Research Journal of Chemical Sciences ______________________________________________ ISSN 2231-606X Vol. 1(9), 79-82, Dec. (2011) Res.J.Chem.Sci. International Science Congress Association 79 Short CommunicationUltrasonic Study of Binary Liquid Mixtures of Methyl Methacrylate with Alcohols Vadamalar R., Mani D.2 and Balakrishnan R. Department of Physics, Priyadarshini Engineering College, Vaniyambadi, TN, INDIA2 Department of Physics, Hindustan University, Kelambakkam; TN, INDIAAvailable online at: www.isca.in (Received 30th August 2011, revised 13th September 2011, accepted 13th October 2011)Abstract MMA is an important monomer which has a wide range of applications in the field of medicine and industries, while tert-butanol and iso-butanol are widely used as a solvent in chemical reactions, as well as being a useful starting material for organic synthesis. Therefore, physico-chemical properties on such mixtures will be useful in process engineering. Ultrasonic velocity and density have been experimentally determined for binary liquid mixtures of Methyl methacrylate (MMA) with tert-butanol and iso-butanol at three different temperatures. The measured velocities are compared with those obtained from various theoretical models of liquid mixtures. Relative merits and interrelation in these mixing rules have been discussed. Good agreement has been found between the experimental values with the respective values obtained from the mixing rules.Key words:MMA, alcohols, ultrasonic velocity, mixing rules. IntroductionDuring the last two decades, ultrasonic study of liquid mixtures has gained much importance in assessing the nature of molecular interactions present in the mixtures. The deviation from linearity in the values of ultrasound velocity when studied as a function of concentration is found to exhibit interesting variations in the case of liquid mixtures. A number of existing empirical, semi-empirical and statistical mechanical theories proved mixing rules for theoretically predicting the viscosity and ultrasonic velocity of binary liquid mixtures. These parameters give better insight in understanding various intermolecular interactions taking place within the mixtures. This in turn helps us in bringing out the facts, which can have positive implication of both industry as well as the theory building process. Thus, one verifies and modifies the already existing theories and formulations and can lay a solid ground work for the emergence of new theories and formulations of various psysico-chemical phenomena associated with liquid mixtures. A researcher pointed out the theoretical basis and the pertinent relations in the mixing rules (Free Length theory and Collision factor theory). Molecular interactions of MMA with several organic solvents and alcohols4-10 have been studied by several workers through excess property and thermo dynamical calculations. For examining the validity of various mixing rules for predicting the values of ultrasonic velocity, We have applied five mixing rules, Nomoto’s relation, VanDael and Vangeel’s relation, Collision factor theory (CFT), Impedance Dependence relation (IDR) and Junjie’s relation, and based relation for the theoretical prediction of ultrasonic velocity for binary mixtures of MMA with tert-butanol and iso-butanol. Material and MethodsExperimental Section: The chemicals were purchased from Lobochem, and were of analar grade (purity greater than 99%). The mixtures were prepared by mixing the measured volumes of the components in airtight brown bottles to minimize evaporation losses and light effects. Density measurements were made with a (single pan) mettler balance. The experimentally determined values of densities and velocities agreed well with literature data. Ultrasonic velocities were determined using a crystal controlled variable path ultrasonic interferometer operating at a frequency of 1 MHz In all, the accuracy of the determined values of density, viscosity and ultrasonic velocity work out to be ±0.0001 gm/cm, ±0.0001mpa and ±0.2m/s respectively. Ultrasonic Velocities were measured by using multi frequency ultrasonic interferometer (Model – 3, Mittal Enterprises). Theory: Mixing hpgRules for Ultrasonic Velocity Nomoto’s relation11U = ( x R / xi i) 3 …(1) VanDael and Vangeel’s relation(VDV) 12,13U = ( x M) / (x / Mi i -1/2 …(2) Collision Factor Theory (CFT) 1 4 Research Journal of Chemical Sciences __________________________________________________________ ISSN 2231-606X Vol. 1(9), 79-82, Dec. (2011) Res.J.Chem.SciInternational Science Congress Association 80 U = U ( x S ) ( x B ) / ( xi i ) …(3) Impedance Dependence relation (IDR) 15 U = ( x Z / xi ) …(4) Junjie’s equation16 U = ( x V x M1/2 [ / di i 2 )]-1/2 …(5) Where x is the mole fraction, U is ultrasonic velocity, R is molar sound velocity, Vi is molar volume, M is molecular weight, S collision factor, Z is acoustic impedance and B is the actual volume of ith component in the mixture. Collision factors are calculated using S = U/U r, where r is the space filling factor which in turn is given by B/V = r = /V, V is the specific volume of a mol of molecules and V is the molar volume of the liquid. The constant U = 1600 m/s. Results and DiscussionUltrasonic Velocity: The experimentally measured values of density and ultrasonic velocity of the pure liquids are agreed well with the literature are given in table-1. The measured values of ultrasonic velocities of the MMA + tert - butanol and MMA + iso - butanol mixtures are given in table-2. The validity of the different theoretical formulae is checked in terms of average percentage deviation (APD). APD values for all five mixing rules are given in table-3. Examining the validity of mixing rules has been already done 20. The values of the ultrasonic velocity (U), which are predicted by the mixing rules for all the binary mixtures at three different temperatures at 303K, 313K and 323K, are not shown here. But they have deviations from the respective measured values which is very small in magnitude. The approximation and assumption incorporated in the theories on which these mixing rules are based, may have a bearing on the deviations. The five mixing rules holds good at all temperatures. Out of the two binary mixtures, MMA + iso - butanol mixture gives comparatively highest value of all, for Impedance Dependence relation at 313 K. Table-1 Densities and velocities of sound for the components of mixtures System Temperature (K) Density ‘’(gm m-3) Ultrasonic Velocity ‘U’ (ms-1 Exp. Lit. Exp. Lit. MMA 303 0.9323 0.9317 4 1165 117918 0.9323 10 313 0.9215 0.9209 18 1133 1136 18 323 0.9092 0.9084 18 1108 --- tert-butanol303 0.7734 0.7757 17 1110 1114 17 0.7762 19 1104 11 313 0.7637 --- 1068 --- 323 0.7529 --- 1031 --- iso-butanol303 0.7935 0.794217 1177 1179 17 1172 18 313 0.7756 --- 1152 --- 323 0.7529 --- 1127 --- Table-2 The experimental values of ultrasonic velocity of MMA + tert-butanol and MMA + iso-butanol mixture Mole fraction of MMA ‘X’ Ultrasonic Velocity ‘U’ (ms-1) for MMA + tert-butanol mixtureMole fraction of MMA ‘X’ Ultrasonic Velocity ‘U’ (ms-1) for MMA + iso-butanol mixture 303 K 313 K 323 K 303 K 313 K 323 K 0.0000 1110 1068 1031 0.0000 1177 1152 1127 0.0902 1112 1079 1037 0.0881 1175 1149 1126 0.1824 1119 1089 1049 0.1786 1174 1148 1125 0.2767 1122 1091 1052 0.2715 1172 1146 1123 0.3730 1125 1093 1054 0.3670 1169 1143 1121 0.4716 1127 1108 1067 0.4652 1169 1141 1120 0.5724 1129 1116 1077 0.5661 1169 1139 1118 0.6756 1134 1120 1081 0.6699 1168 1137 1114 0.7812 1141 1123 1082 0.7767 1166 1135 1112 0.8893 1145 1127 1095 0.8867 1165 1134 1110 1.0000 1165 1133 1108 1.0000 1165 1133 1108 Research Journal of Chemical Sciences __________________________________________________________ ISSN 2231-606X Vol. 1(9), 79-82, Dec. (2011) Res.J.Chem.SciInternational Science Congress Association 81 Table-3 Average Percentage deviation (APD) *of various theoretical mixing rules at different temperatures System Temperature (K) VDV IDR Junji’s CFT Nomoto MMA + tert-butanol 303 -0.197 -0.716 -0.529 -1.154 0.494 313 1.475 0.277 0.846 0.628 1.509 323 0.976 -0.347 -0.091 -0.371 3.104 MMA +iso-butanol 303 0.515 -0.067 0.075 1.723 1.050 313 0.494 -4.739 0.102 2.792 1.078 323 0.668 0.107 -0.076 -0.271 3.390 Where *APD = [(Utheory-Uexp.)/Utheory]*100 Nomoto based his mixing rules on the assumptions of the linearity of the molar sound velocity and the additivity of the molar volumes in the liquid mixture21. Van Dael and Vangeel method is most suitable for mixtures in which the component molecules are of the same size, it assumes the mixture to be ideal with components having molar specific heat ratios equal to that of the mixture. Also their molar volumes are assumed to be equal. This assumption holds very well for the two binary mixtures. Thus, in terms of relative merits of the mixing rules for ultrasonic velocity, it appears that the Junji’s method is best suited for predicting the ultrasonic velocity, as it gives an overall smaller APD than that given by rest of the mixing rules. One of the researcher also stated that the calculated values are in agreement with the literature values as both Nomotto’s relation and ideal ideal mixing relations gives identical values., but the Collision Factor Theory proves to be better than both of these22. ConclusionsThe study indicates that almost all the mixing rules employed here, give reasonably good results with allowed error less than 5%. The presence of dipole-dipole interactions is observed in both the systems due to the polar nature of alcohols. References1.Pandey J.D. and Shukla A.K.,Ultrasonic study of liquid mixtures.,J. Pure Appl. Ultrason, 15, 37-52 (1993)2.Sorichetti P.A. and Romano S.D. 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