Non-linearity parameter B=A of binary liquid mixtures at elevated pressures

Transcription

1 PRAMANA cfl Indian Academy of Science Vol. 55, No. 3 journal of September 2000 phyic pp Non-linearity parameter B=A of binary liquid mixture at elevated preure J D PANDEY, J CHHABRA, R DEY, V SANGURI and R VERMA Department of Chemitry, Univerity of Allahabad, Allahabad , India MS received 18 March 2000; revied 27 July 2000 Abtract. When ound wave of high amplitude propagate, everal non-linear effect occur. Ultraonic tudie in liquid mixture provide valuable information about tructure and interaction in uch ytem. The preent invetigation comprie of theoretical evaluation of the acoutic non-linearity parameter B=A of four binary liquid mixture uing Tong and Dong equation at high preure and T = 303:15 K. Thermodynamic method ha alo been ued to calculate the non-linearity parameter after making certain approximation. Keyword. Non-linearity parameter; binary liquid mixture; ultraonic velocity. PACS No y; Ba; Introduction Mot of the parameter involved in ultraonic tudie have been deduced by conidering the propagation of acoutic wave of infiniteimal amplitude. But when ound wave of high amplitude propagate, non-linear effect occur uch a harmonic ditortion and acoutic cattering. It ha become of much interet to predict the extent of variou kind of nonlinear effect in acoutic [1 4]. It i poible to obtain certain information about internal preure, clutering, inter-molecular pacing etc., from the value of the non-linearity parameter, which play a ignificant role in non-linear acoutic ranging from underwater acoutic to medicine. A number of experimental and theoretical invetigation have been carried out on the non-linearity parameter of liquid. Tong and Dong [5] determined B=A for pure liquid making ue of the Schaaff [6] equation for ound velocity. Non-linearity parameter of binary a well a multicomponent liquid mixture ha alo been computed by everal worker [7 10]. Recently non-linearity parameter of higher alkane wa computed by Verma et al [11]. To the bet of our knowledge, computation of B=A on varying preure ha not been carried out. In the preent invetigation an attempt in thi field ha been made and B=A i calculated for four binary liquid mixture at T = 303:15 K over a wide range of preure (ranging from 0.1 to 80 Mpa). In thi context, Tong and Dong equation ha been ued to calculate the B=A value. Scarcity of experimental data and it variation with temperature ha hampered worker in thi field to evaluate B=A from the more direct thermodynamic 433

2 J D Pandey et al method. Here an attempt ha thu been made to compute B=A from the thermodynamic equation by making ue of ome approximation for evaluating du=dt. The reult obtained are found to be fairly atifactory taking into account the approximation ued. Furthermore, a comparative tudy of B=A value obtained from the two method ha alo been carried out, and merit and demerit of both the method are dicued in the light of molecular tructure and intermolecular interaction. 2. Theory Since ound propagation i an adiabatic proce, the non-linearity parameter i to be obtained from the adiabatic equation of tate: where 2 P = P 0 + A» ρ ρ0 + B=2» ρ ρ0 + ; (1) ρ 0 ρ A = ρ 0 = ρ 0 u 2 ; ;0 B = ρ 2 2 P ; u3 : ;0 Here uffix 0 indicate the equilibrium value and i entropy. In what follow, uffix 0 i omitted for brevity. The non-linear departure i ymbolized B=A =2ρu : (2) From eq. (2) the non-linearity parameter i calculated by two different method, viz., Tong and Dong method and the thermodynamic method. Tong and Dong [5] applied Schaaff [6] equation for ound velocity, namely;» (1=3)M u 2 = flrt (M ρb) 2 2 (3) (M ρb) for computingthe valueofb=a. From eq (2) and (3), B=A i given by B=A = J(0) + J(x); (4) where J(0) = J(x) = 1 1 fl u2 ρfi T ff T ; 2(3 2x) 2 3(x 1)(6 5x) ; with 434 Pramana J. Phy., Vol. 55, No. 3, September 2000

3 Binary liquid mixture at elevated preure x = M=ρ b: Here ρ i the denity of the mixture, fi T iothermal compreibility, ff coefficient of thermal expanion and x i the real volume of molecule. For the preent work the value of b mix and x mix for liquid mixture were obtained from relation x mix = b mix = nx i=1 nx i=1 y i M i =ρ mix b mix ; y i b i ; where y i i the mole fraction, M i i the molar ma of ith component and ρ mix i the denity of mixture. While computing B=A the iothermal compreibility fi T (mix) and thermal expanion coefficient ff mix have been etimated by uing two recently propoed relationhip [12] fi T (mix) = 1:71 Λ 10 3 T 4=9 u 2 mix ρ4=3 mix and ff 4 mix =0:0191; (5) fi T (mix) where all the term have their uual meaning. In the thermodynamic method the non-linearity parameter B=A of liquid can be obtained from the variation of ound velocity with preure and temperature. Subtituting @T = + T =(fl 1)(fi =ff): B=A can be expreed in the B=A =2ρu +(fl 1) fi ff Thi thermodynamic equation ha alo been ued for etimating B=A. P : P 3. Reult and dicuion The value of non-linearity parameter for binary liquid mixture, viz., toluene + aniline (I), toluene + o-xylene (II), benzene + cyclohexane (III), benzene + nitrobenzene (IV) have been repreented graphically in the figure from 1 to 4 at variou preure and mole fraction. Takagi and coworker [13 15] meaured experimentally the ultraonic peed and denitie at K and high preure. The denitie were repreented in the form of the Tait equation. Thi data and the Tait equation were taken for computing the variou quantitie employed in the equation for B=A. Although the non-linearity parameter have Pramana J. Phy., Vol. 55, No. 3, September

4 J D Pandey et al Figure 1. Plot of B=A (Tong and Dong and thermodynamic) v preure for toluene + aniline. Figure 2. Plot of B=A (Tong and Dong and thermodynamic) v preure for toluene + o-xylene. been calculated over a wider range of preure, carcity of pace ha neceitated the table to be omitted. The complete data can be obtained from the author on requet. For ytem (I) toluene + aniline (non-polar + polar), experiment carried out previouly [13] how that for binary mixture including aniline, fi S E (exce) are negative at atmopheric preure and change progreively to 0 or poitive a the temperature i raied. Furthermore aniline molecule i alo known to be aociated through H bonding in the pure tate and thi elf-aociation decreae when it i mixed with ome other aromatic 436 Pramana J. Phy., Vol. 55, No. 3, September 2000

5 Binary liquid mixture at elevated preure Figure 3. Plot of B=A (Tong and Dong and thermodynamic) v preure for benzene + nitrobenzene. Figure 4. Plot of B=A (Tong and Dong and thermodynamic) v preure for benzene + cyclohexane. compound. Hence we preume that fi S E value would be largely affected by preure change ince molecular interaction between unlike ubtance are weak. The value of the non-linearity parameter are found to decreae with increaing preure at low aniline concentration but in the aniline rich region the non-linearity parameter how a revere trend i.e. it increae with increae in preure. Pramana J. Phy., Vol. 55, No. 3, September

6 J D Pandey et al For the binary liquid mixture toluene + o-xylene (non-polar + non-polar) previouly determined value [13] how that fis E i mall and poitive at atmopheric preure and decreae with rie in preure howing parallel curve. Hence the mixture can be treated in general a regular or ideal a no recognized aociation take place between the unlike molecule. In thi cae the value of the non-linearity parameter from the Tong and Dong equation are again found to decreae with increae in preure at low o-xylene concentration. A the o-xylene concentration increae, the B=A value till decreae but at high value of preure ome increaing trend i alo marked. Ultraonic velocity meaurement for binary liquid mixture benzene + cyclohexane (non-polar + non-polar) how that ultraonic peed increae parabolically with increae in preure throughout the experimental range. Further, large poitive value of exce volume [14] clearly indicate a nearly linear relation with mole fraction and thu the mixture can generally be treated a approximately ideal. Thi obervation i further trengthened by the fact that B=A value for the aforementioned ytem calculated by the Tong and Dong equation exhibit the highet value at all the mole fraction a compared to the other binary liquid mixture under invetigation. The value of the non-linearity parameter from the Tong and Dong equation for thi liquid mixture how a regular decreaing trend with rie in preure. The value of the non-linearity parameter for ytem (IV) benzene + nitrobenzene (nonpolar + polar) decreae a the preure increae. There i a light reveral of thi trend at high nitrobenzene concentration although it i not o remarkable a in the cae of ytem containing toluene. The non-linearity parameter, B=A, calculated by the Tong and Dong equation i made up of two part (eq. (4)). The J(0) term contribute only 16% of B=A at maximum for all four mixture motly due to maller contribution of the J(0) term to the overall value of B=A. TheJ(x) term i important which depend upon x the molar volume. The preent invetigation conit of component having comparative ize and nearly pherical or flat haped tructure. Here the flat or planar tructure prove to be a major inhibitor for interaction to a very large extent. Another caue which upport to inhibit interaction in the cae of benzene i the preence of the de-localized ß electron cloud above and below the molecule which give it extra tability thu preventing a higher degree of interaction. A a reult ytem containing benzene how a gradual drift toward ideality a fact which i well exhibited by the value of B=A obtained from the Tong and Dong method for the binary liquid mixture benzene + cyclohexane. To calculate B=A by the thermodynamicapproach, variationofoundvelocitywith temperature (@u=@t ) P and preure (@u= ) T hould be known. For the above mentioned binary liquid mixture, (@u= ) T wa directly computed from the data but the variation of ultraonic velocity with temperature wa not available o certain approximation were ued. It wa oberved that the variation of ultraonic velocity with denity wa linear in nature. For all the mixture ultraonic velocity wa plotted with repect to denity, it wa found that up to a reaonable extent it wa a traight line, i.e. U = A + Bρ: (7) Here A and B are contant depending upon the mixture tudied. Uing the definition and the value of the thermal expanion coefficient and taking B a the lope of thi line we get du=dt = Bffρ: (8) 438 Pramana J. Phy., Vol. 55, No. 3, September 2000

7 Binary liquid mixture at elevated preure Subtituting the value of ) P in the thermodynamic equation, the non-linearity parameter wa calculated. The value are found to be on the higher ide than from the Tong and Dong equation, a i evident from the graph but thi might be attributed to the approximation involved in the calculation. A comparative tudy of the value of B=A calculated by the Tong and Dong equation and the thermodynamic method propoed here, indicate that the thermodynamic approach may prove to be a valuable tool for determination of the non-linearity parameter from the knowledge of the thermal expanion coefficient. Alo thi method propoed here can be ued directly in the abence of the du=dt value. In the preent invetigation the four binary liquid mixture viz. toluene + aniline (nonpolar + polar), toluene + o-xylene (non-polar+ non-polar),benzene+ cyclohexane (nonpolar + non-polar) and benzene + nitrobenzene (non-polar + polar) have been taken to tudy all the poible type of intermolecular interaction. Molecular interaction play a key role in undertanding the complete picture of the variou liquid mixture taken for the preent tudy and the B=A value of the liquid have been interpreted a the quantity repreenting the magnitude of the hardne of the liquid. Hence the calculated value prove invaluable in explaining the interaction taking place in the ytem taken under conideration. Acknowledgement One of the author (VS) i thankful to the Council of Scientific and Indutrial Reearch, New Delhi for providing financial aitance. Reference [1] R T Beyer, J. Acout. Soc. Am. 32, 719 (1960) [2] R T Beyer and S V Letcher, Phyical Ultraonic (Academic Pre, New York, 1969) p. 202 [3] K P Thakur, Acutica 39, 4, 270 (1978) [4] R P Jain, J D Pandey and K P Thakur, Z. Phy. Chem. (Neue Folge) 94, 211 (1975) [5] Jie Tong and Yanwn Dong, Kexue Tangbao 33, 1511 (1988) [6] W Schaaff, Z. Phy. 115, 69 (1939) [7] A P Sarvazyan and T V Gnalikian, J. Acout. Soc. Am. 88, 1555 (1990) [8] P Kuchhal, R Kumar and D Naringh, Pramana J. Phy. 52, 321 (1999) [9] Endo Harumi, J. Acout. Soc. Am. 83, 2043 (1988) [10] J D Pandey, R Dey and M Upadhyaya, Acou. Lett. 21, 6, 120 (1997) [11] G P Dubey, V Sanguri and R Verma, Int. J. Pure Appl. Phy. 36, 678 (1998) [12] J D Pandey, G P Dubey, A K Singh and N Tripathi, Int. Acad. Phy. Sci. 1, 117 (1997) [13] T Takagi and H Teranihi, J. Chem. Thermodynamic 17, 1057 (1985) [14] T Takagi and H Teranihi, J. Chem. Thermodynamic 14, 1167 (1982) [15] T Takagi, J. Chem. Thermodynamic 12, 1183 (1980) Pramana J. Phy., Vol. 55, No. 3, September