Indian Journal of Chemistry Vol. 41 A, September 2002, pp. 1804-1811

Osmotic and activity coefficient studies on the aqueous solutions of tetramethylurea at 298.15 K

K J Patil*, A M Surgar & D H Dagade

Department ofChelll istry. Shi vaji Uni versity, Kolhapur 416 004. India

Received /0 April 2002; revised 3 Jlllv 2002

The osmotic coeffi cients and densities of good prcc ision of aqucous solutions of tetramethy lurea (TMU) in the concentration range 0.1 to 8.0 11/ at 298. 15 K have been experimentally detennined and the d:.1la used to C1lculate apparent and partial molar volumes, activities and act ivity coe ffi cients of water and TMU as a function of eoneentrat iol1 o f TMU . It has been observed that partial molar vo lumes of solvent and solute go through a maximum and a minimum, respecti vely, at about 0.055 mole fracti on o f TMU. The activ ity coeffi cient values for 1-1 "0 incn:ase, while those 01' T MU decrease with increase in concentration of TMU. These results arc compared w ith those of aqueous urea so lutions and arc in agreement with literature va lues indicating the presence of hydrophobic interacti ons in I-I "O-TMU so lu tions. Exce '; ' free energy of mixing of TMU in water has been calculated using act ivity data at 298. 15 K and is found to decrease as a functi on of TM U concentration in the stud ied concentration range. T he va lues for the attractive and repul sive contributions to the so lute­so lvent interaction ha ve becn estimated and data is compared w ith other non-electrol y tes. Further, appl y ing M cMillan­Mayer theory of solutions to thc data, osmotic second and third viri al coeffi cients for TMU ha ve been obtainc: c1. T he va lues of vi rial coefficient s, on decompos ition into attracti ve and repulsive contributions to solute-solute intcracti ons. indicate that pairwi se interacti on between TMU molecules and water structure making effect is more prominent th an tr iplet nnd higher order interactions in the studi ed concentration range of nqueous-TMU so lutions.

The thermodynamic properties of aqueous urea solutions are well-known I. Consideri ng the importance of urea as denaturing agent for aqucous bio-polymer so lu tions, many basic studi cs were conducted to obtain information about molecular interaction in solutions". It has been postulated that urea mixes ideally with a postulated 'dense' (non­hydrogen bonded) spec ies of water with a slight structure breaking effect via H-bond formation i .e. so lute-so l vent interactions3

. Stokes has ex plai ned the concentration dependence of the thermodynamic properties in terms of association of urea mo l ec ul es~ . There is much controversy regarcli ng the interpretation of urea acting as structure-making or structure-breaking sol ute and a lot depends upon the unique structural properties o f waters. It is known that the alkyl substitution in a molecule alters the thermodynamic properties of so lutions and th e effec ts can be explained in terms o f hydrophobic hydration and interactions6

.7

. M ethyl substitution on amino group in urea has three effects: ( i) contribut ion rrom methyl group itself (intrinsic and hyclrophobic), (i i) a hindrance of H-bonding ability of the substit uted ami no group and (ii i) a decrease of H-bonding abili ty or the carbonyl group as indicated by the dipole momentss. Therefore, it is interesting to compare thermodynamic properties of urea-water so lutions

with that of aqueous sol utions of lelramethylurea so that useful information about solute-solvent and solute-solute, and hence hydrophobic interacti on in aqueous solutions can be deri ved.

Tetramethy lurea is a typical l iquid at ordinary conditions, also is an excellent sol vent for aromatic organic compounds') It is so luble in water at all proportions. It has been reported that ultrasonic absorption , density and viscosity properti es show a maximum at about 20 mole or TMU in water and attributed to the formation or molec ular complexes of stoichiometry o f 4 : I (water-TMU)l o. Recentl y, the small angle neutron scattering stu dies in aqueous soluti ons of TMU have indicated th e presence o f hydruphobic interaction, which increase with temperature 1 I . Computer simul ati on or li qu id TM U and its aqueous so luti on studies re\'eal th at free energy of hydra ti on i" much less negat ive th an urea­water so luti ons and the influence ofTMU on energeti cs of water watl' r H-bonding is negligible1c

.

W e have earlier detected hydrophobic associ ation usin!.!. NMR relax ation and se lf-di f fus ion coerfi cient data~in aqueous so utipns (1 1' TM U I1

. T hus, TMU acts a\ hydrophobic so lute in aqueolls SO il tions.

T he nature of so lute-so lu te in teract ions in mi xtures can be inves ti gated by appl y it g lattice and oth er statis ti ca l mechan iea l theories t ~ . 15. The McM i l lan-

PATIL el al.: OSMOTIC ST UD IES OF TETRAMETHYLUREA SOLUTI ONS 1805

Mayer fo rmali sm appears at first sight to be an attracti ve one, as the pair and multiplet interac ti on parameters which can be extracted from thermodynami c data can, under favourable conditions, provide di rect estimates of the di fferent types of solute interacti ons. The theory has been successfull y applied to solutions of alcoholsl6, carbohydrates l7 and of electrolytes 18. Recently, we have made such an analys is fo r aqueous solutions of 18-crown-6 19

. To understand the thermodynami c behav iour of a typical hydrophobic solute like TM U in water, from which solute-solvent as well as solute-solute interac tions can be in vestigated, precise and accurate act ivity coefficient data along with partial molar volume data are required. In thi s context, we are reporting in the present paper the osmoti c, activity coefficient and volumetric studies of aqueous TMU solutions at 298 .1 5 K. The data is used to es timate the attracti ve and repulsive contri butions to the solute-solvent interaction, the magnitude of which can be used to interpret the solute-solvent interactions in terms of H­bonding and hydrophobic hydration. The data is also subj ected to the analysis using McMillan-Mayer theory of solutions20 and the approach evolved by Kozak et al.14

. The in fo rmati on about pairwise and triplet interac ti ons is derived and compared with other non-electrolytes like urea, sucrose, alcohols, etc.

Materials and Methods Tetramethylurea (>99% pure) procured from Merk­

Schuchardt was used wi thout further purification . The salt NaCi of AR grade (BDH) was dried under vacuum for 24 hours before use. All the solutions were prepared in fresh doubly glass-distilled water on molality bas is and converted to molarity scale when required using the density data at 298 .15 K.

The density measurement of aqueous TM U solutions were made using Anton Paar digital densitometer (model DMA 60/602) at 298. 15 ± 0.02 K. The reproducibility of the values was fo und to be better than ± I x 10-2 kg m-3

.

The osmotic cocfficients (C/J) of aqueous TM U solutions were determined using KNA UER K-7000 vapour pressure osmometer at 298. 15 ± 0.001 K. The instrument was kept in specially fabricated refrigerated thermostat working bctween 0 to 40°C. The osmometer was calibrated using aqueous Nae l solutions fo r the measurement of aqueous TM U solutions. The accuracy in C/J meas urements was found to be better than ± I x 10-3 at the lowest concentration studied.

Results The apparent molar volumes (C/Jv) of TMU in water

were obtained using the density data in the concentration range - 0.1 to 8.0 m using the usual equation . These data are in good agreement wi th those reported earlier8

.21

.

The partial molar volume (V2 ) of TM U at various

concentrati ons were es timated using Eq. (1)

V2 = C/Jv +m --- [dC/Jv ) dm

.. . (l)

The parameter (dC/Jv/ dm) was estimated by di fferenti ating the appropriate polynomi al of the plot of C/Jv against m. The partial molar volumes of water (V;) III aqueous TMU solutions at different

concentrations were calculated using Eq. (2) given below

- I [ 0 2 [dC/Jv )] VI = - Il IVI -11l --

III dm .. . (2)

where nl is the number of moles of water and VIO is

the molar volume of pure water. The data for V2 and

VI along with the density data are collected in Table I

and their variation as a function of concentration of tetramethylurea is shown in Fig. 1. The smooth extrapolati on of the curve V2 against concentrati on of

TM U in Fig. I to infinite dilution yielded the value of

limiting parti al molar volume (\1;0 ) of TM U. The

errors in volved in C/Jv and V2 values are of the order of

± 0.1 x 103 and ± 0.5 x 103 mm3mol- l, respecti vely at the lowest concentration.

The osmotic coefficients (C/J ) of aqueous telramethylurea so lutions were determined over the range 0.1 to 8.0 mol kg- I at 298. 15 K. Since the TMU is high boiling liquid (bp=449.65 K), its contri bution to total vapour press ure over the so lution at 298. 15 K is assumed to be negligible. The data are well represented by Eq. (3)

C/J = 1- 0.5267111 + 0.435611? - 0.18 1 1m3

+ 0.0382/1/4-0.0039//15 + 0.00021116

and are collected in Table 2.

.. . (3)

1806 IND IAN J CHEM, SEC A, SEPTEM BER 2002

18.20 115 .0

18.10 114.0

-0 18.00 113.0 .< 8

~ -8 ~ B~ -; 17.90 112.0

~

17.80 111.0

17.70 110.0

0.0 1.0 2.0 3.0 4.0 S.O

c / moldm·'

fi g. I- Variation of parti al molar volume of solven t (L. H.S.) and solute (R.H.S. ) as a function of concentration of TMU in aqueous solutions at 298.15 K

The solvent act ivity coefficients were calculated from the experimental os motic coeffici ent data using express ion

... (4)

where XI and X2 are the mole frac ti ons of solvent and solute respectively, and al is solvent activity. The

ac tivity coefficien t of solute (Y2) has been calcul ated lI sing Eg . (5)

... (5)

Since the osmotic coefficient is expressed as a power

Table I- Volume properties of TMU + H20 system at 298. 15 K

11/ C d 10-3 X 1/1. 10-3 X V; 10-3 X V;

mol kg- l mol dm-:1 kg m-3 mm' mor l

mm3 mor l mm3 mol- I

0.0000 0.0000 997.047 114.9* 114.9* 18.07*

0. 1018 0. 1003 997.2 18 114.8 114.7 18.07

0.2098 0.2043 997.410 114.7 11 4.6 18.07

0.4854 0.4586 997.943 11 4.5 114.2 18.07

0.9993 0.8945 999.068 114.2 113.7 18.08

1.5592 1.3207 1000.4 16 11 3.9 11 3.2 18.09

2.9486 2.2048 1003.859 11 3.4 112.6 18. 13

4.4758 2.9655 1007.049 11 3. 1 11 2.7 18. 12

5.7053 3.46 12 1008.7 18 11 3.1 113.2 18.05

6.77 19 3.8273 1009.758 11 3.2 11 3.7 17.94

7.7924 4. 1326 1010.385 11 3.3 114.3 17.80

*Values at infinite dilution.

Table 2--0smotic and act ivity coefficients of TMU + H20 system at 298. 15 K

III 1/1 OW YI Y2 I1GE

mol kg'l 1 mor l

0.1018 0.9846 0.9982 1.0000 0.9042 -0.39

0.2098 0.8836 0.9967 1.0004 0.8233 -0.75

0.4854 0.8181 0.9929 1.001 6 0.6822 -4.40

0.9993 0.7735 0.9862 1.0039 0.5498 - 16.69

1.5592 0.7439 0.9793 1.0068 0.4828 -32.9

2.9486 0.6993 0.9635 1.0147 0.3920 -82.7

4.4758 0.6838 0.9463 1.0227 0.3322 -152.4

5.7053 0.6945 0.931 1 1.0268 0.3 144 -207.9

6.77 19 0.7203 0.9159 1.0276 0.2996 -264.7

7.7924 0.7592 0.8989 1.0251 0.2930 - 320.8

PATIL e/ al.: OSMOTIC STUDIES OF TETRAMETHYLUREA SOLUTIONS 1807

0.030 r--------- ----------,

0.025

0.020

;. 0.0 15

0.010

0.005

0.000 i#--~-~--~-~--~-~----'

0.00 0.02 0.()4 0.06 0.08 0.10 0.12 0.14

x,

Fig. 2a--Variati on of water acti vity coc ffi cient YI as a fun cti on of mole frac tion of TM U at 298. 15 K

series on the molality scale of the solute by Eq.(6)

II

cfJ = I + L Ai mi " . (6) i= 1

where the coefficient Ai can be obtained by the method of least squares, Eq . (5) takes the form , after solving the right hand side integral , as

II (i + I) . Iny 2 = L -.- Ailll' i= 1 l

" . (7)

The data for the activity coefficients of solvent and solute at various concentrations are collected in Table 2. Figures 2a and 2b respectively represen t the variation of activity coeffici ent of solvent and solute as a function of concentration of solute at 298. 15 K. It is observed that the activity coefficient of solvent increases, while that of solute decreases as the so lu te concentration is increased.

The activ ity data, wh ich have been converted into the mole fraction scale , were used to calcu late the

excess free energy change of mixing (f.,C E) of TMU

with water using Eq. (8)

" . (8)

where XI and X2 are the mo le fracti ons of so lvent and solute respec tive ly. It is observed that the va lues are negative and deCl-eases with increase in concentration of TMU as shown in Fig . 3. The data are a lso inc luded in Table 2.

Discussion Examination of data in Table I and Fig. I reveals

that VI and V2 goes through a maxi mum and a

minimum respectively at -0.055 mole fraction of

0.0

~. 2

~.4

~.6 ;:. .5

~. 8

-1.0

-1.2

·1.4

0 4

Fi g. 2b--Variation of acti vity coeffi cient of TMU Y~ in aqueous solutions as a functi on of molality at 298. 15 K

-so

-100

-ISO

~ '" -200 "b <l -250

-300

-350

400 L-_~ __ ~_~ __ ~_~~_~ _ __J

0.00 0.02 0.()4 0.06 0.08 0.10 0.12 0.14

Fig. }--Variation of excess free cnergy of mi xing tJ.CE of aqueous TMU solut ions as a function of mole frac ti on of TM at

298. 15 K

TMU. S imil ar observations are well known for mo nofunctional so lutes like alcoho ls, amines and ethers as well as for the aqueous so lutions of tetraa lky lammonium salts22-24 . The partia l mo lar vo lume study of aqueous 18-crown-6 so luti ons at 298 .15 K a lso shows such behaviour25

. These observations indicate that the hydrophobic hydratio n is predominent in the studied concentration range. The negative slope in the lower concentration region can be attributed to th e reduction in hydrophobic hydration per mole of solute through an o verlap of the co-spheres26 (so lu te-so lvent-so lu te interactions). The

increase of V2 at hig h concentration range g ives an

indication of TMU-TMU inte ractions in so lution 7.

The li miting excess part ial mol ar vo lume (v:,0E =

V;o - V2o, where V20 is the mo lar vo lume of pure TMU

at 298. 15 K) of TM U is found to be nega tive and of magn itude 5.6 x 10J mm]mo l- I

. The negat ive

1808 INDIAN J CHEM, SEC A, SEPTEMBER 2002

magnitude is comparable with monofunctional non­electrolytes like t-butanol, higher amines etc. and indicates the extent of solute-solvent interaction , which occur with a volume loss for the solute27

.

The solute-solvent cluster integral , blIO, is related to the partial molecular vo lume of the solute at infinite dilution b/8

-3o

.. . (9)

where k is the Boltzmann constant, T is the abso lute temperature and K is the isothermal compressibility coefficient of the pure solvent. The values for solute­solvent interaction NB ll o' (where Bllo' = -bll o) for aqueous TMU solutions calculated usi ng Eq . (9) are given in Table 3a. The values for other non­electrolytes in aqueous solutions at 298.15 K are also included in Table 3a for comparison.

The solute-solvent cluster integral in the above equation is related to the potential of mean force (w") between one molecule of solute and one of solvent in the pure solvent by the expression (10)

.. . (10)

where r is the distance apart of the centres of the molecules. It was shown that thi s integral could be split into attractive and repulsive parts as

Blo; = 4n f;[l-exp(-w" / kT)]r 2dr

+ f; [1 -exp(-w" / kT)] r 2 dr

=S+cP A

... (11)

where R is the distance of closest approach of the two molecules, S is the repulsive and ¢ A is the attractive contribution .

If the form of potential w (ref. I I ) is known, then the integration could be performed to y ield B ll

o' . The simplest potential function regards the molecules as rigid spheres . For two hard spheres of diameters RI and R2,

_ .. (12)

The water molecule can be considered to be a sphere of diameter 0.304 nm (although one may use the diameter of water as 0.276 nm, we recained the value equal to 0.304 nm as the comparison of the data for other solutes can be made) and taking the diameter of TMU molecule as 0.725 nm (calculated on the basis of molar volume and assuming a spherical shape), the repulsive contribution to the solute-solvent interaction comes out as NS = 344.2 cm3mor l ancl the attractive contribution at 298. 15 K can be obtained as

The data of attractive and repulsive contributions to the solute-solvent interaction in water for other H­bonding non-electrolytes at 298.15 K are given in Table 3a for comparison . The attractive contribution increases with increase of H-bonding sites. The value of ¢ A for TMU is much larger than that for urea indicating the stabilization of the structure of solvent in aqueous TMU sol utions. Urea-water hydrogen bond interactions exist but may be short-lived. The

Table 3a--Attrac ti vc contributions to solute-solvent interac tion coefficient at 298.15K

10-3 x V;O 10-3 X RTK 1O-3 x NB 11 .

10-3 X NS 10-3 X (-Net>"")

mm3mol- 1 mm3mol- 1 mm3mol- 1 mm3mol- 1 mm3mor l

TMU + H2O 114.9 1.11 113.8 344 230.2

18C6+H2O# 223.2 1.1 I 222 .1 699 477

Sucrose +H2O* 2 11 .5 1.11 210.4 476 266

Glucose + H2O* 112.2 1.11 111.1 358 246

Hexamethy lene- 110.6 1.11 109.5 300 191 tetramine + H2O*

Urea* 44.2 1.l1 43.1 176 143

# Data from reference 19; * Data from reference 30

PATIL el (/1.: OSMOTIC STUDIES OF TETRAMETHYLUREA SOLUTIONS 1809

magnitude of ¢A is small compared to other non­electrolytes like sucrose but is comparable to hexamethylenetetramine and glucose having more H­bonding sites than TMU. Thus along with H-bonding with oxygen atom of the carbonyl group of TMU, there is large hydrophobic hydration. The minimum and maximum observed in partial molar volume of TMU at - 0.055 mole fraction indicate that in aqueous TMU solutions 1: 17 type clatherate hydrates equilibria may exist supporting the estimated ¢A

value which is larger than the expected one for the available H-bonding sites.

In aqueous tetramethylurea solutions, the logarithms of activity coefficients of water at 298.15 K are positive in the studied concentration range indicating the positive deviation from ideality. Such type of positive deviation from ideality was also reported in case of alcohol-water mixtures l4 . The negative I1C£ obtained in aqueous solutions may be indicative of H-bonding of water molecules with carbonyl oxygen . However, we restrained to discuss it in detail, since the data of excess enthalpy and excess entropy for solutions are not available.

According to the theory of McMillan and Mayer20

for a solution of a solute in a solvent, the osmotic pressure, IT, is given by

00. (13)

where It is the number density. It can be shown that the osmotic second and third virial coefficients, B2'

and B3' respecti vely, for the osmotic pressure of non­electrolyte solutions can be calculated from experimental activity data and the partial molar volume of solute and solvent as 14

00. (14)

(15)

o -0 where V, and V2 are the partial molar volumes of

solvent and solute respectively at infinite dilution, b

and g are the coefficients in equation of expansion of partial molar volume of solvent and solute at concentration C mol dm·3 given as

V, =V,o +aC+bC 2

- -0 V 2 = V 2 + gC + hC 2

(\6)

(17)

The Band C in Eqs (14) and (15) are the coefficients in the following Eq. (18) in which the solvent activity coefficient is expressed as a power series in the mole fraction scale of solute as,

Iny, =Bxi +Cx~ + .. . • 00 (18)

The Band C coefficients appearing in Eq. (18) with their sign and magnitude are of special importance in understanding the thermodynamic behaviour since they are related to solute-solvent association, solute­solute interactions and solute size'4.

Kozak et at. '4 have shown that the osmotic second virial coefficient can be decomposed into attractive and repulsive components. The minimum attractive (A 2min) and minimum repulsive (R2min) contributions to the osmotic second virial coefficient have been calculated by following equations

-0 R 2min =! ( 4 V 2 )

A2min = R2 min - NB;

(\ 9)

(20)

where! is the factor which is measure of the ellipticity of the molecule. For spherical molecule! is unity. In much the same way as the second virial coefficient, the third virial coefficient can be decomposed into attractive and repulsive components. The minimum attractive (A 3min ) and minimum repulsive (R3min )

contributions of these two components have been calculated using Eqs (21) and (22).

-0 R3min =10(V2)2 (21)

.00 (22)

The values of osmotic second and third virial coefficients as well as the minimum attractive and repulsive contributions to the solute-solute interactions are given in Table 3b. The value for osmotic second virial coefficient of TMU is estimated to be + 35.1 cm3 mol- ' and is large positive than the

1810 INDIAN J CHEM, SEC A, SEPTEMBER 2002

Table 3b-Attracti vc con tributi ons to solute-solute interaction coefficicnt at 298.15 K

NB2* N2B,* -A2min R1min -A3 min R3mi ~1

TMU+H2O 35. 1 4934 424.5 459 .5 13 1974 127040

18C6+H2O# 278 226998 615 893 498048 271051

Sucrose + H2O* 286 87000 558 783 360000 447000

G lucose + H2O * IJ7 403 520

Hexamethy lene- tetramine + 338 58 396 H2O+

Urca + H2O* 2.2 3800 175 177 16000 19800

Glycolamide + H2O* 20 7100 205 225 24000 31 100

#Data from referencc 19; *Data from re ference 14 +Data from reference 30

value reported earlier by Bezzabotno el al. II as small negative using small ang le neutron scattering data . The data for other non-e lectrolytes in aqueous medium, collected from the literature, are also included in Table 3 for comparison . The discrepancy in 8 2* value obtained in the present work with that obtained from neutron scatteri ng data may be attributed to the limitation of spectroscopic techniques to obtain infinitely dilute solution properties.

The minimum attractive contribution to the solute­solute interactions for TMU in aqueous solutions is

found to be - 424.5 cm3mor l, which is a measure of

pairwise interactions between two TMU molecules in water at 298.15 K. Since the magnitude of the attractive contribution increases with the number of functiona l groups capable of H-bonding as we ll as hydrophobic interactions with another so lute molecules , it reveals that one TMU molecule may interact strongly with another TMU molecule by means of hydrophobic interaction. Comparing the magnitude of minimum attractive contributio ns to solute-solute inte ractions for aqueous TMU solutions to that of other aqueous non-electrolytes at 298.15 K, it seems that the solute-solute pairwi se interacti o ns in aqueous TMU solutions are larger than those in urea, ami no acids and amides but are of smaller magnitude than the polyfunctional solutes like sucrose.

A relative importance of pairwi se verses trip let inte ractions can be derived by writing

... (23)

where r > 0 signifies that triplet c lustering is more pronounced than that wou ld be predicted from the

summation of three pairwise imeractions l4. For

tetramethylurea r is negative indicating that the pairwise interactions are predominent than the triplet and higher order clustering. Comparing the magnitude of A211lill and A311lill which have reflected in the val ue of

r for urea and TMU in their aqueous solutions at 298.15 K reveals that favourable pairwise interactions in aqueous TMU solutions are due to the increased number of hydrophobic a lkyl groups.

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