Indian l ourn al of Pure & Applied Ph ysics Vol. 40, May 2002, pp. 3 15-322

Study of intermolecular interactions in binary liquid mixtures through ultrasonic speed measurement

A Ali *, A Yasmin & A K Nain

Depart ment of Chemistry, l amia Milli a Islami a, New Delh i 11 0025

Received 2 August 200 1; revised 27 December 200 1; accepted II March 2002

Dens ity p. and ult rason ic speed II , have been measured in pure benzyl alcohol (BA), cyclohexane, toluene and ehl orobenzene and in their binary mixtures with BA as common co mponent at 308 K. From these experiment al data. isentropic compressi bility K" intermolecul ar free length Lr, acousti c impedance Z, molecular association R!\, mo lar sound speed Rill ' excess isent rop ic compress ibility K,E, excess free length LrE , excess acoustic impedance ZE, and e~cess ult raso ni c speed It are calculated for all the three binary liq uid mi xtures, over the entire compositi on range. The vari ati ons of these parameters, part icularly the sign and magn itude of excess func tions, wit h composition of the mixtures suggest dipole-induced-dipole interac ti on between BA and cyclohexane, and weak to medium-strength rc--- H hond between BA and chlorobenzene/toluene molecules. Theo retical values of ultrasonic speed in binary liquid mix tures are ca lcul ated us in !.! different theori es and empirical relations. The relati ve meri ts o f these theories and relati ons have been discussed. ~

1 Introduction

As a part of ongoing research programme l .. 1 on

thermodynamic, acousti c and transport properties of non-aqueous binary and te rnary liquid mixtures, the autho rs report he re the results of the ir stud y on bin ary mi xtures of benzy l a lcoho l w ith cyc lohexane, toluene and chlorobenzene, cover ing the who le compos iti on range, at 308 K . Mi xed so lvents, rathe r th an pure liquids, find prac tical appli cations in many chemica l and industri a l processes, as they enabl e us to change the ph ys ico-che mica l properties in a continuous manner to have a large number of reacti ve medi a (so lvents) at our di sposal. Therefore, a J eeper know ledge of the influence of the solvent at a molecul ar is essenti a l for the understanding o f many chemi ca l and bi o logical processes in these medi a. The mo lecules o f BA and c hl orobenzenc are po lar, w hil e th ose of to luene and cyc lohexane are weakl y po lar and no n-po lar, respect ive ly. M oreover, BA mo lecules are se lf-assoc iated th rough inte rmo lecul ar hydrogen bonding in the pure state. B A forms este rs w hich are used in pe rfumery . T he uses of to luene for blending of pe tro l, as a so lvent fo r pa int s, res ins and rubber, as a starting mate ri a l for benzy l de ri va ti ves, benzoic ac id and benzaldchyde, are we ll known. Ch lorobenz ne is a lso an import ant compound used for the preparati on of pheno l and ni trobenzenes w hi ch are

required for the manu fac ture o f azo and sul phur dyes , fung ic ides and prese rvati ves. A survey o f lite rature indicates tha t the re has been practica ll y no study o f the binary mi xtures of these sys tems from the po int o f view o f the ir ultrasonic be hav iour.

In the present paper, the authors report densit ies and ultrasonic speeds of pure liquids and those of the ir binary mi xtures w ith B A as a common component over the entire compos iti on range at

308 K . Us ing the experimenta l va lues o f p and II the va lues o f isentropi c compress ibility K" inte rmo lecul ar free length Lr. acoustic impedance Z, mo lecul ar a."soc iati on RA , mo lar sound speed Rill' excess isent ro pi c compress ib ility K/", excess f ree length Lr

E, excess acousti c impedance 7f, and excess

ultrasonic speed l.t E, a re ca lcul ated for a ll the three bin ary mi xtures. These de ri ved paramete rs offer a convenicnt method for thc study o f the rmodynamic properti es of liquid mi xtures not eas il y ob ta ined by other means . Moreover, theore ti ca l va lues of ultrasoni c speeds in a ll the binary mi xtures have bee n calcu lated uSing d ifferent theories and empirical re lati ons. The re lati ve me rit s of these theori es and re lati ons are di scussed.

2 Experimental Details

Benzy l alco ho l, cyclohexane, to luene and chl orobenzen ' (s.d . fine, A R G rade) were purified

316 INDIAN J PURE & APPL PHYS , VOL 40, MAY 2002

by standard meth ods-l. All the chemi ca ls were kept in spec ia l a ir-ti ght bottles . Be fore use, they were stored over 0.4 nm mo l.ecular sie ves to minimi ze the wate r content , if any. The binary mi xtures of BA with cyc lo hexane, to luene and chl orobenzene were

prepared by mass in a dry box . The weighings were done on A fcoset ER-1 20A e lectro ni c ba lance

prec ise ly up to I x 10-4 gm.

T he dens ities o f pure liquids and of the ir binary mi xtures were measured using a s ing le-capill ary pycno mete r made o f Boros il g lass hav ing a bulb

capac ity o f 8 x 10-(' m' . The capill ary, with gradu ated marks, has uniform bore and could be c losed by we ll-fitting glass cap. The marks on the capill ary were cal ibrated using known density of tripl e di still ed wate r. The accuracy of the density

measurement was ± 0.0001 g cm-' . The ultrasoni c speeds in pure liquid s and in thei r binary mixtures were measured using a s ingle c rys ta l variable-path inte rferomete r at 3 M Hz as reported in earli e r works l --''- T he accuracy 1Il ultrasonic speed

measurement was found to be ± 0.05% . The temperature of the liquids and of the ir binary

mixtures was ma inta ined at 308 ± 0 .02 K in an e lectronicall y contro lled the rmostati c wate r bath .

3 Results and Discussfion

The experimenta l values o f density p and ultrasonic speed u were used to calcul ate the va lues

of K" L" Z, RA and Rm with the he lp o f fo ll owing re lati ons 1--' :

Lr= KI up v,

Z =IIP

R,, = (p Ip.,)(u.,lu) 111

Rill = U l/-' V

... ( I )

... (2)

... (3)

... (4)

. . . (5)

where K is te mperature-dependent constant (' ; p" and lI" are the de nsity and ultrasonic speed of the so lvent , cyc lohexane/to luene/c hl orobenzene; and V IS the molar vo lume of the mi xture. The

experimenta l va lues of p and u and calcul ated va lues o f K" L" Z , R" and Rill o f the binary liquid mi xtures at d iffe rent mo le fractions x of BA at 308 K have been recorded in Tabl e I . It is c lear from T ab le I tha t, for a ll the systems stud ied , the va lues of K, and Lr dec rease, while those of Z ex hibit

opposite trend as x of BA inc reases. A lmost linear inc rease in RA for BA + cyclohexane/to luene and a reverse trend for BA + chl orbenzene sys tems is observed . The va lues of Rill fi rs t dec rease then inc rease for the mi xtures of BA w ith cyc lohexane and to luene, while a continuous inc rease in Rill is observed for the sys tem BA + c hl oroben zene with inc reas ing mole fracti ons x of B A in the present systems. The observed decreaselinc rease in K" LI, Z, R" and Rill w ith compos iti on is an e vidence of s ignificant inte rac tion between the component molecules in the binary liquid mi xtures. Such a conclusion was a lso arrived at by Ali & Na in 7 and Me hta et a /.x fo r bina ry liquid mi xture . Furthe r, the observed inc rease in u and the corresponding decrease in Lr with x (T able I ) fo r a ll the three sys tems is in accordance with the views proposed by A li el a /.Y, according to w hic h the ultrasonic speed increases with decrease in free le ngth , and vice-versa.

The excess properties yE (K,E, LrE, C and U E), which are found to be more sensiti ve towards inte rmolecul ar interac ti on, have been ca lcul ated with the he lp of the equati on:

yE = Y- [( I-x) YI + x YJ ... (6)

w here Y stands for the property K" L" Z and u of the liquid mixture and subscripts I and 2 represent the components I and 2, respective ly ; vo lume fraction ,

ALI et al.: BINARY LIQUID MIXTURES 317

0.8

-+-Tolucne 0.6 -It-Chlorobenzene

-.-Cyclohexane

0.4 ~

1 Me 0 0.2 b '-'

'" tJ 0.0

-0.2

-0.4 L--_-'-_--'-__ "--_-'-_--'

0.0 0.2 0.4 0.6 0.8 1.0

x (BA)

Fig. I - Variation of excess isentropic compressibility, K,E with mole fracti on of benzy l alcohol for the binary mixtures

e ~ 0 ~ "'~ ...l

4.0 ...------------..,

3.2

2.4

1.6

0.8

0.0

.{l.8

0.0 0.2 0.4

-+-Toluene ..... Chlorobenzene -.-Cyclohexane

0.6 0.8

x (BA)

1.0

Fig. 2 - Vari al ion of excess intcrnm lecular frec length. L," wi th mole fr3ction of bell zyl alco lwl for the hillary mixture~

0.2 ,----,:========::;---, -+-Toluene ---Chloroben >.ene

0.0 ......... Cyclohexa:·1C

-0.8

0.0 0.2 0.4 0.6 0.8 1.0

x (BA)

Fi g. 3 - Vari ation of excess acoustic impedance, ZE with mole fraction of benzyl alcohol for the binary mi xtures

0

·16

-32

_ ....... -48 I rtl

g to

-64 ::s

-80

·96 -+-Toluene ___ Chlorobenzene

...... Cyc!ohexane

·112 0.0 0.2 0.4 0.6 0.8 1.0

x (SA)

Fig. 4 - V al iati on ui' exce~s ultra sonic speed, It with mole fraction o f benzy l alcohol f

318 INDIAN J PURE & APPL PHYS, VOL 40, MAY 2002

The curves in Fig. I show that, the behaviour of K,E with composition of the mixtures is also reflected in the behaviour of LrE (Fig. 2). Both K,E and LrE change sign from positive (in BA-poor region) to negative (in BA-rich region) for BA+ cyclohexane, become entirely negative for BA + toluene and turn entirely positive for BA + chlorobenzene system with increasing mole fraction of BA. The behaviours of the present systems have been qualitatively examined. Mixing of BA with cyclohexane will induce the breaking up of the associated structure of BA releasing several dipoles which, in tum, can induce a dipole moment in the neighbouring cyclohexane molecules, resulting in dipole-induced - dipole interaction between BA and cyclohexane molecules. The former effect (breaking up of associated structure of BA) leads to an expansion in volume, hence, an increase in K,E and Ll, whereas, the latter effect (dipole-induced-dipole interaction) is responsible for contraction in volume, hence, a decrease in K,E and LIE values . The observed positive K,E and LIE values up to x - 0.43 (Fig. I) and x - 0.64 (Fig. 2) suggest that the effect due to breaking up of BA-BA associates dominates over that of BA-cyclohexane interaction. Beyond this (in BA-rich region), dipole-induced-dipole interaction between BA and cyclohexane molecules seems to outweigh the effect due to dissociation of BA-BA structure. Small negative K,E (Fig. I) and LrE (Fig. 2) values for the system BA + toluene over the whole mole fraction range indicate that the effect of BA-toluene interaction dominates over that of the breaking up of associated structure of BA. According to Ali & Nain1, K,E and LIE become increasingly negative as the strength of interaction between component molecules increases.The added toluene causes dissociation of associated stmcture of BA and forms IT---H bond of medium strength involving of BA IT-electrons of benzene ring and H-atom of -OH group of BA, yielding small negative values of K,E and Lr This is due to the fact that the IT-electron density of benzene ring in toluene is significantly by the presence of electron releasing group -CH, in its molecule, making the availability of these electrons easier for the proton of -OH group of BA, and, thus, accounting for greater interaction between BA and toluene molecules. Unlike -CH, group in toluene, chlorine atom in chlorobenzene is an electron-withdrawing atom,

tends to attract the IT-electrons of the benzene ring, thereby, decreases the electron density of the ring. As a result, the benzene ring in chlorobenzene becomes relatively poor electron-donor towards the electron-seeking proton of -OH group of BA. This results in a relatively weak IT---H bonding between toluene and BA molecules, which is too weak to compensate the effect due to rupture of associated structure of BA, and this makes l(,E and LIE positive over the entire mole fraction range. The importance of weak to medium-strength IT---H bonding involving IT -electrons of benzene ring and proton of NH, and tert-butylalcohol molecules has also been reported by others'l.I2. The curves in Figs 3 and 4 clearly indicate that the behaviours of 7!- and uE, both being negative over the whole range of mole fraction, support each other. Negative deviations in 7!- and uE from linear dependence on mole fraction x of BA suggest the presence of weak interaction between the component molecules. Similar result was also reported for the binary mixtures of dimethylsulphoxide with toluene!1.

Theoretical values of ultrasonic speed in the present binary mixtures were evaluated using different theories and empirical relations. Comparison of theoretical values of ultrasonic speeds with those obtained experimentally in the present binary liquid mixtures is expected to reveal the nature of interaction between the component molecules in the mixture. Such theoretical study is useful in building the comprehensive theoretical model for the liquid mixtures. Theoretical values of ultrasonic speed in the mixtures : BA + cyclohexane, + toluene and + chlorobenzene at different mole fractions of BA were calculated using the following theories and relations:

Free length theory (FL T)~:

u (FLT) = K/(Lrp "2 ) Collision factor theory (CFT)1 4:

u (CFT) = u~ (x,S, + X2S2) [(X,B I+X2B2)/V] Nomoto (NOM) relation' 5:

... (9)

... (10)

u (NOM) = [(X,R,+X2R2)/(XI V,+X2 V2)Y ... ( I I) Van Dael and Vangeel (VDV) ideal mixing

u (VDV)=

All el al.: BINARY LIQUID MIXTURES 319

Tab le I - Density p, ultrasonic velocit y u, isentropi c compressibility K,. intermolecul ar free length Llo acousti c impedance Z. relati ve association RA, and mol ar sound speed6 Rrn of bin ary mixtures of BA wi th toluene, chl orobenzene and cyc lohexane as a functi on of mole fracti on, x of BA at 308 K

x P II K, L, Z RA Rill (BA) (kg m-' ) (m S- I) ( 10- 111 m2 W i) ( 10- 11 m) ( IO

h kg m-2s- ') [1 0- 11 m' mol-I (m S-I)]

BA + to luene

0.0000 852.9 1262.0 7.36 18 5.6809 1.0764 1.0000 1.1 674

0.0685 880. 1 1275.0 6.9895 5.5354 1.1221 1.0284 1.1 487

0. 160 1 904.2 1293.4 6.6110 5.3834 1.1695 1.05 I 5 1.1 411

0.23 11 920.0 1307.5 6.358 1 5.2795 1.2029 1.0660 1.1391

0.3339 939.8 1328.4 6.0299 5.1 414 1.2484 1.0832 1.1402

0.433 1 958.4 1350.2 5.7234 5.0090 1.2940 1.0987 1.1 425

0.5217 974.4 1368.5 5.4799 4.9013 1.3335 1.11 20 1. 1450

0.6496 998. 1 1400.2 5.11 03 4.733 1 1.3975 1.1 304 1.1 493

0.7781 1021.0 1438.5 4.7332 4.5551 1.4687 1.1460 1564

0.8786 1037.0 1470.3 4.4608 4.422 1 1.5247 1.1 555 1645

1.0000 1057.0 1512.0 4. 1383 4.2593 1.5982 1.1668 1743

BA + 'chlorobenzene

0.0000 1117.0 1252.0 5.711 3 5.0037 1.3985 1.0000 1.086 1

0.0935 11 09 .8 1255.4 5.7173 5.0063 1.3932 0.9927 1.090 1

0.2 111 1101.9 127 1.2 5.6160 4.96 18 1.4007 0.98 15 1.0974

0.2967 1097.3 1284.6 5.5225 4.9203 1.4096 0.9740 1.1 021

0.4 130 1091.8 1308.6 5. 3486 4.8422 1.4287 0.963 1 1. 1094

0.5176 1086.4 1333 .3 5.1779 4.7643 1.4485 0.9524 1. ll n

0.6050 108 1.5 1356.3 5.0265 4.694 1 1.4668 0.9427 1. 1247

0.7224 1074.6 1390.2 4.8150 4.5944 1.4939 0.9290 I 1359

0.83 12 1067.6 1428.5 4.5902 4.4858 1.5251 0.9 147 1487

0.9104 1062 .5 1462 .3 4.40 I 5 4.3926 1.5537 0.9032 1595

1.0000 1057 .0 15 12.0 4.1383 4.2593 1.5982 0.8886 1743

BA + cyc lohexane

0.0000 766.4 120 1.0 9.0460 6.2973 0.9204 1.0000 1. 1673

0.0770 797.2 11 84.4 8.9420 6.2610 0.9442 1.0450 1.1 415

0.1196 8 14.4 I 166.4 90254 6.290 1 0.9499 1.0730 J. 1249

0.22 11\ 845.1\ 11 68 .4 1\.6606 6.1617 0.9882 I . I 138 1.1 143

0.3015 869.7 11 85.4 8. 1828 5.9893 1.0309 I. I 397 1.1 121

0.3952 896.8 1224.6 7.4356 5.7093 1.0982 1.1 626 1. 11 71

0.4964 925 .3 1279.4 6.6024 5.3799 I. I 838 I . I 822 1.1 270

0.6 165 959.3 1336.3 5.8376 5.0588 1.28 19 1.2079 1. 136 I

0.7369 99 1.3 1393.2 5.1972 4.7732 1. 38 11 1.23 10 . 1473

08632 1024.0 1451.2 4.637 1 4.5087 1.4860 1.2544 I . 1593

1.0000 1057.0 1512.0 4 . I 383 4.2593 1.5982 1.2773 1743

320 INDlAN 1 PURE & APPL PHYS , VOL 40, MA Y 2002

... ( 12)

The details of the dev iations and terms used may be obtai ned from the I ite rature"· I ~.17. Theoretically calculated ultrason ic speed along with the experimental values and the percentage errors in the calculated val ues for all the th ree mixtures at different moie fractions of BA at 308 K are listed in Table 3. The acoust ical behaviour of the binary liquid mixtures unde r invest igation may be analysed in the light of the afore-menti oned theo ries and relatio ns .

BCII-:.r/ o/coho/ + cvc/ohexane (p%r + lIoll-po/ar) 1I/1.\ lllre - A c lose perusal of Tab le 3 indicates that Van Dael-Vangee l idea l mi xing re lation , with minimum devia tions in the range 0.06 to 5.84%, predicts the ex perimental data well , fo ll owed by Nomoto's re lat ion, with deviati ons in the range 0.87 to 8.43 %, then by co lli sion factor theory showing deviati ons in the range 2.1 8 to 11 .79%. The free-length [heory, however, is found to show the max i mum deviati ons, 2.0 I to 12. 14 %, over the whole mole fracti on range of BA. The finding by the authors is in good agreement with the conclusion arrived at by Palaniappan el al. l x for 117-creso l + cyclohexane (po lar + non-polar) binary mi xture, as in their case. During their acoustical

study of the above system, they found that ideal mixing relation is best suited with the ex peri mental results, followed by Nomoto 's relation . Thus , the addit ivity of the isentropic compressibil ity (Table I), as suggested by Van Dael and Vangeel , has been observed in the bi nary mixture BA + cyclohexane.

BeIl ZY/ a/coho/ + toluene (po/ar + \\"(!okl\" fl%r) lIIixture - For the above mixture, aga in, it is the ideal mixi ng relat ion, with minimum deviat ions in the range from 0.20 to 0.72 CIa, which is best suited with the experimental result s, followed b Nomoto's relation, with deviations in the ra nge 0.1 9 to 1.26%, then by coll ision fac tor theory, with dev iations in the range 1.36 to 3.64°/e and lastly by the free- length theory show ing maximum deviati ons, 2.38 to 9.87%, over the entire mole fraction range of BA. Thi s, furt her, substantiates the finding by the au thors that fo r po lar + non polar or weak ly polar (some auth ors ha ve treated toluene as a non-polar17 I iqu id) systems idea l mi x i ng relat ion prov ides the best result foll owed by Nomoto' s re lati on.

Benzyl a/coho/ + chlorobenzene (po /ar + polar) mixture - For thi s mixture, Table 3 reveals that percentage deviations for free length theory, Van Dael-Vangeel ideal mixing re lation, Nomoto' s relation and co lli sion factor theory are, respecti ve ly, in the range 0.17 to 0.93 ; 1.28 to 2.79; 1.58 to 3.76

Table 2 - Coemcients, Ai of Eq . (7) along with the standard devi ations. (J (yE) of least-squares fit

Property Ao AI A2 A, A~ (J (yE)

BA + toluene K,E (10- 10 m2 Wi ) -1.0194 -0.7030 -0.3660 -0.4242 -0.8669 0.0046 LrE (10- 12 m) -1.7692 -2 .85 12 -1.3298 -1.0479 -3.009 1 0.0 189 ZE (10' kg m-2 S-I) -0.51 85 1.0275 0.4615 O .~IO 0.9428 0.0055 Il(m 5- 1) -9 1.285 55.406 -7.995 -48.960 30.506 0.4051

FA + chlorobenzene

K,E (10- 10 m2 N- I) 1.1490 0.1554 0.7693 0.0234 0.03 19 0.0021 LrE (10- 12 m) 5.8371 0.2862 3.4 173 -0.071 8 0.5028 0.0094 ZE (1 05 kg m-2 S-I) -2 .1280 0.0765 - 1.2338 0.2748 -0.1920 0.0029 Il (m S-I) -211.56 34.356 -90.840 17.818 -28.503 0.2028

FA + cyclohexane

K,E ( 10- 111 m2 N- I ) -0.6625 4.3404 10.82 10 0.2647 -13.194 0.0284 LrE (10-12 rn) 3.5 184 19.603 1 30.9774 -7.3803 -39.360 0.0957 ZE ( 105 kg 111-2 5-1) -2.9362 -3.2515 -3.0882 2. 1098 4.91 9 1 0.0 139 HE (m S-I) -300.85 -4 11 . 19 -543.52 154.630 696.677 2.4880

ALI et at.: BINARY LIQUID MIXTURES 32 1

Table 3 - Theoretical va lues of ultrason ic speed calculated from CFf, FLT, Nomoto ' s and Van Dael and Vangeel ' s ideal mi xing relation along with experimental va lues of ultrasonic speed and percentage error for binary mi xtures

(SA)

0.0000

0.0685

0.1601

0.23 11

0.3339

0.433 1

0.52 17

0.6496

0.778 1

0.8786

1.0000

0.0000

0.0935

0.2 111

0.2967

0.4 130

0.5 176

0.6050

0.7224

0.83 12

0.9 104

1.0000

0.0000

0.0770

0.1196

0.22 18

0.3015

0.3952

0.4964

0.6 165

0.73 69

0.8632

1.0000

Exp.

1262.0

1275.0

1293.4

1307.5

1328.4

1350.2

1368.5

1400.2

1438.5

1470.3

15 12.0

1252.0

1255.4

127 1.2

1284.6

1308.6

1333.3

1356.3

1390.2

1428.5

1462.3

1512.0

1201.0

11 84.4

1166.4

1168.4

1185.4

1224.6

1279.4

1336.3

1393.2

145 I. 2

1512.0

CFf

1262.0

1356.4

1411.4

1436.5

1449.6

1460.9

1467.4

1491.6

15 14.8

1505.3

1512.0

1252.0

1253.3

1260.4

1273.0

1298.7

1323.7

1345.8

13 80.4

1415.3

1449.8

1512.0

1201.0

1252.7

1286.9

13 10.3

1328.7

1347.9

1368.3

1406.8

1438.0

1480.4

151 2.0

FLT

1262.0

1299.7

133 1.6

135 1.9

1376.5

1399.2

141 8.3

1446.4

1472.7

1490.2

1512.0

1252.0

1274.6

1304.2

1327.1

1359. 1

1387.4

14 10.6

144 1.3

1468.9

1489.0

1512.0

1201.0

1240.2

1262.0

1298.2

1325. 1

1354.7

1385.0

1420.3

145 1. 8

1482.8

1512.0

NOM VDV

SA + toluene 1262.0 1262.0

1277.4

1298.3

13 14.8

1339.2

1363.3

1385.3

141 7.8

1451.5

1478.5

15 12.0

1272.4

1287.4

1300.0

13 19.7

1340.8

136 1.4

1394.5

1432.5

1466. 1

151 2.0

SA + chlorobenzene

1252.0

1275 .3

1304.8

1326.6

1356.4

1383.5

1406.3

1437.4

1466.4

1487.7

15 12.0

1252.0

127 1.4

1297.0

1316.5

1344.3

1370.5

1393.6

1426.2

1458.2

1482.8

15 12.0

SA + cyC\o hexane

120 1.0

122 1.9

1233.6

1262.3

1285.4

13 13. 1

1343.9

138 1. 8

1421.0

1463 .8

15 12.0

120 1.0

12 12.0

1218.7

1236.7

1252.6

1273 .9

1300.3

1337. 1

138 1.1

1436.9

1512.0

FLT

0.00

6.39

9. 13

9.87

9.1 2

8.20

7.23

6.53

5.30

2.38

0.00

0.00

0. 17

0.85

0.90

0.76

0.72

0.77

0.7 1

0.93

0.85

0.00

0.00

5.77

10.33

12. 14

1209

10.07

6.95

5.27

3.22

2.0 1

0.00

CFf

0.00

1.93

2.95

3.40

3.62

3.63

3.64

3.30

2.38

1.36

0.00

0.00

1.53

2.59

3.3 1

3.86

4.06

4.00

3.68

2.83

1.82

0.00

0.00

4.7 1

8. 19

I I. I I

11 .79

10.63

8.25

6.29

4.2 1

2. 18

0.00

% error

NOM

0.00

0.19

0.38

0.56

0. 81

0.97

1. 23

1.26

0.90

0.56

0.00

0.00

1.58

2.64

3.27

3.65

3.76

3.69

3.39

2.65

1.74

0.00

0.00

3. 16

5.76

8.04

8.43

7.23

5.04

3.40

2.00

0.87

0.00

VDV

0.00

0.20

0.46

0.58

0.65

0.70

0.52

0.41

0.42

0.29

0.00

0.00

1.28

2.03

2.49

2.73

2.79

2.75

2.59

2.08

1.40

0.00

0.00

2.33

4.49

5.84

5.67

4.03

1.64

0.06

0.87

0.98

0.00

322 [NOlAN J PURE & APPL PHYS , VOL 40, MAY 2002

and 1.53 to 4.06, over the whole mole fract ion range of BA. Thus, fo r the above mixture, the free-length theory seems to predict the experimental data well , followed by ideal mIx II1 g relati on. Nomoto ' s re lat ion and co lli s ion facto r theory are equally good in pred ict ing the ex perimental data for thi s mixture.

Acknowledgement

One or the authors (AA) is thankful to Department of Science & Technology, New Del hi . for the award of maj or research project. Other auth ors (A Y and AKN) are th ankful to CS[R , New De lhi , fo r the award of research assoc iateship.

References

A li A. Tiwari K . Nai n A K & Chakravortt y V . Ph.".\' Chelll Liq. 38 (2000) 459 ; h/(lian .I PhI'S, 74B (2000) 35 I .

2 Ali A & ;"\Jain A K,.1 Pllre AI'I'I PhI'S, 35 ( 1996) 729.

lain A K , Al i A & A lalll M , .I Chelll Th e/'ll /Od\'ll , 30 ( 1998) 127; Nai n A K & Ali A , Z PhI'S Chelll , 2 10 ( 1999) 185.

..\ Voge l A I. Te.rlbouk o./' I'raclical organic chelllisllT, 5'" ed (Longman. London). 1989.

5 Ali A, Hyder S & Nain A K, AeollSI Le/l , 2 1 ( 1997) 77 ; J Mol Liq, 79 ( 1999) 89 .

6 Kannappan A N & Palani R, India n .I Phrs. 70B (1996) 59.

7 Ali A & Nain A K, 81111 Clleln Soc (.Japan ), (in press ).

8 Mehta S K , Chauhan R K & Dewan R K . .I ChcllI Soc, Faraday TrailS, 92 ( 1996) 1167.

9 A li A . Nain A K & Kamil M. The/'ll/Ochilll Ac((/. 27,,\ ( 1996) 209.

10 Pitzer K S, Th el'lllud \'llalllics. 3'" ed (M cGraw lIill Book Co. Singapore), 1995.

I I Rodham D A, Suzuki S, Suenralll R D el (I I .. Nm II rl', 362 ( 1993) 735.

12 Larsen G, Ismail Z K . Hen'eros B & Parra R D, .I PhI'S Chelll , 102 ( 1998) 4734.

13 Tiwari K , Patra C & Chakr:lVortty V . Acollsi Lell , 19 ( 1995) 53 .

14 SchaalTs W. ACllslica. 30 ( 1974) 275 ; 33 ( 1975 ) 272.

15 Nomoto 0 , J Phrs Soc .lpn , 13 ( 1958) 1528 .

16 Van Dael W & Vangeel E. Proceedillgs of' Firsl hllernolional CrJ/l{eren('(' on talorilllelrl' Th l' l'Inodynolllics. Warsaw. 1969.

17 Pandey J D, Dey R & Dwi vedi D K. Prw/w /IO , 52 (2000) 187.

18 Palaniappan P R, Piehai muthu A & Kannappnn A Indian J PhI'S, 72B ( 1998) 175.