International Journal of Chemical & Petrochemical Technology (IJCPT) ISSN 2277-4807 Vol. 3, Issue 4, Oct 2013, 15-26 TJPRC Pvt. Ltd. THEORETICAL EVALUATION OF ULTRASONIC VELOCITY IN BINARY MIXTURES OF ALCOHOLS WITH ANISIC ALDEHYDE P. B. SANDHYA SRI, ZAREENA BEGUM, M. NAGESWARA RAO & C. RAMBABU Department of Chemistry, Acharya Nagarjuna University, Guntur, Andhra Pradesh, India ABSTRACT Theoretical values of ultrasonic velocity in binary liquid mixtures of anisic aldehyde + pentanol, anisic aldehyde + hexanol and anisic aldehyde+ heptanol have been evaluated at 303.15,308.15,313.15 and 318.15K using Nomoto s relation, ideal mixing relation (IMR) impedance dependence relation (IDR), Rao s velocity method (RVM) Junjie s method (JM) and Danusso method (DM). The relative merits of these theoretical relations were examined by comparing the theoretical values of ultrasonic velocity with the values obtained experimentally. The validity of the theories was checked by applying the chi-square test for goodness of fit and by calculating the average percentage error (APE). KEYWORDS: Ultrasonic Velocity, Anisic Aldehyde, Alcohols, Chi-Square Test INTRODUCTION In recent years an increasing variety of research techniques are being employed to get an insight into the molecular behavior of liquids. In the present stage of development, ultrasonic techniques are yielding fruitful results comparable with those of other methods in the elucidation of molecular mechanisms. Measurement of sound velocity has been used for many years in connection with the determination of elastic and thermodynamic properties of gases, liquids and solids. Intimate relations between the values of sound velocity and chemical or structural characteristics of molecules of liquids or liquid mixtures have been found. This gives sound velocity the primary quantity in the molecular theory of liquids. Theoretical evaluation of ultrasonic velocity in binary liquid mixtures and its comparison with the experimental values reflects the molecular interaction in liquid mixtures, which is very useful to build comprehensive theoretical model for liquids. Several researchers [1-9] carried out investigations on liquid mixtures and correlated the experimental results of ultrasonic velocity with the theoretical relations like Nomoto s relation[10], ideal mixing relation (IMR) [11], impedance dependence relation (IDR) [12], Rao s velocity method (RVM) [13] Junjie s method (JM) [14] and Danusso[15]. Further, the best suitable theory for the given studied system is also picked out by computing the average percentage error and Chi-Square test. In the present investigation anisic aldehyde is mixed with alcohols at different mole fractions to study the interactions between the component molecules. The results are explained and discussed in terms of molecular interactions present in the investigated systems. The deviation in the variation of U 2 exp/ U 2 imx, average percentage error, (APE), Chi-square test for goodness of fit, from unity have also been evaluated to further explain the non-ideality of the system. The ratio of U 2/ exp U 2 imx gives an idea of extent of interaction taking place between molecules of the mixtures, positive values of which infer strong interactions between the components.
16 P. B. Sandhya Sri, Zareena Begum, M. Nageswara Rao & C. Rambabu EXPERIMENTAL Anisic aldehyde, pentanol, hexanol and heptanol from Merk were purified as described in the literature [16, 17]. The pure chemicals were stored over activated 4Å molecular sieves to reduce water content before use. The mixtures are prepared gravimetrically using an electronic balance (Shimadzu AY120) with an uncertainty of ±1x10-7 kg and stored in airtight bottles. The uncertainty on mole fraction is estimated to be 1x10-4.It is ensured that the mixtures are properly mixed and the measurement of the required parameters was done within one day of preparation. The densities, ρ, of pure liquids and their mixtures are determined using a 10-5 m 3 double-arm pycnometer, and the values from triplicate replication at each temperature are reproducible within 2 x 10-1 kg m 3 and the uncertainty in the measurement of density is found to be 2 parts in 10 4 parts. The reproducibility in mole fractions was within ±0.0002 Temperature control for the measurement of viscosity and density is achieved by using a microprocessor assisted circulating water bath, (supplied by Mac, New Delhi) regulated to ±0.01 K, using a proportional temperature controller. Adequate precautions were taken to minimize evaporation losses during the actual measurements. The ultrasonic velocity of sound (U) is measured using an ultrasonic interferometer (Mittal Enterprises, New Delhi model F05) operating at 2 MHz The measured speeds of sound have a precision of 0.8 m.sec -1 and an uncertainty less than ± 0.1 m.sec -1. The temperature stability was maintained within 0.01K.by circulating water bath around the measuring cell through a pump. THEORETICAL CONIDERATIONS Nomoto Equation Rao [18] proposed the relation that the ratio of temperature coefficients of sound velocity U and molar volume V remains almost constant for pure liquids: [(1/U) (du/dt)] / [(1/V) (dv/dt)] = -3 (1) where T is the absolute temperature. Integration the above equation, we get VU 1/3 = const = M/ U 1/3 = R (2) Where U and are determined experimentally and M is the mean molecular weight in a binary liquid mixture M = (X 1 M 1 + X 2 M 2 ) ( where M 1 and M 2 are molecular weights of constituent components. Simple manipulation yields the following relation U Nomoto = [(X 1 R 1 +X 2 R 2 ) / (X 1 V 1 +X 2 V 2 )] 3 (4) The Van Dael and Vangeel Equation Van Dael [11] obtained the relation for ultrasonic velocity in liquid mixtures as 1/(X 1 M 1 +X 2 M 2 )*1/U 2 imx = X 1 /M 1 U 1 2 +X 2 /M 2 U 2 2 (5) where U imx is the ideal mixing ultrasonic velocity in liquid mixture.u 1 and U 2 are ultrasonic velocities in species.
Theoretical Evaluation of Ultrasonic Velocity in Binary Mixtures of Alcohols with Anisic Aldehyde 17 The Impedance Relation Impedance relation U = X i Z i / X i i (6) where X i mole fraction, is the density of the mixture and Z i is the acoustic impedance. The Rao s Specific Velocity Method Relation Rao s specific velocity method 14 U = ( X i r i ) 3 (7) where X i mole fraction, U i is the ultrasonic velocity, is the density of the mixture, r i is the Rao s specific sound velocity = Ui 1/3 / i and Z i is the acoustic impedance. The Junjie Equation Junjie equation U J = (X 1 M 1 / 1 +X 2 M 2 / 2 )/[{X 1 M 1 +X 2 M 2 } 1/2 {X 1 M 1 / 1 U 2 1 +X 2 M 2 / 2 U 2 2 )} 1/2 ] (8) where M 1, M 2 are molecular weights of constituent components.. 1 and 2 are the densities of constituent components. Danusso Model Danusso model of velocity of ultrasonic waves is given by U D = (1/ mix) (1/M eff (X 1 M 1 / 2 1 U 2 1 +X 2 M 2 / 2 2 U 2 2 )) -1/2 (9) Chi-Square Test for Goodness of Fit formula According to Karl Pearson [19] Chi-square value is evaluated for the binary liquid mixtures under study using the N 2 = ( U mix(obs) - U mix(cal) ) 2 / U mix(cal) ) (10) i=1 where n is the number of data used. Average Percentage Error (APE) The Average percentage error [21] calculated using the relation APE = 1/n ( U mix(obs) - U mix(cal) ) / U mix(obs) ) X100% (11) where n is the number of data used. U mix(obs) = experimental values of ultrasonic velocities U mix(cal) = computed values of ultrasonic velocities Molecular Association The degree of intermolecular interaction or molecular association is given by U exp U imx DISCUSSIONS Anisic Aldehyde, also known as para methoxy benzaldehyde is slightly polar (CH=O group). Oxygen is more electronegative than carbon so it has a tendency to pull electrons in a carbon-oxygen bond towards itself. Alcohols are
18 P. B. Sandhya Sri, Zareena Begum, M. Nageswara Rao & C. Rambabu polar (- OH group) protic compounds. The covalent bonds of this functional group are polarized so that oxygen is electron rich and both carbon and hydrogen are electrophilic. This group is less electron-withdrawing nature than hydrogen and is therefore considered as electron-releasing. The experimental values of ultrasonic velocity for the system along with theoretical values and percentage deviations for Nomoto s Relation (U NR ), Vandeal Vangael Ideal Mixing Relation (U imx ), Impedance Dependence Relation (U I ), Rao s specific velocity method (U Rao ) Junjie s relation (U J ) and Danusso (U D ) are compared for all the three binaries. The agreement between theoretical velocities of Nomoto s relation in all the three binary systems suggests that R is additive property in all the three systems. It is observed that the experimental values show deviation with the theoretical values of ultrasonic velocities which confirms the existence of molecular interactions. Tables 1, 2, and 3 show the values of ultrasonic velocity computed by various theories along with experimental values (U).There are variations between the evaluated and experimental values. From the observed values of all three systems, there is a good agreement between theoretical and experimental values through Impedance relation followed by Nomoto Relation for all the three systems. There are higher variations in some intermediate concentration range suggesting the existence of strong tendency of association between component molecules as a result of hydrogen bonding. [2] Nomoto s theory proposes that the volume does not change upon mixing. Therefore, no interaction between the components of liquid mixtures has been taken into account. Similarly, the assumption for the formation of ideal mixing relation is that, the ratios of specific heats of ideal mixtures and the volumes are also equal. Again no molecular interactions are taken into account. But upon mixing, interactions between the molecules occur because of the presence of various types of forces such as dispersion forces, charge transfer, hydrogen bonding dipole-dipole and dipole-induced dipole interactions. Thus, the observed deviation of theoretical values of velocity from the experimental values shows that the molecular interactions are taking place between the unlike molecules [1] Tables 4, 5, and 6 show the percentage deviations and interaction parameters (α) for the systems anisic aldehyde (AA) + pentanol, hexanol and heptanol, at all four measured temperatures. The evaluated interaction parameters are positive for all the systems, indicating stronger interactions between the mixing molecules, which is high for pentanol. This suggests somewhat stronger interaction of Anisic Aldehyde with pentanol in comparison to other alcohols [3].The negative values indicate the dominance of dispersion forces arising from the breakage of hydrogen bonds in the associates and vice versa. A positive value of in all the system clearly indicates the existence of strong tendency for the formation of association in mixture through dipole-dipole interactions higher values of percentage deviation indicates maximum departure of the particular theory from experiment at that particular concentration and magnitude of the chi-square value finally determines the overall validity of the theory [20].The chi square values along with average percentage error are given in table 7and figures 1,2 and 3 give the variation of (U 2 /U 2 imx) for the systems AA + pentanol, Hexnol and heptanol respectively at temperatures 303.15K,308.15K,313.15Kand 318.15K against the mole fraction of anisic aldehyde. On the whole, all the theoretical models fairly predicted ultrasonic velocities, are reasonably close to the experimental values for and the three binary mixtures reported in this work, thus showing the validity of studied theoretical models for binary mixtures. The predictive abilities of various ultrasonic theories discussed above, depend upon the strength interaction prevailing in a system [21]; In general the predictive ability of various ultrasonic theories depends upon the strength of interactions that exist in a binary system. In case strong interactions exist between the molecules of the mixtures there is much deviation in theoretical prediction of velocity than the molecules of the mixture where less interaction are present, and the average absolute percentage relative deviation is small in systems where the interactions are less or nil.
Theoretical Evaluation of Ultrasonic Velocity in Binary Mixtures of Alcohols with Anisic Aldehyde 19 REFERENCES 1. Rambabu, C., Sandhya Sri, P.B., & Zareena Begum, International Scholarly Research Network ISRN Physical Chemistry Volume 2012, Article ID 943429, 12 pages doi:10.5402/2012/943429 2. Rambabu, C., Rama Rao, G. V., Viswanatha Sarma, A., & Siva Rama Krishna, J., (2005) Theoretical evaluation of ultrasonic velocities in binary liquid mixtures of o-chlorophenol at different temperatures, Indian Journal of Pure & Applied Physics May 43, 345 3. Santhi, N., Sabarathinam, P.L Emayavaram, ban. M., Gopi, C. &.Manivannan, C., (2010). Molecular Interaction Studies in Binary Liquid Mixtures from Ultrasonic Data, E J. Of Chemistry, 7(2) 648 4. Singh, J., Mohanthy G.C., &.Acharya, S. (2013). Evaluation of ultrasonic parameters in binary mixtures of ethyl methyl ketone and alcohols vis à vis molecular interaction, J of Pure and Appl. Physics, 51,542 5. Raju, K. &.Karpagavalli, K. (2009). Theoretical evaluation of ultrasonic velocity in binary mixtures of aprotic and inert solvents. Journal of convergence in engineering, Technology and science Vol 1(1) pp 31 6. Sahu, S.,.Nath, G., & Paikaray, R., (2012). Study on Molecular Interactions in Binary Mixture at Variable Frequencies Using Ultrasonic Technique Research Journal of Chemical Sciences Vol. 2(11), 64 7. Yuva Rani & S. Punitha (2009).Theoretical Prediction of Ultrasonic Velocity in Organic Liquid Mixtures, E J. Of Chemistry, 6(SI), S235 8. Santhi N., Sabarathinam, P. L., Madhumitha, J., Alamelumangai, G., Emayavaramban,M., (2013). Theoretical Evaluation of Ultrasonic Velocity in Binary Liquid Mixtures of Alcohols [S] + Benzene, International Letters of Chemistry, Physics and Astronom, 2 18 9. Indhumathi, M., Meenakshi, G., Priyadharshini, VJ., Kayalvizhi, R & Thiyagaraj, S., (2013). Research Journal of Pharmaceutical, Biological and Chemical Sciences, April-June RJPBCS Volume 4 Issue 2 Page No. 1382 10. Nomoto O (1958) Empirical Formula for Sound Velocity in Liquid Mixtures J Phys Soc 13: 1528-1532. 11. Van Dael W. & Vangael, E (1955),. Pro Int Conf on Calorimetric and Thermodynamics, Warsaw 555. 12. Shipra Baluja &.Parsania, P.H., (1995). "Acoustical properties of 3-α-furyl acrylic acid in aqueous methanol system, Asian J Chem., 7,417. 13. Gokhale V.D. & Bhagavat, N.N., (1989). J Pure Appl Ultrason 11, 21. 14. Z.Junjie, (1984). J China Univ Sci Techn, 14,298. 15. Suhasini Ernest &.Kavitha P.(2011).Theoretical evaluation of Ultrasonic velocity in Binary mixtures of an edible oil with alkyl Acetates, Chemical Environmental and Pharmaceutical Research, Vol No 2,92 16. Bunger, W.B., Reddick, J. A. & Sankano, T. K. (1986).Organic Solvents, VolII4 th Ed, Weissberger A Ed, Wiley Interscience, New York, 17. Weissberger, A. Proskaner, E.S, Riddick J. A & Jr, Toops. E.E. (1955)., Organic Solvents, Vol II 2 nd Ed, Weissberger A Ed, Wiley Interscience, New York 18. Rao, R, (1940).Velocity of Sound in Liquids and Chemical Constitution, Indian J Phys, 14 109 & J Chem Phys, 9 (1941) 682.
20 P. B. Sandhya Sri, Zareena Begum, M. Nageswara Rao & C. Rambabu 19. Pearson, K. (1973). Fundamentals of Mathematical Statistics, Eds. Gupta S G, Kapoor V K, S.Chand and Company, New Delhi, India,, 903. 20. Meenakhshi K & Palani, R., (2007). Investigation of molecular interaction in ternary liquid mixtures using ultrasonic velocity Indian Journal of Chemistry, 46A,, 252 21. Anwar Ali, Anil Kumar Nain, Vinod Kumar Sharma & Shakil Ahmed Molecular interactions in binary mixtures of tetrahydrofuran with alkanols (C6,C8,C10): An ultrasonic and volumetric study Indian J of Pure &Appl Phys, 42 (2004) 666. APPENDICES Table 1: Experimental Velocities (U/m.sec -1 ), Theoretical Velocities ((Ux/m.sec -1 ) for the System Anisic Aldehyde (AA) + Pentanol X 1 U exp U NR U imx U IR U R U j U D ms -1 ms -1 ms -1 ms -1 ms -1 ms -1 ms -1 303.15K 1284.90 1316.50 1346.50 1377.00 1406.70 1433.20 1460.45 1488.50 1515.00 1274.00 1305.00 1333.60 1361.20 1389.90 1415.00 1440.70 1467.54 1492.41 1253.50 1285.20 1315.20 1344.60 1374.80 1401.20 1429.12 1458.00 1485.10 1201.40 1236.10 1267.50 1297.90 1326.90 1357.50 1384.20 1412.00 1441.00 1468.40 1282.08 1309.54 1337.40 1365.64 1394.28 1423.32 1452.76 1482.60 1512.85 1269.21 1295.28 1321.71 1348.50 1375.66 1403.18 1431.07 1459.34 1487.98 1246.96 1274.51 1302.45 1330.80 1359.54 1388.69 1418.25 1448.22 1478.60 1201.40 1228.71 1256.40 1284.49 1312.95 1341.81 1371.06 1400.70 1430.74 1461.17 1258.19 1264.85 1275.38 1290.31 1310.39 1336.62 1370.42 1413.86 1469.97 1246.24 1252.36 1262.23 1276.36 1295.44 1320.42 1352.64 1394.01 1447.34 1223.20 1230.03 1240.67 1255.68 1275.79 1302.02 1335.83 1379.28 1435.52 1201.40 1204.92 1211.85 1222.57 1237.64 1257.79 1284.06 1317.90 1361.43 1417.81 1290.11 1323.57 1355.48 1385.97 1415.11 1443.00 1469.71 1495.32 1519.90 308.15K 313.15K 318.15K 1276.81 1308.55 1338.82 1367.72 1395.35 1421.78 1447.10 1471.36 1494.65 1255.01 1288.57 1320.60 1351.19 1380.44 1408.44 1435.27 1460.99 1485.68 1201.39 1236.61 1270.20 1302.29 1332.97 1362.32 1390.44 1417.40 1443.27 1468.12 1375.28 1444.14 1507.24 1554.16 1582.34 1606.89 1612.64 1609.39 1594.68 1543.48 1371.24 1448.25 1507.06 1556.87 1588.03 1612.92 1610.41 1602.61 1577.63 1517.01 1352.34 1433.99 1499.05 1547.59 1588.69 1616.10 1612.08 1597.58 1577.49 1201.40 1344.47 1427.76 1499.73 1549.17 1592.22 1616.66 1610.75 1596.84 1568.53 1492.01 1264.91 1277.74 1293.76 1313.30 1336.83 1364.93 1398.40 1438.28 1485.99 1252.75 1264.82 1279.97 1298.51 1320.87 1347.60 1379.43 1417.32 1462.58 1229.88 1242.84 1258.95 1278.56 1302.14 1330.29 1363.80 1403.76 1451.61 1201.40 1211.77 1224.99 1241.33 1261.13 1284.85 1313.10 1346.67 1386.61 1434.39 1248.11 1258.96 1272.62 1292.02 1317.97 1346.67 1383.00 1425.18 1475.27 1252.75 1264.82 1279.97 1298.51 1320.87 1347.60 1379.43 1417.32 1462.58 1208.98 1216.16 1229.40 1248.43 1270.90 1298.85 1337.78 1383.22 1435.18 1201.40 1187.46 1194.36 1205.90 1224.85 1246.96 1275.80 1315.23 1360.50 1414.92
Theoretical Evaluation of Ultrasonic Velocity in Binary Mixtures of Alcohols with Anisic Aldehyde 21 Table 2: Experimental Velocities (U/m.sec -1 ), Theoretical Velocities ((Ux/m.sec -1 ) for the System Anisic Aldehyde (AA) +Hexanol X 1 U exp U NR U imx U IR U R U j U D ms -1 ms -1 ms -1 ms -1 ms -1 ms -1 ms -1 303.15K 1319.30 1350.00 1379.00 1407.20 1433.98 1456.80 1479.50 1501.40 1521.90 1279.00 1308.80 1338.00 1365.30 1391.30 1416.50 1437.70 1459.00 1480.20 1498.70 1287.50 1318.50 1346.60 1374.40 1401.70 1424.40 1447.60 1470.50 1491.20 1237.00 1271.40 1301.90 1330.80 1357.65 1385.00 1407.80 1430.83 1454.30 1475.20 1313.54 1337.88 1362.52 1387.46 1412.70 1438.24 1464.09 1490.25 1516.72 1279.00 1301.57 1324.40 1347.51 1370.89 1394.54 1418.47 1442.68 1467.17 1491.94 1278.15 1302.62 1327.38 1352.45 1377.83 1403.52 1429.52 1455.83 1482.46 1237.00 1261.13 1285.57 1310.30 1335.34 1360.68 1386.33 1412.28 1438.55 1465.12 1300.26 1313.49 1329.34 1348.05 1369.91 1395.28 1424.63 1458.57 1497.85 1279.00 1289.00 1301.36 1316.23 1333.82 1354.38 1378.23 1405.81 1437.64 1474.41 1264.86 1278.17 1294.10 1312.87 1334.80 1360.25 1389.72 1423.82 1463.36 1237.00 1247.86 1261.15 1277.04 1295.78 1317.65 1343.04 1372.45 1406.49 1445.98 1324.19 1356.17 1385.75 1413.18 1438.70 1462.49 1484.73 1505.56 1525.11 308.15K 1278.99 1311.53 1341.52 1369.25 1394.96 1418.86 1441.15 1461.98 1481.48 1499.79 313.15K 1288.84 1320.98 1350.70 1378.28 1403.94 1427.87 1450.25 1471.21 1490.89 318.15K 1236.99 1271.74 1303.80 1333.46 1361.00 1386.62 1410.52 1432.87 1453.82 1473.49 1387.72 1444.14 1494.28 1531.87 1554.01 1574.67 1581.36 1583.58 1577.79 1543.49 1279.00 1384.66 1447.00 1493.29 1533.29 1558.33 1579.85 1579.55 1577.52 1562.80 1365.16 1431.45 1484.15 1523.36 1557.94 1581.29 1581.09 1572.94 1561.88 1237.00 1357.71 1426.10 1485.28 1525.59 1561.96 1584.25 1581.01 1572.89 1554.35 1298.27 1309.72 1324.07 1341.60 1362.67 1387.74 1417.42 1452.51 1494.07 1279.00 1286.99 1297.58 1310.95 1327.36 1347.14 1370.72 1398.65 1431.65 1470.68 1262.97 1274.59 1289.08 1306.73 1327.89 1353.05 1382.82 1418.02 1459.73 1237.00 1246.06 1257.76 1272.29 1289.95 1311.10 1336.21 1365.90 1400.98 1442.53 1283.65 1292.55 1304.58 1321.65 1344.82 1370.48 1402.87 1440.03 1484.14 1279.00 1269.69 1275.65 1287.49 1302.37 1322.96 1346.38 1378.40 1414.09 1457.71 1244.13 1250.25 1261.73 1278.50 1298.26 1323.26 1357.59 1397.87 1443.78 1237.00 1224.17 1229.75 1239.47 1255.95 1275.21 1300.43 1335.41 1375.46 1423.39
22 P. B. Sandhya Sri, Zareena Begum, M. Nageswara Rao & C. Rambabu Table 3: Experimental Velocities (U/m.sec -1 ), Theoretical Velocities ((Ux/m.sec -1 ) for the System Anisic Aldehyde (AA) +Heptanol X 1 U exp U NR U imx U IR U R U j U D ms -1 ms -1 ms -1 ms -1 ms -1 ms -1 ms -1 303.15K 1312.00 1342.00 1372.70 1400.70 1427.40 1452.00 1471.90 1491.40 1509.60 1526.05 1323.00 1353.80 1382.30 1406.40 1430.20 1449.80 1468.50 1485.00 1501.00 1314.00 1345.50 1372.10 1397.70 1422.20 1441.65 1461.00 1479.80 1495.55 1255.40 1295.00 1326.00 1353.75 1382.30 1407.80 1429.20 1447.50 1465.60 1480.70 1312.00 1334.03 1356.31 1378.83 1401.60 1424.62 1447.89 1471.41 1495.19 1519.22 1314.37 1335.96 1357.79 1379.84 1402.12 1424.63 1447.37 1470.35 1493.56 1300.40 1322.63 1345.10 1367.80 1390.74 1413.92 1437.33 1460.98 1484.87 1255.40 1277.97 1300.78 1323.84 1347.13 1370.67 1394.45 1418.47 1442.73 1467.24 1312.00 1328.90 1347.05 1366.48 1387.24 1409.37 1432.95 1458.05 1484.76 1513.20 1309.39 1326.99 1345.82 1365.93 1387.37 1410.19 1434.47 1460.29 1487.76 1295.19 1313.22 1332.54 1353.18 1375.20 1398.68 1423.69 1450.33 1478.72 1255.40 1272.52 1290.93 1310.66 1331.76 1354.30 1378.37 1404.05 1431.45 1460.72 1312.00 1347.15 1378.47 1406.56 1431.89 1454.84 1475.75 1494.86 1512.41 1528.57 1543.51 308.15K 1326.95 1357.23 1384.39 1408.89 1431.11 1451.35 1469.86 1486.86 1502.52 313.15K 1313.29 1344.42 1372.36 1397.59 1420.46 1441.31 1460.39 1477.92 1494.07 318.15K 1255.40 1291.13 1323.02 1351.67 1377.55 1401.03 1422.44 1442.03 1460.04 1476.64 1312.01 1392.03 1436.03 1475.90 1506.44 1525.28 1545.15 1554.02 1562.35 1565.39 1379.39 1428.86 1465.90 1499.76 1522.26 1543.85 1547.53 1553.17 1548.92 1517.01 1369.90 1423.19 1465.73 1497.78 1528.20 1550.63 1553.80 1551.76 1549.17 1255.39 1356.10 1411.41 1460.38 1494.59 1527.67 1550.06 1551.13 1550.18 1541.62 1492.01 1312.00 1319.81 1330.17 1343.27 1359.35 1378.70 1401.74 1428.97 1461.04 1498.84 1300.60 1310.69 1323.43 1339.04 1357.83 1380.17 1406.52 1437.53 1474.00 1286.47 1297.04 1310.27 1326.42 1345.77 1368.71 1395.75 1427.54 1464.91 1263.55 1274.60 1288.33 1304.98 1324.86 1348.39 1376.08 1408.61 1446.85 1312.00 1306.56 1314.39 1325.18 1340.64 1361.75 1385.15 1414.98 1448.83 1489.08 1285.07 1290.75 1301.82 1315.64 1334.86 1356.80 1387.00 1420.30 1461.19 1269.43 1274.61 1284.74 1299.81 1317.49 1340.01 1371.17 1407.73 1449.24 1255.40 1244.09 1249.28 1258.20 1273.31 1290.95 1314.20 1346.67 1383.71 1428.01
Theoretical Evaluation of Ultrasonic Velocity in Binary Mixtures of Alcohols with Anisic Aldehyde 23 Table 4: Percentage Deviations and Interaction Parameters (α) for the System Anisic Aldehyde (AA) + Pentanol X 1 %U NR %U imx %U IR %U R %U J %U D U 2 /U 2 imx α -0.2194-0.5284-0.6760-0.8248-0.8827-0.6893-0.5267-0.3964-0.1421-0.3757-0.7447-0.8915-0.9329-1.0248-0.8353-0.6682-0.5588-0.2968-0.5221-0.8322-0.9694-1.0266-1.1098-0.8925-0.7604-0.6706-0.4374-0.5979-0.8754-1.0336-1.0511-1.1558-0.9494-0.8003-0.7123-0.4924-2.0791-3.9234-5.2818-6.2952-6.8467-6.7391-6.1644-5.0147-2.9725-2.1791-4.0337-5.3514-6.2326-6.7961-6.6839-6.1122-5.0106-3.0198-2.4172-4.2929-5.6665-6.6131-7.2019-7.0781-6.5281-5.3989-3.3388-2.5221-4.3904-5.8036-6.7271-7.3453-7.2348-6.6642-5.5218-3.4454-0.0001 0.4054 0.5367 0.6672 0.6512 0.5978 0.6836 0.6342 0.4584 0.3234 0.0002 0.2206 0.2719 0.3914 0.4792 0.3921 0.4794 0.4441 0.2606 0.1499 0.1207 0.2625 0.4104 0.4900 0.4104 0.5168 0.4302 0.2052 0.0392 0.0412 0.2134 0.3383 0.4571 0.3551 0.4508 0.3824 0.1575-0.0194 303.15K -0.0006 7.0339 9.6951 11.9375 12.8657 12.4858 12.1190 10.4210 8.1215 5.2597-0.0011 308.15K 7.6326 10.9768 13.0066 14.3751 14.2549 13.9874 11.7796 9.2042 5.7100 313.15K 7.8852 11.5775 13.9787 15.0964 15.5576 15.3370 12.8024 9.5737 6.2210 318.15K 8.7667 12.6435 15.5502 16.7511 17.2908 16.7937 14.0761 10.8145 6.8191-1.5556-2.9438-3.9169-4.6259-4.9672-4.7634-4.2488-3.3741-1.9152-1.6683-3.0788-4.0216-4.6055-4.9666-4.7632-4.2530-3.4222-1.9991-1.8845-3.2961-4.2770-4.9113-5.2851-5.0608-4.5703-3.7201-2.2548-1.9680-3.3535-4.3586-4.9567-5.3515-5.1365-4.6270-3.7742-2.3164-2.8633-4.3707-5.4869-6.1714-6.3076-6.0375-5.3032-4.2539-2.6224-3.1926-4.9192-5.9266-6.5650-6.8003-6.5623-5.7034-4.6436-2.8779-3.5514-5.3719-6.5235-7.1524-7.5575-7.3041-6.3912-5.1292-3.3613-3.9353-5.7706-7.0881-7.6909-8.1429-7.8310-6.8532-5.5865-3.6418 1.0429 1.0833 1.1146 1.1389 1.1524 1.1497 1.1357 1.1084 1.0622 1.0450 1.0858 1.1163 1.1374 1.1512 1.1484 1.1344 1.1083 1.0632 1.0502 1.0917 1.1237 1.1466 1.1612 1.1581 1.1446 1.1174 1.0703 1.0524 1.0939 1.1270 1.1494 1.1648 1.1621 1.1479 1.1203 1.0726 0.0429 0.0833 0.1146 0.1389 0.1524 0.1497 0.1357 0.1084 0.0622 0.0450 0.0858 0.1163 0.1374 0.1512 0.1484 0.1344 0.1083 0.0632 0.0502 0.0917 0.1237 0.1466 0.1612 0.1581 0.1446 0.1174 0.0703 0.0524 0.0939 0.1270 0.1494 0.1648 0.1621 0.1479 0.1203 0.0726
24 P. B. Sandhya Sri, Zareena Begum, M. Nageswara Rao & C. Rambabu Table 5: Percentage Deviations and Interaction Parameters (α) for the System Anisic Aldehyde (AA) +Hexanol X 1 %U NR %U imx %U IR %U R %U J %U D U 2 /U 2 imx α -0.4363-0.8976-1.1951-1.4029-1.4841-1.2738-1.0413-0.7424-0.3402-0.5527-1.0162-1.3030-1.4670-1.5500-1.3372-1.1183-0.8802-0.4509-0.0004-0.7259-1.2048-1.4273-1.5969-1.7029-1.4660-1.2491-0.9976-0.5863-0.8075-1.2545-1.5401-1.6431-1.7557-1.5250-1.2962-1.0833-0.6835-1.4429-2.7047-3.6010-4.2031-4.4679-4.2228-3.7084-2.8530-1.5802-1.5128-2.7384-3.5939-4.1315-4.3858-4.1362-3.6455-2.8751-1.6207-1.7581-3.0587-3.8989-4.4765-4.7727-4.5033-3.9983-3.1743-1.8668-1.8514-3.1301-4.0395-4.5575-4.8630-4.6000-4.0805-3.2877-1.9806 0.0002 0.3708 0.4572 0.4894 0.4251 0.3290 0.3906 0.3534 0.2770 0.2111 0.0002-0.0004 0.2088 0.2632 0.2891 0.2629 0.1669 0.2401 0.2042 0.0867 0.0727 0.0001-0.0003 0.1042 0.1877 0.3046 0.2825 0.1600 0.2439 0.1828 0.0481-0.0211-0.0002-0.0005 0.0269 0.1458 0.2002 0.2465 0.1168 0.1933 0.1428-0.0330-0.1159-0.0002 303.15K 0.0001 5.1862 6.9734 8.3595 8.8596 8.3705 8.0910 6.8846 5.4735 3.6721-0.0006 308.15K 0.0006 5.7959 8.1467 9.3747 10.2057 10.0125 9.8874 8.2627 6.5748 4.2773 0.0007 313.15K 0.0008 6.0315 8.5665 10.2146 10.8384 11.1468 11.0146 9.2217 6.9663 4.7397 0.0014 318.15K 0.0007 6.7887 9.5401 11.6079 12.3696 12.7770 12.5338 10.4961 8.1546 5.3651 0.0005-1.5944-2.9838-3.9833-4.6618-4.9732-4.7407-4.1959-3.2561-1.8289-1.6663-3.0211-3.9809-4.5957-4.8965-4.6588-4.1363-3.2797-1.8697-1.9054-3.3303-4.2714-4.9239-5.2658-5.0093-4.4749-3.5688-2.1106-1.9927-3.3906-4.3965-4.9867-5.3360-5.0854-4.5380-3.6663-2.2147-2.7020-4.2555-5.3967-6.0793-6.2176-5.9251-5.1798-4.0875-2.4813-0.0002-2.9879-4.6599-5.6989-6.3916-6.6034-6.3520-5.5243-4.4665-2.7348-3.3685-5.1767-6.3024-6.9779-7.3796-7.1006-6.2179-4.9391-3.1798-3.7146-5.5421-6.8630-7.4912-7.9269-7.6269-6.6688-5.4214-3.5118 1.0295 1.0564 1.0761 1.0897 1.0957 1.0901 1.0785 1.0596 1.0324 1.0310 1.0571 1.0759 1.0880 1.0938 1.0882 1.0771 1.0601 1.0332 1.0361 1.0641 1.0828 1.0959 1.1028 1.0965 1.0850 1.0666 1.0384 1.0381 1.0657 1.0860 1.0978 1.1048 1.0988 1.0869 1.0691 1.0408 0.0295 0.0564 0.0761 0.0897 0.0957 0.0901 0.0785 0.0596 0.0324 0.0310 0.0571 0.0759 0.0880 0.0938 0.0882 0.0771 0.0601 0.0332 0.0361 0.0641 0.0828 0.0959 0.1028 0.0965 0.0850 0.0666 0.0384 0.0381 0.0657 0.0860 0.0978 0.1048 0.0988 0.0869 0.0691 0.0408
Theoretical Evaluation of Ultrasonic Velocity in Binary Mixtures of Alcohols with Anisic Aldehyde 25 Table 6: Percentage Deviations and Interaction Parameters (α) for the System Anisic Aldehyde (AA) + Heptanol X 1 %U NR %U imx %U IR %U R %U J %U D U 2 /U 2 imx α -0.5938-1.1942-1.5614-1.8074-1.8856-1.6311-1.3400-0.9545-0.4474-0.0001-0.6525-1.3175-1.7733-1.8886-1.9634-1.7360-1.4386-0.9866-0.4958 0.0001-1.0351-1.6996-1.9678-2.1391-2.2120-1.9238-1.6203-1.2719-0.7142-1.3149-1.9017-2.2097-2.5443-2.6377-2.4317-2.0057-1.5602-0.9087-0.9762-1.8686-2.4429-2.8135-2.9357-2.6462-2.2362-1.6452-0.8418-1.0289-1.9806-2.6389-2.8773-2.9947-2.7320-2.3173-1.6637-0.8818-1.4317-2.3990-2.8834-3.1854-3.3047-2.9809-2.5540-1.9915-1.1252-1.7357-2.6450-3.1833-3.6563-3.8001-3.5568-3.0020-2.3299-1.3494 0.0004 0.3839 0.4205 0.4183 0.3143 0.1959 0.2615 0.2323 0.1862 0.1654 0.0007-0.0004 0.2987 0.2532 0.1511 0.1773 0.0638 0.1070 0.0929 0.1254 0.1015 0.0001-0.0002-0.0539-0.0802 0.0192-0.0082-0.1220-0.0233-0.0416-0.1274-0.0992-0.0004-0.2991-0.2244-0.1534-0.3439-0.4810-0.4732-0.3777-0.3794-0.2741-0.0002 303.15K 0.0008 3.7283 4.6136 5.3687 5.5370 5.0468 4.9765 4.1985 3.4945 2.5776-0.0011 308.15K 0.0005 4.2624 5.5441 6.0481 6.6385 6.4366 6.4873 5.3814 4.5903 3.1927 0.0004 313.15K 0.0004 4.2542 5.7742 6.8239 7.1602 7.4531 7.5594 6.3522 4.8628 3.5854-0.0011 318.15K -0.0007 4.7178 6.4412 7.8769 8.1233 8.5149 8.4562 7.1592 5.7711 4.1140 0.0005-1.6538-3.0983-4.1000-4.7677-5.0480-4.7666-4.1863-3.2165-1.7831-1.6931-3.1847-4.2591-4.7892-5.0599-4.8030-4.2203-3.1965-1.7988-2.0951-3.6019-4.5059-5.1001-5.3744-5.0594-4.4659-3.5317-2.0485-2.3990-3.8492-4.8079-5.5714-5.8714-5.6372-4.9203-3.8788-2.2804-2.6412-4.2475-5.3918-6.0781-6.2155-5.8939-5.1240-4.0255-2.4224-2.8671-4.6571-5.8220-6.4536-6.6664-6.4149-5.5502-4.3570-2.6523-0.0046-3.3916-5.2690-6.3668-7.0036-7.3623-7.0505-6.1487-4.8699-3.0963-3.9311-5.7855-7.0584-7.8846-8.3005-8.0468-6.9660-5.5873-3.5586 1.0198 1.0384 1.0507 1.0587 1.0614 1.0551 1.0463 1.0337 1.0171 1.0209 1.0408 1.0549 1.0601 1.0627 1.0570 1.0480 1.0341 1.0179 1.0293 1.0498 1.0603 1.0669 1.0695 1.0624 1.0531 1.0411 1.0229 1.0356 1.0551 1.0668 1.0773 1.0806 1.0751 1.0629 1.0483 1.0275 0.0198 0.0384 0.0507 0.0587 0.0614 0.0551 0.0463 0.0337 0.0171 0.0209 0.0408 0.0549 0.0601 0.0627 0.0570 0.0480 0.0341 0.0179 0.0293 0.0498 0.0603 0.0669 0.0695 0.0624 0.0531 0.0411 0.0229 0.0356 0.0551 0.0668 0.0773 0.0806 0.0751 0.0629 0.0483 0.0275
26 P. B. Sandhya Sri, Zareena Begum, M. Nageswara Rao & C. Rambabu Table 7: Values of Chi Square Test and Average Percentage Error for Studied Binary Mixtures at Different Temperatures AA+pentanol AA+Hexanol AA+Heptanol T/K Nomoto Imx IR Rao s Junjie Danusso χ 2 APE χ 2 APE χ 2 APE χ 2 APE χ 2 APE χ 2 APE 303.15K 0.4428 0.0037 35.5300 0.2936 0.4005 0.0033 133.5612 1.1038 18.0736 0.1494 31.5303 0.2606 308.15K 0.6828 0.0056 35.0036 0.2893 0.1632 0.0013 167.0512 1.3806 18.1954 0.1504 36.6152 0.3026 313.15K 0.8460 0.0070 39.3505 0.3252 0.1585 0.0013 190.1329 1.5713 20.7026 0.1711 44.4443 0.3673 318.15K 0.9318 0.0077 40.5828 0.3354 0.1181 0.0010 229.6608 1.8980 21.0330 0.1738 51.0705 0.4221 303.15K 1.6344 0.0135 14.6334 0.1209 0.1793 0.0015 61.8700 6.8744 63.9424 0.5284 30.6978 0.2537 308.15K 1.6400 0.0136 14.1816 0.1172 0.8939 0.0074 87.1238 0.7200 17.8158 0.1472 34.6956 0.2867 313.15K 2.0313 0.0168 16.8538 0.1393 0.0453 0.0004 101.9553 0.8426 20.6416 0.1706 34.6956 0.2867 318.15K 2.2043 0.0182 17.4901 0.1445 0.0287 0.0002 130.8193 1.0812 21.1593 0.1749 48.9887 0.4049 303.15K 2.3946 0.0198 6.1177 0.0506 0.1158 0.0010 26.0305 0.2151 18.9888 0.1569 30.7381 0.2540 308.15K 2.7013 0.0223 6.4791 0.0535 0.0355 0.0003 48.5822 4.4166 19.1103 0.1579 35.2872 0.2916 313.15K 3.6290 0.0300 8.1662 0.0675 0.0076 0.0001 47.8746 0.3957 21.9291 0.1812 42.9089 0.3546 318.15K 5.1451 0.0425 10.7483 0.0888 0.1552 0.0013 61.1379 0.5053 26.0044 0.2149 54.2057 0.4480 Figure 1, 2, 3: Showing the Variation of (U 2 /U 2 imx) for the Systems AA + Pentanol, Hexanol and Heptanol Respectively at Temperatures 303.15K, 308.15K, 313.15 K and 318.15K against the Mole Fraction of Anisic Aldehyde