Anal. Chem. 1989, 61, 349-355
(26) (29) (30)
(31) (32)
00227, University of Waterloo Research Institute, Waterloo, ON, Canada, December 1980. Lubman, 0. M.; Kronick, M. N. Anal. Chem. 1982, 5 4 , 1546. Leasure, C. S.; Fielscher, M. E.; Anderson, G. K.; Eiceman, 0. A. Anal. Chem. 1988, 58, 2142. StimC, R. M.; Cohen, M. J.; Wernlund, R. F. ”Tandem Ion Mobility Spectrometer for Chemical Agent Detection, Monitoring and Alarm”; PCP, Inc., West Palm Beach, FL, Contract NO. D A A K ~1-844-0017, December 1984. Knorr, F. J.; Eathetton, R. L.; Siems, W. F.; Hill, H. H., Jr. Anal. Chem. 1985, 5 7 , 402. Proctor, C. J.; Todd, J. F. Anal. Chem. 1984, 5 6 , 1794.
349
(33) Spangler, G. E.; Carrico, J. P.; Campbell, D. N. J . Test. Eval. 1985, 13(3), 234. (34) Roehl, J. E. Opt. Eng. 1985, 24(6), 985.
RECEIVED for review August 5,1988. Accepted November 11, 1988. This Paper was Presented in Part at the Third Chemical Congress of North America, June 5-10,1988, Toronto, Canada. The financial support of the Public Safety Project Office of NRC is gratefully acknowledged.
Methanol-Water Association and Its Effect on Solute Retention in Liquid Chromatography E. D.Katz The Perkin-Elmer Corporation, 761 Main Avenue, Norwalk, Connecticut 06859 C. H. Lochmuller
Duke University, Department of Chemistry, Durham, North Carolina 27706 R. P. W . Scott*
Georgetown University, Department of Chemistry, Washington, D.C. 20057
Previous work on the association of methanol with water in methanol-water mixtures has been extended. With the use of published data on the volume change on mixlng, density, and refractive index, the mean value for the association constant for methanol and water is found to be 5.22 X lo-’ at 23 O C . Curves relating the associated water concentration, associated methanol concentration, and the concentration of the methanol-water associate against the original volume composition of the solvent mixture are given. The predicted composition of the “ternary” solvent mixtures thus formed is used to explain the magnitude of the distribution coefficient of a number of different solutes between n-hexadecane and a range of methanol-water mixtures. I t is shown that for solutes distributed largely in the aqueous phase, the dlstribution of the solute is controlled almost exclusively by the concentration of the methanol unassoclated with water. For those solutes distributed prlmarity in the hydrocarbon phase, the distribution coefficient has a secondorder dependence on the methanol unassociated with water, probably due to the need for two methanol molecules to associate with the solute to render it soluble in the aqueous mixture.
INTRODUCTION It is important to know the exact nature of methanol-water solutions when they are used as mobile phases in liquid chromatography (LC) in order to be able to predict solute retention from solvent composition and, in particular, to be able to optimize solvent composition for maximum resolution and minimum analysis time. Generally, methanol-water mixtures have been, and to some extent still are, considered to contain only two chemical species despite the report by Katz et al. (1) demonstrating strong association between methanol and water. This work indicated that methanol-water mixtures contained three distinct chemical species with which a solute could react. Thus from a chromatographic point of view the 0003-2700/89/036 1-0349$01.50/0
methanol-water solvent mixtures constitute “ternary” systems and should be treated as such if accurate prediction of solute retention is to be practical. The word “ternary” in this paper is placed in quotation marks to differentiate it from a ternary system where the individual components are independently variable. The concept that water associated with methanol constitutes a solvent component itself and exists independently of the water or methanol is by no means novel. In fact as long ago as 1968, Taylor (2) stated “...water may not simply be a random or ordered arrangement of individual molecules with uniform characteristics and bonding. On the contrary, water may consist of two or more different molecular species, each structure being organized in its distinctive way...” Thus, Taylor suggested that water associated with water to form a distinct substance in much the same way that Katz et al. suggested that the association of methanol and water formed a distinct complex having properties different from that of associated water or associated methanol. As a result of strong hydrogen bonding, Katz et al. considered methanol-water mixtures to consist of water associated with itself, methanol associated with itself, and both in equilibrium with water associated with methanol, the relative proportion of each depending on the equilibrium constant. A value for the equilibrium constant for the association of methanol with water was determined from changes in volume on mixing measurements, and the value of 4.5 X at 23 “C that was obtained confirmed the very strong interaction between water and methanol. The strong association between methanol and water, if indeed present, is extremely important as, due to its effect on solute retention, it will have a profound effect on solvent optimization. The magnitude of the equilibrium constant for water-methanol association, therefore, requires further substantiation. In this paper the magnitude of the equilibrium constant will be determined by two further separate and distinctly differing procedures employing different physical data. The results will be applied to a number of different distribution systems. 0 1989 American Chemlcal Society
350
ANALYTICAL CHEMISTRY, VOL. 61, NO. 4, FEBRUARY 15, 1989
THEORY Relationship between the Equilibrium Constant for a Methanol-Water Mixture, the Volume Change on Mixing, and the Density. The equation for the equilibrium between associated water, associated methanol, and water associated with methanol (1) is restated as (W)(M)/(MW) = k
(1)
where (W) is the molar concentration of associated water, (M) is the molar concentration of associated methanol, (MW) is the molar concentration of the methanol-water associate, and k is the “association” constant. For convenience the molar concentrations will be defined as moles per milliliter before mixing. To be precise, as there is a volume change on mixing, eq 1 should be expressed in moles per milliliter after mixing, i.e.
([(x)/il/l[(M)/il/lJ/[(MW)/il/I = k where $ is the fractional volume change on mixing or
(W)(M)/(MW) = il/k However, as ($) ranges between 0.967 and 1.00 (1) (i.e. a maximum of 3% change in volume), the value of k will also be modified by about 3%. Furthermore, it will be shown later that the standard deviation between measurements of k is greater than 10%; consequently, the effect of the 3% change in volume on mixing on k can be ignored and eq 1 employed in the form given. The term “association” constant is employed as opposed to the more conventional “dissociation” constant, as in the case being considered, a stable compound does not dissociate into other substances (for example a weak acid or a weak base in solution), but the two stable substances methanol and water are interacting to form a single associate. Equation 1assumes that the three component solutions are regular; that is to say, the activity coefficients are unity and the equilibrium constant is independent of composition. The regular nature of the solutions is difficult to establish by independent experiment. However, the assumption is subsequently justified by the fact that the association constants derived from each of the three different experimental data sets are, within experimental error, numerically the same. Equation 1 also assumes that the interaction between water and methanol is on a 1:l basis. Higher orders of interaction produce polyfunctional equations that can also be fitted to the data. However, the results show that higher orders of interaction need not be invoked, as the experimental data can be explained accurately on the assumption that the associate contains water and methanol in the molecular ratio of unity. Now if the methanol-water mixture was originally made up with a volume fraction (a) of methanol, then there will be a volume fraction (1- a ) of water. Consequently, as the molar volume of a substance is the ratio of the molecular weight to the density, the original molar concentration of methanol and water will be a / V M and (1 - a ) / V,, respectively, where VM is the molar volume of methanol and V, is the molar volume of water. It follows that (M) + (MW) = ~ / V M
(2)
(W) + (MW) = (1 - a)/Vw
(3)
and By simple algebraic manipulation employing eq 1-3, it can be shown that (W) = (-b
+ (b2 + 4 ~ ) ” ’ ) / 2
where
b =k
+ u/VM + a/Vw
- 1/Vw
(4)
and
c = k(l/V,
- a/Vw)
Furthermore (MW) = [ ( I - a)/Vwl - (W)
(5)
(M) = ~ / V M - (MW)
(6)
and It should again be noted that (M), (W), and (MW) have for convenience been defined in units of moles per milliliter. Thus the volume of the solution after mixing (vi) (which will not be the sum of the original volumes that were mixed due to the volume change on mixing) will be given by u, = (W) Vw
+ (M) VM + (MW) VMW
(7)
where VMwis the molar volume of the methanol-water associate. Furthermore, the weight of water contained in the solvent mixture (ww)will be given by
ww = ( W M w
(8)
The weight of methanol contained in the solvent mixture, ( w M ) , is given by WM
=
(MWM
(9)
and the weight of associated methanol contained in the solvent mixture, (wMw), by WMW
= (MWWMW
(10)
where Mw, MM, and M m are the molecular weights of water, methanol, and the methanol-water associate, respectively. Thus the weight (mi)of the mixture originally containing the volume fraction (ai) of methanol and the volume fraction (1- ai) of water, which together made up the solvent mixture ( i ) is given by
m, = W W
+ WM + WMW
and consequently the density (di)of solvent mixture (i)is given by di = m , / q (11) where v i is obtained from eq 7. It is clear that by assuming values for k and VMWfor a mixture of methanol-water, having a given initial volume fraction of methanol, one can calculate the molar concentrations of associated water, associated methanol, and water associated with methanol. From these values, with use of eq 7 and 11,the volume of the mixed solvent and its density can also be determined. If this is carried out for a series of methanol/water mixtures and the calculated values for the volume on mixing and solvent density are compared with those measured experimentally, then the assumed values of k and V, that provide the minimum error between calculated and experimental values will provide the best values for k and vMW.
Relationship between the Equilibrium Constant of Methanol- Water Mixtures and the Molar Refractivity. Refractive index measurements can also provide an independent measure of the equilibrium constant k . The additive and constitutive properties of the molar refraction of a substance have been well-known for nearly a century ( 3 , 4 ) ,and the molar refraction is defined by the following equation:
R = (n2- l ) V / ( n 2 + 2 )
(12)
where R is the molar refractivity of the substance, n is the refractive index, and V is the molar volume. As the molar refractivity is additive and constitutive, the molar refractivity of a mixture of n solvents is given by
ANALYTICAL CHEMISTRY, VOL. 61, NO. 4, FEBRUARY 15, 1989 @)I,,
= Xl(R1) + Xz(R2)
+ .**X,(R,)
(13)
where (R)l,, is the molar refractivity of the mixture, (RJ is the molar refractivity of component 1, (R2) is the molar refractivity of component 2, (R,) is the molar refractivity of component n, XI is the molar fraction of component 1,X2 is the molar fraction of component 2, and X, is the molar fraction of component n. The molar fractions of water, methanol, and water associated with methanol, XM, Xw, and XMW, respectively, can be derived from eq 4-6 and thus
XM= (M)/((M) + (W) + ( M W )
(14)
+ (MW) + (W +
(15)
Xw = (W)/((M) + (W)
XMW= (MW)/((M)
(16)
Thus, for a mixture of methanol and water
(RJ = XM(RM)+ Xw(Rw)
+ XMW(RMW)
(17)
where (R,) is the molar refractivity of solvent mixture (i), (Rw) is the molar refractivity of water, (RM) is the molar refractivity of methanol, and (RMW) is the molar refractivity of the water-methanol associate. Consequently
(n,2 - l)V,/(n,Z
+ 2) =
XM(RM)+ X w W W + XMW(RMW) (18) where n,is the refractive index of the solvent mixture and V, is the equivalent molar volume of the mixture taken as the ratio of the effective molecular weight to the mixture density. Thus Vl = ((M)MM+ (W)Mw
+ (MW)MMW)/((M) + (W) + (MW))d, (19)
Substituting into eq 18 from eq 14-16 and 19, and simplifying, one obtains
(n: - 1)/(nL2+ 2) = (M)(RM)+ (W)(Rw) + ( M W ) ( R M W ) ~ , / ( ( M ) M+M( W M w + (MWMMW) =2 (20) Thus
n, = ((22
+ i)/(i- 2 p 5
(21)
It is clear that, in a manner similar to the treatment of the volume change on mixing and solvent mixture density, by knowing the molar refractivities of water and methanol and assuming a range of values for the equilibrium constant k and the refractive index of the methanol-water associate, the actual magnitude of these parameters can be identified. Those values assumed for the equilibrium constant and the refractive index of the methanol-water associate that provide the minimum error between the experimentally determined and calculated data will give the best estimate of the true values for k and (RMw).
RESULTS AND CALCULATIONS Determination of the Equilibrium Constant from the Volume Change on Mixing. The data employed for the volume change on mixing was that published by Katz et al. (I),and the mathematical procedure used was the same as that described in their original paper. The experimental data is included in Table I. From eq 4-7 the values of k and V m were identified that gave the minimum error between the calculated results and experimental values for the volume change after mixing. The calculations were carried out over the range from 0% to 100% (v/v) methanol in steps of 10% (v/v), and the difference between the calculated and experimental values was squared and added for each concentration level. The calculated and experimental values of the volume
351
Table I. Calculated and Experimental Values for the Volume Change on Mixing for Solvent Mixtures of Different Composition
solvent compn, %' c (v/v)
vol on mixing (calcd)
vol on mixing (exptl)
0 10 20 30 40 50 60 70 80 90 100
1.000 0.9925 0.9853 0.9785 0.9723 0.9674 0.9647 0.9663 0.9734 0.9853 1.0000
1.000 0.995 0.986 0.979 0.970 0.967 0.965 0.968 0.974 0.984 1.000
Table 11. Calculated and Experimental Values for the Densities of Methanol-Water Mixtures of Differing Composition
solvent compn, % ' (v/v) methanol 0 1.26 2.51 3.75 4.99 6.23 7.45 8.67 9.88 11.09 12.29 13.49 14.68 15.86 17.04 18.21 19.37 20.53 21.68 22.83 23.97 26.24 28.49 30.71 32.91 35.09 37.24 39.39 41.12 43.60 45.68 49.77 53.80 57.74 61.62 65.42 69.16 72.83 76.43 79.98 83.46 86.88 90.24 100 ~. .
density (exptl), g/mL
density (calcd), g/mL
0.998 23 0.986 43 0.994 74 0.993 04 0.991 34 0.989 65 0.988 05 0.986 35 0.984 75 0.983 16 0.981 66 0.980 06 0.978 57 0.977 97 0.975 47 0.973 97 0.972 47 0.970 98 0.969 48 0.967 98 0.966 49 0.963 59 0.960 60 0.957 50 0.954 51 0.951 41 0.948 82 0.945 02 0.941 63 0.938 24 0.934 74 0.927 36 0.919 37 0.911 48 0.903 20 0.89461 0.885 53 0.876 25 0.866 66 0.856 88 0.846 80 0.836 62 0.825 94 0.791 44
0.998 23 0.986 46 0.995 07 0.991 92 0.991 92 0.980 33 0.988 76 0.987 18 0.985 61 0.984 04 0.982 46 0.980 88 0.979 31 0.977 74 0.976 16 0.974 59 0.973 02 0.971 44 0.969 87 0.968 28 0.966 70 0.963 53 0.960 34 0.957 14 0.953 93 0.950 69 0.947 43 0.944 12 0.941 40 0.937 42 0.934 00 0.927 00 0.91969 0.91207 0.904 00 0.895 47 0.886 42 0.876 86 0.866 85 0.856 42 0.845 74 0.834 89 0.823 97 0.791 44
on mixing are shown in Table I and the values obtained for the equilibrium constant and molar volume of the watermethanol associate included in Table IV. Determination of the Equilibrium Constant k from Density Data. The density data employed was obtained from
352
ANALYTICAL CHEMISTRY, VOL. 61, NO. 4, FEBRUARY 15, 1989
0 Calculated
I 00
+ Experimental
0 Experimental
*
Calculated
20
40
I
0
20
40
80
60
120
100
Figure 1. Graph of volume change on mixing against solvent composition: horizontal axis, solvent composition, YO (v/v) methanol; vertical axis, volume on mixing, mL.
i
0 7 4 , 0
I
,
60
, 80
.
3
100
Figure 3. Graph of calculated and experimental values of solvent density against solvent composition: horizontal axis, solvent composition, % (v/v) methanol; vertical axis, density, g/mL.
lo]
099j
0 9 6 - v . 096
I
097
'
, 098
'
, 099
'
, 100
'
I
ioi
Figure 2. Graph of theoretical values of the volume on mixing against experimental values: horizontal axis, calculated values; vertical axis, experimental values. ref 4 and is given in Table 11. Equations 4-6 and 8-11 were employed again with a simple iterative procedure to calculate the density of a series of methanol-water mixtures for a range of values of the equilibrium constant k and the molar volume of the water-methanol associate, Vw The calculated values were again taken over the range of 0%-100% (v/v) methanol in the steps given in (4), and the densities obtained were compared with those obtained experimentally. As before, the computer program stored the total error and then proceeded to repeat the calculations by employing the next value for k or VMW. In this way the values for k and VMw that gave the minimum error between experimentally based and calculated values for the solvent density were identified. These values were taken as the best estimate for the equilibrium constant and for the molar volume of the water-methanol associate and are included in Table IV. The results for the calculated and experimental density values are included in Table 11. Determination of the Equilibrium Constant from Refractive Index Data. The refractive index data that was employed was also obtained from ref 4 and is given in Table 111. The computer iteration program was developed from eq 4-6,20, and 21. The calculations were carried out, again over a range of water-methanol mixtures from 0% to 100% (v/v) methanol, employing the specific concentrations given in ref 4. The experimental and calculated values for the refractive indices of the different mixtures are shown in Table I11 and the values obtained for k and ( R M W ) included in Table IV. R E S U L T S A N D DISCUSSION The results given in Table I are shown as graphs in Figure 1relating volume on mixing against composition of the original mixture. Both the calculated and experimental results are included, and it is observed that there is close agreement between the two sets of data. In Figure 2, the experimental values are plotted against the calculated values, and it is also
07Y
I
08
07
10
09
Flgure 4. Graph of calculated values of solvent density against experimental values: horizontal axis, calculated values; vertical axis, experimental values.
0
20
40
60
80
100
Figure 5. Graph of calculated and experimental values of refractive index against solvent composition: horizontal axis, solvent composition, % (v/v) methanol; vertical axis, refractive index. seen that the expected straight line is produced with a slope close to unity, again confirming the closeness of the fit and the validity of the values for k and VMw derived by this procedure. In Figure 3 the calculated and experimental values of the density of the solvent mixtures are plotted against solvent composition, and it is again seen that there is closed agreement between the two sets of data. In Figure 4 curves relating the experimental and calculated values of the densities of the mixtures wxhibit good linearity with a slope close to unity and with a very small intercept. In Figure 5, the calculated and experimental values for the refractive index of the solvent mixture are plotted against solvent composition. It is seen that the agreement is as good as that obtained from the density and volume change on mixing data. The linear curve shown in Figure 6, relating the experimental values of the refractive index to the experimental
ANALYTICAL CHEMISTRY, VOL. 61, NO. 4, FEBRUARY 15, 1989
353
Table 111. Calculated and Experimental Values for the Refractive Indices of Methanol-Water M i x t u r e s of D i f f e r i n g Composition
solvent compn, [ (v/v)
refractive index (exptl)
refractive index (calcd)
1.3330 1.3332 1.3334 1.3337 1.3339 1.3341 1.3344 1.3346 1.3349 1.3352 1.3354 1.3357 1.3360 1.3363 1.3365 1.3368 1.3371 1.3374 1.3376 1.3379 1.3382 1.3388 1.3393 1.3398 1.3403 1.3408 1.3412 1.3416 1.3420 1.3423 1.3426 1.3429 1.3430 1.3431 1.3430 1.3426 1.3421 1.3414 1.3405 1.3396 1.3384 1.3372 1.3357 1.3288
1.3330 1.3332 1.3335 1.3337 1.3339 1.3342 1.3344 1.3347 1.3349 1.3352 1.3355 1.3358 1.3361 1.3367 1.3366 1.3369 1.3372 1.3374 1.3377 1.3380 1.3383 1.3388 1.3394 1.3399 1.3404 1.3408 1.3412 1.3417 1.3417 1.3423 1.3425 1.3429 1.3429 1.3430 1.3427 1.3424 1.3418 1.3411 1.3402 1.3392 1.3380 1.3367 1.3351 1.3288
0
1.26 2.51 3.75 4.99 6.23 7.45 8.67 9.88 11.09 12.29 13.49 14.68 15.86 17.04 18.21 19.37 20.53 21.68 22.83 23.97 26.24 28.49 30.71 32.91 35.09 37.24 39.39 41.12 43.60 45.68 49.77 53.80 57.74 61.62 65.42 69.16 72.83 76.43 79.98 83.46 86.88 90.24 100.00
y' 1321 32
-00124t10093~ R - 1 0 0 I
1 34
1.33
1 35
Flgure 6. Graph of experimental values of refractive index against calculated values: horizontal axis, calculated values of RI; vertical axis, experimental values of R I .
0 +
80
+
Water Methanol Methanol-water
0 20 40 60 BO 100 Flgure 7. Graph of concentration of methanol, water, and methanol-water associate against composition of original solvent mixture: horizontal axis, original methanol concentration, % (v/v); vertical axis, component concentration, % (v/v).
values, supports the credibility of the procedure; the slope is close to unity and the intercept close to zero. The value of k obtained from the refractive index data is shown in Table IV and is comparable to that obtained from the density and volume change on mixing data. The results of all three sets of data are summarized in Table IV. I t is seen that all three values for k vary from 0.00443 obtained from the volume change on mixing experiments to 0.005 65 obtained from density measurements, giving an average value from all three methods of 0.005 04. The values for the density of the water-methanol associate were taken as the ratio of the molar volume to the sum of the molecular weights of water and methanol. The two values obtained are in reasonable agreement and have a magnitude that could be
expected for the hydrogen-bonded associate. The molar refractivity of 11.88 is also in accordance with that expected, considering the molar refractivities of water and methanol are 3.72 and 8.28, respectively. The refractive index of the associate was calculated from the molar refractivity and its mean molar volume determined from the density and volume change on mixing experiments. It is seen that, as would be expected, the refractive index of the associate (1.3502) is higher than that of either water or methanol. From eq 4-6 the actual composition of a series of methanol-water mixtures was calculated by employing the mean values of 0.005 04 and 55.18 for the equilibrium constant and molar volume of the water-methanol associate, respectively. The numerical data are shown in Table V, and the curves relating component concentration as a percentage (v/v) against the original percentage of methanol (v/v) used in making up the mixture are shown in Figure 7. The curves in Figure 7 given a clear indication of the nature of methanol-water mixtures and the strong degree of association between the water and the methanol that takes place. The curves are very similar to those published by Katz et al. (I),although the mean value for the equilibrium constant is slightly larger than that previously employed. This again reflects the relative insensitivity of the composition of the solvent mixture to slight
Table IV. Summary of E q u i l i b r i u m D a t a
source of data vol change on mixing density refractive index mean
molar vol equilibrium constant ( k ) of associate 0.004 43 0.005 65 0.005 04 0.005 04
density of associate
55.46 54.90
0.9024 0.9118
55.18
0.9071
molar refractivity of associate
refractive index of associate
11.88 11.88
1.3502 1.3502
354
ANALYTICAL CHEMISTRY, VOL. 61, NO. 4, FEBRUARY 15, 1989
Table V. Composition of Methanol-Water Mixtures initial solvent metha-
compn, %
(v/v)
water %
nol, %
methanol
(v/v)
(v/v)
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
100.0 93.3 86.7 80.0 73.2 66.5 59.8 53.2 46.6 40.1 33.8 27.8 22.2 17.2 12.8 9.1 6.2 4.0 2.3 1.0 0
0 0.5 1.0 1.6 2.4 3.2 4.3 5.5 7.1 9.1 11.6 14.8 19.0 24.5 31.4 40.0 50.1 61.4 73.7 86.7 100.0
associated methanol-water, b/V)
0 6.2 12.3 18.4 24.4 30.3 35.9 41.3 46.3 50.8 54.6 57.4 58.8 58.3 55.8 50.9 43.7 34.6 24.0 12.3 0
8-
6-
4-
21 ,oo
OW. 0
I
'
20
I
'
.
'
I
60
40
G
'
I
'
100
80
1
120
Table VI. Distribution Data for a Number of Solutes between Methanol-Water Mixtures and n -Hexadecane 0
associated methanol, % (v/v)
1-penta-
0 1.0 2.4 4.3 7.1 11.6 19.0 31.4 50.1 73.8 100.0
2.80 3.45 4.12 4.63 7.46 8.58 13.9 21.9 34.4
no1
benzonitrile 0.111 0.146 0.183 0.260 0.400 0.766 1.41 2.55 3.97 6.28 8.66
vinyl
acetate 0.33 0.35 0.33 0.54 0.42 0.74 1.05 1.47 2.15 2.97
IO
30
20
50
40
60
Figure 8. Graph of distribution coefficient against concentration of methanol unassociated with water: horizontal axes, unassociated methanol, % (v/v); vertical axes, distribution coefficient (k).
anisole benzene 0.008 0.012 0.018 0.026 0.042 0.072 0.14 0.25 0.45 0.86 1.49
0.008 0.007 0.010 0.021 0.024 0.045 0.084 0.142 0.290 0.515 0.990
changes in the value of k when association is particularly strong and consequently, the magnitude of 12 very small. It must again be emphasized that solutions made up with 50% (v/v) of methanol or less contain very little methanol unassociated with water, whereas mixtures initially made up with more than 50% (v/v) methanol contain very little water unassociated with methanol. A solution containing initially 60% (v/v) of methanol actually contains 50% (v/v) of the water-methanol associate. Thus, as it will be seen later, if methanol unassociated with water is the active eluent in liquid chromatography, then the increase in elution rate at very high concentrations of methanol is to be expected. It is now interesting to consider the effect of the complex "ternary" system that is formed in methanol-water mixtures on the distribution of a solute between such mixtures and n-hexadecane. The solvent n-hexadecane is chosen to simulate the character of a reverse phase and, by employing a liquidliquid system, to eliminate any uncertainty that may arise from the preferential adsorption of methanol on the surface of a reverse phase. Such a situation could introduce, in effect, another layer of phase between the mobile phase and the reverse phase and thus produce a different type of solutesolvent interaction. The data used was that for 1-pentanol and vinyl acetate as reported by Katz et al. (1) together with similar data for benzonitrile, anisole, and benzene determined
31
/n3 0
vinyl acetate
2
Y
y = 0 2995 + 0 0365~ R = 1 00
04 0
I
20
40
60
80
Flgure 9. Graph of distribution coefficient against concentration of methanol unassociated with water: horizontal axis, unassociated methanol, % (v/v); vertical axis, distribution coefficient (k).
by the same procedure (1). The data obtained are given in Table VI. The distribution coefficients (all of which are given with respect to the aqueous phase) of 1-pentanol and benzonitrile are shown in Figure 8 plotted against the percentage of methanol (v/v) unassociated with water in the methanol-water mixture. It is seen that the distribution coefficient of both solutes seems to be exclusively controlled in a linear manner by the percentage of methanol (v/v) unassociated with water. It should also be noted that the distribution coefficients of the two solutes are farily large (ranging from 3 to 34 and 0.1 to 8.7 for 1-pentanol and benzonitrile, respectively), which corresponds to the majority of the conditions of elution in the practive of liquid chromatography. In Figure 9 a similar curve for vinyl acetate behaves in the same manner as that for 1-pentanol and benzonitrile. There is a linear relationship between the distribution coefficient and the percentage of methanol (v/v) unassociated with water in the solvent mixture. For anisole and benzene (shown in Figure lo), however, the linear relationship breaks down, and
ANALYTICAL CHEMISTRY, VOL. 61, NO. 4, FEBRUARY 15, 1989
solute molecule must interact with two solvent molecules in order to become sufficiently hydrophilic to be solvated by the aqueous phase. The interaction of one solute molecule with two solvent molecules leads directly to a second-order equation in terms of concentration of the interacting solvent and could be treated in a similar manner to a second-order chemical reaction.
/ y-00138 t 0.0034x+ 1 128e-4x.2 R. 1.00 l
0
20
’
40
l
’
8
60
80
’
r
’
l
100
120
1 000-
-
0.800
0 600
0
benzene
-
y = 0 0143
t
0 O O l x + 8 529e-Sx’2
0 000 0
20
40
60
80
R
-
355
1 00 I
100
Flgure 10. Graph of distribution coefficient against concentration of methanol unassoclated with water: horizontal axes, unassociated methanol, % (vlv); vertical axes, distribution coefficient (k).
this occurs for solutes that are very poorly distributed in the aqueous system and in fact are substances that are almost insoluble in water. The distribution coefficients ranged from 0.01 to 1.49 and 0.001 to 0.99 for anisole and benzene, respectively. This range of values of distribution coefficients is smaller than that generally encountered in liquid chromatography. However, it can be demonstrated that the curves for anisole and benzene accurately fit a quadratic function in percentage of methanol (v/v) unassociated with water, and thus this parameter is still the one that controls retention. The reason for the quadratic relationship will not be discussed in this paper, and it will be sufficient to say that there is poor interaction between the solute and solvent (albeit with methanol unassociated with water). It would appear that the
CONCLUSIONS Data from density, volume change on mixing, and refractive index measurements all strongly indicate that the association that takes place in methanol-water mixtures is binary in that the ratio of methanol molecules to water molecules is unity. This results in a “ternary” mixture of associated water, associated methanol, and water associated with methanol. The concentration of methanol unassociated with water increases nonlinearly and rapidly with the methanol content of the original mixture. The concentration of methanol unassociated with water appears to be the major, if not the only, factor controlling solute elution in liquid chromatography where a mixture of methanol and water is employed as the mobile phase. Under most practical conditions it appears that the distribution of a solute with respect to the aqueous phase is linearly related to the concentration of methanol unassociated with water in the mixture, not the concentration of methanol originally added. The unique character of aqueous solvent mixtures employed in liquid chromatography makes it essential to take into account solvent-water association if retention is to be predicted from solvent composition on a general and rational basis. It has been shown that solventwater interactions also take place to a very significant extent with tetrahydrofuran and to a lesser extent with acetonitrile ( I ) . It follows that the “ternary” nature of aqueous mixtures of such solvents must also be taken into account in any solvent optimization procedure or in any attempt to develop a rational explanation of solute retention in reversed-phase liquid chromatography. LITERATURE CITED (1) Katz, E. D.; Ogan, K.; Scott, R. P. W. J . Chromatogr. 1986, 352, 67. (2) Taylor, D. Gases, Liquids and Solids; Penguin Llbrary of Physical Sclences: 1968, p 206. (3) Elsenlohr, S. Z . Phys. Chem. 1910, 75, 585. (4) The Handbook of Chemistry and Physics, 51st ed.;Weast, Robert C., Ed.; CRC Press: Boca Raton, FL, 1970-1971; p D194.
RECEIVED for review November 4,1987. Resubmitted October 28, 1988. Accepted November 8, 1988.
