In dian Jo urn al of P ure & Applied Ph ys ics
Vol. 4 1, February 2003, pp. 11 3- 120
Ultrasonic speeds and isentropic functions of mixtures of
N-methyl-2-pyrrolidinone and branched alcohols at 298.15 K
Amalendu Pal*", Harsh Kumar", B R Arbadb& A B Tekaleb
"Department of C hemistry, Ku rukshetra Universi ty, Ku rukshetra 136 119
hDepa rtment of C hemistry, Dr B A Marath wada Uni versit y, Aurangabad 43 1 004
*[e-mai l: search @vidya.kuk.ernet.i n]
Received 8 February 2002; re vi sed 9 September 2002; accepted I November 2002
Ult rasonic speeds have been measured for bi nary mix tures of N- meth yl-2-pyrroli di no ne with 2-propanol , 2-meth yl-1propa nol, 2-methyl-2-propanol, and 3-mcthyl- 1-b utanol, as a fun cti o n o f co mpositio n at 298 .1 5 K. T he values have been
combined with those of densities deri ved fro m excess mo lar vo lu mes to give esti mates o f the product Ks.m of the molar
vo lumes and the isent ropic compressibility Ks and the excess quan tit y K
entire range of composi tion fo r all mixtu res. The deviations
11D
f m. T he K f m va lues are negative over the
of the speeds of so und fro m their val ues in an ideal mixture
were also evaluated for all meas ured mo le fracti o ns. Graphs of uD , and K
f magainst co mposition are presen ted as a basis
for a qu anti tat ive discussio n of the resu lts. Va ri o us thermodynamic parameters have been derived from the speed o f sound
data. Theoretical values of speeds of sound 11 have also been determined using empirical relations.
1 Introduction
Results of measurements of some vo lumetric
N-methyl-2and
transport
properti es
of
pyrro lidinone with branched alcoho ls at 298. 15 K
have been presented in an earlier paper 1• In a
continuing effo rt to co ll ect further thermodynamic
qu antiti es of these mi xtures and al so to extend the
ava il able database for N-methyl-2-pyrrolidinone +
branched alco ho l mi xtures, new experimental
speeds of sound u for the mixtures of N-meth yl-2pyrrolidin one
with
2-propano l,
2-meth yl- 1propano l, 2-methyl-2-propanol, or 3-meth yl- 1butano l over the wh o le mo le fracti on range at the
temperature 298. 15 K and atmosphe ri c pressure are
reported in thi s paper.
The isentropic compress ibility Ks for all
mi xtures were estimated by combining the densities
deri ved from the excess mo lar vo lumes 1 and the
measured ultrasonic speeds. The molar volumes
were multipli ed by the values of isentropic
co mpress ibility, to obta in estimates of Ks.rn· The
auth ors have also ca lcul ated deviati ons u D o f th e
speeds of soun d u from th ose in th e idea l mi xtures
uid,
to 0crether with the excess molar qu antiti es K 5E,m
.
To in vesti gate the nature of interac ti ons, vari ous
thermodynami c parametersv have been ca lcul ated,
which are sens itive to interacti ons between so lute
and so lvent. Theoretica l va lues of speeds of soun d
have been es timated using different e mpiri ca l
equ ations.
2 Experimental Details
2.1Materials
Materi als were of the same ori g in and purity, as
used in the earlier study' . All liquids were kept in
ti ghtly sealed bottl es to minimi ze the abso rpti on of
atmospheri c moisture and C0 2, and dri ed over 0.4
nm mo lecul ar sieves to reduce water content Before
measurements, all liquids were parti a ll y de-gassed
at low pressure. By co mparing the de ns ities at
(298. 15 ± 0 .0 I ) K and atmospheri c pressure with
the ir corresponding literature valu es 4• 11 (T able I ) the
purity of the liquids was chec ked . A lso g iven in
Table l are the measured or literature va lu es of
those quantiti es which we re required in the
estimati on of Ks. 111 , K
J
111
,
and uD . The co mpos iti on
of each mi xture was obtained with an un certain ty of
I x I 0-4 from the measured ap parent masses of one
of the component s. All the mass measurements we re
perfo rmed on an e lectrica l balance (Dho na 2000,
In d ia), accurate to ± 0. 1 mg. Correcti ons were made
11 4
INDIAN J PURE & APPL PHYS , VOL 41 , FEBRUARY 2003
Table I - Observed and li terature values of densities p*; isobari c thermal expansivities ar *; molar isobari c heat capac ities
Cr* m; ult rasoni c speeds u*; and th e product Ks.* m of th e molar vo lu me and isen tropi c compressibili ty of pure liquid co mponents
at 298. 15 K
U*/m s· 1
cr.*nl
Component
Obs.
Li t.
Obs.
N-Methy l-2-pyrro lidinone
1027 .9
1027.9 4
1027.29 5
0 .884"
2-Propanol
78 1.5
78 1. 26 4
78 1.6 7
1.087"
2-Methy l-1-propano l
797 .6
797 .8 4
798.07
308.30"
Ks.*m
/mm·1 mo l" 1 MPa· 1
J K-1 mo l" 1
Li t.
1546.1
39.25
11 38.2
75.95
11 86 . 72~
180.99x
11 87 .0
146 .6 lx
11 20.0
96 .95
1234.0
89.24
82. 70
7 9 7.77 ~
797. 82 10
2-Meth yl-2-propanol
780.7
78 1. 2 4
780.9 7
3-Methyl- 1-butanol
805.4
807.1 x
808.25 11
1.245"
"calc ul ated fro m our measured densities
for buoyancy . A ll mo lar quantities were based upon
the IUPAC ta b~ of atomi c weights 12 .
II
u = I, a;x 1;
. .. ( I )
i=O
3 Apparatus and Procedure
Densities of pure solvents were measured with a
bicapillary pycnometer. The pycnometer was
calibrated at 298. 15 K with double-di stilled water.
The sensitivity of the pycnometer corresponded to a
prec iSIOn in density of I X I0-2 kg m-·1. The
reproduci bility of the den sity estimates was found to
be ::: l x i 0- 1 kg m-' .
Ultrasonic speeds of pure liquids and their
mi xtures at 298. 15 K were measured using s
NUSONIC (Mapco, Model 6080 Concentrati on
Analyser) vel oc imeter based on the sing-around
tec hnique " with 4 MHz acousti c waves. The
maxima l error in the measurements of the sound
speed re lati ve to water ( 1496.687 m s· 1 at 298 . 15
K ) 14 is estimated to be less than 0 .2 m s- 1• Further
detail s concerning the apparatu s, experimental setup and operationa l procedures have been given
prev iousl/ 5 • All the measurements were carried out
in a well-stirred water-bath with temperature
contro lled to ± 0 .0 I K.
by the method of least-squ ares wi th eac h point
weighted equally . The values of coeffic ients a; and
standard devi ations a are summari zed in T ab le 2.
-~.o
,_
Me -a .o
E
e·
'E
UJ . -
:>::
-12 .0
-16 .o .____.___....._--''----'--....__.____.__
o.o
o. ~
0.6
KJ
_,__.____,
08
1.0
fo r x N-methyl -2-pyrrolidin one + ( I
4 Results and Discussion
Fig. l -
The measured speeds of sound u were fitted to a
polynomi al of type:
- x) 2-propanol, o; + ( I - x) 2- meth yl- 1-propano l, L'1 ; + ( I - x)
Values o f
111
2- meth yl-2- propanol, ; + ( I - x ) 3-meth yl-1 -bu tano l, o at
298. 15 K. Continuous curves have been drawn from Eq . (7)
PAL et a/.:BINARY MIXTURES
115
Table 2 - Values of coefficients ai and standard devi ati ons o
Parameter
/Unit
(J
(a) Parameters of Eq . ( I) and th e stand ard deviations o
x N-M eth yl- 2-pyrrolidinone + ( I - x) 2-propanol
11
I m s·'
11 38.3 16
11
I m s·'
11 87. 198
562.970
-359.29 1
334.431
- 129.994
0.93
-98.235
0.37
-361.846
1.02
-43.089
0.63
x N-Methyl-2-pyrrolidinone + ( I - x) 2-meth yl-1-propano l
442.3 32
-230.3 12
245 .350
x N-Methyl-2-pyrrolidinone + ( I - x) 2-methyl-2-propanol
11
I m s- 1
1120.702
602.695
-663.230
848 .1 80
x N-Methyl-2-pyrrolidinone + ( I - x) 3-methyl-1-butanol
11
I m s·'
1233.608
301.02 1
(b) Parameters of Eq . (7) and the standard de viations
-49 .1 64
104.964
o
x N-Methyl-2-pyrrolidinone + ( I - x) 2-propanol
HDI m s·'
1
KE
S ,m I mm· -mo 1-'MP a ·'
LEI A
381.305
-32.240
16.605
13.546
62.682
-8 . 150
16.714
2.884
0.94
0.09
-0.1 336
0.0493
-0.0287
0.0061
0.0004
60.289
-26.074
28.333
11.592
0.83
J
z EX
10._1 /kg m·2 s· l
x N-Methyl-2-pyrrolidinone + ( I - x) 2-methyl-1-propanol
uD/ m s· '
K SE,lll I mm·1 -mo r'MP a-1
LE /A
321 .636
-29.2 11
50.299
9.856
57.951
-4.462
13.1 67
3.1 76
-0.08 18
0.0254
-0.0184
0.0057
-25.659
-21.290
13.022
0.81 1
-0.39 1
0.0002
J
z Ex
10-3 / kgm·2 s· '
0.39
0.04
26.5 16
0.3 5
x N-Methyl-2-pyrrolidinone + ( I - x) 2-methyl -2-p ropanol
uDI m s·'
3
K f m /mm -mor ' MPa· '
LEI A
522.958
-53.884
90.418
20.478
129.504
- 13. 198
15. 11 3
14.447
110.074
-13.869
0.94
0.08
-0.1049
0.0410
-0.0340
0.0343
-0.0444
0.0003
-71.7 13
-46.291
58.744
-21.755
6 1.798
0.81
48.257
0.74
0.06
I
z E X IQ-_1
/kg
Ill-:
s· l
x N-Meth yl-2-pyrrolidinone + ( I - x) 3-methyl-1-butano l
11 D
I m s· '
K SE,m I mm·' -mo r' MP a_,
E
Lf I A
z EX
10' 3 I kg m' 2 s' 1
25 1.759
-25.289
79.959
5. 162
27. 190
-2. 165
39.4 14
-0.938
-0.0329
0.0059
-0.006 1
-0.0067
-126 .235
- 19.948
-9.6 18
24.6 15
Products Ks.m of the molar volume and the isentropic
compres sibility were calcu lated from
. . . (2)
0.0003
42.962
0.72
where xi and M j are the mol e fraction and mola r
mass of component, respective ly, in a mixture with
de nsity p.
The e xcess qua ntiti es were calcu lated from :
K S.m
E = KS, m - K S.id m
... (3)
INDIAN J PURE & APPL PHYS , VOL 41 , FEBRUARY 2003
116
II
F(x) = x(l - x) I.
I
a; (2x- I Y
. . . (7)
i =O
K~'~~~ =I.x; [K ,_ ,-TA 'r.i { (I.xA '"./I.x;C'r;)(A 'r.IC'r;) }]
... (4)
where, A' "; is the product of the molar volume and
the isobaric expansivity, C'p.i the isobaric molar heat
capacity, and Ks.'; the product of the molar volume
V;' qnd the isentrop ic compressibility Ks.';. The p of
the mixture at the appropriate mol e fraction used in
the ultrasonic speed measurements were obtained
from molar volumes of pure components and excess
molar volumes' from the cubic-spline interpolation .
_0_01
140
-0 02
•4
'
120
-O.Q3
'•
E
',
0
60
-o.o 4
o.o
40
L - - - ' - _ L - . _ _ , _ _ L - . _ _ . _ _ L _ _ _ j _ _L__j____j
02
0.4
06
08
1.0
20
Fig. 3 - Values of
0.2
0.4
0.6
08
1.0
Fig. 2 - Values of ,p for x N-methyl -2-pyrrolidinone + ( I - x)
2-propanol, o; + (I - x) 2-methyl-1-propanol , ~; + (I - x) 2meth yl-2-propano l, ; + ( I - x) 3- methyl-1-butano l, oat 298.15
K. Continuous cu rves have been drawn from Eq. (7)
The deviations of the ultrasonic speeds from
their values tn an ideal mixture were calculated
from 17 :
.. .(5)
where
U
"' = v miet
I ( K S;",m ·I.xM)"2
• •
The values of
Kffm , and
... (6)
u 0 were fitted for each
mixture by an equation of the type:
L}
for x N-methyl-2-pyrrolidinone + ( I -
x) 2-propanol, o; t ( I - x) 2-methyl-1-propanol, ~ ; + ( I - x) 2methyl-2-propanol , ; + ( I - x) 3- methyl-1-butano l, oat 298. 15
K. Continuous curves have been drawn from Eq . (7)
Values of coefficients a; and standard deviations <J
are summarized in Table 2. Experimental resu lts for
Kffm and u 0
are plotted against x in Figs I and 2.
The authors have attempted to explain the
physico-chemical behaviour of the mixtures, such as
molecular association and dissociation, as well as
the strength and nature of the interaction between
the components, by deriving variou s thermodynamic
parameters from the ultrasonic speed and den sity
data. Parameters such as, inter-molecular free
length' x L, , van der Waal' s constant b, molecular
radiu s 'x r, geometrical volume B, colli s ion factor 19 S,
specific acoustic impedance 211 Z, and mol ecu lar
association 2 1 M A were computed us ing th e following
relations :
PAL et ai.:BINARY MIXTURES
117
1600
0
11.00
12.0
1200
0
....
0
1000
0
0
0
'· 800
' 1600
. E
~
11.00
1200
0
0
1000
0
••
0
800
00
o.o
0.2
01.
0.6
08
1-0
Fig. 4 - Values of zE for X N-methyl-2-pyrrolidinone + ( I - x)
2-propano l, o; + ( I - x) 2-methyl-1-propanol , 1'1; + ( I - x) 2methyl-2-propanol, : + ( I - x) 3-methyl-1-butanol, oat 298.15
K. Co ntinu o us curves have been drawn rrom Eq. (7)
L 1 = K I (up 112 )
. .. (8)
b=(Mip)-(RT!pu 2 ){ [I +(Mu 2 !3RT)] 112-1 }
... (9)
6rrN) 11-'
. .. ( I 0)
B = ( 4/3 )nr'N
... ( I I )
=uV, I u ~B
.. . ( 12)
S
0.6
o.s
. ...
10
Fig. 5 - Experimental and calculated ultrasonic speeds 11 . noo ;
llcrr. ----; 11 1, - - -: li N, - - - : ll r-u·. ooo fur x N-methyl-2pyrrolidinone + ( I - .r) 2-propano l, (a): + ( I - x) 2-mcthyl-1propanol, (b)
-30-0
r = (3b I l
0-2
••
Z=up
M" = [(u I L.x;u()l - I ]
. . . ( 13)
... ( 14)
w here L1 is th e free length of id ea l mixing, M the
mo lar mass of the mi xture, K th e Jacobson 's
constant {(= ( 93.875 + 0.375 T) x I o·T x and u~
taken as 1600 m s· 1 • These para1.1eters are li sted in
Table 3 for the pure components.
It is observed that, K5 _, and L 1 decrease with mo le
fraction of x for a ll mixtures, whi le Z ex hibit s
reverse trends. The decrease in Ks.m that is, increase
in u and the corresponding decrease in L 1 w ith x
indicates signifi cant interaction between cyc li c
amide and bran ched alcohol mo lecul es . Mi xin g of
-met hy l-2-pyrro lidin one w ith branched a lcohols
te nd s to break the assoc iates present in a lco hol
molecules . However, because of s imulta neous
inte raction s, ma inl y due to possibl e association
throug h weak hydroge n-bo ndin g inte ract ion s of th e
type 0 - H--0 between unlike mol ecul es, th e re is a
co mpe nsating effect resu lting in an ove ra ll decrease
in Ks.m and L1 or increase in u with x .
The values of th e acoust ic impedance Z in c rease
with increasing x for a ll mixtures. Similarly, for the
mixtures
of
N-met hy l-2-py rrolidinone
with
branched a lco hols, the large deviations in M" (not
s hown in Table) are obta in ed with 2-propanol and
th ese deviations decrease in th e orde r: 2-propa nol >
2-methyl-2-propanol > 2-methy l-1-propanol > 3methyl-1-butanol. This suggests that, the non-
INDIAN J PURE & APPL PHYS, VOL 4 1, FEBRUARY 2003
11 8
Table 3 - Values of th e deri ved para meters of th e pure compo nents at 298. 15 K
h x 10 6/ m·'
Component
91.67
71.05
86.58
88.17
102.65
N-Meth yl- 2- pyrrol id inone
2-Pro panol
2-Meth yl- 1-propa nol
2-M eth yl-2-p ropano l
3- Methyl-1-butanol
rl
nm
B
10 6/
m mor 1
s
Lrl
A
Zx I o-'1
kg m·2 s· 1
0 .209
0.192
0.205
0.206
0.2 17
23.02
17.85
21.72
22.04
25 .77
4.05
3.07
3. 17
3.02
3.28
0.4 156
0 .6474
0.6145
0.6583
0.5882
1589.24 '
889.50
946.75
874.38
993.86
ideality in these systems varies in the o rde r: 3methyl-1-butanol < 2-methyl -1-propanol < 2methyl-2-propanol < 2-propanol. It shows that , M A
is mo re posi tive for the mixtures w ith 2-methyl-2propano l and 2-propano l, which may be due to the
ex istence of weak interact ions. The mol ecul ar
assoc iat ion MA is less positive for the mixtures with
an d
2-methyl-1-propa nol ,
3-mcthyl-1-butanol
indicating that, the strength of interaction be tween
unlike molecules becomes important. The results for
M A support the conclusion d rawn from the excess
vo lumes and viscosity data 1 of these mixtu res.
The excess functions of inter-mo lecu lar free
length and acoust ic impedance Z were calculated
using th e relation:
L~ = L 1 - [x Lu + ( I - x) Lu]
7! =
z-
[x
zl + ( l
-
X )Z"]
X
3
co mpos!ti on. Th e be haviour is s imilar to th at of u 0
(Fig. 2), but of o ppos ite si .?,n.
::: f___ ·__ ___ ___ ---- --->
.1200
1000
BOO
{b)
... . . .. .
. . . . ..
. ....
"£ 15oo
'1~0 0
... ( 15)
... ( 16)
E
The results of L 1 and 7!- were fitted to a
polynomial, sim il ar to that given by Eq. (7). Values
of parameter a, along with standard deviations a, arc
presented in Table 2 and are graphically represented
in Figs 3 and 4.
1000
be negat ive for all mixtures , while excess acoust ic
impedance 7!- value~ are negative with 3-methyl- 1butanol, positive with 2-propanol, and change sign
from positive to negative with 2-met hyl-1-propanol
and 2-methyl-2-propanol over the comp lete mole
fraction range. Negative and positive deviations in
these functions from rectilinear dependence on mole
fraction indi cate the extent of association between
unlike molecules. For all the mixtures studied,
(Fig.
I)
K:
J.lll
is negative over the enti:-e range of
.. ... ....
BOO .
o.o
02
o.~
o.a
0.6
1-0
Fi g. 6 - Experimental and calculated ultr· son ic speeds 11 . ooo:
- - ; IIFLT• ooo for .r N-methyl-2pyrrol idinone + (I - x) 2-methyl-2-propanol. (a), ( I - .r) 3mcthyl- 1- butano l (b)
IICf-T· ----; 111, - - - ; li N, -
The curves tn Figs 3 and 4 show that, excess
inter-molecular free lengt h L~ values are found to
(0)
. .,
However, the behaviour of
Kf., , u
0
and
L'J are
inconsistent with V"~· for 2-methyl-2-propanol and
2-propanol. A minimum value fo r K
f, a nd
L~· and
a maximum value for u 0 are observed for 2-methyl 2-p ropanol and 2-propanol. T hi s is normal bec&use
u is generally higher when the struct ure has high
rigidity. Negative vaiues of K ;"," indicate that. the
mixture is less compressible than the corresponding
ideal
mixture, suggest in g stronger specific
interactions wit h 2-methyl-2-propano l and :?.propanol. As the cyclic amide is added to alcohol,
PAL et a i. :B INARY MIXTURES
breakdown of self-assoc iated alco hol takes pl ace
contributing to a denser packing of the mol ecul es
through inter-mo lecu lar inte raction s. Speed of sound
£
d ecreases . H oweve r,
K s.m
111
·
ts
mo re negative for 2-methy l-1-propano l and
3-
increases an d
v £
11 9
Junji e eq u ati o n 2 .~:
u1 = {(x1M/p1)+x2M/p2}I[ {x1M 1+
X2 M2}112 { (x1 M1I p 1u12) + x 2 M2l p 2u/} 112 ]
••• (
19)
No moto equati on 25 :
= [{ xl R1 +x2 R2}l{ x1 VI +x2 V2lf
. ..(20)
methyl-1-butan o l, a lthough K ffm is negative and u 0
u N
like-wise positive, in the sequence: 3-methyl-1 butan ol < 2-methyl-1-propanol < 2-propat_lOI < 2meth yl-2-propano l, indicatin g that, when the
mixture is c reated, free vo lume increases and is
hi g her
in
mixtures contammg N-methyl-2pyrrolidinone with 2-meth yl-2-propanol. The effect
is that, whil e go ing from secondary alcohol to
te rtiary a lcohol , th at is, 2-methyl-1-propanol to 2met hyl-2-prop ano! ,
inertial
accommodation
becomes less impo rtant, and th at th e molecul es of
th e two compo nents cann ot be accommodated
eas il y.
The computed ucFr, u FLT• uh and u N values a re
shown in Figs 5 and 6, for compari son with
experimental values, for all the mixtures. As can be
seen, the simple Nomoto express io n and co lli s ion
factor theory predict the experimenta l results,
extreme ly we ll , for a ll the mixtures, whereas th e
Junji e express ion shows the maximum deviati o n at
lower mol e fraction range, and th e free le ngth
theory g ives larger dev iation for a ll the present
bin ary mixtures .
Again, with inc reas in g bra nc hing in the
mol ecul e, the -C=O group of cycl ic amide is more
hinde red and less act ive to break the self-assoc iation
of 2-methyl-2-propanol. This additional ri g idity is a
good reason for the positive values of u 0 and
Acknowledgement
One of the authors (ABT) g ratefull y
acknowledges the University Grant s Commiss io n
(WRO), Pune, for award of teac her fellowship and
financial ass istance.
References
negative values of K ffm for 2-me thy l-2-propan o l.
So, the main contributi on to large negati ve
and
less
negative
viii·£
K.fm
to th e earlier view of the auth ors, from K %:,, and u
Pal A, Sharma S & Kumar A , In dian .I Pure & Appl Phys,
38 (2000) 174.
3
Pal A & Kumar H. In dia n .I Phys, 758 (200 I ) 419 .
4
Riddi ck J A. Bunger W S & Sakano T. Organic solvenls.
!echniques of chemislrv. Vol II , 4'h Ed: (John Wil ey &
Sons, New York), 1986.
5
Davis M I, Th ennochim Acla , 120 ( 1987) 299.
6
CRC handbook of physics and chemis1ry. 80'h Ed. , 2000.
7
Nikam P S, Jad har M C & Hasan M , J Chem En g Dala . 41
( 1996) I 028 .
8
Riddick J A , & Bunger W S, Or[:ianic solvenls, tecl111iques
of chemi.w y, Vol II , 3'" Ed. : (John Wil ey, New York),
1970.
9
Troncoro J, Carball o E, Cerdeiri na C A. Gonzalez D &
Romani L , J Chem Eng Daw, 45 (2000) 594.
10
Francesconi R & Comclli F. J Chem Eng Da!a , 44 ( 1999)
44.
II
Joshi S S, Aminabha vi T M . Balundgi R H & Shukl a S S,
Indian 1 Chem Techno/, 29 ( 199 1) 425 .
12
I UPAC, Commission on atomic weights &
abundances, Pure Appl Chem , 58 ( 1986) I 677.
0
data .
For comparison, the authors have ca lculated the
theoreti ca l valu es of the ultrasoni c speeds from the
following empiri cal equations:
Colli sion Factor Theory'·1 :
H.cn =u_{xiSI + x2S2}[{ x1 B1 + x2B2} IV]
Free le ngth th eory x:
2
values for 2-methyl-2-
propan o l and 2-propanol appears to be du e to the
different s izes and shapes of the co mponents which
tend to break the assoc iates present in brancheda lcoho ls
with
subseque nt
complex-forming
interactions, whic h seems to domin ate over that of
hydrogen-bonding effect. Further, increasin gly
negative values of ZE with x (Fig. 4) is indicative of
the decreas ing strength of inte racti on between the
component molecul es of th e mi xtures, as suggested
by Tiwari et al .22 . Thi s behavior also finds support
1
Pal A , Kumar A, Arbad B R &Tekalc A B. Indian 1 Chem,
41A (2002) 1593.
... ( 17)
isotopic
13 Garnsey R, Boe R J, M ahoney R & Litovitz J A, .I Chem
Phys, 50 ( 1969) 5222.
INDIAN J PURE & APPL PHYS, VOL 41, FEBRUARY 2003
120
14
Del Grosso V A & Mader C W , J Acousl Soc A111 , 52
(1972) 1442.
20
D ewan R K , Gupta C M & Mehta S K . A c usl im , 65 ( 19XH)
245.
15
Pal A & Singh Y P. India n J Pure & AJlpf Ph1•s , 35 ( 1997)
310.
21
M eh ta S K , Chau han R K & Dewan R K , .I Cften1 Soc
Faradm• Trans , 92 ( 1996) II 67 .
16
Benson G C & Ki yohara 0 , .I C!teiJI T!temwd\'11 , I I ( 1979)
1061.
22
Tiwari K , Patra C & Chakravortty V. Acousl Lell. 19
( 1995)53.
Douheret G. Pal A & Davi s M I, J Cften 1 Tliemwdrn , 22
23
Schaaffs W , Acuslica , 33 ( 1975) 272.
24
Junjie Z , J Clr i11a UniF Sci Tec!tn , 14 (I 9X4) 29X.
25
Nomoto 0 , .I Pln•s Soc
17
( I<)<)() ) lJ9.
I 1:>
Jacobson B . .I C!ten1 P!trs. 20 ( 1952) 927.
19
SchaaiTsW , ZP/n·s. ll4(1974 ) 110.
.It"'·
13 ( 195X) 20X.