Research Journal of Chemical Sciences ______________________________________________ ISSN 2231-606X Vol. 4(8), 42-45, August (2014) Res. J. Chem. Sci. International Science Congress Association 42 Theoretical Evaluation of Speeds of Sound in Liquid Mixtures Containing Diethyl carbonate and Aniline at Various TemperaturesNarendra K., Sudhamsa B. and Sarath Babu M.Department of Physics, V.R. Siddhartha Engineering College (Autonomous), Kanuru, Vijayawada – 520007, INDIA Department of Chemistry, MIC College of Technology, Kanchikacharla, INDIA Department of Chemistry, MIC College of Technology, Kanchikacharla, INDIA Available online at: www.isca.in, www.isca.me Received 24th July 2014, revised 8th August 2014, accepted 17th August 2014Abstract Speeds of sound and density values of the liquid mixtures containing diethyl carbonate and aniline have been measured at different temperatures (293.15, 298.15, 303.15, 308.15, 313.15 and 318.15) K over the entire range of mole fraction. The theoretical values of speeds of sound were evaluated with the help of Nomoto’s relation (uNR), impedance relation (uIR), ideal mixing relation (uIMR), Junjie’s relaiton (uJR) and Rao’s specific velocity relation (u). The theoretical values are compared with the experimental values. The molecular association () has been evaluated from the values of experimental and theoretical speeds. Keywords: Diethyl carbonate, aniline, mixing rules. IntroductionIn determining the Physico-chemical behaviour of liquid mixtures, speeds of sound data is very important and it have many applications in industry. Speeds of sound investigations has been carrying by many researchers1-4 from several years and correlating the experimental results with the theoretical relations of Nomoto, impedance, ideal mixing relation, Junjie and Rao’s specific velocity. Due to its non-destructive nature, speeds of sound of liquid mixtures have been extensively carrying out in the last two decades in different branches of science. These measurements are helpful in measuring thermodynamic properties which in turn are useful to predict the nature of molecular interactions present between molecules in a mixture. Here we report the experimental values of speeds of sound along with theoretical values evaluated using ideal mixing relation, Nomoto’s relation, Junjie’s relation, impedance relation and Rao’s specific velocity relation for diethyl carbonate and aniline at temperatures (293.15, 298.15, 303.15, 308.15, 313.15 and 318.15) K over the entire mole fraciton range. Relative applicability of these theories to the system considered in the present study has been checked including the necessary discussion. Material and Methods The present investigation used the chemicals obtained from Aldrich Chemicals with purity �99% and they were used as-received without any further purification. Purity of the samples was checked by comparison of the observed values of densities and speeds of sound with those in literature reports. Anton Paar DSA 5000 density and sound analyser provided with two Pt 100 platinum thermometer was used for measuring densities and speeds of sound of pure liquids as well as liquid mixtures. The apparatus was controlled to 0.001 K by a built-in solid state thermostat since density shows extreme sensitivity to temperature. The stated accuracy in speed of sound and density are 0.5 m/s and 5x10-3 kgm-3 respectively. Known masses of pure liquids were mixed in order to get the binary liquid mixtures and they were stored in airtight-stoppered bottles to minimize evaporation losses. The weighings were done using an electronic balance with a precision of 0.01mg. Theory: Nomoto’s relation, According to Nomoto, following is the relation for speed of sound in binary liquid mixtures, which was established based on the assumption of the additivity of molar sound speed (R) and no change in volume on mixing: R = M /1/3 (1) where u and are determined experimentally, and M is the mean molecular weight in a binary mixture. M = (x + x) (2) Here M, M, x and x are molecular weights and mole fractions of constituent components. NR = [(x + x)/(x+x)] (3) In the above equation, V and V are the molar volumes of 1stand 2nd components of the liquid mixture. Impedance relaiton Research Journal of Chemical Sciences ___________________________________________________________ ISSN 2231-606XVol. 4(8), 42-45, August (2014) Res. J. Chem. Sci. International Science Congress Association 43 IR = / i (4) where x is the mole fraction, the density and Z is the acoustic impedance of the mixture. Junjie equation J = (x + x)/[{x + x1/2 {x + x1/2] (5) Rao’s specific velocity = (3 (6) where x = mole fraction, = density and r = Rao’s specific sound velocity of the mixture. Ideal Mixing relation 1/(x + x)*uimx = x/M + x/M (7) The degree of molecular interaction given as interaction parameter, is calculated using the relation, = (uexp/uimx) – 1 (8) Results and Discussion The experimentally obtained values of speeds of sound for the binary system and the corresponding theoretical values at various temperatures are presented in table-1. Data reveals that the speeds of sound calculated from Ideal Mixing relation (IMR) exhibit more satisfactory agreement with the experimental values in all the temperatures studied than other approaches in the binary system. From table-2 it is observed that there is a deviation between experimental and theoretical values which confirms the existence of molecular interactions. Higher variations are observed at some intermediate concentrations suggesting the strong tendency of association between component molecules of the mixture due to hydrogen bonding10. Interactions between different components of the binary mixture were not taken into account in view of the assumption in Nomoto’s theory, that there is no change in the volume on mixing. In case of ideal mixing relation, the ratios of specific heats of ideal mixtures and the volumes are also equal and hence no molecular interactions are considered. However, upon mixing the components, interactions between the molecules occur due to the presence of various types of forces like hydrogen bonding, charge transfer, dispersion forces and interactions of dipole-dipole and dipole-induced dipole. The deviations observed in case of theoretical values of speeds of sound from the experimental values, thus, indicate that there are molecular interactions between the unlike molecules11. The negative and positive magnitudes of percentage deviations in speeds of sound indicating non ideal behavior of liquid mixtures. The positive value of at all temperatures clearly indicates the existence of strong tendency for the formation of association in mixture through dipole-dipole interactions. All the theoretical models fairly predicted the speeds of sound are reasonably close to the experimental values. Conclusion Speeds of sound values are measured at different temperatures and using various theoretical models speeds of sound is evaluated. Experimental values are compared with the theoretical results and it is observed that Ideal Mixing relation provides good results when compared to other relations. References 1.Mishra Sujata and Paikaray Rita, Ultrasonic and theoretical study of binary mixture of two polar-liquids at different temperatures, Res.J.Chem.Sci.,3(6), 24-31 (2013)2.Gangwar Munendra Kumar and Sacena Ashish Kumar, Ultrasonic study of molecular interactions in binary mixtures of isopropylbenzene (Cumene) with benzene, toluene and acetone at 303K, Res.J.Chem.Sci.,3(2), 27-30 (2013)3.Kolla Narendra, Chintalapati Srinivasu, Piratla Narayanamurthy, Experimental and theoretical ultrasonic velocities of binary liquid mixtures at temperatures (303.15, 308.15, 313.15 and 318.15)K – Comparative study, Pak.J.Sci.Ind.Res.Ser.A: Phys.Sci., 55(2), 59-67 (2012) 4.Saravanakumar K, and Kubendran T.R., Density and viscosities for the binary mixtures of 1,4-dioxane and benzene or chlorobenzene at 303.15, 308.15, 313.15K and a pressure of 0.1M Pa, Res.J.Chem.Sci.,2(4), 50-56 (2012)5.Nomoto O., Empirical formula for sound velocity in liquid mixtures, J Phys Soc Japan, 13, 1528-1532 (1958)6.Baluja S., Parsania P.H., Acoustical properties of 3-and alpha-furyl acrylic acid in protic and aprotic solvents, Asian J Chem., , 417 (1995)7.Van Dael W., Vangael E., Proc Int Conf on Calorimetry and Thermodynamics Warsaw, 555 (1955)8.Junjie Z., J China Univ Sci Techn, 14, 298 (1984)9.Gokhale V.D., Bhagavat, J Pure Appl Ultrason., 11, 21 (1989)10.Meenakshi K., Palani R., Investigation of molecular interactions in ternary liquid mixtures using ultrasonic velocity, Indian J Chem., 46A, 252-257 (2007)11.Begum Z., Sandhya Sri P.B., Rambabu C., Theoretical evaluation of ultrasonic velocities in binary liquid mixtures of anisaldehyde with some alcoxyethanols at different temperatures, ISRN Physical Chemistry, 12 (2012) Research Journal of Chemical Sciences ___________________________________________________________ ISSN 2231-606XVol. 4(8), 42-45, August (2014) Res. J. Chem. Sci. International Science Congress Association 44 Table-1 Experimental and theoretical values of speeds of sound for diethyl carbonate + aniline at different temperatures uexpt uNR uIR uIMR uJR u uexpt uNR uIR uIMR uJR u 293.15 K 298.15 K 0.0000 1656.02 1656.02 1656.02 1656.02 1656.02 1656.02 1636.79 1636.79 1636.79 1636.79 1636.79 1636.79 0.0730 1613.70 1608.31 1624.00 1610.52 1585.99 1621.09 1594.43 1588.81 1604.72 1590.86 1565.85 1601.75 0.1652 1562.65 1552.43 1583.28 1556.69 1513.50 1576.35 1543.34 1532.64 1563.93 1536.62 1492.70 1556.87 0.2537 1516.89 1502.81 1543.82 1508.37 1456.18 1534.35 1497.74 1482.80 1524.40 1488.01 1435.05 1514.72 0.3387 1475.49 1458.60 1505.67 1464.87 1409.74 1494.76 1455.94 1438.42 1486.17 1444.31 1388.48 1475.01 0.4432 1427.55 1408.25 1458.32 1414.79 1361.40 1447.05 1407.88 1387.92 1438.69 1394.07 1340.11 1427.15 0.5468 1381.13 1362.29 1410.90 1368.50 1320.87 1399.34 1361.32 1341.85 1391.13 1347.70 1299.65 1379.30 0.6546 1335.93 1318.20 1361.08 1323.56 1284.82 1350.64 1315.96 1297.69 1341.16 1302.75 1263.72 1330.37 0.7559 1294.35 1279.86 1313.82 1284.02 1255.44 1305.27 1274.23 1259.32 1293.73 1263.24 1234.49 1284.98 0.8840 1242.96 1235.18 1253.36 1237.34 1223.26 1249.50 1222.58 1214.61 1233.04 1216.66 1202.51 1229.05 1.0000 1198.01 1198.01 1198.01 1198.01 1198.01 1198.01 1177.46 1177.46 1177.46 1177.46 1177.46 1177.46 303.15 K 308.15 K 0.0000 1617.52 1617.52 1617.52 1617.52 1617.52 1617.52 1598.27 1598.27 1598.27 1598.27 1598.27 1598.27 0.0730 1575.11 1569.26 1585.41 1571.16 1545.66 1582.36 1555.8 1549.75 1566.13 1551.49 1525.49 1563.00 0.1652 1523.92 1512.81 1544.56 1516.51 1471.85 1537.34 1504.55 1493.04 1525.24 1496.44 1451.04 1517.87 0.2537 1478.31 1462.77 1504.96 1467.62 1413.89 1495.08 1458.49 1442.79 1485.58 1447.27 1392.79 1475.46 0.3387 1436.36 1418.23 1466.65 1423.72 1367.20 1455.24 1416.83 1398.11 1447.21 1403.20 1345.99 1435.54 0.4432 1388.18 1367.59 1419.06 1373.33 1318.81 1407.23 1368.52 1347.34 1399.52 1352.67 1297.61 1387.41 0.5468 1341.47 1321.42 1371.38 1326.90 1278.43 1359.27 1321.69 1301.09 1351.73 1306.19 1257.32 1339.33 0.6546 1295.96 1277.20 1321.27 1281.94 1242.63 1310.33 1276.04 1256.82 1301.48 1261.25 1221.68 1290.28 0.7559 1254.09 1238.80 1273.68 1242.49 1213.56 1264.74 1234.06 1218.41 1253.76 1221.86 1192.78 1244.61 0.8840 1202.27 1194.09 1212.77 1196.02 1181.81 1208.67 1182.09 1173.71 1192.64 1175.52 1161.25 1188.43 1.0000 1156.96 1156.96 1156.96 1156.96 1156.96 1156.96 1136.62 1136.62 1136.62 1136.62 1136.62 1136.62 313.15 K 318.15 K 0.0000 1579.10 1579.10 1579.10 1579.10 1579.10 1579.10 1559.95 1559.95 1559.95 1559.95 1559.95 1559.95 0.0730 1536.56 1530.33 1546.94 1531.90 1505.39 1543.73 1517.56 1510.93 1527.79 1512.34 1485.33 1524.50 0.1652 1485.25 1473.36 1506.01 1476.44 1430.31 1498.47 1466.00 1453.73 1486.83 1456.50 1409.63 1479.13 0.2537 1439.08 1422.92 1466.31 1427.01 1371.78 1455.94 1419.76 1403.12 1447.10 1406.81 1350.85 1436.50 0.3387 1397.37 1378.11 1427.87 1382.77 1324.88 1415.93 1377.98 1358.19 1408.62 1362.42 1303.87 1396.41 0.4432 1348.95 1327.22 1380.11 1332.13 1276.52 1367.69 1329.49 1307.20 1360.79 1311.68 1255.56 1348.07 0.5468 1302.02 1280.90 1332.22 1285.61 1236.35 1319.51 1282.46 1260.82 1312.82 1265.14 1215.51 1299.82 0.6546 1256.26 1236.59 1281.84 1240.69 1200.87 1270.36 1236.61 1216.50 1262.34 1220.27 1180.21 1250.57 0.7559 1214.18 1198.17 1233.98 1201.37 1172.14 1224.62 1194.46 1178.08 1214.36 1181.04 1151.68 1204.80 0.8840 1162.07 1153.50 1172.67 1155.18 1140.86 1168.35 1142.22 1133.46 1152.88 1135.02 1120.65 1148.43 1.0000 1116.45 1116.45 1116.45 1116.45 1116.45 1116.45 1096.47 1096.47 1096.47 1096.47 1096.47 1096.47 Research Journal of Chemical Sciences ___________________________________________________________ ISSN 2231-606XVol. 4(8), 42-45, August (2014) Res. J. Chem. Sci. International Science Congress Association 45 Table-2 Percentage deviations and interaction parameters (aa) for diethyl carbonate + aniline at different temperatures %uNR %uIR %uIMR %uJR %uaa%uNR %uIR %uIMR %uJR %uaa 293.15 K 298.15 K 0.0000 0.00 0.00 0.00 0.00 0.00 0.0000 0.00 0.00 0.00 0.00 0.00 0.0000 0.0730 0.33 -0.63 0.20 1.72 -0.46 0.0040 0.35 -0.64 0.22 1.79 -0.46 0.0045 0.1652 0.66 -1.30 0.38 3.15 -0.88 0.0077 0.70 -1.32 0.44 3.28 -0.88 0.0088 0.2537 0.94 -1.74 0.56 4.00 -1.15 0.0113 1.01 -1.75 0.65 4.19 -1.13 0.0131 0.3387 1.16 -2.00 0.72 4.46 -1.31 0.0145 1.22 -2.03 0.80 4.63 -1.31 0.0162 0.4432 1.37 -2.11 0.89 4.63 -1.37 0.0181 1.44 -2.14 0.98 4.81 -1.37 0.0199 0.5468 1.38 -2.11 0.91 4.36 -1.32 0.0185 1.45 -2.14 1.00 4.53 -1.32 0.0203 0.6546 1.35 -1.85 0.93 3.83 -1.10 0.0188 1.41 -1.88 1.00 3.97 -1.10 0.0204 0.7559 1.13 -1.48 0.80 3.01 -0.84 0.0162 1.18 -1.51 0.86 3.12 -0.84 0.0175 0.8840 0.63 -0.83 0.45 1.59 -0.53 0.0091 0.66 -0.85 0.48 1.64 -0.53 0.0097 1.0000 0.00 0.00 0.00 0.00 0.00 0.0000 0.00 0.00 0.00 0.00 0.00 0.0000 303.15 K 308.15 K 0.0000 0.00 0.00 0.00 0.00 0.00 0.0000 0.00 0.00 0.00 0.00 0.00 0.0000 0.0730 0.37 -0.65 0.25 1.87 -0.46 0.0050 0.39 -0.66 0.28 1.95 -0.46 0.0056 0.1652 0.73 -1.34 0.49 3.42 -0.88 0.0098 0.77 -1.36 0.54 3.56 -0.89 0.0109 0.2537 1.06 -1.77 0.72 4.36 -1.13 0.0146 1.09 -1.82 0.77 4.50 -1.16 0.0156 0.3387 1.28 -2.07 0.88 4.81 -1.31 0.0178 1.34 -2.10 0.96 5.00 -1.32 0.0195 0.4432 1.51 -2.18 1.07 5.00 -1.37 0.0217 1.57 -2.22 1.16 5.18 -1.38 0.0236 0.5468 1.52 -2.18 1.09 4.70 -1.33 0.0221 1.58 -2.22 1.17 4.87 -1.33 0.0239 0.6546 1.47 -1.92 1.08 4.11 -1.11 0.0220 1.53 -1.95 1.16 4.26 -1.12 0.0236 0.7559 1.23 -1.54 0.93 3.23 -0.85 0.0188 1.28 -1.57 0.99 3.35 -0.86 0.0201 0.8840 0.69 -0.87 0.52 1.70 -0.53 0.0105 0.71 -0.88 0.56 1.76 -0.54 0.0112 1.0000 0.00 0.00 0.00 0.00 0.00 0.0000 0.00 0.00 0.00 0.00 0.00 0.0000 313.15 K 318.15 K 0.0000 0.00 0.00 0.00 0.00 0.00 0.0000 0.00 0.00 0.00 0.00 0.00 0.0000 0.0730 0.41 -0.67 0.30 2.03 -0.47 0.0061 0.44 -0.67 0.34 2.12 -0.46 0.0069 0.1652 0.81 -1.38 0.59 3.70 -0.89 0.0120 0.84 -1.40 0.65 3.84 -0.90 0.0131 0.2537 1.14 -1.86 0.84 4.68 -1.17 0.0170 1.19 -1.89 0.91 4.85 -1.18 0.0185 0.3387 1.40 -2.14 1.05 5.19 -1.33 0.0212 1.46 -2.18 1.13 5.38 -1.34 0.0230 0.4432 1.64 -2.26 1.25 5.37 -1.39 0.0254 1.71 -2.30 1.34 5.56 -1.40 0.0273 0.5468 1.65 -2.27 1.26 5.04 -1.34 0.0257 1.72 -2.31 1.35 5.22 -1.35 0.0276 0.6546 1.59 -2.00 1.24 4.41 -1.12 0.0253 1.65 -2.04 1.32 4.56 -1.13 0.0270 0.7559 1.34 -1.60 1.05 3.46 -0.86 0.0214 1.39 -1.64 1.12 3.58 -0.87 0.0229 0.8840 0.74 -0.90 0.59 1.83 -0.54 0.0120 0.77 -0.92 0.63 1.89 -0.54 0.0127 1.0000 0.00 0.00 0.00 0.00 0.00 0.0000 0.00 0.00 0.00 0.00 0.00 0.0000