joumal of M OLEC ULAR

LIQUIDS E L S E V I E R Journal of Molecular Liquids 88 (2000) 183-195

www.elsevier.nl/Iocate/molliq

V A R I A T I O N O F V O L U M I C P R O P E R T I E S W I T H T E M P E R A T U R E AND C O M P O S I T I O N O F 2-BUTANONE + 1,2-PROPANEDIOL BINARY M I X T U R E S

Andrea Marchetti, Gyula P~ilyi, Lorenzo Tassi,* Alessandro Ulrici and Claudia Zucchi

Department of Chemistry, University of Modena, via G. Campi 183, 41100 Modena, Italy

Received 22 November 1999; accepted 01 August 2000

ABSTRACT

In this work we present experimental values of the density (p), and some related quantities such as excess molar volumes (I,~), of the 2-butanone + 1,2-propanediol binary mixtures at various temperatures in the - 1 0 < t / °C _< 80 range and as a function of mole fraction. The experimental results have been fitted to some relationships of the type p = 9(73, p = p(xi), and p = p(T, xi) to estimate the property in correspondence of the experimental data gaps. The observed behaviour has been interpreted on the basis of specific interactions and molecular features of the components. © 2000 Elsevier Science B.V. All rights reserved.

KEYWORDS : density; excess molar volumes; binary mixtures; 2-butanone; 1,2-propanediol.

* corresponding author. Fax : 059-373543. E-mail : Tassi.Lorenzo@unimo.it

0167-7322/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII S0167-7322(00) 00153-7

184

INTRODUCTION

The thermophysical behaviour of ketones J-4 and diols, 59 both as pure species or in binary mixtures, have been studied extensively in recent years, due to their applications as solvents for chemical industry, as additives, and for many other employments in the scientific context. The type and nature of the specific intermolecular interactions have been studied in terms of derived quantities such as excess molar mixing properties. The variation of these properties with temperature and composition provides important information concerning architecture of self-organization and associative processes in these solvent mixtures.

As a part of a research program on thermodynamic properties of binary and temary solvent systems, l°'ll we report here experimental data of densities for the 2-butanone (methyl- ethyl-ketone, MEK, component 1) + 1,2-propanediol (12PD, component 2) solvent system, which were measured at different temperatures in the -10 < t / °C < 80 range and at atmospheric pressure, employing the two pure species and their mixtures covering the whole range of composition expressed by the condition 0 < xi < 1.

Some properties derived from the experimental values, i.e. excess molar volumes (V a)

and the related partial molar quantities ( ~ and ~L- ) of the components, were calculated and

interpreted on the basis of molecular features, geometric effects and specific interactions.

EXPERIMENTAL

M a t e r i a l s - The solvents MEK and 12PD (containing < 0.05% and < 0.10% by mass of water, respectively, found by Karl-Fischer titrations) were high-purity grade reagents from Carlo Erba (Milan). MEK was further purified by double fractional distillation over anhydrous NaKCO3 to eliminate the traces of acids and to reduce the total amount of water, keeping only the middle fraction (b.p. 79.6 °C) for the measurements. The purified solvents were stored over 3A type molecular sieves for many days before use. The final purity was checked by gas chromatography (99.8% and 99.7% by mass for MEK and 12PD, respectively), confirming the absence of other organic components.

A p p a r a t u s a n d P r o c e d u r e s - All binary mixtures were prepared, just before use, by weight on a Mettler PM 480A-range balance, operating in a dry box to avoid the atmospheric moisture. The probable error in each mole fraction (xi) is estimated to be less than 1.5x10 4.

The apparatus, procedures and experimental details for the density measurements have been described elsewhere, l0

RESULTS AND DISCUSSION

The values of the measured experimental densities at each temperature are reported in Table 1, along with binary composition of the solvent mixtures. Some values at the highest temperature and in the MEK rich-region are absent because of phase separation.

Our density values for the pure species have been compared with some literature data (Table 2), and a fairly good agreement is observed.

185

0

~J

0

.o

+

v

0

S &

a .

"1:I

! &

0 ° ~

r3~

u.l

0

c~

d d d d d o o d d o o d o o d d o

d d d d d o d d o d d d d d d d d

o ~ d d o d o o d d d d d d o ~

I ~I~ ~ o ~ o~ o ~ o ~ o ~ o~ o~ o~ o

I

186

TABLE 2. Reference Density Values (p/g em 3) for MEK and 12PD at Some Selected Temperatures

MEK 12PD

t / °C p Ref. this work p Ref. this work

5 0.820582 (4) 0.820633

15 0.8103 (20) 0.810305

20 0.80592 (21) 0.805129

25 0.79974 (23) 0.799891

27

30 0.79449 (25) 0.794671

40 0.784326 (4) 0.784122

45 0.7785 (20) 0.778826

50 0.774846 (4) 0.773531

1.0364 (22) 1.035936

1.0327 (8) 1.032228

1.0308 (24)

The density data were processed, following literature suggestions, by empirical equations which relate the properties of the mixtures to those of the pure species, in order to improve our knowledge about these interpretative models and to perform predictive calculations of the investigated properties in correspondence of the experimental data gaps.

At first, the variation of p with temperature (T / K) was examined by applying the fitting equation : x2

4

p(T) = ~a,T ' (1) i=O

whose ai coefficients for each mixture have been evaluated by TSP multilinear regression package, 13 and are listed in Table 3 along with the standard deviation ~(p). Equation (1) seems to be adequate to fit the experimental data and allows us to calculate the density values within the limits of the experimental error at each temperature, with an average uncertainty

% = + 0.0018 g cm "3, evaluated by the relation

- - o 100 ~ , Ap yo - - - e Ipo,=,, - pco,c l (2)

where N is the number of experimental points (204) of Table 1, and taking values in the 0.0000 _< Ap % / g c m -3 -< 0.0038 range.

The next step in this study concerned with an empirical investigation of the trend of p against binary composition, expressed as the mole fraction of one component. Therefore the isothermal densities have been fitted to the relationship:

187

TABLE 3. Coefficients ai and Standard Deviations t~(p)/g cm -3 of Eq. (1) for the MEK (1) + 12PD (2) Binary Mixtures.

xl ao 104al 107a2 109a3 101~a4 105 ~(p)

1 1.090239 -11.624 21.901 -7.5178 7.6942 2.0

0.9025 1.720632 -93.562 428.89 -96.412 79.918 2.5

0.8050 1.435688 -54.516 239.77 -55.473 46.673 2.3

0.7044 1.126481 -12.411 37.646 -12.295 12.245 2.4

0.5894 1.401185 -45.245 196.32 -45.912 38.850 2.6

0.5048 0.798083 35.891 -200.09 39.920 -30.447 2.7

0.4030 0.414218 88.589 -457.91 96.228 -76.494 2.1

0.3108 1.298397 -25.554 104.39 -26.178 23.120 2.5

0.2049 1.276195 -19.225 69.323 -17.144 14.517 2.6

0.1045 1.189979 -5.8243 6.5108 -3.7699 3.8960 2.4

0 1.058957 13.939 -89.524 17.352 -13.461 2.0

4

p(x,) = ~ .b jx ( (3) ./=0

whose bj coefficients are shown in Table 4, together with the standard deviation or(p) / g cm 3

at each temperature. Equation (3) reproduces the experimental data of Table 1 within Ap % =

+ 0.0032 g cm -3, and always in the interval 0.0000 < Ap % / g cm "3 < 0.0083. By using multiple linear regression analysis, a bivariant equation has been obtained

which correlates p with T and xi. By combining equations (1) and (3), after algebraic manipulation we can write:

This equation, whose calculated c o coefficients are listed in Table 5, allows us to fit p for any value of T and xi of the binary solvent system investigated here, reproducing the

experimental values with an average uncertainty A--p % = 4- 0.0034 g c m "3 (and always in the

limits 0.0000 _< Ap % / g cm "3 _< 0.0092) over all the specific temperature (-10 ___ t / °C < 80) and composition (0<_ xi < 1) ranges.

Particular attention must be given when using equations (1), (3) and (4) for predictive calculations, in order to avoid extrapolated values without any physical meaning in temperature and composition ranges where phase separation occurs.

188

TABLE 4. Coefficients bj and Standard Deviations cr(p)/g cm "3 of Eq. (3) for the MEK (1) + 12PD (2) at Various Temperatures.

t / °C bo 10bj I02b2 10~b3 104b4 10sex(p)

-10 1.057446 -2.4782 1.8536 12.016 -42.625 4.2

-5 1.053972 -2.4976 1.9521 10.971 -38.495 3.5

0 1.050442 -2.5206 2.1002 10.206 -38.387 3.8

5 1.046867 -2.5407 2.1034 11.652 -48.492 3.3

10 1.043249 -2.5621 2.1121 13.419 -61.062 2.7

15 1.039602 -2.5791 1.9808 16.841 -80.250 2.1

20 1.035925 -2.5959 1.8595 19.886 -96,810 2.1

25 1.032214 -2.6165 1.8604 21.390 -106.50 2.8

30 1.028485 -2.6333 1.7615 23.714 -118.04 3.2

35 1.024723 -2.6572 1.9610 21.716 -109.07 4.4

40 1.020931 -2.6770 2.0251 21.168 -105.11 4.9

45 1.017114 -2.7012 2.2804 17.857 -88.140 4.1

50 1.013253 -2.7240 2.5010 14.834 -71.567 3.4

55 1.009372 -2.7470 2.7522 11.124 -51.029 3.1

60 1.005482 -2.7757 3.1539 5.8978 -24.904 2.4

65 1.001528 -2.7963 3.3752 2.1137 -2.4007 2.9

70 0.997548 -2.8166 3.6021 -1.8574 21.362 3.9

75 0.993563 -2.8392 3.8382 -5.2069 40.128 4.6

80 ~989561 -2.8689 4.7026 -26.672 220.98 8.4

THE EXCESS FUNCTION

In order to take into account that the p values for these polar binary mixtures have a non- linear dependence on composition, the corresponding excess molar volumes (Ifi) were calculated, expressing the deviations from ideality as given by the following equation:

2

v ~ = ~ x y , ( p - ' - p ; ' ) (5)

where Mi are the molar masses (Ml = 72.107 and M2 = 76.095 g molq), and 9 and pi are the densities of the mixtures and of the pure species at each experimental temperature, respectively.

T A B L E 5. Coefficients cij and Standard Deviat ion cr(p)/g cm "3 o f Eq. (4) for the M E K (1) + 12PD (2) Solvent System.

189

ij Variable cij

00 1.083192

01 xl 4.0102

02 xl 2 -26.291

03 xt 3 47.5831

04 xl 4 -25.2074

10 T 1.08 x 10 -3

11 Txl -5.52 × 10 -2

12 Txl 2 3.46 × 10 "l

13 Txl 3 -6.26 × 10 "t

14 Txl 4 3.32 × l i f t

20 /,2 -7.43 × 10 -6

21 7axa 2.70 × 10 -4

22 7~xl 2 -1.69 × 10 -3

23 Taxi 3 3.07 × 10 -3

24 TZxl 4 -1.63 × 10 -3

30 7o 1.41 x 10 -8

31 /°xl -5.86 × 10 .7

32 /~xl 2 3.67 x 10 -6

33 TSxl 3 -6.66 × 10 "6

34 T3xt 4 3.54 × 10 -6

40 T 4 -1.08 × 10 "11

41 T~xl 4.76 x 10 q°

42 T~xl 2 -2.96 × 10 -9

43 T4xl 3 5.38 × 10 -9

44 T4xl 4 -2.86 × 10 .9

or(p) = 3.3 x 10 .5

According to Redl ich and Kister, excess molar volumes were fitted, at each temperature, by a smooth ing equat ion o f the type 14

V E ~-- XlX2 Z N k (x 2 _ Xl )k (6) k

190

TABLE 6. Coefficients dk and Standard Deviations g(Ve)/cm s mol l of Eq. (6) for the MEK (I) + 12PD (2) Binary Mixtures at Different Temperatures.

t / °C 10d0 102dl 102d2 103cr(V E)

-10 -9.2809 -25.956 -4.2646 2.9

-5 -9. 8979 -23.478 -2.7395 2.6

0 - 10.466 -20.785 -3.9363 2.9

5 -11.013 -18.491 -7.6064 2.6

10 -I 1.551 -15.852 -11.127 2.2

15 -12.071 -13.527 -15.539 2.2

20 -12.604 -11.887 -18.566 2.4

25 -13.121 -10.633 -21.883 2.8

30 -13.672 -9.9882 -23.689 3.3

35 - 14.240 -9. 8070 -23.305 3.6

40 - 14. 809 - 10.431 -22. 543 3.9

45 -15.409 -11.970 -19.225 3.8

50 -16.026 -13.323 -14.657 3.7

55 -16.666 -16.224 -10.029 3.7

60 -17.328 - 18.679 -3.8833 4.0

65 -17.992 -21.783 2.0121 4.6

70 -18.674 -24.748 7.6421 5.1

75 - 19.376 -27.976 12.918 5.9

which allows us to reproduce the excess values within the limits of experimental error of p measurements for each binary mixture. Table 6 reports the dk coefficients and the standard deviation cr(V~)/cm 3 mol "l of the smoothing equation (6). This fitting procedure gives an

average uncertainty ~-~E = + 0.003 cm 3 mol -l (0.000 _< AV e / cm 3 mol q < 0.013).

Figure 1 shows the trend of the excess quantity against x2 and, as it is evident, Ve is always negative at all experimental conditions. For reasons of clarity, only the experimental points at one temperature (25 °C) are represented in the figure. According to literature suggestions, t5 the contraction of molar volume due to mixing process may be attributed to the presence of strong intermolecular interactions, such as hydrogen bonding, appearing between components. Furthermore, V E passes through a minimum centered at x2 -= 0.5 which becomes deeper as temperature increases. This minimum suggests the probable existence of a eomplex structure of the type MEK : 12PD = 1 : 1.

191

Figure 2 shows equimolar values of ~ at different temperatures. These values may be obtained from Table 6 since

V~(x~ = 0.5) = 0.25. do (7)

It is evident that dVE/dT is negative (d/~/dT = -2.7 x 10 -3 cm 3 tool -I K "l at 25 °C) and that its value decreases around circa 30 °C. Since ~ reaches a minimum at this composition ratio (xi = 0.5), the related variation is certainly the maximum observable in this solvent system. This quantity represents the change during mixing of the expansibility, E or otV, i.e.

E z = (ctV) E = dI/e/dT (8)

0 L ~

7 0

-0.1

-0.21

-0.3

-0.4

-0.5

I I I I

0 0.2 0.4 0.6 0.8 1

X2

FIGURE 1 - Isothermal excess molar volume ( ~ ) vs xa for MEK (1) + 12PD (2) binary mixtures at different temperatures from -10 to 75 °C.

192

where a is the thermal expansion coefficient of the equimolar solution. From the point of view ofthermomechanical behaviour of mixed solvent systems, the thermal expansibility of the liquids may be usefully correlated to other properties such as internal energy contribution and internal pressure, compressibility, and some derivedl6quantities which can be fruitfully employed in modelling and solving engineering problems.

To deepen our knowledge about this solvent system, a further aspect have been taken into account. By deriving the equation (6) with respect to xi and after algebraic manipulation, it is

- - E possible to obtain the partial molar excess volumes ( V, ) and the partial molar volumes ( ~ ) of the components :17

-E Ve aV E V , = + ( l - x , ) - - (9)

&,

V,. = Vj + ~e (10)

7 0

-0.2

-0.3

-0.4

-0.5 I I I

-10 20 50 80

t/°C

FIGURE 2 - Plot of equimolar V E (xi = 0.5) against temperature for MEK (1) + 12PD (2). Points are from temperature-dependent dk coefficients of Eq. (6) in Table 6.

where Vi is the molar volume of the i-th pure component at each temperature. Therefor using the Redlich-Kister equation with the coefficients reported in Table 6 for experimental condition, it is possible to determine the partial molar quantities by calcul

the ~V--~e terms. A numerical inspection of ~ quantities shows that the dependenc 0x~

composition of the apparent molar volumes of MEK and 12PD is similar at all tempera1

Gradually, the V, values of both species decrease while reducing their recip

concentration. Furthermore, we observe that an increasing temperature results in a pa

increase of V~. Probably, the partial molar volume contraction of these species is relat

their molecular features, steric hindrances and rotational conformers that become more s under certain conditions, l s.19

0

0.5 0

-lO oo

-1.5 75 "C ~ -i.0

-1.5 -2.0

i i t

0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6

X2

(a) (b)

FIGURE 3 - Partial excess molar volumes (V~) vs x2 for MEK (1) + 12PD (2) binary mixtures at different temperatures : (a) MEK ; (b) 12PD.

194

In Figure 3a, b are represented the V,~ trends for the two components in the mixtures, at all measuring temperatures. These plots should significantly help in understanding which kind of effects and driving contributions are mainly responsible for the macroscopic behaviour of

this solvent system. In the extremely dilute MEK region the ~e values show a marked and continuous decrease with increasing temperature, passing from -1.230 at -10 °C to -2.088 cm 3 mol "~ at 75 °C. This observation indicates that for these mixtures the breaking of the weak dipolar interactions involving self-associated MEK molecules is very effective when a hydrogen bonding network between the two components occurs, this causing a negative contribution to V ~.

__f,, Considering 12PD, Figure 3b depicts the trend of V2 at the same experimental

conditions above mentioned. In the dilute 12PD region (x2 ~ 0), where the degree of intermolecular association is low, the breaking-off of hydrogen-bonding between 12PD molecules is very probable, and the homocooperative network is progressively substituted by the heterocooperative one, which should be more and more effective (involving -OH groups of 12PD and =C=O group of MEK), and providing a liquid structure with a greater packing degree than that observable in the pure species. This behaviour should be the responsible one

for the most negative contribution to ~ and is reflected in the significant decrease of V~ in - - E

this region. However, starting from the lower temperature, V2 decreases with increasing temperature up to around 40 °C, reaching a minimum (-1.615 cm 3 mol "l) which becomes

- - E almost insensitive with changing temperature up to 75 °C. The invariableness of V2 over 40 °C probably suggests that the 12PD molecule reaches a maximum contraction of its free volume in correspondence with the possible presence of a conformer that should be more stable than the other molecular rotameric configurations.

ACKNOWLEDGEMENTS

The authors are grateful to MURST of Italy for financial support.

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