -3.0 cm3 this value of ( V E o - v B o ) and the values of P(elect), calculated by various methods (Table VII), the nH values were estimated from eq 15. Individual values of nH range, respectively (columns a to c, Table VII), from 3.9 to 13.0 (av 7.4 f 2.4), from 2.9 to 9.8 (av 5.4 f 1.8),and from 3.6 to 5.0 (av 4.4 f 0.3). Although these values are in reasonable agreement, the values of nH calculated from p(elect) in column a, Table VII, are probably too large. For all the methods used, the higher values of nH occur for amino acids with side chains which can hydrogen bond with water. By differentiating eq 15 with respect to pressure, one obtains (assuming a V E o / a P and a n H / a P = 0) Eo(elect) = - [aVo(elect)/aP] = nH(avBo/aP)(16) where (aVBn/aP) = -/3BoVBo is related to the compressibility @Bo) of bulk water. Upon rearranging and substituting for aVBo/aP, we have 12H =
-KO(elect)/PB"Bo
(18) Since one would expect P ( i n t ) to be small (it is less than 5 X cm3 mol-I b a r 1 for ionic crystals and many dissolved organic solutes in water), as a first approximation, one can assume Ro(int) = 0. The Eto for a few amides have been measured and are all -3 X cm3 mol-' Thus, one might expect P ( i n t ) for the amino acids to be equal to -3 X lo4 cm3mol-l bar-l. The values of P(e1ect) calculated from eq 18 assuming Ro(int) 3.0 X cm3mol-l bar-' are given in Table VIII. For glycine and alanine, we have used Ro(isomer) = 2.70 X lo-* and 3.35 X cm3mol-' b a r Lfor glycolamide and lactamide, re~pectively.'~For P ( i n t ) = 0, the values of P(e1ect) are those given in Table 11. The values of nH calculated from eq 17 using the Ro(elect) values determined by these two methods are also given in Table VIII. Individual values of nH range from 2.9 to 4.5 (av 3.6 f 0.5) for P ( i n t ) = 0, and from 3.2 to 4.8 (av 4.0 f 0.5) for Ro(int) = 3 X cm3 mol-' bar-'. These values are in good agreement with the values calculated from P(e1ect). The hydration model as well as the continuum modellg indicate that P(e1ect) is directly proportional to P(e1ect):
-
NH
H,N-C-NH(CH,),- -0.38
The Ro(elect) can be calculated from the experimental values of Ro(amino acid) from
(17)
-
Vo(elect) = k Ro(elect)
(19)
where, for the hydration model and for the continuum model for ionic solutes (a l n D / a P ) k= (a2 In D/aP2)- 2(a In D/aP)2
At 25 " C , using (a In D / a P ) = 47.10 X lo4 and (a2 In D / a P ) = -71.53 X given by Owen et al.57the continuum model yields k = 4.1 X lo3 bar. [In previous studies19 eq 21 was given without the factor of 2 in front of the term (a In D / a P ) 2 which gives a slightly higher value of k, i.e., h = 5.0 X l o 3 bar.] Differentiation of eq 14 with respect to pressure and substituting into eq 19 yields eq 21 for a zwitterion in a
The Journal of Physical Chemistry, Vol. 82, No. 7, 1978 791
Molal Volumes and Compressibilities of Aqueous Amino Acids
TABLE VIII:
Values of K s o ( e l e c t ) a n d n H for Amino A c i d s E s t i m a t e d by V a r i o u s M e t h o d s nH
Amino a c i d
d-A l a n i n e 1-Alanine dI- A l a n i n e l-Arginine dl-Aspartic acid 1-Cysteine Glutamic acid Glycine Histidine 1-Leucine dI-Methionine Phenylalanine I-Proline d-Tryptophan 1-Valine Average
-104Kso(elect),a c m 3 m o l - ' bar-'
28.88 28.91 28.37 29.62 36.12 35.82 39.17 29.70 34,84 34fi78 34.18 3%54 26.25 33.24 33.62 32.74 i 3.84
From c o m p r e s s i b i l i t y
From v o l u m e
b
C
d
e
3.16 3.16 3.09 3.29 4.09 4.06 4.48 3.34 3.94 3.93 3.85 4.28 2.87 3.72 3.78 3.67 i. 0.49
3.57 3.57 3.51 3.66 4.46 4.43 4.84 3.67 4.29 4.30 4.22 4.64 3.24 4.11 4.16 4.04 i 0.47
3.41 3.41 3.41 5.40 4.85 4.95 5.41 2.63 6.83 4.96 6.16 5.22 2.89 8.83 3.43 4.79 ~t 1.67
3.94 3.94 3.94 3.94 3.94 3.94 3.94 3.97 3.27 3.94 3.94 4.15 4.18 4.58 3.94 3.97 i 0.26
a Fs'(elec4) = z ' ( a m i n o acid) - ffO(int) w h e r e ff"(int) = K o ( i s o m e r ) for g l y c i e (2.7 X 1 0 ' 4 1 a n d alanineJ3.35 X ref 17, a n d Ko(int)= 3 X l o T 4for t h e o t h e r a m i n o acids. QH = -Kso(elect)/VBoflp,o where Ks'(e1ect) = K o ( a m i n o acid). n H = - r s o ( e l e c t ) / v B 0 p B o w h e r e r s o ( e l e c t ) given in c o l u m n 1. n H = v 0 ( e l e c t ) / - 3 . 3 where v o ( e l e c t ) = v ' ( a m i n o a c i d ) ( 0 . 7 / 0 . 6 3 4 ) ~ o ( c r y s t ) , c o l u m n b of T a b l e VII. e n H = v 0 ( e l e c t ) / - 3 . 3 whereV'(e1ect) = v o ( a m i n o acid) - V o ( i s o m e r ) , c o l u m n c of T a b l e VII.
*
continuum. Thus, at 25 "C, h = 4.1 X lo3 bar for both dipolar ions and ionic solutes in a continuum model. The results are too scattered for a plot of i"(e1ect) vs P(e1ect) to be meaningful. However, the slope, h = V'(elect)/ Ko(elect), calculated for our best average estimate of i"(e1ect) and P(elect), is found to be 4.5 (f0.5) X lo3 bar which is in reasonable agreement with the continuum model h value. For various electrolytes the hydration model yields h = 3.6 X l o 3 bar, whereas for ion pair formation, and for ionization of weak acids and bases, h is 3.7 X l o 3 and 4.7 X lo3 bar, respe~tive1y.l~The experimental values of these slopes, h , are in reasonable agreement with the continuum model. The calculated value from h = 4.1 X lo3 bar yields a value of ( VEo- VBO) = -hT'Bo/3Bo = -3.3 cm3 mol-l which is smaller than the value (-2.7 cm3mol-l) for ions. By using this lower value, (VEo - VBo) = -3.3 cm3 mol-I, and the P(e1ect) listed in columns b and c, Table VII, the nH values were recalculated from eq 15. The results are given in Table VIII, along with the nHvalues determined from the compressibility data. The values of nH calculated, by several methods, from the volume and compressibility data are in good agreement. For the volume data individual values of nH range from 2.6 to 8.9 (av 4.8 f 1.7) and from 3.3 to 4.6 (av 4.0 f 0.3), columns c and d, Table VIII, respectively. Combining the values of nH from the compressibility and volume data, we obtain an average of 4.1 water molecules hydrated to the NH3+CHC(=O)Ogroup. In summary, volume and compressibility data have been determined for aqueous amino acids solutions and the results have been used to estimate the number of hydrated water molecules. The electrostriction partial molal volume and compressibility were determined from the measured i" and KO, and i"(int) and P ( i n t ) . The V(int) were and i" of estimated from the crystal volume (i"cry,t) uncharged isomers. Group contributions for i" and Eto have been determined by several methods. The volume results are in good agreement with the values calculated by other workers. This simplistic approach of relating the volume and compressibility behavior with purely Coulombic interactions seems successful in obtaining credible values for such properties as apparent hydration numbers
when applied to electrolytes and amino acids in aqueous solutions. However, this approach tends to mask contributions from other types of interactions (i.e., hydrophobic hydration) particularly in the case of proteins, amino acids, and soluble organic solutes which have side chains that can hydrogen bond with water.
Acknowledgment. The authors gratefully acknowledge the valuable comments provided by Professor John T. Edsall. They also acknowledge the support of the Office of Naval Research (N00014-75-C-0173) and the Oceanographic Section of the National Science Foundation (OCE73-00351-A01) for this study. Supplementary Material Available: Table I consists of experimental data for 15 amino acids in water at 25 O C . The data are relative density and sound speed, and apparent molal volume and adiabatic compressibility (6 pages). Ordering information is available on any current masthead page. References and Notes (1) E. J. Cohn and J. T. Edsall, "Proteins, Amino Acids and Peptides as Ions", Reinhold, New York, N.Y., 1943. ( 2 ) J. P. Greenstein and M. Winitz, "Chemistry of the Amino Acids", Vol. I,Wiley-Interscience, New York, N.Y., 1961. 1 J. W. Larson and L. G. Hepler, "Solute-Solvent Interactions", J. F. Coetzee and C. D. Richie, Ed., Marcel Dekker, New York, N.Y., 1969. 1 G. Ling in "Water and Aaueous Solutions". R. A. Horne. Ed.. Wiley-Interscience, New York, N.Y., Chapter 16, 1972. H. Chick and C. J. Martin, Biochem. J., 7, 92 (1913). T. L. McMeekin, M. Groves, and N. J. Hipp, J . Polym. Sei., 12, 309 (1954). E. Berlin and M. J. Pallansch, J. Phys. Chem., 72, 1887 (1968). J. Bernhardt and H. Pauly, J . Phys. Chem., 79, 584 (1975). M. 0. Dayhoff, G. E. Perlmann, and D. A. MacInnes, J . Am. Chem. Soc., 74, 2515 (1952). M. J. Hunter, J. Phys. Chem., 70, 3285 (1966). H. B. Bull and K. Breese, J. Phys. Chem., 72, 1817 (1968). F. J. Millero, G. K. Ward, and P. V. Chetirkin, J. Bid. Chem., 251, 4001 (1976); ibid., in press. A. A. Yayanos, J. Phys. Chem., 76, 1783(1971). J. Kirchnerova, P. G. Farrell, and J. T. Edward, J. Phys. Chem., 80, 1974 (1976). F. J. Millero, Chem. Rev., 71, 147 (1971). F. J. Millero, G. K. Ward, and P. V. Chetirkin, J . Sol. Chem., to be submitted. F. T. Gucker, Jr., and R. M. Haag, J . Acousf. SOC.Am., 25, 470 (1953). E. J. Cohn, T. L. McMeekin, J. T. Edsall, and M. H. Blanchard, J. Am. Chem. Soc., 56, 784 (1934).
792
The Journal of Physical Chemistry, Vol. 82,No. 7, 1978
(19) F. J. Millero, G. K. Ward, F. K. Lepple, and E. V. Hoff, J. Phys. Chem., 78, 1636 (1974). (20) Available as supplementary material. See paragraph at the end of the paper. (21) G. S. Kell, J. Chem. f n g . Data, 15, 119 (1970). (22) F. J. Millero, D. Lawson, and A. Gonzalez, J . Geophys. Res., 81, 1177 (1976). (23) V. A. Del Grosso and C. W. Mader, J . Acoust. SOC.Am., 52, 961 (1972). (24) F. J. Millero and T. Kubinski, J . Acoust. SOC.Am., 57, 312 (1975). (25) H. D. Ellerton, G. Reinfelds, D. E. Mukahy, and P. J. Dunlop, J. Phys. Chem., 68, 398 (1964). (26) F. T. Gucker, Jr., and T. W. Ailen, J. Am. C h m . Soc., 64, 191 (1942). (27) F. T. Gucker, Jr., W. L. Ford, and C. E. Moser, J. Phys. Chem., 43, 153 (1939). (28) H. F. V. Tyrrell and M. Hennerby, J . Chem. Soc. A , 2724 (1968). (29) J.-D. C. Ahluwalia, C. Ostiguy, G. Perron, and J. E. Desnoyers, Can. J. Chem., 55, 3364 (1977). (30) J. Traube, Samm. Chem. Vortr., 4, 255 (1899). (31) J. E. Desnoyers and M. Arel, Can. J. Chem., 47, 547 (1969). (32) W.-Y. Wen, A. Lo Surdo, C. Jolicoeur,and J. Boileau, J. Phys. Cbem., 80, 466 (1976). (33) C. Jolicoeur and G. Lacroix, Can. J . Chem., 54, 624 (1976). (34) S. Cabanl, V. Mollica, L. Lepori, and S.T. Lobo, J . Phys. Chem., 81, 987 (1977). (35) J. E. Desnoyers and M. Arel, Can. J . Chem., 45, 359 (1967). A. Horne, Ed., (36) F. J. Millero in “Water and Aqueous Solutions’> Wiley-Interscience,New York, N.Y., 1972. [ P(H ) - -5.4 cm3 mol-’ reported by R. Zana and E. Yeager, J. Phys. Chem., 70,954 (1966); 71, 4241 (1967)]. (37) C. Jolicoeur, J. Boileau, S. Banzinet, and P. Picker, Can. J . Chem., 53, 716 (1975). (38) H. Hailand, Acta Chem. Scand., Ser. A , 28, 699 (1974).
A. Ben-Nalm H H~iland,J . Chem. Sac., Faraday Trans. 7 , 71, 797 (1975). R. Zana, J . Phys. Chem., 81, 1817 (1977). Reference 1, Chapter 4, p 85. Professor J. T. Edsall, personal communication. H. Heiland and E. Vikingstad, Acta Chem. Scand., Ser. A , 30, 692 (1976). (44) L. H. Laliberte and B. E. Conway, J . Phys. Chem., 74,4116 (1970). (45) T. L. McMeekin, E. J. Cohn, and J. H. Weare, J. Am. Chem. SOC., 57, 626 (1935). (46) J. P. Greenstein and J. Wyman, Jr., J . Am. Chem. SOC.,58, 463 (1936). (47) J. P. Greenstein, J. Wyman, Jr., and E. J. Cohn, J. Am. Chem. SOC., 57, 637 (1935). (48) J. Daniel and E. J. Cohn, J. Am. Chem. Soc., 58, 415 (1936). (49) J. T. Edsall and J. Wyman, Jr., J. Am. Chem. Soc., 57, 1964 (1935). (50) J. B. Dalton and C. L. A. Schmide, J. Bo/. Chem., 103, 549 (1933); 109, 241 (1935). (51) E. J. King, J . Phys. Chem., 73, 1220 (1969). (52) (a) W. L. Masterton, J . Chem. Phys., 22, 1830 (1954); (b) R. Kobayashi and D. L. Katz, Ind. f n g . Chem., 45, 440 (1953). (53) (a) R. E. Verrall and B. E. Conway, J. Phys. Chem., 70, 3961 (1966); (b) B. E. Conway, R. E. Verrall, and J. E. Desnoyers, Trans. faraday SOC.,62, 2738 (1966); (c) S. D. Hamann and S.C. Lim, Aust. J . Chem., 7, 329 (1954). (54) (a) G. D. Scott, Nature (London), 185, 68 (1960); (b) J. D. Bernal and J. L. Flnney, Discuss. Faraday SOC.,43, 62 (1967); (c) W. C. Duer, J. R. Greenstein, G. B. Oglesby, and F. J. Millero, J . Chem. Ed., 54, 139 (1977). (55) R. M. Fuoss, J . Am. Chem. SOC.,58, 982 (1936). (56) J. K. Kirkwood, Chem. Rev., 19, 275 (1936). (57) B. B. Owen, R. C. Miller, C. E. Milner, and H. L. Cogan, J. Phys. Chem., 65, 2065 (1961). (39) (40) (41) (42) (43)
Standard Thermodynamics of Transfer. Uses and Misuses A. Ben-Nalm Department of Physical Chemistry, The Hebrew Universify of Jerusalem, Jerusalem, Israel (Received July 29, 1977; Revised Manuscript Received December 16, 1977)
The standard free energy of transfer of a solute A between two solvents a and b is discussed at both a thermodynamic and a statistical mechanical level. It is shown that whereas thermodynamics alone cannot be used to choose the “best” standard quantity, statistical mechanics can help to make such a choice. It is shown that A ~ A O P ,the standard free energy of transferring A, computed by the use of the number density (or molarity) scale, has the following advantages: (1)it is the simplest and least ambiguous quantity; (2) it is the quantity that directly probes the difference in the solvation properties of the two solvents with respect to the solute A; (3) it can be used, without any change of notation, in any solution, not necessarily a dilute one, and including even pure A; (4) by straightforward thermodynamic manipulations on’e obtains the entropy, enthalpy, volume changes, etc. for the same process. All of these quantities have advantages similar to the ones indicated for the free energy change. Because of the advantages of this particular choice of standard quantities, we propose to “standardize” the use of the standard thermodynamic quantities of transfer and refer to them as the local-standard quantities. Some common misconceptions and misinterpretations of other standard quantities are indicated.
1. Introduction The purpose of this paper is to examine critically some thermodynamic quantities which are ubiquitous in the field of aqueous solutions. Part of the material presented here has already been published before,1’2but here we shall present the issue in more detail. Also some new and more fundamental arguments are given which have not been presented previously. Today, there are a growing number of articles ranging from solution chemistry to biochemistry and biology in which standard thermodynamic quantities of transfer are used. In many of these papers the authors make certain statements concerning the interpretation of these concepts without taking the trouble of checking their validity. 0022-3654/78/2082-0792$0 1.OO/O
The central issue of this paper is to show that standard thermodynamic quantities of transferring a solute between two phases, based on the molar concentration scale, have unique advantages over all other standard quantities. The main reason for that is that these standard quantities are completely devoid of any contribution from the translational degree of freedom of the solute. Therefore they are referred to as the local-standard quantities of transfer. The local character of these quantities are quite easy to see in the standard free energy of transfer. Here a mere choice of the correct concentration scale leads directly to the required standard quantity. The identification of the local-standard entropy, enthalpy, or volume of transfer is more intricate and involves some subtle arguments. To 1978 American Chemical Society
