J Solution Chem (2010) 39: 808–819DOI 10.1007/s10953-010-9546-5

Ultrasound Speeds and Molar Isentropic Compressionsof Aqueous 2-(Ethylamino)ethanol Mixtures from 283.15to 303.15 K

Isabel M.S. Lampreia · Ângela F.S. Santos

Received: 27 October 2009 / Accepted: 12 January 2010 / Published online: 9 June 2010© Springer Science+Business Media, LLC 2010

Abstract Ultrasound speeds in 31 aqueous binary mixtures of 2-(ethylamino)ethanol(EEA) were experimentally determined over the entire composition range at 283.15, 288.15and 303.15 K. Isentropic compressibilities, κS , were calculated by combining the ultra-sound speed with density data. Excess molar isentropic compressions, KE

S,m, referred to athermodynamically-defined ideal liquid mixture, were estimated. Excess partial molar isen-tropic compressions, KE

S,i , of both components and their respective limits at infinite dilution,K

E,∞S,i , were analytically obtained using Redlich-Kister type equations. The temperature and

composition dependences of KES,i were analyzed, especially in the water and EEA rich re-

gions. The present KE,∞S,i values are compared with those for water + 2-diethylaminoethanol

(DEEA) and water + diethylamine (DEA) mixtures, as a function of temperature. Althoughthe K

E,∞S,2 values for EEA and DEEA increase with temperature, the opposite trend is ob-

served for DEA. Results for aqueous EEA and aqueous DEEA seem to support the idea thatthe driving force for hydrophobic hydration relies on solute-solvent hydrophilic interactionrather than on enhancing the water structure. On the other hand, different temperature de-pendent behavior is observed for the differential volumetric properties K

E,∞S,i and limiting

excess partial molar isobaric expansion, EE,∞P,i , which are attributed to the different sensitiv-

ity of these properties to hydration.

Keywords Ultrasound speed · Isentropic compressions · Aqueous solutions ·2-(ethylamino)ethanol · Hydration · Intermolecular interactions

1 Introduction

It is generally acknowledged that the process of mixing of amphiphile solutes with wateris usually accompanied by interesting volumetric changes as a function of composition,

I.M.S. Lampreia (�) · Â.F.S. SantosDepartamento de Química e Bioquímica, Centro de Ciências Moleculares e Materiais, Faculdadede Ciências, Universidade de Lisboa, 1749-016, Lisboa, Portugale-mail: milampreia@fc.ul.pt

J Solution Chem (2010) 39: 808–819 809

temperature and pressure [1–3]. These changes are mainly due to a combination of differenttypes of hydration that play a crucial role in the conformational stability of the amphiphilemolecules in water. Establishing links between those volumetric changes and phenomenasuch as hydrogen bonding, self-assembly, dissociation, or conformational changes has beenan important part of efforts carried out to understand hydration in real systems with industrialand biological interest, starting with model systems [4–9].

Partial molar properties such as volumes, isobaric expansions, and isentropic or isother-mal compressions are volumetric properties that give important insights on hydration mecha-nisms, mainly when studies are carried out on series of compounds differing in chain length,polar head groups, or branching [7, 10–15].

Continuing our volumetric study of binary and ternary aqueous mixtures containing am-phiphilic compounds having amine, alcohol and alkoxy hydrophilic groups in their struc-tures, [13, 14, 16–22] we report here the speed of sound in 31 aqueous binary mixturesof 2-(ethylamino)ethanol (EEA) at 283.15, 288.15 and 303.15 K. Excess molar and excesspartial molar compressions, and their values at infinite dilution, have been derived and in-terpreted in terms of intermolecular interactions occurring in solution.

The combination of the these results, either with volumetric information concerning ex-cess partial molar volumes or isobaric expansions obtained for the same system [22], or withsimilar results for the systems water + 2-(diethylamino)ethanol (DEEA) [21] and water +diethylamine (DEA) [13], leads to interesting information concerning the effects on hydra-tion and on aggregation patterns induced by changes in branching and head polar groups, asfunctions of both composition and temperature.

2 Experimental

2-(Ethylamino)ethanol, supplied by Agros Organics (>98% quoted purity), was further pu-rified by drying over potassium hydroxide pellets, refluxed with barium oxide and fraction-ally distilled at reduced pressure. Its purity (better than 99%) has been tested by GC-MS andby density measurement yielding ρ = 912.47 kg·m−3 at 298.15 K. This value compares wellwith 912.48 kg·m−3 previously published by us [22] and with Mather and co-workers’ valueof 912.78 kg·m−3 [23], both at 298.15 K. High purity water was prepared by ion exchange(resistivity, 18 M�·cm) using a Milli-Q reagent grade system supplied by Millipore.

Speed of sound measurements were made according to a previously described procedure[24, 25]. In short, a commercial sing-around ultrasound velocimeter supplied by NusonicMapco Inc. (model 6080), and fitted with a double transducer system operating at 1.8 MHz,was used. The velocimeter had been modified in order to furnish the pulse repetition fre-quency directly and with suitable resolution. The frequency was measured using a ten-digitfrequency counter supplied by Hewlett-Packard (model HP 53181A 225 MHz). A tight cellmade of Pyrex glass and specially designed to prevent evaporation was used. The apparatuswas calibrated with pure water and methanol, using speed of sound data calculated from thefitting equation of Del Grosso and Mader [26], and corrected to the ITS-90 temperature scalefor water [27, 28]. Reliable values for speed of sound in methanol used are: u = 1120 m·s−1

at 293.15 K [29, 30] and u = 1104 m·s−1 at 298.15 K [31]. The cell was introduced into awater bath with a temperature control to within ±0.005 K. Temperature was measured witha standard uncertainty of 0.01 K with a platinum resistance thermometer, calibrated againsta SPRT (standard platinum resistance thermometer), which in turn was calibrated with astandard uncertainty of 0.005 K on the ITS-90 temperature scale. All measurements weremade at ambient pressure.

810 J Solution Chem (2010) 39: 808–819

The calibration of the velocimeter and uncertainty evaluation procedure has been re-ported elsewhere [32]. The reproducibility and accuracy of the present measurements werefound to be 0.02 and 0.2 to 1.0 m·s−1, respectively. All solutions were prepared by weightin volumetric flasks specially designed to prevent evaporation. Buoyancy corrections weremade. The uncertainty in solution composition, expressed as mole fraction, was found to beless than ±0.00005.

3 Results and Discussion

3.1 Ultrasound Speeds and Isentropic Compressibilities

Experimental values of the ultrasound speed, u, in water(1) + EEA(2) mixtures, at 283.15,288.15, and 303.15 K and covering the entire composition range, are reported in Table 1.

Isentropic compressibilities, κS , also shown in Table 1, have been obtained by combiningu values with density values, ρ, using the Newton-Laplace equation, Eq. 1:

κS = 1

ρu2(1)

Density values used in these calculations were estimated using previously reported polyno-mial equations and parameters [22]. Figure 1 shows the κS values as a function of tempera-ture and composition at five experimental temperatures. Data at 293.15 and 298.14 K werepublished previously [24, 25].

Figure 1 shows minima in the κS values at all temperatures, that decrease in magnitudeand are displaced to the more water-rich region as the temperature rises. Minimum values,which are usually observed in aqueous amphiphilic mixtures, have been attributed to thehydrophobic effect [33]. We can also observe in this figure that the effect of temperature israther small in the water-rich region, and that at x2 ≈ 0.04 (see inset of Fig. 1) an intersectionpoint occurs, revealing that two opposing temperature dependent effects, which cancel outat this composition, are operating.

3.2 Excess Molar and Excess Partial Molar Isentropic Compressions

The molar isentropic compression is defined by KS,m = VmκS = −(∂Vm/∂p)S , where V m isthe molar volume of the mixture. Plots of the excess molar isentropic compression, KE

S,m, as

Fig. 1 Composition dependenceof the isentropiccompressibilities, κS in thewater(1) + EEA(2) system at:(�) 283.15 K; (�) 288.15 K;(�) 293.15 K; (�) 298.15 K; and(•) 303.15 K

J Solution Chem (2010) 39: 808–819 811

Table 1 Ultrasound speeds, u (m·s−1), and isentropic compressibilities, κS (Pa−1), of the water(1) +EEA(2) system from 283.15 to 303.15 K

x2 T = 283.15K T = 288.15K T = 303.15 K

u κS × 1010 u κS × 1010 u κS × 1010

0.00000 1447.28 4.776 1465.94 4.658 1509.14 4.410

0.00550 1474.13 4.606 1490.63 4.508 1528.41 4.303

0.01107 1499.55 4.454 1514.01 4.372 1546.71 4.205

0.01933 1535.72 4.248 1547.02 4.189 1571.92 4.075

0.02953 1577.72 4.024 1585.36 3.989 1600.37 3.934

0.03482 1600.29 3.911 1605.95 3.888 1615.86 3.860

0.03841 1613.15 3.848 1617.55 3.832 1624.51 3.820

0.04446 1633.96 3.749 1636.16 3.745 1637.39 3.761

0.05983 1679.38 3.546 1676.76 3.564 1665.27 3.639

0.07083 1701.99 3.451 1696.77 3.480 1678.76 3.582

0.08079 1723.18 3.366 1715.34 3.405 1690.29 3.535

0.08238 1726.07 3.354 1717.75 3.395 1691.13 3.532

0.10318 1744.51 3.284 1733.37 3.336 1699.78 3.502

0.12833 1751.83 3.260 1738.82 3.320 1699.57 3.512

0.14441 1748.98 3.275 1735.54 3.337 1695.02 3.537

0.17126 1742.51 3.308 1728.50 3.374 1685.20 3.590

0.19558 1730.17 3.365 1715.65 3.436 1672.05 3.659

0.24850 1705.80 3.487 1690.87 3.562 1644.72 3.809

0.29332 1683.37 3.601 1668.19 3.681 1621.11 3.944

0.36240 1651.62 3.772 1635.91 3.860 1587.93 4.146

0.39618 1636.67 3.856 1621.12 3.946 1572.43 4.244

0.44468 1613.63 3.988 1597.85 4.083 1549.28 4.396

0.48174 1599.96 4.072 1583.82 4.172 1534.98 4.496

0.57873 1567.82 4.279 1552.18 4.383 1504.11 4.725

0.69031 1536.27 4.496 1519.57 4.615 1469.92 4.993

0.74456 1520.50 4.609 1503.71 4.732 1453.98 5.125

0.79928 1511.51 4.682 1494.64 4.808 1444.21 5.215

0.82503 1502.47 4.746 1485.63 4.875 1435.16 5.290

0.84682 1500.09 4.767 1482.72 4.900 1430.88 5.328

0.89306 1490.26 4.841 1472.97 4.977 1421.90 5.409

0.91738 1484.99 4.882 1467.46 5.021 1415.97 5.462

0.95951 1479.14 4.933 1461.73 5.073 1411.09 5.514

1.00000 1473.71 4.979 1456.23 5.124 1404.67 5.577

a function of the composition give a first indication of how values of this property, for realmixtures, deviate from those of a well defined ideal state. A more powerful tool is the excesspartial molar property, which allows the separation of KE

S,m into the individual contributionsof the components in the equilibrium mixture. It has been pointed out that the excess partialmolar isentropic compressions, KE

S,i can give important insights on changes in different fea-tures such as packing effects, aggregation patterns, configurations and/or solvation producedby modifications in composition, temperature and pressure [34, 35].

812 J Solution Chem (2010) 39: 808–819

In this work, the KS,m values were therefore calculated and used to estimate the excessquantity, KE

S,m, defined by Eq. 2:

KES,m = KS,m − K id

S,m (2)

In this equation, K idS,m is the molar isentropic compression of a thermodynamically ideal

mixture at the same temperature, pressure and composition as KS,m and KES,m. This quantity

for the experimental compositions, at different temperatures, was estimated by using Eq. 3,

K idS,m = K id

T ,m − T (Eidp,m)2/C id

p,m (3)

where K idT ,m,Eid

p,m and C idp,m are the ideal molar isothermal compression, isobaric expansion

and isobaric heat capacity, respectively. Ideal molar values of these Gibbsian properties [36]were obtained by the following simple mixing rule,

Qidm = x1Q

∗m,1 + x2Q

∗m,2 (4)

where Qidm stands for K id

T ,m,Eidp,m or C id

p,m. Q∗m,1 and Q∗

m,2 are the corresponding molar prop-erties for pure water and EEA, respectively, whose values are reported in Table 2 at thetemperatures of interest.

Estimated excess molar isentropic compressions at 283.15, 288.15, 293.15, 298.15 and303.15 K are plotted in Fig. 2 as a function of the EEA concentration. As can be seen inthis figure, moderate negative values, which decrease in absolute value as the temperatureincreases, are obtained at all of the temperatures studied. In addition, in the amphiphilerich-region no noticeable changes are observed with temperature. The Redlich-Kister fittingmethod, in the form of Eq. 5, was applied to represent the KE

S,m values:

KES,m = x1x2

k=n∑

k=0

Bk(2x2 − 1)k (5)

The number of Bk parameters was varied, and the F -test indicated that five terms (n = 4) isthe appropriate number. These analytical correlations are also represented in Fig. 2 as fulllines. Values of the Bk parameters along with the standard deviation of the fits are shown inTable 3.

Aiming to separate the contributions of each component to the excess molar isentropiccompression, excess partial molar isentropic compressions of both components, KE

S,i , overthe entire composition range were then obtained from Eq. 6:

KES,i = KE

S,m + (1 − xi)dKE

S,m

dxi

(6)

To evaluate the derivative shown in the right hand side of Eq. 6, we have differentiated Eq. 5with respect to x2. The resulting excess partial molar isentropic compressions of water andEEA at the extreme temperatures (283.15 and 303.15 K) are shown in Fig. 3.

Negative KES,i values found for both components at all mixture compositions indicate that

there is a better packing of the components in the liquid mixture than in their pure states.In the water-rich region the principal reasons for the marked negative values of KE

S,2 maybe the changes in amphiphile configuration, when this molecule is transferred from the purestate to water, and the hydrophobic effect. In a previous paper [13] involving a similar mole-cule diethylamine (DEA), we have advanced that a displacement of equilibrium between

J Solution Chem (2010) 39: 808–819 813

Tabl

e2

The

rmod

ynam

icpr

oper

ties

ofpu

rew

ater

and

pure

2-et

hyla

min

oeth

anol

(EE

A)

Com

pone

ntT

ρu

Cp,m

Ep,m

KT

,mK

S,m

(K)

(kg·m

−3)

(m·s−

1)

(J·K

−1·m

ol−1

)(m

m3·K

−1·m

ol−1

)(m

m3·M

Pa−1

·mol

−1)k

(mm

3·M

Pa−1

·mol

−1)l

Wat

er28

3.15

999.

699a

1447

.28c

75.5

25g

1.58

54i

8.61

538.

6059

288.

1599

9.09

7a14

65.9

4c75

.410

g2.

7211

i8.

4266

8.39

83

293.

1599

8.20

1a14

82.3

6c75

.339

g3.

7333

i8.

2823

8.22

81

298.

1599

7.04

1a14

96.7

0c75

.298

g4.

6497

i8.

1755

8.08

99

303.

1599

5.64

3a15

09.1

4c75

.278

g5.

4899

i8.

1008

7.97

95

EE

A28

3.15

924.

713b

1473

.71d

227.

40h

85.0

56j

57.0

0647

.998

288.

1592

0.36

0b14

56.2

3d22

7.01

h84

.780

j58

.746

49.6

23

293.

1591

6.58

4b14

38.8

8e22

6.98

h84

.480

j60

.463

51.2

46

298.

1591

2.48

3b14

21.4

9f22

7.29

h84

.180

j62

.276

52.9

81

303.

1590

8.74

4b14

04.6

7d22

7.92

h83

.900

j64

.067

54.7

05

a Ref

eren

ce[3

7]

bR

efer

ence

[22]

c Ref

eren

ce[2

7]

dT

his

wor

ke R

efer

ence

[24]

f Ref

eren

ce[2

5]gR

efer

ence

[38]

hR

efer

ence

[39]

i Cal

cula

ted

from

the

expr

essi

onof

the

rela

tive

dens

ityas

afu

nctio

nof

tem

pera

ture

give

nin

refe

renc

e[4

0]

j Cal

cula

ted

from

data

ofre

fere

nce

[22]

kC

alcu

late

dfr

omK

S,m

(eig

hth

colu

mn)

usin

gE

q.3

l Cal

cula

ted

from

ρan

du

(thi

rdan

dfo

urth

colu

mns

)

814 J Solution Chem (2010) 39: 808–819

Fig. 2 Composition dependenceof the excess molar isentropiccompressions, KE

S,m, in thewater(1) + EEA(2) system at:(�) 283.15 K; (�) 288.15 K;(�) 293.15 K; (�) 298.15 K; and(•) 303.15 K. Full lines are fromthe Redlich-Kister equations

Table 3 Least squares fitting coefficients, Bk (mm3·MPa−1·mol−1), of Eq. 5 in the form of polynomial fitsof the 4th degree, and corresponding standard deviations of the fits, σfit(mm3·MPa−1·mol−1), for the water+ EEA system from 283.15 to 303.15 K

T = 283.15 K T = 288.15 K T = 293.15 K T = 298.15 K T = 303.15 K

B0 −25.3688 −25.2772 −25.1681 −25.2604 −25.2882

B1 12.5572 11.9977 11.4472 10.9552 10.5788

B2 −7.1089 −6.7790 −6.5655 −6.1124 −5.6612

B3 16.5029 14.7094 13.6994 12.4895 11.8970

B4 −13.0021 −11.1957 −9.1616 −8.1840 −6.9091

σfit 0.055 0.051 0.049 0.046 0.047

Fig. 3 Composition dependenceof the excess partial molarisentropic compressions, KE

S,i, in

the water(1) + EEA(2) system:(—), EEA at 283.15 K; (– – –),water at 283.15 K; (—), EEA at303.15 K; (- - -), water at303.15 K

different rotamers of the amphiphile molecule, towards forms with a larger number of 1–4non-bonded gauche interactions, would be favorable in a solvent such as water. Figure 3also shows that while the KE

S,2 values in the water rich-region present a neat displacement toless negative values at higher temperatures, the KE

S,1 curves for the two temperatures almostoverlap. This fact may be due to solute-solvent interactions in the water very-rich region,and at slightly higher compositions to the hydrophobic effect that varies with temperaturebecoming more evident at lower temperatures.

J Solution Chem (2010) 39: 808–819 815

3.3 Limiting Partial Molar Isentropic Compressions

Using now the concept of apparent molar properties, limiting excess partial molar isentropiccompressions of water in EEA, K

E,∞S,1 , and of EEA in water, K

E,∞S,2 , can easily be obtained

from Eq. 5. As the excess apparent molar isentropic compressions of both components,KE

S,φ,i , can be expressed as a function ofKES,m, by Eq. 7:

KES,φ,i = KE

S,m

xi

(7)

Substituting KES,m in Eq. 7 with the expression given in Eq. 5, and letting xi tend to zero,

shows that the limiting excess partial molar isentropic compressions can be expressed interms of the Bk coefficients. The resulting Eqs. 8 and 9 were first obtained by Maham et al.[41] and subsequently were used by many authors, including ourselves [22, 42].

limx1→0

KES,φ,1 = K

E,∞S,1 =

∑

k

Bk, (8)

limx2→0

KES,φ,2 = K

E,∞S,2 =

∑

k=even

Bk −∑

k=odd

Bk (9)

The KE,∞S,i values thus obtained are presented in Table 4, together with their standard devia-

tions calculated on the basis of the standard deviation of the Bk coefficients.K

E,∞S,1 has negative values, which seem to be constant within their standard uncertainty.

This fact reveals that there is better packing of water in an EEA environment in relationto the pure state. The constancy of K

E,∞S,1 with temperature may indicate that, if infinitely

dilute water is hydrogen bonded to EEA, then this quantity would not sense the variation ofthis interaction strength with temperature. By contrast, this constancy is not apparent in thecorrespondent limiting excess partial molar isobaric expansion, E

E,∞P,1 , which was found to

increase as the temperature increases [22], indicating that the strength of solute-solvent in-teractions decreases as the temperature increases. This fact shows that these two parent prop-erties sense the process of mixing differently. On the other hand, the larger negative valuesof K

E,∞S,2 would result from the two aforementioned factors, namely the changes of the EEA

conformation when it is infinitely diluted in water and the solute-solvent interactions. Thefirst factor would result in a decrease of the intrinsic compression of the amphiphile mole-cule, and at the same time the second effect would stiffen the surrounding water moleculesin relation to the pure state.

In order to support the tentative explanations given before, we compare the temperaturedependence of K

E,∞S,i of the present aqueous system with those of aqueous systems where

the amphiphile molecules can be derived from EEA by substituting either the head OH

Table 4 Limiting excess partialmolar compressions,K

E,∞S,i

(mm3·MPa−1·mol−1),and standard deviations,σi(mm3·MPa−1·mol−1), for thewater(1) + EEA(2) system from283.15 K to 303.15 K

T/ K KE,∞S,1 σ1 K

E,∞S,2 σ2

283.15 −16.4 1 −74.5 3

288.15 −16.5 2 −70.0 6

293.15 −15.8 2 −66.0 6

298.15 −16.1 2 −63.0 6

303.15 −15.4 2 −60.3 6

816 J Solution Chem (2010) 39: 808–819

Fig. 4 Molecular structure of:(ethylamino)ethanol (EEA),diethylamine (DEA) and2-(diethylamino)ethanol (DEEA)

Fig. 5 Temperature dependenceof the limiting excess partialmolar isentropic compressions,K

E,∞S,2 , of: (•) EEA; (�) DEEA;

and (�) DEA for the respectiveaqueous systems

Fig. 6 Temperature dependenceof the limiting excess partialmolar isentropic compressions,K

E,∞S,1 , of water(1) for the

aqueous systems: (◦) EEA;(�) DEEA; and (�) DEA

group by H, leading to DEA, or substituting the H of the secondary amine group by thehydrophobic CH3CH2 group, leading to 2-(diethylamino)ethanol, DEEA (see Fig. 4).

For comparison, Figs. 5 and 6 show the profiles of the temperature dependence of KE,∞S,i

for the three mentioned systems. Figure 5 shows that, although all the three systems presentnegative K

E,∞S,2 values, curves for EEA and DEEA follow the same profile, increasing as

the temperature increases. Conversely, the DEA values show a tendency to decrease withincreasing temperature, probably due to the increase with temperature of the degree of hy-drolysis as discussed in a previous paper [13]. The behavior of EEA and DEEA seems tobe in accordance with the view that, at infinite dilution, the driving force for hydrophobic

J Solution Chem (2010) 39: 808–819 817

hydration depends on solute-solvent hydrophilic interactions rather than on the enhancingthe water structure [43–45]. In fact, Finney and co-workers using isotope-labeled neutrondiffraction measurements concluded that there is no significant perturbation of the structureof the first hydration shell of the hydrophobic moiety of the amphiphile molecules from thatfound in liquid water, contrary to what has been advanced to explain most of experimentalresults for thermodynamic properties. The present K

E,∞S,2 temperature dependences for EEA

and DEEA, showing a similar net increase as the temperature increases, led us to concludethat a weakening of the solute-solvent interaction (H-bonding) is the prevailing effect, sincehydrophobic hydration should increase with temperature. Otherwise, Fig. 6 shows that whileK

E,∞S,1 , corresponding to water infinitely diluted in EEA, is almost constant, in the cases of

DEEA and DEA it decreases as the temperature increases. Considering that these trendsreflect the behavior of water in the amphiphile-rich region, these results suggest that in thisregion water-amphiphile hydrogen bonding would prevail in solvents with a higher densityof –OH groups, whereas in mixtures of solvents whose the accessible surface area is dom-inated by the non-polar alkyl chain, water clustering would be more favorable. This is theexplanation given by Koga and coworkers [46] to interpret values obtained for excess partialmolar volumes, enthalpies and entropies of aliphatic alcohols from methanol to decanol andfor some alkoxyalcohols in water-poor solutions.

Acknowledgements We are grateful to Fundação para a Ciência e a Tecnologia and FEDER for finan-cial support. We thank Mr. Pedro S. Carvalho for performing some of the experiments. A.F.S. Santos andI.M.S. Lampreia thank the University of Lisbon for granting sabbatical leave in the academic years 2007/2008and 2009/2010, respectively.

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