J. Phys. Chem. 1993,97, 4601-4607
Solvation of Nonelectrolytes in Water Probed by
170NMR
4601
Relaxation of the Solvent
Alessandro Bagno,' Giancarlo Lovato, Gianfranco Scorrano, and Jan Willem Wijnent Centro CNR Meccanismi Reazioni Organiche, Dipartimento di Chimica Organica, Universith di Padova, via Marzolo 1 , 351 31 Padova, Italy Received: December 21, 1992
The concentration dependence of the 1 7 0NMR spin-lattice relaxation rate of the solvent water in nonelectrolyte solutions has been determined for a series of alcohols, amides, ethylene glycol, urea, and dimethyl sulfoxide. The values of TlO/TI are linearly related to the solute mole fraction or molality with a slope B. This parameter is shown to depend on the number of solvation sites of the solute and on the change in the correlation time of water molecules between bulk and solvation shell. The possible dependence on changes in nuclear quadrupole coupling constant is ruled out by a b initio theoretical calculations, which show that the electric field gradient at the oxygen nucleus of water does not change appreciably between water dimer and methanol- or formamidewater complexes. The B parameter is correlated with the enthalpy of hydration of the solute within a given family (alcohols, primary, secondary, or tertiary amides). It is shown that if TlO/T1values are corrected for the solution viscosities, the new B,, values thus obtained correlate with the enthalpy of hydration regardless of the family.
Introduction The enormous importance of aqueous solutions to chemistry and biochemistry has made them the object of a large number of studies. These studies have focused on both the macroscopic and microscopic aspects of the various phenomena that occur in aqueous solutions, Le., the thermodynamics of the solution and solvation of ions and molecules and the detailed study of the structure and motion of solutes and solvent in the solvation shell.] Thermodynamicdata on hydration energetics are now available for a large number of neutral molecules, either experimentally or from empirical group contributions;2free energies of solvation can also be obtained from molecular dynamics simulations.3 However, the effort put into partitioning experimental data into group or bond contributions attests that availability of more data is desirable. For example, despite the relevance of the amide group to protein chemistry, their hydration energies are experimentally available for relatively few compounds.2d Solvation phenomena can be investigated by NMR, employing the relaxation rates of the magnetic nuclei (IH, 2H, I7O) in the water molecule and in the solute^;^ much work has been done to elucidate the motion of water molecules in the hydration shell, especially of inorganic ions.+ll In most cases, solvent chemical shifts and spin-lattice relaxation rates have been determined as a function of temperature and solute concentration. If the concentration is not too high (< 2 mol kg-I), for both electrolyte and nonelectrolyte solutions, a linear relationship is observed between the ratio of T Ivalues in pure water and a given solution, and the solute molality m (eq 1); the slope of this line is called the NMR B coefficient. A similar (but generally quadratic) relationship holds for the concentration dependence of viscosity (eq 2):4b Tlo/Tl = 1 q/qo =
1
+ Bm
+ B,m + Cm2
(1)
(2)
Fister and Hertz5 proposed that structure-breaking ions lengthen the T I of I7O of water (B > 0), whereas structuremaking ions shorten it (B < 0). B values of electrolyte solutions have also been dissected into singleion contributionsand correlated
' Visiting student from the Department of Organic Chemistry, University of Groningen (The Netherlands) under the ERASMUS program. 0022-3654/93/2097-4601$04.00/0
withviscosity coefficients,partial molar volumes, and electrostatic entropies of solvation.1 The analogous work on nonelectrolytes has been much less systematic. Some sparse data are available for aqueous solutions of alcohols,cyclicethers, amines,nitriles, carboxylicacids, ketones, dimethyl sulfoxide, amides, urea, monosaccharides, and quaternary ammonium salts, obtained by a variety of techniques (relaxation of IH or 2H in solvent or solute, chemical shifts, diffusion coefficients).4a The general conclusion is that, with the exception of urea, all nonelectrolytes with alkyl groups increase the relaxation rate of water because of decreased motion in the hydration shell; in a homologous series the sensitivity (B) increases with increasing chain length.4a Recently, Uedaira et al. found a good correlation of the B coefficients of carbohydrates with the average number of equatorial OH groups and diffusion coeffic i e n t and ~ ~ ~suggested that other molecular properties of thesolute reIated to hydration might be accounted for by B values. Indeed, the most obvious and useful possibility would be to investigate the existence of a correlation between B values and thermodynamic functions of solvation of neutral solutes, because these also reflect the influence of solutes on the dynamic behavior of water. This approach might yield a different empirical approach to the determinationof useful thermodynamicquantities and possibly provide some insight to the factors relating the motion of water molecules in the solvationshell to the solvationenergetics.
Method The 170nucleus (I = 5 / 2 ) possesses an electric quadrupole moment eQ; thus, an asymmetry in the electronic distribution around the nucleus (characterized by nonzero components of the electric field gradient (efg) traceless tensor q, the largest of which is denoted qrr) causes the quadrupole moment-electric field gradient to dominate the relaxation of I7O,leading to very short relaxation times.14 This mechanism is normally intramolecular; in the extreme narrowing limit (generally satisfied for small molecules in a low-viscositymedium), this contribution (and the only significant one for 1 7 0 ) to the relaxation rate is given by
l/Tl = 1/T2 = (3/125)(1
+ e2/3)x27,
(3)
where x = e2qZzQ/h is the nuclear quadrupolar coupling constant (NQCC), E is the asymmetry parameter of the efg tensor (defined 0 1993 American Chemical Society
4602 The Journal of Physical Chemistry, Vol. 97, No. 18, 1993
Bagno et al.
TABLE I: Water ''0 Relaxation Times in Aaueous Nonelectrolyte Solutions and Correspondhip B Valuesa m (molkg-I)
X
TI
CH3OH
Bm
0.083 (0.005)
0.57 1 .oo 1.62 2.07
0.0102 0.0177 0.0284 0.0360
6.99 6.64 6.39 6.19
0.0102 0.0184 0.0277 0.0343
6.64 6.14 5.62 5.32
0.00804 0.0163 0.0270 0.0351
6.63 6.03 5.33 4.91
0.0103 0.0167 0.0260 0.0338
6.38 5.83 5.22 4.74
0.00981 0.0189 0.0256 0.0333
5.95 5.14 4.55 4.10
0.00916 0.0178 0.0264 0.0350
6.95 6.62 6.30 6.03
0.0105 0.0170 0.0261 0.0356
6.70 6.35 5.96 5.60
0.0103 0.0182 0.0297 0.0363
7.23 7.29 7.26 7.25
0.00981 0.0177 0.0260 0.0355
6.94 6.66 6.44 6.15
0.00855 0.0177 0.0265 0.0338
7.27 7.33 7.26 7.36
0.00981 0.0189 0.0258 0.0368
7.03 6.71 '6.44 6.22
0.00928 0.0175 0.0277 0.0363
6.74 6.17 5.60 5.25
CH3CH20H
0.185 (0.005)
0.57 1.04 1.58 1.97
CH3CH2CH20H 0.45 0.92 1.54 2.02
0.236(0.005)
(CH3)2CHOH
0.272(0.008)
0.58 0.94 1.48 1.94
0.401 (0.008)
(CH3hCOH 0.55 1.07 1.46
0.101 (0.003) 1 .oo 1.51 2.01
CH3SOCH3
0.143 (0.002)
0.59 0.96 1.49 2.05
HCONH2
-0.002 (0.002)
0.58 1.03 1.70 2.09
CH3CONH2
0.086 (0.002)
0.55 1 .oo 1.48 2.04
-0.007 (0.004)
CO(NH2)2 0.48 1 .oo 1.51 1.94
HCONHCH3
0.081 (0.006)
0.55 1.07 1.47 2.12
CH3CONHCH3
0.186 (0.007)
0.52 0.99 1.58 2.09 0
TIvalues (in ms)obtained with 5 0 - Hline ~ broadening.
BX m (molkg-') X TI Bm BX 4.8 (0.3) CH3CH2CONHCH3 0.269 (0.007) 15.5 (0.4) 0.50 0.00893 6.46 1.04 0.0184 5.74 1.52 0.0268 5.13 1.99 0.0346 4.73 10.6 (0.3) n-CsH7CONHCH3 0.35 (0.01) 19.9 (0.8) 0.51 0.00905 6.31 1.01 0.0178 5.50 1.49 0.0262 4.83 2.00 0.0347 4.28 13.6 (0.4) i-C3H7CONHCH3 0.395 (0.007) 22.7 (0.3) 0.50 0.00894 5.93 0.99 0.0175 5.18 1.50 0.0263 4.50 1.89 0.0329 4.13 15.6 (0.5) n-C.+H&ONHCH3 0.34(0.01) 19.9 (0.6) 0.50 0.00889 6.22 1 .oo 0.0177 5.29 1.50 0.0262 4.71 2.00 0.0348 4.31 23.0 (0.5) HCONHC2Hs 0.155 (0.008) 8.9 (0.5) 0.49 0.000875 6.86 1.02 0.0181 6.37 1.53 0.0268 5.91 1.98 0.0344 5.58 5.8 (0.2) CH3CONHC2Hs 0.281 (0.008) 16.1 (0.5) 0.50 0.00893 6.50 1.02 0.0181 5.66 1.49 0.0262 5.15 2.01 0.0350 4.64 8.2 (0.1) CHjCONH-n-CjH7 0.307 (0.009) 17.7(0.6) 0.5 1 0.00906 6.41 0.0176 1 .oo 5.63 1.49 0.0261 5.02 1.99 0.0347 4.50 -0.1 (0.1) CH3CONH-n-CdHg 0.36 (0.01) 20.6 (0.7) 0.50 0.00894 6.25 0.99 0.0176 5.30 1.49 0.0262 4.66 2.00 0.0348 4.26 5.0 (0.1) HCON(CH3)2 0.144(0.002) 8.3 (0.1) 0.42 0.00751 6.78 1.02 0.0180 6.29 1.43 0.0251 5.96 2.03 0.0353 5.59 -0.4 (0.2) CH3CH2CON(CH3)2 0.320 (0.009) 18.4(0.6) 0.50 0.00892 6.38 1 .oo 0.0177 5.56 1.50 0.0262 4.96 2.01 0.0349 4.41 4.6 (0.3) HCON(C2Hsh 0.261 (0.008) 15.0(0.5) 0.54 0.00965 6.42 0.99 0.0175 5.86 1.50 0.0263 5.23 1.97 0.0343 4.78 10.7 (0.4) CH~CON(C~HS)~ 0.351 (0.009) 20.1 (0.6) 0.51 0.00907 6.29 0.99 0.0175 5.40 1.46 0.0256 4.81 1.73 0.0303 4.52 B values calculated with Tl0 = 7.23 ms. Errors from least-squares analysis in parentheses.
as c = lqxx- qyyJ/qrr in which qxx,qyy,and qzrare its three principal components), and T , is the molecular correlation time. The electronicdistribution in most organic molecules leads to TIvalues in the millisecond range.].+ The correlation time defines the rate at which the molecule tumbles in solution, which depends essentially on the viscosity of the medium ( v ) and the hydrodynamic radius of the molecule (r),or the equivalent molecular volume ( V , ) ;the latter property is difficult to define precisely. A simplified way to express it is the Debye-Stokes-Einstein equation: T,
= 4avr3/3kT = vV,,,/kT
(4)
In aqueous solutions, the I7O nuclei of water molecules are distributed between two motional states (hydration and bulk water) with different relaxation rates. Since the residence time in any of these states is much shorter than TI,7 a weighted-average T I will be observed
where T I ,TI0,and Tlhare the observed relaxation times in the solution, in bulk water (assumed to be identical to that in pure water), and in the hydration shell, respectively, while xh is the mole fraction of water in the hydration shell. Combining eqs 3
Solvation of Nonelectrolytes in Water
The Journal of Physical Chemistry, Vol. 97, No. 18, 1993 4603
SCHEME I
Lf
0
/
r(0H) = 0.941W &OH = 1M.W E = -76.055943821
/
\H
H
Hl
-
r(W 1349%
