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Ultrasonic velocities, densities, and excess molar volumes of binary mixtures of N,N-dimethyl formamide with methyl acrylate, or ethyl acrylate, or butyl acrylate, or 2-ethyl hexyl acrylate at T = 308.15 K
J. Chem. Thermodynamics 43 (2011) 1844–1850
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Ultrasonic velocities, densities, and excess molar volumes of binary mixtures of N,N-dimethyl formamide with methyl acrylate, or ethyl acrylate, or butyl acrylate, or 2-ethyl hexyl acrylate at T = 308.15 K M. Kondaiah a, D. Sravana Kumar b, K. Sreekanth a, D. Krishna Rao a,⇑ a b
Department of Physics, Acharya Nagarjuna University, Nagarjuna Nagar 522510, Andhra Pradesh, India Dr. V.S. Krishna Govt. Degree College, Visakhapatnam, Andhra Pradesh, India
a r t i c l e
i n f o
Article history: Received 26 March 2011 Received in revised form 17 June 2011 Accepted 19 June 2011 Available online 29 June 2011 Keywords: Ultrasonic velocity Density Redlich–Kister type polynomial Excess molar volume Partial molar volumes Theoretical models
a b s t r a c t Ultrasonic velocities, u, densities, q, of binary mixtures of N,N-dimethyl formamide (DMF) with methyl acrylate (MA), ethyl acrylate (EA), butyl acrylate (BA), and 2-ethyl hexyl acrylate (EHA), including pure liquids, over the entire composition range have been measured at T = 308.15 K. Using the experimental results, the excess molar volume, V Em , partial molar volumes, V m;1 , V m;2 , and excess partial molar volumes, V Em;1 , V Em;2 have been calculated. Molecular interactions in the systems have been studied in the light of variation of excess values of calculated properties. The excess properties have been fitted to Redlich– Kister type polynomial and the corresponding standard deviations have been calculated. The positive values of V Em indicate the presence of dispersion forces between the DMF and acrylic ester molecules. Further theoretical values of sound velocity in the mixtures have been evaluated using various theories and have been compared with experimental sound velocities to verify the applicability of such theories to the systems studied. Theoretical ultrasonic velocity data have been used to study molecular interactions in the binary systems investigated. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The study of properties of liquid mixtures and solutions finds direct applications in chemical and biochemical industry. The measurement of speed of sound in liquids enables determination of some useful acoustic and thermodynamic parameters that are found to be very sensitive to molecular interactions. Hence, such measurements are useful to study the strength of molecular interactions in liquid mixtures. Acrylic esters are important industrial chemicals and are widely used as precursors in the production of technically important special type polymers. Methyl acrylate is a contact allergen present in nail lacquer. It can also be used as a co-polymer in the process of polymerization of poly anionic cellulose (PAC) polymers, to reduce the glass transition temperature of the PAC polymers. Ethyl acrylate is a very important industrial chemical and is widely used commercially for the production of high polymeric and latex compounds. Butyl acrylate is a very useful feedstock for chemical synthesis, because it readily undergoes addition reaction with a wide variety of organic and inorganic compounds and N,N-dimethyl formamide is used as a solvent in
⇑ Corresponding author. Tel.: +91 863 6458142 (R); fax: +91 9440712142. E-mail address: [email protected] (D. Krishna Rao). 0021-9614/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2011.06.011
peptide coupling for pharmaceuticals, in the development and production of pesticides, in the manufacture of adhesives, synthetic leathers, fibers, films, and surface coatings and other applications of pure solvents. A survey of the literature indicates that Francesconi and Comelli [1], Gonzalez and Ortega [2], and Liau et al. [3] reported density and viscosity data for binary mixtures of esters with alkanols. Peralta et al. [4–7] measured densities of ethyl acrylate, butyl acrylate, methyl methacrylate, and styrene with toluene/cyclohexane/benzene/1,4-dioxane at temperature 298.15 K. Recently some researchers have reported the ultrasonic, volumetric, and viscometric studies of esters with alcohols [8–13]. The study of intermolecular interactions in (N,N-dimethyl formamide + acrylic esters) would be interesting owing to their industrial and pharmaceutical applications. In the present paper, ultrasonic velocities, u and densities, q of binary mixtures of N,N-dimethyl formamide (DMF) with methyl acrylate (MA) or ethyl acrylate (EA) or butyl acrylate (BA) or 2-ethyl hexyl acrylate (EHA) besides those of pure liquids at temperature 308.15 K covering the entire composition range have been reported. The excess molar volume, V Em , partial molar volumes, V m;1 , V m;2 , and excess partial molar volumes, V Em;1 , V Em;2 have been calculated. The variations of excess properties with composition of the mixtures have been discussed in terms of molecular interactions in the mixtures. The experimental values of u and q of pure liquids at
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M. Kondaiah et al. / J. Chem. Thermodynamics 43 (2011) 1844–1850 TABLE 1 Comparison of experimental values of ultrasonic velocity, u, and density, q, of pure liquids with the corresponding literature values at 308.15 K. u/(m s1)
Liquid
N,N-dimethylformamide Methyl acrylate Ethyl acrylate Butyl acrylate 2-Ethylhexyl acrylate
q/(kg m3)
Present work
Literature
Present work
Literature
1433.68 1141.78 1119.12 1158.33 1229.40
1434.40 1140.00 1118.70 1159.30
935.88 937.13 903.78 885.40 875.00
935.717 [15] 937.70 [8] 904.90 [8] 884.60 [17]
T = 308.15 K along with their literature [8,14–17] values are presented in table 1. 2. Experimental The N,N-dimethyl formamide (mass fraction purity 0.99) and butyl acrylate (mass fraction purity 0.99) were obtained from LOBA Chemicals, and methyl acrylate (mass fraction purity 0.99), ethyl acrylate (mass fraction purity 0.99), and 2-ethyl hexyl acrylate (EHA) (mass fraction purity 0.99), obtained from KEMPHASOL Company, Bombay. All are Analytical Reagent grade (AR grade) used in the present investigation and are further purified by standard methods [18]. The solutions of binary mixtures of DMF with MA, EA, BA, and EHA have been prepared in the specially designed glass bottles with air tight stoppers and adequate precautions have been taken to minimize evaporation losses. The weighing of solutions has been made using a METTLER TOLEDO (Switzerland make) ABB5-S/FACT digital balance with an accuracy of ±0.01 mg. The uncertainty in the mole fraction is 105. The ultrasonic velocity of pure liquids and their binary mixtures has been measured by using a multi-frequency ultrasonic interferometer (M-82 Model) supplied by Mittal enterprise, New Delhi at a fixed frequency of 2 MHz with an accuracy of ±0.2%. The temperature of liquid sample in the interferometer cell is maintained constant by circulating water pumped from constant temperature water bath. In the present study, the constant temperature water bath (digital electronic) supplied by Concord Instruments Co. Ltd., Chennai (RAAGA type) has been used. The instrument can maintain temperature to ±0.01 K as per its specifications. The density has been measured using a two stem pyknometer of Parker & Parker type [19–21] having a bulb volume of 5 cm3. A traveling microscope is used to determine the height of liquid level in the stems of pyknometer. In this method, the volume of the pyknometer cell is calibrated using triply distilled deionised water [22], as it is not practicable to determine the volume of pyknometer cell exactly from its geometry. The capillary of the pyknometer is calibrated using mercury. The pyknometer filled with the liquid/ liquid mixture that is free from air bubbles. The temperature of the liquid/liquid mixture is maintained constant by immersing the pyknometer in the transparent-walled constant temperature bath for at least 30 min to attain thermal equilibrium. The density of liquid mixture at each composition is determined three times and the average of the experimental values is reported in this paper. The constant temperature water bath maintained the temperature fluctuations within ±0.01 K while the density of the liquid mixtures was measured. The estimated accuracy in the density measurement is 3 in 105 parts.
[14] [16] [8] [8]
where M1, M2 and q1, q2 are the molar masses and densities of the pure components used in the present work; q is the density of the liquid mixture. The values of q, V Em and partial molar volumes V m;1 , V m;2 are presented in table 2. The values of V Em have been fitted to the Redlich–Kister type polynomial equation [23].
Y E ¼ x1 x2
n X
Ai ðx2 x1 Þi ;
where Y E ¼ V Em . The values of Ai are the adjustable parameters of the function and are determined using the least squares method. In the present investigation, ‘i’ values were taken from 0 to 4. The coefficients Ai and the corresponding standard deviation (r) of all the binary mixtures are presented in table 3. Figure 1 represents the variation of excess molar volume with mole fraction of DMF. The sign of V Em depends upon the contraction and expansion of volume of the liquids due to mixing. The factors that are mainly responsible for the volume expansion, i.e. positive values of V Em are due to (i) loss of dipolar association between the molecules (dispersion forces). (ii) The geometry of molecular structures which does not favor the fitting of molecules of one component into other molecules of second component. (iii) Steric hindrance of the molecules. The negative values of V Em are due to the (i) association of molecules through the formation of hydrogen bond, i.e. strong specific interactions and (ii) accommodation of molecules because of large differences in their molar volumes. The variation of excess molar volume is found to be positive over the entire composition range in the present investigation. Such positive V Em values suggest that the loss of association of the acrylic ester molecules due to the addition of DMF. Further, it is noticed that from figure 1, for all the binary mixtures investigated, the values of V Em become less positive as we move from MA to EHA. Over the entire composition range of binary mixture (DMF and acrylate), V Em follows the order (MA + DMF) > (EA + DMF) > (BA + DMF) > (EHA + DMF). This observation supports the prediction that fitting of molecules of one component into the voids in the structure of second component is less favorable if the difference in molar volumes of component liquids is less. Peralta et al. [5,24] reported similar studies on positive values of V Em . The existing molecular interactions in the systems are well reflected in the properties of partial molar volumes. The partial molar volumes V m;1 of component 1 (DMF) and V m;2 of component 2 (acrylic ester) in the mixtures over the entire composition range have been calculated by using the following relations.
V m;1 ¼
V Em
þ
V 1
þ x2
3. Results and discussion The excess molar volume, V Em was calculated using the relation
V Em ¼
x1 M 1 þ x2 M 2
q
x1 M 1
q1
þ
x2 M 2
q2
;
ð1Þ
ð2Þ
i¼0
V m;2 ¼
V Em
þ
V 2
x1
@V Em @x @V Em @x
! ;
ð3Þ
;
ð4Þ
T;P
! T;P
where V 1 and V 2 are the molar volumes of the pure components of DMF and acrylic esters respectively. The derivates ð@V Em =@xÞT;P in
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TABLE 2 Densities, excess molar volumes, and partial molar volumes of all the binary systems at 308.15 K.
q (kg m3)
V Em (106 m3 mol1)
V m;1 (106 m3 mol1)
0.00000 0.11751 0.22835 0.33863 0.44010 0.54157 0.63671 0.73224 0.82577 0.91949 1.00000
937.13 924.97 915.96 913.50 914.67 916.46 918.70 922.32 926.11 931.65 935.88
MA + DMF 0.0000 1.1737 2.0260 2.2195 2.0600 1.8462 1.5996 1.2360 0.8711 0.3698 0.0000
86.5455 87.8630 83.6419 80.2711 78.9475 78.6914 78.6486 78.4184 78.1091 78.0209 78.1080
91.8660 91.9149 92.8177 94.1248 94.9394 95.1685 95.2350 95.7571 96.8563 97.3211 94.3941
0.00000 0.13626 0.25387 0.38050 0.48592 0.59136 0.67931 0.76745 0.84752 0.92761 1.00000
903.78 897.04 895.06 896.08 900.90 906.50 912.27 917.97 924.68 930.43 935.88
EA + DMF 0.0000 1.1799 1.7098 1.9100 1.6560 1.3614 1.0429 0.7716 0.4203 0.1950 0.0000
88.1558 85.2954 81.9097 79.4479 78.4770 78.1388 78.0745 78.0644 78.0671 78.0877 78.1080
110.7790 111.0395 111.8586 112.9777 113.7019 114.0822 114.1894 114.2143 114.2002 114.0179 113.4596
0.00000 0.16988 0.30775 0.44561 0.54877 0.65275 0.73279 0.81323 0.88759 0.94275 1.00000
885.40 882.93 883.92 891.03 897.06 904.42 910.66 917.38 924.71 930.00 935.88
BA + DMF 0.0000 1.1323 1.5812 1.2452 1.0062 0.7167 0.5125 0.3388 0.1460 0.0685 0.0000
81.6101 84.1502 79.6943 77.7442 77.7287 77.9976 78.0634 78.0111 77.9921 78.0485 78.1080
144.7590 144.8993 146.2902 147.3939 147.3857 146.9816 146.8437 147.0308 147.1136 146.4445 144.0355
0.00000 0.22421 0.38077 0.53704 0.63443 0.73403 0.79928 0.86454 0.89800 0.96093 1.00000
875.00 877.06 881.30 889.40 895.86 903.77 909.72 917.00 924.93 929.69 935.88
EHA + DMF 0.0000 0.7912 0.9096 0.6135 0.4211 0.2540 0.1821 0.0839 0.0620 0.0160 0.0000
78.2398 81.0405 78.3833 77.7068 77.8455 77.9968 78.0374 78.0532 78.0635 78.0951 78.1080
210.6060 210.7783 211.9022 212.4068 212.2024 211.8787 211.7482 211.6702 211.5920 211.1303 210.4098
Mole fraction of DMF (x1)
TABLE 3 Coefficients Ai of Redlich–Kister type polynomial equation (2) and the corresponding 1 standard deviation of V Em =ð106 m3 mol Þ in all the systems. A0
A1
A2
A3
A4
r
7.7672 6.5798 4.5147 2.7985
5.2878 5.3956 6.3454 4.3423
6.1153 1.7741 4.9313 1.5024
2.3331 1.6620 4.2326 4.1783
8.3997 2.0397 8.0567 4.3331
0.0273 0.0329 0.0327 0.0329
0.25
V m;1 ¼ V 1 þ x22
j X
Ai ðx2 x1 Þi 2x1 x22
i¼0
V m;2 ¼ V 2 þ x21
j X i¼0
j X
Ai ðx2 x1 Þi1 ;
ð5Þ
i¼1
Ai ðx2 x1 Þi þ 2x21 x2
j X i¼1
/(10 E Vm
equations (3) and (4) are obtained by differentiating equation (2) which lead to the following equations for V m;1 and V m;2 .
0.15
3
-1
m .mol )
0.20
-5
MA + DMF EA + DMF BA + DMF EHA + DMF
V m;2 (106 m3 mol1)
0.10 0.05 0.00 0
0.2
0.4
0.6
0.8
1
mole fraction, x1
Ai ðx2 x1 Þi1 ;
ð6Þ
FIGURE 1. Plots of excess molar volume against mole fraction of DMF for binary mixtures of DMF with MA (), EA (d), BA (N), and EHA (j).
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M. Kondaiah et al. / J. Chem. Thermodynamics 43 (2011) 1844–1850
using the above equations V Em;1 , V Em;2 have been calculated using,
ð8Þ
The values of V m;1 and V m;2 are furnished in table 2. From this table, the values of V m;1 and V m;2 for both the components in the mixtures are greater than their respective molar volumes in the pure state, i.e. an expansion of volume takes place on mixing DMF with acrylic esters. These results also support the observed positive values of V Em in all the binary systems. Figures 2 and 3 represent the variation of excess partial molar volumes of DMF and MA/EA/BA/EHA in the binary mixtures respectively. Examination of figures 2 and 3 reveals that, indicating dispersion forces exist between the unlike molecules. These figures support the conclusions drawn from V Em values. The variation of ultrasonic velocity with the mole fraction of DMF is shown in figure 4. The ultrasonic velocity increases non-linearly in all the systems investigated. This non-linear variation indicates the existence of molecular interactions between the unlike molecules in the binary mixtures. In the present study, theoretical sound velocities have been evaluated by considering acrylates as one component and DMF as the other component in the binary mixture. Such an evaluation of theoretical sound velocity is useful to verify the applicability of various postulates of the theories of liquid mixtures and to arrive at some useful inferences regarding the (strength of) molecular interactions between component liquids in some cases. The theoretical values of ultrasonic velocity obtained using various theories along with the experimental velocity are summarized in table 4. Nomoto [25] established the following relation for sound velocity based on the assumption of the linearity of the molecular sound velocity and the additivity of molar volume.
UN ¼
X
xi R i
.X
xi V i
o3
n .X o X xi M i f1=U V g2 ; ðxi M i =u2i Þ ¼ 1
ð10Þ
where Mi is the molar mass of ith component in the liquid mixture. The Impedance Dependence Relation used by Shipra Baluja and Parrania [27] is given below
U imp ¼
xi Z i
.X
4 3 2 1 0 -1
0
xi q i ;
ð11Þ
0.2
0.4
0.6
0.8
1
mole fraction, x1 FIGURE 3. Plots of excess partial molar volumes of MA, EA, BA, EHA for the binary mixtures of DMF with MA (), EA (d), BA (N), and EHA (j).
1500 1450 1400 1350 1300 1250 1200 1150 1100 0
ð9Þ
;
where xi is the mole fraction, Ri = ui1/3Vi the molar sound velocity, Vi the molar volume, and ui is the sound velocity of the ith component. Van Dael and Vangeel [26] obtained the Ideal Mixture Relation
X
_E V m 2 /(10 -6 m3.mol-1)
V Em;2 ¼ V m;2 V 2 :
5
-1
ð7Þ
¼ V m;1
6
u /(m.s )
V 1 ;
V Em;1
0.2
0.4 0.6 mole fraction, x1
0.8
1
FIGURE 4. Plots of variation of ultrasonic velocity against mole fraction of DMF for binary mixtures of DMF with MA (), EA (d), BA (N), and EHA (j).
where Zi is the acoustic impedance and qi is the density of the ith component of the mixture. Junjie’s [28] equation is given by
U Jun ¼
X
xi V i
X
xi M i
1=2 nX
ðxi V i =qi u2i Þ
o1=2
:
Jacobson’s [29] equation is given by
U J ¼ K q1=2 L1 f ; 11
_E V m1 /(10 -6 m3.mol-1)
ð13Þ
where Lf is the ideal free length of the mixture. Rao’s (specific sound velocity) [30] relation is given by
9
UR ¼ 7
X
xi r i q
3
ð14Þ
;
where ri = ui1/3/qi is Rao’s specific sound velocity of the ith component of the mixture.
5
The experimental results have been fitted to two types of polynomials which describe the ultrasonic velocity data quantitatively as well as qualitatively even in the specific interaction predominant region where non-ideal behavior of the system is noticed. The polynomial equations used are [31,32]
3 1 -1
ð12Þ
0
0.2
0.4 0.6 0.8 mole fraction, x1
1
FIGURE 2. Plots of excess partial molar volumes of DMF for binary mixtures of DMF with MA (), EA (d), BA (N), and EHA (j).
f ðxÞ ¼ UðxÞ ¼
X
gðxÞ ¼ ln UðxÞ ¼
ak xk
and
X ðln U k Þxk ;
ð15Þ ð16Þ
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M. Kondaiah et al. / J. Chem. Thermodynamics 43 (2011) 1844–1850
TABLE 4 Experimental and theoretical values of ultrasonic velocity from equations (9)–(16). Mole fraction of DMF (x1)
Uexp
UN
UV
0.00000 0.11751 0.22835 0.33863 0.44010 0.54157 0.63671 0.73224 0.82577 0.91949 1.00000
1132.60 1157.43 1182.22 1208.25 1233.91 1261.50 1290.15 1321.60 1354.67 1390.53 1424.30
1132.60 1160.25 1187.69 1216.38 1244.11 1273.20 1301.79 1331.86 1362.73 1395.16 1424.30
1132.60 1160.31 1187.77 1216.46 1244.16 1273.21 1301.76 1331.80 1362.65 1395.10 1424.30
0.00000 0.13626 0.25387 0.38050 0.48592 0.59136 0.67931 0.76745 0.84752 0.92761 1.00000
1122.00 1150.91 1177.45 1208.75 1236.96 1267.64 1295.45 1326.70 1357.33 1391.54 1424.30
1122.00 1150.21 1176.93 1208.54 1237.40 1268.94 1297.55 1328.59 1359.11 1392.10 1424.30
0.00000 0.16988 0.30775 0.44561 0.54877 0.65275 0.73279 0.81323 0.84700 0.94275 1.00000
1168.56 1194.70 1219.52 1246.50 1269.20 1297.09 1323.00 1350.34 1362.47 1401.26 1424.30
0.00000 0.22421 0.38077 0.54100 0.64200 0.73403 0.79928 0.86454 0.91274 0.96093 1.00000
1229.40 1247.20 1263.00 1285.80 1304.03 1328.38 1345.68 1366.27 1386.59 1404.89 1424.30
UImp
UJun
UJ
UR
f(x)
g(x)
MA + DMF 1132.60 1166.80 1199.12 1231.28 1260.88 1290.48 1318.25 1346.13 1373.44 1400.81 1424.30
1132.60 1154.41 1176.97 1201.63 1226.58 1254.06 1282.50 1314.11 1348.55 1387.18 1424.30
1132.60 1157.43 1182.22 1208.25 1233.91 1261.51 1290.15 1321.60 1354.67 1390.54 1424.30
1132.60 1161.28 1189.23 1218.85 1247.13 1276.43 1304.59 1334.31 1363.78 1394.70 1424.31
1132.57 1157.55 1182.15 1208.15 1233.86 1261.74 1290.21 1321.36 1354.59 1390.77 1424.21
1132.61 1157.57 1182.13 1208.11 1233.83 1261.74 1290.22 1321.36 1354.57 1390.71 1424.15
1122.00 1155.09 1185.33 1219.80 1250.14 1282.12 1310.14 1339.55 1367.50 1396.72 1424.30
EA + DMF 1122.00 1164.37 1200.60 1239.31 1271.30 1303.09 1329.44 1355.71 1379.45 1403.07 1424.30
1122.00 1143.33 1164.49 1190.84 1216.28 1245.74 1274.14 1306.95 1341.50 1381.73 1424.30
1122.00 1150.91 1177.45 1208.75 1236.96 1267.64 1295.45 1326.70 1357.33 1391.54 1424.30
1122.00 1146.65 1171.05 1201.26 1229.89 1260.84 1288.82 1318.65 1349.97 1386.73 1424.31
1122.03 1150.75 1177.65 1208.77 1236.83 1267.51 1295.65 1326.63 1357.52 1391.29 1424.39
1122.04 1150.79 1177.68 1208.70 1236.82 1267.50 1295.69 1326.63 1357.50 1391.31 1424.39
1168.56 1192.49 1215.42 1242.38 1265.86 1293.12 1317.10 1344.40 1356.97 1396.88 1424.30
1168.56 1195.53 1221.03 1250.33 1275.16 1303.08 1326.85 1353.00 1364.73 1400.68 1424.30
BA + DMF 1168.56 1214.01 1250.29 1286.02 1313.40 1338.68 1358.71 1378.67 1386.99 1410.43 1424.30
1168.56 1186.89 1205.28 1228.03 1248.92 1274.56 1298.45 1327.34 1341.31 1388.70 1424.30
1168.56 1194.71 1219.52 1246.50 1269.20 1297.09 1323.00 1350.34 1362.47 1401.26 1424.30
1168.56 1182.05 1200.80 1225.84 1247.84 1273.77 1297.30 1324.83 1336.82 1387.76 1424.31
1168.54 1194.81 1219.37 1246.33 1269.62 1297.32 1322.17 1350.35 1363.05 1401.04 1424.33
1168.53 1194.76 1219.26 1246.38 1269.65 1297.38 1322.13 1350.32 1363.08 1401.08 1424.25
1229.40 1247.44 1264.16 1286.67 1304.96 1325.59 1343.31 1364.41 1382.79 1404.19 1424.30
1229.40 1208.44 1212.63 1233.33 1256.00 1284.32 1309.63 1340.08 1366.43 1396.59 1424.30
EHA + DMF 1229.40 1275.41 1306.72 1338.09 1357.52 1374.52 1387.26 1399.42 1408.33 1417.19 1424.30
1229.40 1243.68 1257.47 1276.94 1293.58 1313.29 1331.07 1353.38 1373.88 1399.11 1424.30
1229.40 1247.20 1263.00 1285.80 1304.03 1328.38 1345.68 1366.27 1386.59 1404.89 1424.30
1229.40 1224.42 1231.61 1260.71 1274.29 1282.87 1302.61 1327.54 1352.19 1383.93 1424.30
1229.39 1247.30 1262.79 1285.65 1305.10 1327.12 1345.73 1367.30 1385.44 1405.74 1423.98
1229.42 1247.38 1262.82 1285.62 1305.05 1327.16 1345.74 1367.31 1385.48 1405.71 1423.96
where k in the summation assumes values from 0 to 5, x is the mole fraction of the DMF and ak, ln Uk are constant coefficients to be determined using numerical methods. The values of sound velocities (after determining the coefficients in the above polynomial equations by applying least squares method) have been compiled in table 4. The standard deviations corresponding to sound velocity values calculated using the polynomial equations from their experimental values have been evaluated using the relation:
nX o1=2 r¼ ðU E U P Þ2 =n ;
ð17Þ
where UE is the experimental sound velocity. The UP is the calculated sound velocity from the polynomial equations f(x) and g(x) and n is the number of mole fractions at which experimental and theoretical velocities have been determined. These standard deviations are presented in table 5 and these values are small. The percentage deviations of theoretical velocities from the experimental ultrasonic velocity values are plotted in figures 5–8 for all the systems investigated. Among all the empirical theories
TABLE 5 Standard deviation of ultrasonic velocity calculated using polynomial equations from experimental values. Name of the liquid system
Polynomial form
Standard deviation
r/(m s1) MA + DMF EA + DMF BA + DMF EHA + DMF
f(x) g(x) f(x) g(x) f(x) g(x) f(x) g(x)
0.1831 0.2086 0.3407 0.3031 0.6370 0.6393 0.8954 0.8884
Jacobson’s relation gives the best estimate of experimental values of sound velocity in all the systems followed by Nomoto’s relation. In the present binary systems, the difference between experimental and theoretical velocities is greater where the mole fraction of DMF varies in the region 0.5 to 0.7. Hence it can be qualitatively inferred that the strength of interaction in the binary mixtures is more in this range of composition of binary mixtures.
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M. Kondaiah et al. / J. Chem. Thermodynamics 43 (2011) 1844–1850
2
5
1
4
-1 0
3
0.2
0.4
0.6
0.8
1
% (uexp-ucal)/uexp
% (uexp-ucal)/uexp
0 -2 -3 -4 -5
0 -1 0
0.2
0.4
0.6
0.8
1
-3
-7
-4
-8
-5
mole fraction, x 1
mole fraction, x1
FIGURE 5. Percentage deviations of theoretical ultrasonic velocities of MA + DMF mixture with mole fraction of DMF, Nomoto (), Van Dael (h), Impedance (N), Junjie (j), Jacobson (s), and Rao’s (d).
4 3 2 % (uexp-ucal)/uexp
1
-2
-6
1 0 -1 0
2
0.2
0.4
0.6
0.8
1
-2 -3
FIGURE 8. Percentage deviations of theoretical ultrasonic velocities of EHA + DMF mixture with mole fraction of DMF, Nomoto (), Van Dael (h), Impedance (N), Junjie (j), Jacobson (s), and Rao’s (d).
are positive in all the binary mixtures, indicating dispersion forces between the acrylate and DMF molecules and it follows the order (MA + DMF) > (EA + DMF) > (BA + DMF) > EHA > DMF. The observed higher partial molar volumes in the liquid mixture when compared to the respective molar volumes of pure components indicate weak interactions present in the systems. The ultrasonic velocities computed from different velocity theories were correlated with the experimentally measured ultrasonic velocities. Jacobson’s equation gives the good agreement between the theoretical and experimental ultrasonic velocity values.
-4
Acknowledgements
-5 -6
Authors are grateful to University Grants Commission, New Delhi for providing infrastructure facilities under DRS Scheme to the Department of Physics, Acharya Nagarjuna University.
mole fraction, x1 FIGURE 6. Percentage deviations of theoretical ultrasonic velocities of EA + DMF mixture with mole fraction of DMF, Nomoto (), Van Dael (h), Impedance (N), Junjie (j), Jacobson (s), and Rao’s (d).
References [1] [2] [3] [4]
4 3
[5]
% (uexp-ucal)/uexp
2 [6]
1
[7]
0 -1 0
0.2
0.4
0.6
0.8
1
-2 -3 -4
[8] [9] [10] [11] [12] [13] [14] [15]
-5 mole fraction, x 1 FIGURE 7. Percentage deviations of theoretical ultrasonic velocities of BA + DMF mixture with mole fraction of DMF, Nomoto (), Van Dael (h), Impedance (N), Junjie (j), Jacobson (s), and Rao’s (d).
[16] [17] [18] [19] [20]
4. Conclusions The ultrasonic velocities and densities for (MA or EA or BA or EHA + DMF) binary mixtures have been measured and the values of V Em , V m;1 , V m;2 , and V Em;1 , V Em;2 have been calculated. The V Em values
[21] [22] [23] [24]
R. Francesconi, F. Comelli, J. Chem. Eng. Data 42 (1997) 45–48. E. Gonzalez, J. Ortega, J. Chem. Eng. Data 4 (1996) 53–58. W.R. Liau, M. Tang, Y.P. Chen, J. Chem. Eng. Data 43 (1998) 826–829. J. Wisniak, G. Cortez, R.D. Peralta, R. Infante, L.E. Elizakde, J. Solution Chem. 31 (2007) 997–1022. R.D. Peralta, R. Infante, G. Cortez, L. Villarreal, J. Wisniak, Thermochim. Acta 390 (2002) 47–53. R.D. Peralta, R. Infante, G. Cortez, A. Cisneros, J. Wisniak, Thermochim. Acta 398 (2003) 39–46. R.D. Peralta, R. Infante, G. Cortez, R.R. Ramirez, J. Wisniak, J. Chem. Thermodyn. 35 (2003) 239–250. A. Ali, F. Nabi, M. Tariq, Int. J. Thermophys. 30 (2009) 464–474. K. Dharmalingam, A. Jalbout, J. Mol. Liq. 141 (2008) 17–18. A.K. Nain, T. Srivastava, J.D. Pandey, S. Gopal, J. Mol. Liq. 149 (2009) 9–17. A.K. Nain, R. Sharma, A. Ali, S. Gopal, J. Mol. Liq. 144 (2009) 124–130. A.K. Nain, R. Sharma, A. Ali, S. Gopal, J. Mol. Liq. 144 (2009) 138–144. A.K. Nain, R. Sharma, A. Ali, S. Gopal, Int. J. Thermophys. 31 (2010) 1073–1091. Shipra Baluja, Nayan Vekariya, Jagdish Movaliya, Iran. J. Chem. Chem. Eng. 27 (2008) 129–135. L. Marcheselli, A. Marchetti, M. Tagliazucchi, L. Tassi, G. Tosi, J. Chem. Soc. Faraday Trans. 88 (1992) 3159–3163. J. George, N.V. Sastry, S.R. Patel, M.K. Valand, J. Chem. Eng. Data 47 (2002) 262– 269. N.V. Sastry, M.K. Valand, Int. J. Thermophys. 18 (1997) 138–1403. A.I. Vogel, A Text Book of Practical Organic Chemistry, English Language Book Society, London, 1983. H.C. Parker, E.W. Parker, J. Phys. Chem. 29 (1925) 130–137. U.B. Kadam, A.P. Hiray, A.B. Sawant, M. Hasan, J. Chem. Thermodyn. 38 (2006) 1675–1683. M.K. Mohammad Ziaul Hyder, M.A. Saleh, S. Akhtar, J. Mol. Liq. 159 (2011) 204–210. S.Z. Mikhail, W.R. Kimel, J. Chem. Eng. Data 6 (1961) 533–537. O. Redlich, A.T. Kister, Ind. Eng. Chem. 40 (1948) 345–348. R.D. Peralta, R. Infante, G. Cortez, J.L. Angulo, J. Wisniak, Phys. Chem. Liq. 40 (2002) 649–660.
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[25] O. Nomoto, J. Phys. Soc. Jpn. 13 (1958) 1528–1532. [26] W. Van Dael, Vangeel, in: Proceedings of the First International Conference on Calorimetry and Thermodynamics, Warsaw, 1969, p. 556. [27] Shipra Baluja, P.H. Parrania, Asian J. Chem. 7 (1995) 417–423. [28] Z. Junjie, J Chem. Univ. Sci. Technol. 14 (1984) 298–300. [29] V. D Gokhale, N.N. Bhagavat, J. Pure Appl. Ultrason. 11 (1989) 21–24. [30] B. Jacobson, J. Chem. Phys. 20 (1952) 1927–1928.
[31] D. Sravana Kumar, D. Krishna Rao, Indian J. Pure Appl. Phys. 45 (2007) 210– 220. [32] A. Ali, A.K. Nain, N. Kumar, M. Ibrahmim, J. Pure Appl. Ultrason. 24 (2002) 27– 32.
JCT 11/111
Contents lists available at ScienceDirect
J. Chem. Thermodynamics journal homepage: www.elsevier.com/locate/jct
Ultrasonic velocities, densities, and excess molar volumes of binary mixtures of N,N-dimethyl formamide with methyl acrylate, or ethyl acrylate, or butyl acrylate, or 2-ethyl hexyl acrylate at T = 308.15 K M. Kondaiah a, D. Sravana Kumar b, K. Sreekanth a, D. Krishna Rao a,⇑ a b
Department of Physics, Acharya Nagarjuna University, Nagarjuna Nagar 522510, Andhra Pradesh, India Dr. V.S. Krishna Govt. Degree College, Visakhapatnam, Andhra Pradesh, India
a r t i c l e
i n f o
Article history: Received 26 March 2011 Received in revised form 17 June 2011 Accepted 19 June 2011 Available online 29 June 2011 Keywords: Ultrasonic velocity Density Redlich–Kister type polynomial Excess molar volume Partial molar volumes Theoretical models
a b s t r a c t Ultrasonic velocities, u, densities, q, of binary mixtures of N,N-dimethyl formamide (DMF) with methyl acrylate (MA), ethyl acrylate (EA), butyl acrylate (BA), and 2-ethyl hexyl acrylate (EHA), including pure liquids, over the entire composition range have been measured at T = 308.15 K. Using the experimental results, the excess molar volume, V Em , partial molar volumes, V m;1 , V m;2 , and excess partial molar volumes, V Em;1 , V Em;2 have been calculated. Molecular interactions in the systems have been studied in the light of variation of excess values of calculated properties. The excess properties have been fitted to Redlich– Kister type polynomial and the corresponding standard deviations have been calculated. The positive values of V Em indicate the presence of dispersion forces between the DMF and acrylic ester molecules. Further theoretical values of sound velocity in the mixtures have been evaluated using various theories and have been compared with experimental sound velocities to verify the applicability of such theories to the systems studied. Theoretical ultrasonic velocity data have been used to study molecular interactions in the binary systems investigated. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The study of properties of liquid mixtures and solutions finds direct applications in chemical and biochemical industry. The measurement of speed of sound in liquids enables determination of some useful acoustic and thermodynamic parameters that are found to be very sensitive to molecular interactions. Hence, such measurements are useful to study the strength of molecular interactions in liquid mixtures. Acrylic esters are important industrial chemicals and are widely used as precursors in the production of technically important special type polymers. Methyl acrylate is a contact allergen present in nail lacquer. It can also be used as a co-polymer in the process of polymerization of poly anionic cellulose (PAC) polymers, to reduce the glass transition temperature of the PAC polymers. Ethyl acrylate is a very important industrial chemical and is widely used commercially for the production of high polymeric and latex compounds. Butyl acrylate is a very useful feedstock for chemical synthesis, because it readily undergoes addition reaction with a wide variety of organic and inorganic compounds and N,N-dimethyl formamide is used as a solvent in
⇑ Corresponding author. Tel.: +91 863 6458142 (R); fax: +91 9440712142. E-mail address: [email protected] (D. Krishna Rao). 0021-9614/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2011.06.011
peptide coupling for pharmaceuticals, in the development and production of pesticides, in the manufacture of adhesives, synthetic leathers, fibers, films, and surface coatings and other applications of pure solvents. A survey of the literature indicates that Francesconi and Comelli [1], Gonzalez and Ortega [2], and Liau et al. [3] reported density and viscosity data for binary mixtures of esters with alkanols. Peralta et al. [4–7] measured densities of ethyl acrylate, butyl acrylate, methyl methacrylate, and styrene with toluene/cyclohexane/benzene/1,4-dioxane at temperature 298.15 K. Recently some researchers have reported the ultrasonic, volumetric, and viscometric studies of esters with alcohols [8–13]. The study of intermolecular interactions in (N,N-dimethyl formamide + acrylic esters) would be interesting owing to their industrial and pharmaceutical applications. In the present paper, ultrasonic velocities, u and densities, q of binary mixtures of N,N-dimethyl formamide (DMF) with methyl acrylate (MA) or ethyl acrylate (EA) or butyl acrylate (BA) or 2-ethyl hexyl acrylate (EHA) besides those of pure liquids at temperature 308.15 K covering the entire composition range have been reported. The excess molar volume, V Em , partial molar volumes, V m;1 , V m;2 , and excess partial molar volumes, V Em;1 , V Em;2 have been calculated. The variations of excess properties with composition of the mixtures have been discussed in terms of molecular interactions in the mixtures. The experimental values of u and q of pure liquids at
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M. Kondaiah et al. / J. Chem. Thermodynamics 43 (2011) 1844–1850 TABLE 1 Comparison of experimental values of ultrasonic velocity, u, and density, q, of pure liquids with the corresponding literature values at 308.15 K. u/(m s1)
Liquid
N,N-dimethylformamide Methyl acrylate Ethyl acrylate Butyl acrylate 2-Ethylhexyl acrylate
q/(kg m3)
Present work
Literature
Present work
Literature
1433.68 1141.78 1119.12 1158.33 1229.40
1434.40 1140.00 1118.70 1159.30
935.88 937.13 903.78 885.40 875.00
935.717 [15] 937.70 [8] 904.90 [8] 884.60 [17]
T = 308.15 K along with their literature [8,14–17] values are presented in table 1. 2. Experimental The N,N-dimethyl formamide (mass fraction purity 0.99) and butyl acrylate (mass fraction purity 0.99) were obtained from LOBA Chemicals, and methyl acrylate (mass fraction purity 0.99), ethyl acrylate (mass fraction purity 0.99), and 2-ethyl hexyl acrylate (EHA) (mass fraction purity 0.99), obtained from KEMPHASOL Company, Bombay. All are Analytical Reagent grade (AR grade) used in the present investigation and are further purified by standard methods [18]. The solutions of binary mixtures of DMF with MA, EA, BA, and EHA have been prepared in the specially designed glass bottles with air tight stoppers and adequate precautions have been taken to minimize evaporation losses. The weighing of solutions has been made using a METTLER TOLEDO (Switzerland make) ABB5-S/FACT digital balance with an accuracy of ±0.01 mg. The uncertainty in the mole fraction is 105. The ultrasonic velocity of pure liquids and their binary mixtures has been measured by using a multi-frequency ultrasonic interferometer (M-82 Model) supplied by Mittal enterprise, New Delhi at a fixed frequency of 2 MHz with an accuracy of ±0.2%. The temperature of liquid sample in the interferometer cell is maintained constant by circulating water pumped from constant temperature water bath. In the present study, the constant temperature water bath (digital electronic) supplied by Concord Instruments Co. Ltd., Chennai (RAAGA type) has been used. The instrument can maintain temperature to ±0.01 K as per its specifications. The density has been measured using a two stem pyknometer of Parker & Parker type [19–21] having a bulb volume of 5 cm3. A traveling microscope is used to determine the height of liquid level in the stems of pyknometer. In this method, the volume of the pyknometer cell is calibrated using triply distilled deionised water [22], as it is not practicable to determine the volume of pyknometer cell exactly from its geometry. The capillary of the pyknometer is calibrated using mercury. The pyknometer filled with the liquid/ liquid mixture that is free from air bubbles. The temperature of the liquid/liquid mixture is maintained constant by immersing the pyknometer in the transparent-walled constant temperature bath for at least 30 min to attain thermal equilibrium. The density of liquid mixture at each composition is determined three times and the average of the experimental values is reported in this paper. The constant temperature water bath maintained the temperature fluctuations within ±0.01 K while the density of the liquid mixtures was measured. The estimated accuracy in the density measurement is 3 in 105 parts.
[14] [16] [8] [8]
where M1, M2 and q1, q2 are the molar masses and densities of the pure components used in the present work; q is the density of the liquid mixture. The values of q, V Em and partial molar volumes V m;1 , V m;2 are presented in table 2. The values of V Em have been fitted to the Redlich–Kister type polynomial equation [23].
Y E ¼ x1 x2
n X
Ai ðx2 x1 Þi ;
where Y E ¼ V Em . The values of Ai are the adjustable parameters of the function and are determined using the least squares method. In the present investigation, ‘i’ values were taken from 0 to 4. The coefficients Ai and the corresponding standard deviation (r) of all the binary mixtures are presented in table 3. Figure 1 represents the variation of excess molar volume with mole fraction of DMF. The sign of V Em depends upon the contraction and expansion of volume of the liquids due to mixing. The factors that are mainly responsible for the volume expansion, i.e. positive values of V Em are due to (i) loss of dipolar association between the molecules (dispersion forces). (ii) The geometry of molecular structures which does not favor the fitting of molecules of one component into other molecules of second component. (iii) Steric hindrance of the molecules. The negative values of V Em are due to the (i) association of molecules through the formation of hydrogen bond, i.e. strong specific interactions and (ii) accommodation of molecules because of large differences in their molar volumes. The variation of excess molar volume is found to be positive over the entire composition range in the present investigation. Such positive V Em values suggest that the loss of association of the acrylic ester molecules due to the addition of DMF. Further, it is noticed that from figure 1, for all the binary mixtures investigated, the values of V Em become less positive as we move from MA to EHA. Over the entire composition range of binary mixture (DMF and acrylate), V Em follows the order (MA + DMF) > (EA + DMF) > (BA + DMF) > (EHA + DMF). This observation supports the prediction that fitting of molecules of one component into the voids in the structure of second component is less favorable if the difference in molar volumes of component liquids is less. Peralta et al. [5,24] reported similar studies on positive values of V Em . The existing molecular interactions in the systems are well reflected in the properties of partial molar volumes. The partial molar volumes V m;1 of component 1 (DMF) and V m;2 of component 2 (acrylic ester) in the mixtures over the entire composition range have been calculated by using the following relations.
V m;1 ¼
V Em
þ
V 1
þ x2
3. Results and discussion The excess molar volume, V Em was calculated using the relation
V Em ¼
x1 M 1 þ x2 M 2
q
x1 M 1
q1
þ
x2 M 2
q2
;
ð1Þ
ð2Þ
i¼0
V m;2 ¼
V Em
þ
V 2
x1
@V Em @x @V Em @x
! ;
ð3Þ
;
ð4Þ
T;P
! T;P
where V 1 and V 2 are the molar volumes of the pure components of DMF and acrylic esters respectively. The derivates ð@V Em =@xÞT;P in
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M. Kondaiah et al. / J. Chem. Thermodynamics 43 (2011) 1844–1850
TABLE 2 Densities, excess molar volumes, and partial molar volumes of all the binary systems at 308.15 K.
q (kg m3)
V Em (106 m3 mol1)
V m;1 (106 m3 mol1)
0.00000 0.11751 0.22835 0.33863 0.44010 0.54157 0.63671 0.73224 0.82577 0.91949 1.00000
937.13 924.97 915.96 913.50 914.67 916.46 918.70 922.32 926.11 931.65 935.88
MA + DMF 0.0000 1.1737 2.0260 2.2195 2.0600 1.8462 1.5996 1.2360 0.8711 0.3698 0.0000
86.5455 87.8630 83.6419 80.2711 78.9475 78.6914 78.6486 78.4184 78.1091 78.0209 78.1080
91.8660 91.9149 92.8177 94.1248 94.9394 95.1685 95.2350 95.7571 96.8563 97.3211 94.3941
0.00000 0.13626 0.25387 0.38050 0.48592 0.59136 0.67931 0.76745 0.84752 0.92761 1.00000
903.78 897.04 895.06 896.08 900.90 906.50 912.27 917.97 924.68 930.43 935.88
EA + DMF 0.0000 1.1799 1.7098 1.9100 1.6560 1.3614 1.0429 0.7716 0.4203 0.1950 0.0000
88.1558 85.2954 81.9097 79.4479 78.4770 78.1388 78.0745 78.0644 78.0671 78.0877 78.1080
110.7790 111.0395 111.8586 112.9777 113.7019 114.0822 114.1894 114.2143 114.2002 114.0179 113.4596
0.00000 0.16988 0.30775 0.44561 0.54877 0.65275 0.73279 0.81323 0.88759 0.94275 1.00000
885.40 882.93 883.92 891.03 897.06 904.42 910.66 917.38 924.71 930.00 935.88
BA + DMF 0.0000 1.1323 1.5812 1.2452 1.0062 0.7167 0.5125 0.3388 0.1460 0.0685 0.0000
81.6101 84.1502 79.6943 77.7442 77.7287 77.9976 78.0634 78.0111 77.9921 78.0485 78.1080
144.7590 144.8993 146.2902 147.3939 147.3857 146.9816 146.8437 147.0308 147.1136 146.4445 144.0355
0.00000 0.22421 0.38077 0.53704 0.63443 0.73403 0.79928 0.86454 0.89800 0.96093 1.00000
875.00 877.06 881.30 889.40 895.86 903.77 909.72 917.00 924.93 929.69 935.88
EHA + DMF 0.0000 0.7912 0.9096 0.6135 0.4211 0.2540 0.1821 0.0839 0.0620 0.0160 0.0000
78.2398 81.0405 78.3833 77.7068 77.8455 77.9968 78.0374 78.0532 78.0635 78.0951 78.1080
210.6060 210.7783 211.9022 212.4068 212.2024 211.8787 211.7482 211.6702 211.5920 211.1303 210.4098
Mole fraction of DMF (x1)
TABLE 3 Coefficients Ai of Redlich–Kister type polynomial equation (2) and the corresponding 1 standard deviation of V Em =ð106 m3 mol Þ in all the systems. A0
A1
A2
A3
A4
r
7.7672 6.5798 4.5147 2.7985
5.2878 5.3956 6.3454 4.3423
6.1153 1.7741 4.9313 1.5024
2.3331 1.6620 4.2326 4.1783
8.3997 2.0397 8.0567 4.3331
0.0273 0.0329 0.0327 0.0329
0.25
V m;1 ¼ V 1 þ x22
j X
Ai ðx2 x1 Þi 2x1 x22
i¼0
V m;2 ¼ V 2 þ x21
j X i¼0
j X
Ai ðx2 x1 Þi1 ;
ð5Þ
i¼1
Ai ðx2 x1 Þi þ 2x21 x2
j X i¼1
/(10 E Vm
equations (3) and (4) are obtained by differentiating equation (2) which lead to the following equations for V m;1 and V m;2 .
0.15
3
-1
m .mol )
0.20
-5
MA + DMF EA + DMF BA + DMF EHA + DMF
V m;2 (106 m3 mol1)
0.10 0.05 0.00 0
0.2
0.4
0.6
0.8
1
mole fraction, x1
Ai ðx2 x1 Þi1 ;
ð6Þ
FIGURE 1. Plots of excess molar volume against mole fraction of DMF for binary mixtures of DMF with MA (), EA (d), BA (N), and EHA (j).
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M. Kondaiah et al. / J. Chem. Thermodynamics 43 (2011) 1844–1850
using the above equations V Em;1 , V Em;2 have been calculated using,
ð8Þ
The values of V m;1 and V m;2 are furnished in table 2. From this table, the values of V m;1 and V m;2 for both the components in the mixtures are greater than their respective molar volumes in the pure state, i.e. an expansion of volume takes place on mixing DMF with acrylic esters. These results also support the observed positive values of V Em in all the binary systems. Figures 2 and 3 represent the variation of excess partial molar volumes of DMF and MA/EA/BA/EHA in the binary mixtures respectively. Examination of figures 2 and 3 reveals that, indicating dispersion forces exist between the unlike molecules. These figures support the conclusions drawn from V Em values. The variation of ultrasonic velocity with the mole fraction of DMF is shown in figure 4. The ultrasonic velocity increases non-linearly in all the systems investigated. This non-linear variation indicates the existence of molecular interactions between the unlike molecules in the binary mixtures. In the present study, theoretical sound velocities have been evaluated by considering acrylates as one component and DMF as the other component in the binary mixture. Such an evaluation of theoretical sound velocity is useful to verify the applicability of various postulates of the theories of liquid mixtures and to arrive at some useful inferences regarding the (strength of) molecular interactions between component liquids in some cases. The theoretical values of ultrasonic velocity obtained using various theories along with the experimental velocity are summarized in table 4. Nomoto [25] established the following relation for sound velocity based on the assumption of the linearity of the molecular sound velocity and the additivity of molar volume.
UN ¼
X
xi R i
.X
xi V i
o3
n .X o X xi M i f1=U V g2 ; ðxi M i =u2i Þ ¼ 1
ð10Þ
where Mi is the molar mass of ith component in the liquid mixture. The Impedance Dependence Relation used by Shipra Baluja and Parrania [27] is given below
U imp ¼
xi Z i
.X
4 3 2 1 0 -1
0
xi q i ;
ð11Þ
0.2
0.4
0.6
0.8
1
mole fraction, x1 FIGURE 3. Plots of excess partial molar volumes of MA, EA, BA, EHA for the binary mixtures of DMF with MA (), EA (d), BA (N), and EHA (j).
1500 1450 1400 1350 1300 1250 1200 1150 1100 0
ð9Þ
;
where xi is the mole fraction, Ri = ui1/3Vi the molar sound velocity, Vi the molar volume, and ui is the sound velocity of the ith component. Van Dael and Vangeel [26] obtained the Ideal Mixture Relation
X
_E V m 2 /(10 -6 m3.mol-1)
V Em;2 ¼ V m;2 V 2 :
5
-1
ð7Þ
¼ V m;1
6
u /(m.s )
V 1 ;
V Em;1
0.2
0.4 0.6 mole fraction, x1
0.8
1
FIGURE 4. Plots of variation of ultrasonic velocity against mole fraction of DMF for binary mixtures of DMF with MA (), EA (d), BA (N), and EHA (j).
where Zi is the acoustic impedance and qi is the density of the ith component of the mixture. Junjie’s [28] equation is given by
U Jun ¼
X
xi V i
X
xi M i
1=2 nX
ðxi V i =qi u2i Þ
o1=2
:
Jacobson’s [29] equation is given by
U J ¼ K q1=2 L1 f ; 11
_E V m1 /(10 -6 m3.mol-1)
ð13Þ
where Lf is the ideal free length of the mixture. Rao’s (specific sound velocity) [30] relation is given by
9
UR ¼ 7
X
xi r i q
3
ð14Þ
;
where ri = ui1/3/qi is Rao’s specific sound velocity of the ith component of the mixture.
5
The experimental results have been fitted to two types of polynomials which describe the ultrasonic velocity data quantitatively as well as qualitatively even in the specific interaction predominant region where non-ideal behavior of the system is noticed. The polynomial equations used are [31,32]
3 1 -1
ð12Þ
0
0.2
0.4 0.6 0.8 mole fraction, x1
1
FIGURE 2. Plots of excess partial molar volumes of DMF for binary mixtures of DMF with MA (), EA (d), BA (N), and EHA (j).
f ðxÞ ¼ UðxÞ ¼
X
gðxÞ ¼ ln UðxÞ ¼
ak xk
and
X ðln U k Þxk ;
ð15Þ ð16Þ
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M. Kondaiah et al. / J. Chem. Thermodynamics 43 (2011) 1844–1850
TABLE 4 Experimental and theoretical values of ultrasonic velocity from equations (9)–(16). Mole fraction of DMF (x1)
Uexp
UN
UV
0.00000 0.11751 0.22835 0.33863 0.44010 0.54157 0.63671 0.73224 0.82577 0.91949 1.00000
1132.60 1157.43 1182.22 1208.25 1233.91 1261.50 1290.15 1321.60 1354.67 1390.53 1424.30
1132.60 1160.25 1187.69 1216.38 1244.11 1273.20 1301.79 1331.86 1362.73 1395.16 1424.30
1132.60 1160.31 1187.77 1216.46 1244.16 1273.21 1301.76 1331.80 1362.65 1395.10 1424.30
0.00000 0.13626 0.25387 0.38050 0.48592 0.59136 0.67931 0.76745 0.84752 0.92761 1.00000
1122.00 1150.91 1177.45 1208.75 1236.96 1267.64 1295.45 1326.70 1357.33 1391.54 1424.30
1122.00 1150.21 1176.93 1208.54 1237.40 1268.94 1297.55 1328.59 1359.11 1392.10 1424.30
0.00000 0.16988 0.30775 0.44561 0.54877 0.65275 0.73279 0.81323 0.84700 0.94275 1.00000
1168.56 1194.70 1219.52 1246.50 1269.20 1297.09 1323.00 1350.34 1362.47 1401.26 1424.30
0.00000 0.22421 0.38077 0.54100 0.64200 0.73403 0.79928 0.86454 0.91274 0.96093 1.00000
1229.40 1247.20 1263.00 1285.80 1304.03 1328.38 1345.68 1366.27 1386.59 1404.89 1424.30
UImp
UJun
UJ
UR
f(x)
g(x)
MA + DMF 1132.60 1166.80 1199.12 1231.28 1260.88 1290.48 1318.25 1346.13 1373.44 1400.81 1424.30
1132.60 1154.41 1176.97 1201.63 1226.58 1254.06 1282.50 1314.11 1348.55 1387.18 1424.30
1132.60 1157.43 1182.22 1208.25 1233.91 1261.51 1290.15 1321.60 1354.67 1390.54 1424.30
1132.60 1161.28 1189.23 1218.85 1247.13 1276.43 1304.59 1334.31 1363.78 1394.70 1424.31
1132.57 1157.55 1182.15 1208.15 1233.86 1261.74 1290.21 1321.36 1354.59 1390.77 1424.21
1132.61 1157.57 1182.13 1208.11 1233.83 1261.74 1290.22 1321.36 1354.57 1390.71 1424.15
1122.00 1155.09 1185.33 1219.80 1250.14 1282.12 1310.14 1339.55 1367.50 1396.72 1424.30
EA + DMF 1122.00 1164.37 1200.60 1239.31 1271.30 1303.09 1329.44 1355.71 1379.45 1403.07 1424.30
1122.00 1143.33 1164.49 1190.84 1216.28 1245.74 1274.14 1306.95 1341.50 1381.73 1424.30
1122.00 1150.91 1177.45 1208.75 1236.96 1267.64 1295.45 1326.70 1357.33 1391.54 1424.30
1122.00 1146.65 1171.05 1201.26 1229.89 1260.84 1288.82 1318.65 1349.97 1386.73 1424.31
1122.03 1150.75 1177.65 1208.77 1236.83 1267.51 1295.65 1326.63 1357.52 1391.29 1424.39
1122.04 1150.79 1177.68 1208.70 1236.82 1267.50 1295.69 1326.63 1357.50 1391.31 1424.39
1168.56 1192.49 1215.42 1242.38 1265.86 1293.12 1317.10 1344.40 1356.97 1396.88 1424.30
1168.56 1195.53 1221.03 1250.33 1275.16 1303.08 1326.85 1353.00 1364.73 1400.68 1424.30
BA + DMF 1168.56 1214.01 1250.29 1286.02 1313.40 1338.68 1358.71 1378.67 1386.99 1410.43 1424.30
1168.56 1186.89 1205.28 1228.03 1248.92 1274.56 1298.45 1327.34 1341.31 1388.70 1424.30
1168.56 1194.71 1219.52 1246.50 1269.20 1297.09 1323.00 1350.34 1362.47 1401.26 1424.30
1168.56 1182.05 1200.80 1225.84 1247.84 1273.77 1297.30 1324.83 1336.82 1387.76 1424.31
1168.54 1194.81 1219.37 1246.33 1269.62 1297.32 1322.17 1350.35 1363.05 1401.04 1424.33
1168.53 1194.76 1219.26 1246.38 1269.65 1297.38 1322.13 1350.32 1363.08 1401.08 1424.25
1229.40 1247.44 1264.16 1286.67 1304.96 1325.59 1343.31 1364.41 1382.79 1404.19 1424.30
1229.40 1208.44 1212.63 1233.33 1256.00 1284.32 1309.63 1340.08 1366.43 1396.59 1424.30
EHA + DMF 1229.40 1275.41 1306.72 1338.09 1357.52 1374.52 1387.26 1399.42 1408.33 1417.19 1424.30
1229.40 1243.68 1257.47 1276.94 1293.58 1313.29 1331.07 1353.38 1373.88 1399.11 1424.30
1229.40 1247.20 1263.00 1285.80 1304.03 1328.38 1345.68 1366.27 1386.59 1404.89 1424.30
1229.40 1224.42 1231.61 1260.71 1274.29 1282.87 1302.61 1327.54 1352.19 1383.93 1424.30
1229.39 1247.30 1262.79 1285.65 1305.10 1327.12 1345.73 1367.30 1385.44 1405.74 1423.98
1229.42 1247.38 1262.82 1285.62 1305.05 1327.16 1345.74 1367.31 1385.48 1405.71 1423.96
where k in the summation assumes values from 0 to 5, x is the mole fraction of the DMF and ak, ln Uk are constant coefficients to be determined using numerical methods. The values of sound velocities (after determining the coefficients in the above polynomial equations by applying least squares method) have been compiled in table 4. The standard deviations corresponding to sound velocity values calculated using the polynomial equations from their experimental values have been evaluated using the relation:
nX o1=2 r¼ ðU E U P Þ2 =n ;
ð17Þ
where UE is the experimental sound velocity. The UP is the calculated sound velocity from the polynomial equations f(x) and g(x) and n is the number of mole fractions at which experimental and theoretical velocities have been determined. These standard deviations are presented in table 5 and these values are small. The percentage deviations of theoretical velocities from the experimental ultrasonic velocity values are plotted in figures 5–8 for all the systems investigated. Among all the empirical theories
TABLE 5 Standard deviation of ultrasonic velocity calculated using polynomial equations from experimental values. Name of the liquid system
Polynomial form
Standard deviation
r/(m s1) MA + DMF EA + DMF BA + DMF EHA + DMF
f(x) g(x) f(x) g(x) f(x) g(x) f(x) g(x)
0.1831 0.2086 0.3407 0.3031 0.6370 0.6393 0.8954 0.8884
Jacobson’s relation gives the best estimate of experimental values of sound velocity in all the systems followed by Nomoto’s relation. In the present binary systems, the difference between experimental and theoretical velocities is greater where the mole fraction of DMF varies in the region 0.5 to 0.7. Hence it can be qualitatively inferred that the strength of interaction in the binary mixtures is more in this range of composition of binary mixtures.
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2
5
1
4
-1 0
3
0.2
0.4
0.6
0.8
1
% (uexp-ucal)/uexp
% (uexp-ucal)/uexp
0 -2 -3 -4 -5
0 -1 0
0.2
0.4
0.6
0.8
1
-3
-7
-4
-8
-5
mole fraction, x 1
mole fraction, x1
FIGURE 5. Percentage deviations of theoretical ultrasonic velocities of MA + DMF mixture with mole fraction of DMF, Nomoto (), Van Dael (h), Impedance (N), Junjie (j), Jacobson (s), and Rao’s (d).
4 3 2 % (uexp-ucal)/uexp
1
-2
-6
1 0 -1 0
2
0.2
0.4
0.6
0.8
1
-2 -3
FIGURE 8. Percentage deviations of theoretical ultrasonic velocities of EHA + DMF mixture with mole fraction of DMF, Nomoto (), Van Dael (h), Impedance (N), Junjie (j), Jacobson (s), and Rao’s (d).
are positive in all the binary mixtures, indicating dispersion forces between the acrylate and DMF molecules and it follows the order (MA + DMF) > (EA + DMF) > (BA + DMF) > EHA > DMF. The observed higher partial molar volumes in the liquid mixture when compared to the respective molar volumes of pure components indicate weak interactions present in the systems. The ultrasonic velocities computed from different velocity theories were correlated with the experimentally measured ultrasonic velocities. Jacobson’s equation gives the good agreement between the theoretical and experimental ultrasonic velocity values.
-4
Acknowledgements
-5 -6
Authors are grateful to University Grants Commission, New Delhi for providing infrastructure facilities under DRS Scheme to the Department of Physics, Acharya Nagarjuna University.
mole fraction, x1 FIGURE 6. Percentage deviations of theoretical ultrasonic velocities of EA + DMF mixture with mole fraction of DMF, Nomoto (), Van Dael (h), Impedance (N), Junjie (j), Jacobson (s), and Rao’s (d).
References [1] [2] [3] [4]
4 3
[5]
% (uexp-ucal)/uexp
2 [6]
1
[7]
0 -1 0
0.2
0.4
0.6
0.8
1
-2 -3 -4
[8] [9] [10] [11] [12] [13] [14] [15]
-5 mole fraction, x 1 FIGURE 7. Percentage deviations of theoretical ultrasonic velocities of BA + DMF mixture with mole fraction of DMF, Nomoto (), Van Dael (h), Impedance (N), Junjie (j), Jacobson (s), and Rao’s (d).
[16] [17] [18] [19] [20]
4. Conclusions The ultrasonic velocities and densities for (MA or EA or BA or EHA + DMF) binary mixtures have been measured and the values of V Em , V m;1 , V m;2 , and V Em;1 , V Em;2 have been calculated. The V Em values
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JCT 11/111