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Densities and excess volumes of binary mixtures of 1,4-dioxane with either ethyl acrylate, or butyl acrylate, or methyl methacrylate, or styrene at T=298.15 K
J. Chem. Thermodynamics 35 (2003) 239–250 www.elsevier.com/locate/jct
Densities and excess volumes of binary mixtures of 1,4-dioxane with either ethyl acrylate, or butyl acrylate, or methyl methacrylate, or styrene at T ¼ 298:15 K Rene D. Peralta a,*, Ramiro Infante a, Gladis Cortez a, Rogelio R. Ramırez a, Jaime Wisniak b b
a Centro de Investigaci on en Quımica Aplicada, Saltillo 25000, Coahuila, Mexico Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
Received 8 April 2002; accepted 14 October 2002
Abstract Densities of binary mixtures of 1,4-dioxane with either ethyl acrylate, or butyl acrylate, or methyl methacrylate, or styrene have been measured as a function of composition at T ¼ 298:15 K and atmospheric pressure with an Anton Paar DMA 5000 oscillating U-tube densimeter. The calculated excess volumes were correlated with the Redlich–Kister equation and with a series of Legendre polynomials. The excess volumes are positive for the mixtures of 1,4-dioxane with methyl methacrylate and butyl acrylate and negative for the mixtures of 1,4-dioxane and styrene. The excess volumes for the system 1,4-dioxane and ethyl acrylate are negative for mole fractions x of 1,4-dioxane less than or equal to about 0.44 and positive at x greater than about 0.4498 and positive thereafter. Ó 2003 Elsevier Science Ltd. All rights reserved. Keywords: Densities; Excess volumes; Monomers; Acrylic esters; 1,4-Dioxane
*
Corresponding author. Tel.: +52-844-438-9830; fax: +52-844-438-9839. E-mail address: [email protected] (R.D. Peralta).
0021-9614/03/$ - see front matter Ó 2003 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 9 6 1 4 ( 0 2 ) 0 0 3 1 3 - 0
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1. Introduction This work is part of our program to provide excess volumes of solvents and commercially important monomers, and asses the influence of the chemical structure of the solute on the mixtures under consideration. Sastry and Dave [1,2] measured the excess volumes, isentropic compressibilities, and dielectric constant of 15 binary mixtures of either methyl, or ethyl, or butyl methacrylate with hexane, heptane, carbon tetrachloride, chlorobenzene, and o-dichlorobenzene at T ¼ 308:15 K. They found that with aliphatic hydrocarbons the results were controlled by dispersive interactions, with chlorinated solvents the controlling factors were specific interactions (O-Cl and n-p types) [1,2]. Sastry and Valand [3] also measured the excess volumes of mixtures of alkyl (methyl, ethyl, and butyl) acrylates in several alkanols at 298.15 K and 308.15 K, and found that they were always positive. These results were explained on the basis of non-specific interactions between the components. Sastry et al. [4] measured the excess volumes of binary mixtures of methyl methacrylate with either cyclohexane or benzene, or toluene, or ethylbenzene, or (o,m,p)-xylene, at temperatures of 298.15 K and 303.15 K and found that except for toluene all have positive excess volumes. The excess volumes for the binary mixtures of (methyl methacrylate + cyclohexane) showed a non-symmetric behavior with a maximum V E 1:05 cm3 mol1 at x ¼ 0:45. Aminabhavi and Patil [5] measured the density of mixtures of styrene with 1,4-dioxane at the temperatures between 298.15 K and 308.15 K and determined that the excess volumes were negative. No literature data are available on the excess volumes of mixtures of alkyl acrylates used in this work.
2. Experimental The materials used in this work were obtained from Aldrich with the following minimum stated purity: 1,4-dioxane had a purity of 99.9 mass per cent and contained 0.023 mass per cent water while ethyl acrylate, butyl acrylate, methyl methacrylate and styrene had a purity of 99.9 mass per cent. Prior to use, ethyl acrylate, butyl acrylate and methyl methacrylate were vacuum distilled to eliminate the stabilizer about 0.002 mass per cent hydroquinone monomethyl ether. Styrene, which contained as a stabilizer between 10 and 15 parts per millions of 4tert-butylcatechol was degassed by freezing and heating to avoid polymerization. The purity of the solvents was further ascertained by comparing their densities at T ¼ 298:15 K listed in table 1, with the values reported in the literature. The density of the samples was measured with an Anton Paar model DMA 5000 oscillating U-tube densimeter, provided with automatic viscosity correction and two integrated X 100 platinum thermometers (DKD traceable), had a stated accuracy of 5 106 g cm3 . The temperature of the densimeter was regulated to 0:001 K with a solid-state thermostat. The densimeter was calibrated daily with both dry air and bidistilled degassed water and the reproducibility of density measurements was 2 106 g cm3 .
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TABLE 1 Purity of the components used in this work and their densities q measured in this work along with literature densities q(lit.) at T ¼ 298:15 K Component
Purity/mass per cent
q=g cm3
qðlit:Þ=g cm3
1,4-Dioxane Butyl acrylate Ethyl acrylate Methyl methacrylate Styrene
99.9 >99 99 99 99
1.027910 0.893666 0.915930 0.937669 0.901972
1.02792 [10] 0.8941 [3] 0.9163 [3] 0.93766 [11] 0.9015 [12]
All liquids were boiled or heated to remove dissolved air. Solutions of different compositions were prepared by mass in a 10 cm3 rubber-stoppered vial to prevent evaporation, using a Mettler AG 204 balance accurate to 104 g. To minimize the errors in composition, the heavier component was charged first and the sample kept in ice water. The accuracy of the mole fraction so obtained was 5 105 . The temperature was measured with an accuracy of 0:002 K. 3. Results and discussion At least 21 density measurements were performed (with repetition) for each binary system, in the full mole fraction range (0 6 x 6 1). The excess volumes V E of the solutions of molar composition x were calculated from the densities of the pure liquids and their mixtures according the following equation: V E ¼ ½xM1 þ ð1 xÞM2 =q ½xM1 =q1 þ ð1 xÞM2 =q2 ;
ð1Þ
where q, q1 , and q2 are the densities of the solution and pure components 1 and 2, respectively, and M1 and M2 the molar masses of the pure components. The corresponding values of q and V E are reported in tables 1–6 and figure 1. The values of V E were correlated with composition using two procedures. First, the Redlich–Kister expression [6] n X k V E ¼ x1 x2 Ak ðx1 x2 Þ ; ð2Þ k¼0
where the Ak with k ¼ 1; 2; 3; . . . are adjustable parameters. The Redlich–Kister regressor is very powerful and frequently used to correlate vapor–liquid equilibrium data and excess properties. Notwithstanding, it suffers from the important drawback that the values of the adjustable parameters change as the number of terms in the series is increased. Second, a series of Legendre polynomials Lk ðx1 Þ: n X V E ¼ x1 x2 ak Lk ðx1 Þ; ð3Þ k¼0
which for the four first terms with k ¼ 0; 1; 2; 3 is V E ¼ x1 x2 a0 þ a1 ð2x1 1Þ þ a2 ð6x21 6x1 þ 1Þ þ a3 ð20x31 30x21 þ 12x1 1Þ : ð4Þ
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TABLE 2 Experimental densities q, volumes V, calculated excess volumes V E obtained from equation (2), and deviations dV E ¼ V E ðexpt:Þ V E ðcalc:Þ for {x1,4-dioxane + ð1 xÞbutyl acrylate} at T ¼ 298:15 K and mole fraction x x
q=g cm3
V =cm3 mol1
V E 103 =cm3 mol1
dV E 103 =cm3 mol1
0 0.0270 0.0534 0.1015 0.1521 0.1996 0.2510 0.3014 0.3500 0.4003 0.4499 0.5008 0.5500 0.6004 0.6508 0.6998 0.7500 0.7997 0.7997 0.8498 0.9000 0.9492 0.9750 1
0.893666 0.895824 0.897979 0.902029 0.906463 0.910783 0.915675 0.920681 0.925717 0.931207 0.936882 0.943038 0.949301 0.956062 0.963235 0.970635 0.978669 0.987165 0.987167 0.996303 1.006131 1.016424 1.022178 1.027910
143.421 141.870 140.349 137.583 134.672 131.945 128.991 126.097 123.310 120.416 117.570 114.638 111.805 108.904 105.997 103.166 100.266 97.3849 97.3850 94.4754 91.5554 88.6903 87.1779 85.7176
0 4.53 10.4 19.6 30.6 43.1 55.4 69.2 83.7 96.5 107 115 122 127 128 125 120 108 108 92.1 66.4 38.6 18.0 0
0 0.092 1.08 0.252 )0.603 )0.042 )1.27 )0.864 1.06 1.47 1.02 )0.284 )0.943 )0.103 )0.574 )0.926 0.332 0.324 0.014 1.53 )0.834 0.753 )1.64 0
Legendre polynomials belong to the category of orthogonal functions such as Fourier, Bessel, and Chebyshev, which have the valuable feature, that for a continuous series of observations the values of the coefficients do not change as the number of terms in the series is increased. This is an important property because if a physical explanation can be assigned to one of its coefficients, its value remains constant. For the case of discrete measurements, such as determination of volumes of mixing, the values of the coefficients will vary, but slightly. In addition, as shown in table 7, the series of Legendre polynomials have the important characteristic that the structure of its first four terms is the same as that of the first four terms of the Redlich–Kister expression. The mathematical procedure to transform a power expansion, such as that of Redlich–Kister, into an orthogonal series has been described in detail by Tomiska [7,8]. Tomiska provides the iteration formulas for Legendre or ChebyshevÕs series of any order as well as the proof that the procedure is independent of the conversion coefficients from the actual excess property. Equations (2) and (3) were fitted using a least-squares optimization procedure, with all points weighted equally and minimizing the following objective function OF defined by
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TABLE 3 Experimental densities q, volumes V, calculated excess volumes V E obtained from equation (2), and deviations dV E ¼ V E ðexpt:Þ V E ðcalc:Þ, where for {x1,4-dioxane + ð1 xÞethyl acrylate} at T ¼ 298:15 K and mole fraction x x
q=g cm3
V =cm3 mol1
V E 103 =cm3 mol1
dV E 103 =cm3 mol1
0 0.0248 0.0502 0.0998 0.1496 0.2001 0.2500 0.2986 0.3498 0.4001 0.4498 0.5000 0.5503 0.5993 0.6500 0.7002 0.7500 0.8002 0.8498 0.8997 0.9492 0.9750 1
0.915930 0.918155 0.920461 0.925017 0.929662 0.934462 0.939288 0.944089 0.949238 0.954421 0.959662 0.965092 0.970665 0.976232 0.982142 0.988162 0.994288 1.000643 1.007101 1.013803 1.020655 1.024317 1.027910
109.310 108.721 108.116 106.940 105.769 104.570 103.395 102.250 101.048 99.8665 98.6989 97.5190 96.3371 95.1851 93.9925 92.8093 91.6362 90.4516 89.2798 88.0991 86.9242 86.3118 85.7176
0 )4.37 )8.55 )14.7 )18.2 )18.8 )16.8 )14.0 )8.94 )3.75 1.52 5.74 9.80 13.5 16.7 18.7 20.1 19.9 18.9 14.2 9.02 3.59 0
0 0.439 0.429 0.175 )0.324 )0.399 )0.022 )0.419 0.274 0.500 0.696 )0.032 )0.448 )0.477 )0.212 )0.229 0.166 0.309 0.926 )0.456 0.004 )1.34 0
OF ¼
N X
E E Vi;expt: Vi;calc:
2
;
ð5Þ
1
where N is the number of observations. The values of the different adjustable parameters, Ak of equation (2) and ak of equation (3), are reported in tables 8 and 9 for different values of k, together with the pertinent statistics. The standard deviation s was calculated from 1=2 X 2 E E s¼ Vi;expt: Vi;calc: =ðN kÞ ;
ð6Þ
where k is the number of adjustable parameters. The statistical significance of adding one or more terms after the third, was examined with the requirement that the residues be randomly distributed, as suggested by Wisniak and Polishuk [9]. Randomness of the residues was tested using the Durbin–Watson statistic. It was not deemed necessary to perform a step-wise regression. The variation of V E =fxð1 xÞg with composition was used in every case to test the quality of the data; this function is extremely sensitive to experimental errors, particularly in the dilute ranges. In addition, its values at infinite dilution represent
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TABLE 4 Experimental densities q, volumes V, calculated excess volumes V E obtained from and deviations dV E ¼ V E ðexpt:Þ V E ðcalc:Þ for {x1,4-dioxane + ð1 xÞmethyl methacrylate} at T ¼ 298:15 K and mole fraction x x
q=g cm3
V =cm3 mol1
V E 103 =cm3 mol1
dV E 103 =cm3 mol1
0 0.0248 0.0252 0.0497 0.1003 0.1501 0.1996 0.2500 0.3001 0.3500 0.3997 0.4499 0.5000 0.5499 0.5982 0.6500 0.7002 0.7497 0.7993 0.8495 0.8999 0.9487 0.9730 1
0.937669 0.939417 0.939441 0.941202 0.944887 0.948609 0.952367 0.956299 0.960275 0.964324 0.968472 0.972745 0.977135 0.981603 0.986036 0.990923 0.995781 1.000712 1.005784 1.011062 1.016528 1.021994 1.024775 1.027910
106.775 106.259 106.252 105.741 104.685 103.644 102.610 101.555 100.508 99.4652 98.4232 97.3709 96.3172 95.2683 94.2519 93.1588 92.0992 91.0510 89.9996 88.9333 87.8605 86.8165 86.2962 85.7176
0 6.82 7.07 11.3 21.6 28.6 38.5 44.9 52.7 59.7 63.7 68.7 70.8 72.7 73.0 71.5 68.4 63.1 56.1 47.2 34.2 18.9 10.2 0
0 1.35 1.53 0.626 0.797 )1.35 0.144 )1.16 )0.188 0.761 )0.273 0.723 )0.090 0.074 0.136 )0.091 )0.056 )0.379 )0.220 0.600 0.025 )0.233 )0.373 0
the values of the partial excess volume at infinite dilution, Vi E;1 [10], which can be also calculated from the adjustable parameters using V1E;1 ¼ A0 A1 þ A2 ¼ V11 V10 and
ð7Þ
V2E;1 ¼ A0 þ A1 þ A2 þ ¼ V21 V20 ;
ð8Þ
for the Redlich–Kister expression and V1E;1 ¼ a0 a1 þ a2 ¼ V11 V10 and
ð9Þ
V2E;1 ¼ a0 þ a1 þ a2 þ ¼ V21 V20
ð10Þ 0
for the Legendre polynomial. In equations (7)–(10) Vi is the molar volume of pure component i. The values of Vi E;1 are listed in tables 8 and 9. Equations (7) and (8) or (9) and (10) yield the same values of Vi E;1 . Inspection of the results of tables 2–6 and figure 1 indicates that the excess volumes for the binaries 1,4-dioxane with either butyl acrylate or methyl methacrylate are positive for the whole composition range while those for the system 1,4-dioxane and styrene are negative. The mixture 1,4-dioxane and ethyl acrylate shows a
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245
TABLE 5 Experimental densities q, volumes V, calculated excess volumes V E obtained from equation (2), and deviations dV E ¼ V E ðexpt:Þ V E ðcalc:Þ for {1,4-dioxane V + ð1 xÞstyrene} at T ¼ 298:15 K and mole fraction x x1
q=g cm3
V =cm3 mol1
V E 103 =cm3 mol1
dV E 103 =cm3 mol1
0 0.0274 0.0502 0.0998 0.1495 0.1999 0.2483 0.2999 0.3493 0.4000 0.4495 0.5008 0.5500 0.5993 0.6501 0.6998 0.7495 0.8000 0.8498 0.8996 0.9500 0.9750 1
0.901972 0.904613 0.906829 0.911834 0.916950 0.922238 0.927435 0.933093 0.938624 0.944438 0.950249 0.956449 0.962521 0.968816 0.975459 0.982167 0.989107 0.996392 1.003825 1.011502 1.019576 1.023702 1.027910
115.469 114.646 113.963 112.465 110.969 109.456 108.005 106.463 104.992 103.484 102.015 100.493 99.0402 97.5804 96.0811 94.6129 93.1431 91.6482 90.1748 88.7010 87.2053 86.4621 85.7176
0 )7.34 )13.1 )35.1 )53.8 )67.4 )77.9 )84.2 )86.4 )84.7 )80.2 )75.2 )66.1 )59.1 )48.1 )37.0 )28.2 )18.9 )12.4 )5.17 )0.735 )0.112 0
0 0.708 2.78 )0.817 )1.80 )0.236 )0.060 0.462 0.483 0.777 0.883 )0.960 0.092 )1.88 )0.462 1.10 0.614 0.911 )0.718 )0.186 )0.214 )0.466 0
mixed behavior. Our density measurements are in very good agreement with those of Aminabhavi and Patil [5]; the small difference may be attributed to the fact that Aminabhavi and Patil used styrene as purchased, without further treatment, and measured the density with a pycknometer. Interestingly enough, the calculated excess volumes for both data sets shown in figure 2 are in serious disagreement. Several explanations can be offered for this fact. First of all, the measured data have been transformed into excess volumes, using equation (1). It is a well-known fact that small errors in a variable (density) may translate in large ones when the measured variable is modified. Change of the variable will usually lead a different distribution of the error, as has been shown in detail by Wisniak [11] and Shacham et al. [12]. Another possible explanation is obtained by observing the numerical value of the two terms that compose the right-hand side of equation (1). Consider, for example, the x ¼ 0:5500a in table 6. For this concentration the molar volumes of the solution and of the equivalent ideal solution (rounded) are 99:0370 cm3 mol1 and 99:1057 cm3 mol1 , respectively. Hence, calculation of the excess volumes involves taking the difference between two very large numbers of about the same size and yielding, for the specific concentration, V E ¼ 0:0687 cm3 mol1 . It is clear that a
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TABLE 6 Experimental densities q, volumes V, calculated excess volumes V E , and deviations dV E ¼ V E ðexpt:Þ V E ðcalc:Þ for the system {1,4-dioxane + ð1 xÞstyrene} at T ¼ 298:15 K and mole fraction x x1
q=g cm3
V =cm3 mol1
V E 103 =cm3 mol1
dV E 103 =cm3 mol1
0.0000 0.0274 0.0252a 0.0502 0.0502a 0.0998 0.0998a 0.1495 0.1498a 0.1999 0.2001a 0.2483 0.2496a 0.2999 0.3000a 0.3493 0.3503a 0.4000 0.3994a 0.4495 0.4496a 0.5008 0.4963a 0.5500 0.5500a 0.5993 0.5995a 0.6501 0.6495a 0.6998 0.6992a 0.7495 0.7496a 0.8000 0.7998a 0.8498 0.8492a 0.8996 0.8997a 0.9500 0.9486a 0.9750 0.9751a 1.0000
0.901972 0.904613 0.904386 0.906829 0.906842 0.911834 0.911822 0.916950 0.916965 0.922238 0.922249 0.927435 0.927574 0.933093 0.933087 0.938624 0.938739 0.944438 0.944376 0.950249 0.950284 0.956449 0.955909 0.962521 0.962549 0.968816 0.968850 0.975459 0.975411 0.982167 0.982129 0.989107 0.989164 0.996392 0.996394 1.003825 1.003758 1.011502 1.011557 1.019576 1.019388 1.023702 1.023748 1.027910
115.469 114.646 114.714 113.963 113.962 112.465 112.466 110.969 110.962 109.456 109.450 108.005 107.965 106.463 106.462 104.992 104.962 103.484 103.501 102.015 102.009 100.493 100.626 99.0402 99.0370 97.5804 97.5729 96.0811 96.0955 94.6129 94.6253 93.1431 93.1352 91.6482 91.6521 90.1748 90.1897 88.7010 88.6940 87.2053 87.2428 86.4621 86.4559 85.7176
0 )7.34 )5.43 )13.1 )15.0 )35.1 )33.3 )53.8 )52.0 )67.4 )65.7 )77.9 )76.7 )84.2 )82.4 )86.4 )86.2 )84.7 )86.0 )80.2 )82.6 )75.2 )77.6 )66.1 )68.7 )59.1 )59.3 )48.1 )51.1 )37.0 )40.5 )28.2 )31.4 )18.9 )22.5 )12.4 )14.1 )5.20 )8.10 )0.700 )3.71 )0.100 )1.93 0
0 0.708 19.1 2.78 6.23 0.817 0.301 )1.80 )15.0 )0.236 )3.24 )0.060 )3.04 0.462 11.8 0.483 4.42 0.777 1.96 0.883 )0.515 )0.960 )6.81 0.091 )1.30 )1.88 4.71 )0.462 )8.20 1.10 2.25 0.614 )0.554 0.911 1.74 )0.718 7.66 )0.186 0.147 )0.214 )6.53 )0.466 )7.94 0
a
Mixtures prepared with undried 1,4-dioxane.
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247
v
(
( x FIGURE 1. Excess volumes V E at T ¼ 298:1 K. , {x1,4-dioxane + ð1 xÞmethyl methacrylate}; N, {x1,4-dioxane + ð1 xÞethylacrylate}; r, {x1,4-dioxane + ð1 xÞbutylacrylate}; d, {x1,4-dioxane + ð1 xÞstyrene}.
TABLE 7 Legendre polynomial given by equation (3) and Redlich–Kister expression given by equation (2) as a function of polynomial order k Polynomial order, k
Legendre polynomial, 3
Redlich–Kister, expression
0 1 2 3 4
1 2x1 1 6ðx21 x1 þ 16Þ 20ðx31 32x21 þ 35x1 201 Þ 70ðx41 2x31 þ 97x21 27x þ 701 Þ
1 2x1 1 4ðx21 x1 þ 14Þ 8ðx31 32x21 þ 34x1 18Þ 16ðx41 2x31 þ 32x21 12x þ 161 Þ
small error in each of the two large volumes reflects as a very large error in their difference. We have here the same problem present in the calculation of heats of reaction; they can be calculated from heats of formation or from heats of combustion. The second case is usually in large error for the same reason: we are taking the difference between large numbers to obtain a number smaller in one order of magnitude (at least) of the original figures. Another possibility considered was the effect of the small amount of water present in the ether which was suggested by one of the reviewers. In order to study its influence the ether was first dried with metallic sodium, distilled under vacuum and then stored in the presence of molecular sieves. The dried material contained 0.009 mass per cent water as determined by Karl-Fischer. A series of new measurements were performed and their results are reported in table 6 and shown in figure 2, which clearly shows that drying the ether had no significant effect on the results.
248 TABLE 8 P P E , and Vi E;1 at Coefficients Ak of equation (2), standard deviation s defined by equation (6), Durbin–Watson statistic d a ¼ Nu¼2 ðeu eu1 Þ2 = Nu¼1 e2u , Vx¼0:5 T ¼ 298:15 K A0 10 3
1+2 1+3 1+4 1+5
A1 10 1
3
cm mol
cm mol
4.61 0.230 2.83 )2.98
3.35 1.89 0.926 3.01
A2 10 1
3
A3 10 1
cm mol 0.278 )0.722 0.330 0.489
3
s 104
A4 10 1
cm mol 0.241
3
1.86
9.2 5.5 7.2 8.1
V1E;1 10
E Vx¼0:5 10
cm mol 0.540
)1.52
da
1
3
1.9 1.6 1.7 1.6
1
3
cm mol
cm mol
1.15 0.0577 0.709 )0.744
1.540 )2.09 2.24 )2.56
V2E;1 10 1
cm3 mol1 8.24 2.18 4.09 0.429
TABLE 9 E , and Vi E;1 at T ¼ 298.15 K Coefficients ak (equation (3)), standard deviation (equation (5)), Durbin–Watson statistic d, Vx¼0:5 System
a0 10
a1 10
a2 10
a3 10
a4 10
s 104
da
3
1+2 1+3 1+4 1+5
4.71 0.0971 2.95 )2.59
3.35 2.04 0.926 2.10 PN 2 PN a d ¼ u¼2 ðeu eu1 Þ = u¼1 e2u . E E eu ¼ Vu;calc: Vu;expt: .
0.185 )0.176 0.220 1.09
0.0962 )0.607
0.122 0.425
9.4 5.6 7.1 8.4
1.9 1.6 1.7 1.6
V1E;1 10
E 10 Vx¼0:5 1
3
cm mol
cm mol
1.16 0.0577 0.709 )0.743
1.54 )2.09 2.24 )2.56
V2E;1 10 1
cm3 mol1 8.24 2.18 4.09 0.429
R.D. Peralta et al. / J. Chem. Thermodynamics 35 (2003) 239–250
System
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249
v
(
( X
FIGURE 2. Comparison of the calculated excess volume V E for the mixture {x1,4-dioxane + ð1 xÞ styrene} as a function of mole fraction x. s, this work dried 1,4-dioxane; d, this work undried 1,4dioxane; N, reference 5.
Figure 1 shows that the function V E ðxÞ is asymmetric for the four binaries; the maximum specific interaction deviating to the right or to the left of x ¼ 0:5, indicating the presence of a small amount of self association of one of the components. The magnitude and sign of V E is a reflection of the type of interactions taking place in the mixture. This is very well exhibited by the mixtures studied here with the maximum value of V E ranging from about þ0:13 cm3 mol1 for butyl acrylate to 0:09 cm3 mol1 for styrene. The relative intensity depends on the nature of the solute (monomer) and the solvent. In the case of butyl acrylate and methyl methacrylate the overall positive magnitude of V E results from an intercalation effect of 1,4-dioxane that breaks dipole–dipole associations. As shown in figure 1, the mixture of 1,4-dioxane and styrene presents a small contraction effect. This fact might be the result of an inductive effect of the vinyl group in styrene enhancing the electron density of its ring and the electrostatic interaction with the benzene ring, and of the vinyl group introducing a steric effect that operates in the opposite direction. The electron cloud of styrene interacts well with that of the two oxygen atoms present in 1,4dioxane and results in a contraction of the mixture.
Acknowledgements We thank one of the reviewers for suggesting drying 1,4-dioxane and testing the influence of water on the results.
References [1] N.V. Sastry, P.N. Dave, Int. J. Thermophys. 17 (1996) 1289–1304. [2] N.V. Sastry, P.N. Dave, Proc. Indian Acad. Sci. (Chem. Sci.) 109 (1997) 211–220.
250 [3] [4] [5] [6] [7] [8] [9] [10]
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N.V. Sastry, M.K. Valand, Phys. Chem. Liq. 38 (2000) 61–72. N.V. Sastry, S.R. Patel, M.C. Patel, J. Chem.Thermodyn. 31 (1999) 797–809. T.M. Aminabhavi, V.B. Patil, J. Chem. Eng. Data 4 (1998) 497–503. O. Redlich, A.T. Kister, Ind. Eng. Chem. 40 (1948) 345–348. J. Tomiska, CALPHAD 5 (1981) 93–102. J. Tomiska, CALPHAD 8 (1984) 283–294. J. Wisniak, A. Polishuk, Fluid Phase Equilibria 164 (1999) 61–82. H.C. Van Ness, M.M. Abbott, Classical Thermodynamics of Nonelectrolyte Solutions, McGraw-Hill, New York, 1982. [11] J. Wisniak, Fluid Phase Equilibria 89 (1993) 291–303. [12] M. Shacham, J. Wisniak, N. Brauner, Ind. Eng. Chem. Res. 32 (1993) 2820–2825.
AG 02/005
Densities and excess volumes of binary mixtures of 1,4-dioxane with either ethyl acrylate, or butyl acrylate, or methyl methacrylate, or styrene at T ¼ 298:15 K Rene D. Peralta a,*, Ramiro Infante a, Gladis Cortez a, Rogelio R. Ramırez a, Jaime Wisniak b b
a Centro de Investigaci on en Quımica Aplicada, Saltillo 25000, Coahuila, Mexico Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
Received 8 April 2002; accepted 14 October 2002
Abstract Densities of binary mixtures of 1,4-dioxane with either ethyl acrylate, or butyl acrylate, or methyl methacrylate, or styrene have been measured as a function of composition at T ¼ 298:15 K and atmospheric pressure with an Anton Paar DMA 5000 oscillating U-tube densimeter. The calculated excess volumes were correlated with the Redlich–Kister equation and with a series of Legendre polynomials. The excess volumes are positive for the mixtures of 1,4-dioxane with methyl methacrylate and butyl acrylate and negative for the mixtures of 1,4-dioxane and styrene. The excess volumes for the system 1,4-dioxane and ethyl acrylate are negative for mole fractions x of 1,4-dioxane less than or equal to about 0.44 and positive at x greater than about 0.4498 and positive thereafter. Ó 2003 Elsevier Science Ltd. All rights reserved. Keywords: Densities; Excess volumes; Monomers; Acrylic esters; 1,4-Dioxane
*
Corresponding author. Tel.: +52-844-438-9830; fax: +52-844-438-9839. E-mail address: [email protected] (R.D. Peralta).
0021-9614/03/$ - see front matter Ó 2003 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 9 6 1 4 ( 0 2 ) 0 0 3 1 3 - 0
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1. Introduction This work is part of our program to provide excess volumes of solvents and commercially important monomers, and asses the influence of the chemical structure of the solute on the mixtures under consideration. Sastry and Dave [1,2] measured the excess volumes, isentropic compressibilities, and dielectric constant of 15 binary mixtures of either methyl, or ethyl, or butyl methacrylate with hexane, heptane, carbon tetrachloride, chlorobenzene, and o-dichlorobenzene at T ¼ 308:15 K. They found that with aliphatic hydrocarbons the results were controlled by dispersive interactions, with chlorinated solvents the controlling factors were specific interactions (O-Cl and n-p types) [1,2]. Sastry and Valand [3] also measured the excess volumes of mixtures of alkyl (methyl, ethyl, and butyl) acrylates in several alkanols at 298.15 K and 308.15 K, and found that they were always positive. These results were explained on the basis of non-specific interactions between the components. Sastry et al. [4] measured the excess volumes of binary mixtures of methyl methacrylate with either cyclohexane or benzene, or toluene, or ethylbenzene, or (o,m,p)-xylene, at temperatures of 298.15 K and 303.15 K and found that except for toluene all have positive excess volumes. The excess volumes for the binary mixtures of (methyl methacrylate + cyclohexane) showed a non-symmetric behavior with a maximum V E 1:05 cm3 mol1 at x ¼ 0:45. Aminabhavi and Patil [5] measured the density of mixtures of styrene with 1,4-dioxane at the temperatures between 298.15 K and 308.15 K and determined that the excess volumes were negative. No literature data are available on the excess volumes of mixtures of alkyl acrylates used in this work.
2. Experimental The materials used in this work were obtained from Aldrich with the following minimum stated purity: 1,4-dioxane had a purity of 99.9 mass per cent and contained 0.023 mass per cent water while ethyl acrylate, butyl acrylate, methyl methacrylate and styrene had a purity of 99.9 mass per cent. Prior to use, ethyl acrylate, butyl acrylate and methyl methacrylate were vacuum distilled to eliminate the stabilizer about 0.002 mass per cent hydroquinone monomethyl ether. Styrene, which contained as a stabilizer between 10 and 15 parts per millions of 4tert-butylcatechol was degassed by freezing and heating to avoid polymerization. The purity of the solvents was further ascertained by comparing their densities at T ¼ 298:15 K listed in table 1, with the values reported in the literature. The density of the samples was measured with an Anton Paar model DMA 5000 oscillating U-tube densimeter, provided with automatic viscosity correction and two integrated X 100 platinum thermometers (DKD traceable), had a stated accuracy of 5 106 g cm3 . The temperature of the densimeter was regulated to 0:001 K with a solid-state thermostat. The densimeter was calibrated daily with both dry air and bidistilled degassed water and the reproducibility of density measurements was 2 106 g cm3 .
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241
TABLE 1 Purity of the components used in this work and their densities q measured in this work along with literature densities q(lit.) at T ¼ 298:15 K Component
Purity/mass per cent
q=g cm3
qðlit:Þ=g cm3
1,4-Dioxane Butyl acrylate Ethyl acrylate Methyl methacrylate Styrene
99.9 >99 99 99 99
1.027910 0.893666 0.915930 0.937669 0.901972
1.02792 [10] 0.8941 [3] 0.9163 [3] 0.93766 [11] 0.9015 [12]
All liquids were boiled or heated to remove dissolved air. Solutions of different compositions were prepared by mass in a 10 cm3 rubber-stoppered vial to prevent evaporation, using a Mettler AG 204 balance accurate to 104 g. To minimize the errors in composition, the heavier component was charged first and the sample kept in ice water. The accuracy of the mole fraction so obtained was 5 105 . The temperature was measured with an accuracy of 0:002 K. 3. Results and discussion At least 21 density measurements were performed (with repetition) for each binary system, in the full mole fraction range (0 6 x 6 1). The excess volumes V E of the solutions of molar composition x were calculated from the densities of the pure liquids and their mixtures according the following equation: V E ¼ ½xM1 þ ð1 xÞM2 =q ½xM1 =q1 þ ð1 xÞM2 =q2 ;
ð1Þ
where q, q1 , and q2 are the densities of the solution and pure components 1 and 2, respectively, and M1 and M2 the molar masses of the pure components. The corresponding values of q and V E are reported in tables 1–6 and figure 1. The values of V E were correlated with composition using two procedures. First, the Redlich–Kister expression [6] n X k V E ¼ x1 x2 Ak ðx1 x2 Þ ; ð2Þ k¼0
where the Ak with k ¼ 1; 2; 3; . . . are adjustable parameters. The Redlich–Kister regressor is very powerful and frequently used to correlate vapor–liquid equilibrium data and excess properties. Notwithstanding, it suffers from the important drawback that the values of the adjustable parameters change as the number of terms in the series is increased. Second, a series of Legendre polynomials Lk ðx1 Þ: n X V E ¼ x1 x2 ak Lk ðx1 Þ; ð3Þ k¼0
which for the four first terms with k ¼ 0; 1; 2; 3 is V E ¼ x1 x2 a0 þ a1 ð2x1 1Þ þ a2 ð6x21 6x1 þ 1Þ þ a3 ð20x31 30x21 þ 12x1 1Þ : ð4Þ
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TABLE 2 Experimental densities q, volumes V, calculated excess volumes V E obtained from equation (2), and deviations dV E ¼ V E ðexpt:Þ V E ðcalc:Þ for {x1,4-dioxane + ð1 xÞbutyl acrylate} at T ¼ 298:15 K and mole fraction x x
q=g cm3
V =cm3 mol1
V E 103 =cm3 mol1
dV E 103 =cm3 mol1
0 0.0270 0.0534 0.1015 0.1521 0.1996 0.2510 0.3014 0.3500 0.4003 0.4499 0.5008 0.5500 0.6004 0.6508 0.6998 0.7500 0.7997 0.7997 0.8498 0.9000 0.9492 0.9750 1
0.893666 0.895824 0.897979 0.902029 0.906463 0.910783 0.915675 0.920681 0.925717 0.931207 0.936882 0.943038 0.949301 0.956062 0.963235 0.970635 0.978669 0.987165 0.987167 0.996303 1.006131 1.016424 1.022178 1.027910
143.421 141.870 140.349 137.583 134.672 131.945 128.991 126.097 123.310 120.416 117.570 114.638 111.805 108.904 105.997 103.166 100.266 97.3849 97.3850 94.4754 91.5554 88.6903 87.1779 85.7176
0 4.53 10.4 19.6 30.6 43.1 55.4 69.2 83.7 96.5 107 115 122 127 128 125 120 108 108 92.1 66.4 38.6 18.0 0
0 0.092 1.08 0.252 )0.603 )0.042 )1.27 )0.864 1.06 1.47 1.02 )0.284 )0.943 )0.103 )0.574 )0.926 0.332 0.324 0.014 1.53 )0.834 0.753 )1.64 0
Legendre polynomials belong to the category of orthogonal functions such as Fourier, Bessel, and Chebyshev, which have the valuable feature, that for a continuous series of observations the values of the coefficients do not change as the number of terms in the series is increased. This is an important property because if a physical explanation can be assigned to one of its coefficients, its value remains constant. For the case of discrete measurements, such as determination of volumes of mixing, the values of the coefficients will vary, but slightly. In addition, as shown in table 7, the series of Legendre polynomials have the important characteristic that the structure of its first four terms is the same as that of the first four terms of the Redlich–Kister expression. The mathematical procedure to transform a power expansion, such as that of Redlich–Kister, into an orthogonal series has been described in detail by Tomiska [7,8]. Tomiska provides the iteration formulas for Legendre or ChebyshevÕs series of any order as well as the proof that the procedure is independent of the conversion coefficients from the actual excess property. Equations (2) and (3) were fitted using a least-squares optimization procedure, with all points weighted equally and minimizing the following objective function OF defined by
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243
TABLE 3 Experimental densities q, volumes V, calculated excess volumes V E obtained from equation (2), and deviations dV E ¼ V E ðexpt:Þ V E ðcalc:Þ, where for {x1,4-dioxane + ð1 xÞethyl acrylate} at T ¼ 298:15 K and mole fraction x x
q=g cm3
V =cm3 mol1
V E 103 =cm3 mol1
dV E 103 =cm3 mol1
0 0.0248 0.0502 0.0998 0.1496 0.2001 0.2500 0.2986 0.3498 0.4001 0.4498 0.5000 0.5503 0.5993 0.6500 0.7002 0.7500 0.8002 0.8498 0.8997 0.9492 0.9750 1
0.915930 0.918155 0.920461 0.925017 0.929662 0.934462 0.939288 0.944089 0.949238 0.954421 0.959662 0.965092 0.970665 0.976232 0.982142 0.988162 0.994288 1.000643 1.007101 1.013803 1.020655 1.024317 1.027910
109.310 108.721 108.116 106.940 105.769 104.570 103.395 102.250 101.048 99.8665 98.6989 97.5190 96.3371 95.1851 93.9925 92.8093 91.6362 90.4516 89.2798 88.0991 86.9242 86.3118 85.7176
0 )4.37 )8.55 )14.7 )18.2 )18.8 )16.8 )14.0 )8.94 )3.75 1.52 5.74 9.80 13.5 16.7 18.7 20.1 19.9 18.9 14.2 9.02 3.59 0
0 0.439 0.429 0.175 )0.324 )0.399 )0.022 )0.419 0.274 0.500 0.696 )0.032 )0.448 )0.477 )0.212 )0.229 0.166 0.309 0.926 )0.456 0.004 )1.34 0
OF ¼
N X
E E Vi;expt: Vi;calc:
2
;
ð5Þ
1
where N is the number of observations. The values of the different adjustable parameters, Ak of equation (2) and ak of equation (3), are reported in tables 8 and 9 for different values of k, together with the pertinent statistics. The standard deviation s was calculated from 1=2 X 2 E E s¼ Vi;expt: Vi;calc: =ðN kÞ ;
ð6Þ
where k is the number of adjustable parameters. The statistical significance of adding one or more terms after the third, was examined with the requirement that the residues be randomly distributed, as suggested by Wisniak and Polishuk [9]. Randomness of the residues was tested using the Durbin–Watson statistic. It was not deemed necessary to perform a step-wise regression. The variation of V E =fxð1 xÞg with composition was used in every case to test the quality of the data; this function is extremely sensitive to experimental errors, particularly in the dilute ranges. In addition, its values at infinite dilution represent
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TABLE 4 Experimental densities q, volumes V, calculated excess volumes V E obtained from and deviations dV E ¼ V E ðexpt:Þ V E ðcalc:Þ for {x1,4-dioxane + ð1 xÞmethyl methacrylate} at T ¼ 298:15 K and mole fraction x x
q=g cm3
V =cm3 mol1
V E 103 =cm3 mol1
dV E 103 =cm3 mol1
0 0.0248 0.0252 0.0497 0.1003 0.1501 0.1996 0.2500 0.3001 0.3500 0.3997 0.4499 0.5000 0.5499 0.5982 0.6500 0.7002 0.7497 0.7993 0.8495 0.8999 0.9487 0.9730 1
0.937669 0.939417 0.939441 0.941202 0.944887 0.948609 0.952367 0.956299 0.960275 0.964324 0.968472 0.972745 0.977135 0.981603 0.986036 0.990923 0.995781 1.000712 1.005784 1.011062 1.016528 1.021994 1.024775 1.027910
106.775 106.259 106.252 105.741 104.685 103.644 102.610 101.555 100.508 99.4652 98.4232 97.3709 96.3172 95.2683 94.2519 93.1588 92.0992 91.0510 89.9996 88.9333 87.8605 86.8165 86.2962 85.7176
0 6.82 7.07 11.3 21.6 28.6 38.5 44.9 52.7 59.7 63.7 68.7 70.8 72.7 73.0 71.5 68.4 63.1 56.1 47.2 34.2 18.9 10.2 0
0 1.35 1.53 0.626 0.797 )1.35 0.144 )1.16 )0.188 0.761 )0.273 0.723 )0.090 0.074 0.136 )0.091 )0.056 )0.379 )0.220 0.600 0.025 )0.233 )0.373 0
the values of the partial excess volume at infinite dilution, Vi E;1 [10], which can be also calculated from the adjustable parameters using V1E;1 ¼ A0 A1 þ A2 ¼ V11 V10 and
ð7Þ
V2E;1 ¼ A0 þ A1 þ A2 þ ¼ V21 V20 ;
ð8Þ
for the Redlich–Kister expression and V1E;1 ¼ a0 a1 þ a2 ¼ V11 V10 and
ð9Þ
V2E;1 ¼ a0 þ a1 þ a2 þ ¼ V21 V20
ð10Þ 0
for the Legendre polynomial. In equations (7)–(10) Vi is the molar volume of pure component i. The values of Vi E;1 are listed in tables 8 and 9. Equations (7) and (8) or (9) and (10) yield the same values of Vi E;1 . Inspection of the results of tables 2–6 and figure 1 indicates that the excess volumes for the binaries 1,4-dioxane with either butyl acrylate or methyl methacrylate are positive for the whole composition range while those for the system 1,4-dioxane and styrene are negative. The mixture 1,4-dioxane and ethyl acrylate shows a
R.D. Peralta et al. / J. Chem. Thermodynamics 35 (2003) 239–250
245
TABLE 5 Experimental densities q, volumes V, calculated excess volumes V E obtained from equation (2), and deviations dV E ¼ V E ðexpt:Þ V E ðcalc:Þ for {1,4-dioxane V + ð1 xÞstyrene} at T ¼ 298:15 K and mole fraction x x1
q=g cm3
V =cm3 mol1
V E 103 =cm3 mol1
dV E 103 =cm3 mol1
0 0.0274 0.0502 0.0998 0.1495 0.1999 0.2483 0.2999 0.3493 0.4000 0.4495 0.5008 0.5500 0.5993 0.6501 0.6998 0.7495 0.8000 0.8498 0.8996 0.9500 0.9750 1
0.901972 0.904613 0.906829 0.911834 0.916950 0.922238 0.927435 0.933093 0.938624 0.944438 0.950249 0.956449 0.962521 0.968816 0.975459 0.982167 0.989107 0.996392 1.003825 1.011502 1.019576 1.023702 1.027910
115.469 114.646 113.963 112.465 110.969 109.456 108.005 106.463 104.992 103.484 102.015 100.493 99.0402 97.5804 96.0811 94.6129 93.1431 91.6482 90.1748 88.7010 87.2053 86.4621 85.7176
0 )7.34 )13.1 )35.1 )53.8 )67.4 )77.9 )84.2 )86.4 )84.7 )80.2 )75.2 )66.1 )59.1 )48.1 )37.0 )28.2 )18.9 )12.4 )5.17 )0.735 )0.112 0
0 0.708 2.78 )0.817 )1.80 )0.236 )0.060 0.462 0.483 0.777 0.883 )0.960 0.092 )1.88 )0.462 1.10 0.614 0.911 )0.718 )0.186 )0.214 )0.466 0
mixed behavior. Our density measurements are in very good agreement with those of Aminabhavi and Patil [5]; the small difference may be attributed to the fact that Aminabhavi and Patil used styrene as purchased, without further treatment, and measured the density with a pycknometer. Interestingly enough, the calculated excess volumes for both data sets shown in figure 2 are in serious disagreement. Several explanations can be offered for this fact. First of all, the measured data have been transformed into excess volumes, using equation (1). It is a well-known fact that small errors in a variable (density) may translate in large ones when the measured variable is modified. Change of the variable will usually lead a different distribution of the error, as has been shown in detail by Wisniak [11] and Shacham et al. [12]. Another possible explanation is obtained by observing the numerical value of the two terms that compose the right-hand side of equation (1). Consider, for example, the x ¼ 0:5500a in table 6. For this concentration the molar volumes of the solution and of the equivalent ideal solution (rounded) are 99:0370 cm3 mol1 and 99:1057 cm3 mol1 , respectively. Hence, calculation of the excess volumes involves taking the difference between two very large numbers of about the same size and yielding, for the specific concentration, V E ¼ 0:0687 cm3 mol1 . It is clear that a
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TABLE 6 Experimental densities q, volumes V, calculated excess volumes V E , and deviations dV E ¼ V E ðexpt:Þ V E ðcalc:Þ for the system {1,4-dioxane + ð1 xÞstyrene} at T ¼ 298:15 K and mole fraction x x1
q=g cm3
V =cm3 mol1
V E 103 =cm3 mol1
dV E 103 =cm3 mol1
0.0000 0.0274 0.0252a 0.0502 0.0502a 0.0998 0.0998a 0.1495 0.1498a 0.1999 0.2001a 0.2483 0.2496a 0.2999 0.3000a 0.3493 0.3503a 0.4000 0.3994a 0.4495 0.4496a 0.5008 0.4963a 0.5500 0.5500a 0.5993 0.5995a 0.6501 0.6495a 0.6998 0.6992a 0.7495 0.7496a 0.8000 0.7998a 0.8498 0.8492a 0.8996 0.8997a 0.9500 0.9486a 0.9750 0.9751a 1.0000
0.901972 0.904613 0.904386 0.906829 0.906842 0.911834 0.911822 0.916950 0.916965 0.922238 0.922249 0.927435 0.927574 0.933093 0.933087 0.938624 0.938739 0.944438 0.944376 0.950249 0.950284 0.956449 0.955909 0.962521 0.962549 0.968816 0.968850 0.975459 0.975411 0.982167 0.982129 0.989107 0.989164 0.996392 0.996394 1.003825 1.003758 1.011502 1.011557 1.019576 1.019388 1.023702 1.023748 1.027910
115.469 114.646 114.714 113.963 113.962 112.465 112.466 110.969 110.962 109.456 109.450 108.005 107.965 106.463 106.462 104.992 104.962 103.484 103.501 102.015 102.009 100.493 100.626 99.0402 99.0370 97.5804 97.5729 96.0811 96.0955 94.6129 94.6253 93.1431 93.1352 91.6482 91.6521 90.1748 90.1897 88.7010 88.6940 87.2053 87.2428 86.4621 86.4559 85.7176
0 )7.34 )5.43 )13.1 )15.0 )35.1 )33.3 )53.8 )52.0 )67.4 )65.7 )77.9 )76.7 )84.2 )82.4 )86.4 )86.2 )84.7 )86.0 )80.2 )82.6 )75.2 )77.6 )66.1 )68.7 )59.1 )59.3 )48.1 )51.1 )37.0 )40.5 )28.2 )31.4 )18.9 )22.5 )12.4 )14.1 )5.20 )8.10 )0.700 )3.71 )0.100 )1.93 0
0 0.708 19.1 2.78 6.23 0.817 0.301 )1.80 )15.0 )0.236 )3.24 )0.060 )3.04 0.462 11.8 0.483 4.42 0.777 1.96 0.883 )0.515 )0.960 )6.81 0.091 )1.30 )1.88 4.71 )0.462 )8.20 1.10 2.25 0.614 )0.554 0.911 1.74 )0.718 7.66 )0.186 0.147 )0.214 )6.53 )0.466 )7.94 0
a
Mixtures prepared with undried 1,4-dioxane.
R.D. Peralta et al. / J. Chem. Thermodynamics 35 (2003) 239–250
247
v
(
( x FIGURE 1. Excess volumes V E at T ¼ 298:1 K. , {x1,4-dioxane + ð1 xÞmethyl methacrylate}; N, {x1,4-dioxane + ð1 xÞethylacrylate}; r, {x1,4-dioxane + ð1 xÞbutylacrylate}; d, {x1,4-dioxane + ð1 xÞstyrene}.
TABLE 7 Legendre polynomial given by equation (3) and Redlich–Kister expression given by equation (2) as a function of polynomial order k Polynomial order, k
Legendre polynomial, 3
Redlich–Kister, expression
0 1 2 3 4
1 2x1 1 6ðx21 x1 þ 16Þ 20ðx31 32x21 þ 35x1 201 Þ 70ðx41 2x31 þ 97x21 27x þ 701 Þ
1 2x1 1 4ðx21 x1 þ 14Þ 8ðx31 32x21 þ 34x1 18Þ 16ðx41 2x31 þ 32x21 12x þ 161 Þ
small error in each of the two large volumes reflects as a very large error in their difference. We have here the same problem present in the calculation of heats of reaction; they can be calculated from heats of formation or from heats of combustion. The second case is usually in large error for the same reason: we are taking the difference between large numbers to obtain a number smaller in one order of magnitude (at least) of the original figures. Another possibility considered was the effect of the small amount of water present in the ether which was suggested by one of the reviewers. In order to study its influence the ether was first dried with metallic sodium, distilled under vacuum and then stored in the presence of molecular sieves. The dried material contained 0.009 mass per cent water as determined by Karl-Fischer. A series of new measurements were performed and their results are reported in table 6 and shown in figure 2, which clearly shows that drying the ether had no significant effect on the results.
248 TABLE 8 P P E , and Vi E;1 at Coefficients Ak of equation (2), standard deviation s defined by equation (6), Durbin–Watson statistic d a ¼ Nu¼2 ðeu eu1 Þ2 = Nu¼1 e2u , Vx¼0:5 T ¼ 298:15 K A0 10 3
1+2 1+3 1+4 1+5
A1 10 1
3
cm mol
cm mol
4.61 0.230 2.83 )2.98
3.35 1.89 0.926 3.01
A2 10 1
3
A3 10 1
cm mol 0.278 )0.722 0.330 0.489
3
s 104
A4 10 1
cm mol 0.241
3
1.86
9.2 5.5 7.2 8.1
V1E;1 10
E Vx¼0:5 10
cm mol 0.540
)1.52
da
1
3
1.9 1.6 1.7 1.6
1
3
cm mol
cm mol
1.15 0.0577 0.709 )0.744
1.540 )2.09 2.24 )2.56
V2E;1 10 1
cm3 mol1 8.24 2.18 4.09 0.429
TABLE 9 E , and Vi E;1 at T ¼ 298.15 K Coefficients ak (equation (3)), standard deviation (equation (5)), Durbin–Watson statistic d, Vx¼0:5 System
a0 10
a1 10
a2 10
a3 10
a4 10
s 104
da
3
1+2 1+3 1+4 1+5
4.71 0.0971 2.95 )2.59
3.35 2.04 0.926 2.10 PN 2 PN a d ¼ u¼2 ðeu eu1 Þ = u¼1 e2u . E E eu ¼ Vu;calc: Vu;expt: .
0.185 )0.176 0.220 1.09
0.0962 )0.607
0.122 0.425
9.4 5.6 7.1 8.4
1.9 1.6 1.7 1.6
V1E;1 10
E 10 Vx¼0:5 1
3
cm mol
cm mol
1.16 0.0577 0.709 )0.743
1.54 )2.09 2.24 )2.56
V2E;1 10 1
cm3 mol1 8.24 2.18 4.09 0.429
R.D. Peralta et al. / J. Chem. Thermodynamics 35 (2003) 239–250
System
R.D. Peralta et al. / J. Chem. Thermodynamics 35 (2003) 239–250
249
v
(
( X
FIGURE 2. Comparison of the calculated excess volume V E for the mixture {x1,4-dioxane + ð1 xÞ styrene} as a function of mole fraction x. s, this work dried 1,4-dioxane; d, this work undried 1,4dioxane; N, reference 5.
Figure 1 shows that the function V E ðxÞ is asymmetric for the four binaries; the maximum specific interaction deviating to the right or to the left of x ¼ 0:5, indicating the presence of a small amount of self association of one of the components. The magnitude and sign of V E is a reflection of the type of interactions taking place in the mixture. This is very well exhibited by the mixtures studied here with the maximum value of V E ranging from about þ0:13 cm3 mol1 for butyl acrylate to 0:09 cm3 mol1 for styrene. The relative intensity depends on the nature of the solute (monomer) and the solvent. In the case of butyl acrylate and methyl methacrylate the overall positive magnitude of V E results from an intercalation effect of 1,4-dioxane that breaks dipole–dipole associations. As shown in figure 1, the mixture of 1,4-dioxane and styrene presents a small contraction effect. This fact might be the result of an inductive effect of the vinyl group in styrene enhancing the electron density of its ring and the electrostatic interaction with the benzene ring, and of the vinyl group introducing a steric effect that operates in the opposite direction. The electron cloud of styrene interacts well with that of the two oxygen atoms present in 1,4dioxane and results in a contraction of the mixture.
Acknowledgements We thank one of the reviewers for suggesting drying 1,4-dioxane and testing the influence of water on the results.
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