A study on viscosity B-coefficient of some mineral salts in

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A study on viscosity B-coefficient of some mineral salts in
In dian Journal of C he mistry
Vo l. 4 1A, Octo ber 2002, pp, 2032-2038
A study on viscosity B-coefficient of some mineral salts in binary aqueous
solutions of urea at various temperatures
M L Parmar*, D K Dhiman & R C Thakur
Departme nt of Chemi stry, Him achal Pradesh University, Summer Hill , Shimla 171005, India
Received JO Decelllber 200J ; revised 5 Jllll e 2002
Relati ve viscositi es of so me minera l salts viz; sodium s ulphate, potassium sulph a te, a mmon ium sulpha te a nd
magn es iu m sulphate, at di ffe re nt co ncentratio ns hav e been dete rmin ed in bin ary aqueous solutions of urea (mol e-frac ti o ns of
urea, XII!""" = 0.0 10, 0.025 , 0. 040, 0.055 and 0.070) at 308. 15K and in XII!""" = 0.025 at di fferent temperatures. The data have
bee n eva lu ated using l o nes- Do le equ ati on and the obtained pa ramete rs are inte rpreted in te rm s of io n-io n a nd ion-so lve nt
inte rac ti o ns. T he acti va ti o n pa rameters of visco us fl ow have bee n o btain ed whi c h de pic ts th e mec han ism of visco us fl ow.
Ammo niu m sul phate and mag nes ium s ul phate be have as struc ture brea ke rs w hereas sodiu m sulph ate and potass ium sulphate
act as stru ctu re ma ke rs/pro mo ters in th e prese nt syste m.
Studi es on viscosities of ionic solutions are of great
help in characteri sing the stru cture and properties of
soluti ons. Vari ous types of interactions exist between
the ions in th e solutions and of these, ion-ion and ionsolve nt interacti ons are of cUlTent in teres t in all the
branches of chemi stry. These interacti ons help in
better understanding of the nature of solute and
solvent i.e. , whether th e solute modifi es or distorts the
structure of th e solvent. Survey of literature l - Io show
th at although many studi es have been carried out fo r
vari ous electro lyti c solutions, little attention has been
paid to the behaviour of mineral salts in th e solutions
of non-electrolytes . The present mineral salts have
been selected for the study beca use they are the
important constituents I I of biofluid s and soil flu ids.
The main ioni c solutes in biofluid s are the alk ali
. N a+ an d K + WIt. h M g2+ .111 smaII amount,
catt.ons VIZ;
the common ani ons is SO/- which is present in small
amounts. Hence the present investi gation has been
undertaken to prov ide better understandin g of the
nature of th ese mineral salts in th is medium and to
throw light on ion-solvent interactions.
standard solution. The urea- water soluti ons of varying
mole fractions as we ll as the solutions of electrolytes
were made by weight and molalities, 1lI , were
converted into molarities, c, by using the standard
expression 12 : c = 1000 dml(lOOO + mM2 ) , where d is
the solu tion density and M2 molecular weight of th e
electrolyte.
The density was measured with th e help of an
apparatus simil ar to the one described by Ward and
Millero l 3 described elsewhere l 4. I S The accuracy in the
density measurement was of ±1. 10 5 g cm-3 . The
relative vi scosities were meas ured at the desired
temperature using an Ostwald 's suspend ed level type
vi scometer, with a fl ow time 453 seconds for water at
308. 15 K. Run s were repeated until three successive
determinati ons were obtained within ± 0.1 S. since all
the fl ow times were greater th an 100 s, the kineti c
energy correcti on was not necessary. The relati ve
viscosities of the so lutions (/1,",) were calcu lated by
th e usual procedure. 16 -20 The density and viscosity
measurements were carri ed out in a water-bath
(±0.01 DC) .
Materials and Methods
Sodium sulph ate, potass ium sulph ate, ammonium
sulph ate, magnesium sulphate and urea (all of
Analytical Reagent grade) were used after dryin g over
P::Os in a desiccator for more than 48 h. The reagents
we re always placed in the desiccator over P20 S to
keep them in dry atmosphere. Freshly di stilled
co nduc tivity water (sp. Cond o - 10-6 Ohm-I cm-I ) was
used for prepari ng the urea-water soluti ons as well as
Results and Discussion
The relati ve vi scos ities and densities of th e
soluti ons of sodium sulphate, potass ium sulph ate,
ammonium sul phate and magnesium sul phate in
binary aqueous solutions of urea (at mole-fracti ons of
urea, XI/lea = 0.0 10, 0.025 , 0,040, 0.055 and 0.070)
were determined at 308 . 15 K. The experimenral
results of relati ve viscosities of the mineral salts in
2033
PARMAR et al.: VISCOSITY B-COEFFICIENT OF MINERAL SALTS IN BINARY AQUEOUS SOLUTIONS
binary aqueous solutions of urea have been analysed
21
by Jones-Dole equation (Eqn. 1):
160
... (1)
120
where, 1']sp = (1']/1']0 - 1), 1'] and 1']0 are the viscosities of
the solution and solvent (urea + water) respectively,
and c is the molar concentration, A and B are the
constants characteristic of ion-ion and ion-sol vent
interactions respectively. The B-coefficient, which
depends on ion-size and ion-structure, cannot be
calculated a priori. The plots of (1']r - l)/Yc versus Yc
for all the mineral salts, studied here, were found to
be linear, with least scatter. A sample plot for
potassium sulphate in different mole-fractions of urea
in water at 308 .15 K is shown in Fig. 1. The values of
A and B parameters have been calculated using the
least squares method by fitting the experimental
results in the Jones-Doles equation and these values
are given in Table 1, along with standard en-ors.
A perusal of Table 1 shows that the values of Acoefficient are either negative or positive but very
small for all the mineral salts in the entire
composition range of urea in water at 308.15 K,
thereby showing the presence of very weak ion-ion
interactions. In other words these results indicate that
all the mineral salts, studied here, mix ideally with
urea + water and there is a perfect solvation of these
molecules resulting in weak ion-ion interactions.
It is also evident from Table 1 that the Bcoefficient, for all the mineral salts in various molefractions of urea at 308.15 K, is positive and fairly
large thereby suggesting the presence of strong ionsolvent interactions. The value of B-coefficient also
increases with the increase in mole-fraction of urea,
having a minimum at XI/rea = 0.025 for sodium
sulphate, potassium sulphate and X I/rea = 0 .040 for
ammonium sulphate, thereby suggesting that the ionsolvent interactions increase with the increase of urea
in water at 308 . 15 K. The minimum values of Bcoefficient at the respective mole-fractions show that
the ion-solvent interactions are lowest at these molefractions for the respective mineral salt while these
are higher at lower as well as at higher mole-fractions
of urea .
In case of magnesium sulphate the magnitude of Bcoefficient increases with the increase in molefraction of urea, thereby showing that ion-solvent
interactions further improve with the increase of urea
content in water, which results in the improvement of
ionic solvation. In other words, preferential solvation
100
80
20
100
-20
Fi g. I-Plots of
Jc
11 - 1
r;:;
versus ....;C for potassium sulph ate in
different compositions of urea-water at 308.15 K
by urea molecules would also be expected to reduce
the strong interactions of urea molecules with water
thereby resulting in the increase in B value.
The viscosity data have also been analysed on the
basis of transition state treatment of relative viscosity
of electrolytic solutions as suggested by Feakins et.
a!. 22 The B parameter in terms of this theory is gi ven
by Eqn . 2:
- 0
~ [L1 0* _L1 0* ]
1000
/1 2
/1,
- 0
... (2)
- 0
here V, is the mean volume of the solvent and V 2 is
the partial molar volume of the solute. Th e free
energy of activation per mole of the pure solvent
0*
(L1/1! ), and the free energy of activation per mole of
o'
?]
.
solute (L1/12 ) were calculated-' WIth the help of Eqn s.
(3) and (4) respectively:
o'
- 0
L1/1! =RT In (1']0 V , /hN)
. .. (3 )
a nd
O'
0*
L1/1 2 = L1/1! +
RT
- 0
- 0
[1000 B - ( V I
-
- 0
V 2 )]
. .. (4)
V,
where h is the Planck constant, N the Avogadro
number, 1']" the vi scosity of the solvent, R the gas
INDIAN J CHEM, SEC A, OCTOBER 2002
2034
constant and T is the absolute temperature. The values
of .1J-l ~* calculated from the Eqn. (3) are gi ven in
Table 2. For the mixed so lvents, each solvent mixture
was treated as a pure and the molar volume taken as a
mean volume defined as:
-Ii
VI
= (xiM I + x2M2)/dl
- 0
value of V 2, the partial molar volumes at infinite
dilution for different mineral salts, determined from
density data,15 are also recorded in Table 2. The
.1p~* and v~ calculated with the help of
relations (4) and (S) respectively, are also listed in
Table 2.
It is evident from the data (Table 2) that .1p~* is
practically constant at all solvent mole-fractions
implying that .1p~* is dependent main ly on Bcoefficient and
(V~ - V~) terms. It is also clear from
Table 2 that the values of .1p~* are positive and larger
than .1p
r
Urea + water
(Xu,ea)
which suggest that the formation of the
transition state is less favoured in the presence of
these mineral salts, meaning thereby that the
formation of transition state is accompanied by the
breaking and distortion of the intermolecular bonds
between urea and water i.e. solvent.
Recently it has been emphasized by many workers
24
that dB/dT is a better criterion for determin ing the
structure makinglbreaking nature of any electrolyte
rather than simply the B-coefficient. So it means that
in order to follow this criterion, the temperature effect
must be studied.
Effect of temperature
Because of the identical behaviour of an individual
mineral salt in different mole-fractions of urea at
308.1S K, the effect of temperature has been studied
only in X/Ilea = 0.02S . The plots of {fir - I )/Vc versus
Vc have been found to be linear at all temperature
(303.1S, 308.1S, 313.1S and 318.1S K) in accordance
with lones-Dole equation (Eqn. 1) for all the mineral
salts studied. A sample plot is shown in Fig. 2 for
potassium sulphate. The values of A and B parameters
have been calculated by using least squares method
and these values, along with standard errors, are
recorded in Table 3.
A
(dll/IZ lIIor 'I, )
B
(rill/1II0r' )
Sodium sulphate
... (S)
where XI, MI and X2, M2 are the mole-fractions, and
molecular weights of water and urea respectively, and
d l the densi ty of solvent mixture (urea + water). The
values of
Tab le I-Values of A and B parameters of .fones-Dole equation
for sodium sulphate, potassium sulphate, ammonium s ulphate
and magnesium sulphate in various mole-fractio ns of urea
(Xu,,,,,) a,t 308.15 K. Standard errors are gi ven in parentheses.
0.010
0.025
0.040
0.055
0.070
-0. I 26(±0.002)
-0.039(±0.00 I)
-0. I 37(±0.00 I)
-0. 181(±0.004)
-0. I 96(±0.007)
0.754(±0.O22)
0.520(±0.002 )
0.8 I 6(±0.034)
0.938(±O.02 1)
0.943(±0.023)
Potassium su lphate
0.010
0.Q25
0.040
0.055
0.070
0.065(±0.00 I )
0.135(±0.00 I)
0.047(±0.002)
0.034(±0.00 I)
-0.013(±0.002)
0. 127(±0.002)
0.05 3(±0.003)
0.128(±0.003)
0.164(±0.003)
0.264(±0.005)
Ammonium sulphate
0.010
0.025
0.040
0.055
0.070
-0.046(±0.003)
-0.023(±0.002)
-0.045(±0.002)
-0.040(±0.002)
-0.055(±0.002)
0.390(±0.006)
0.334(±0.OO8)
0.276(±0.009)
0.357(±0.005)
0.371 (±0.009)
Magnesium sulphate
0.010
0.Q25
0.040
0.055
0.070
0.161(0.003)
0.123(0.002)
-0.043(0.003)
-0.035(0.002)
-0.333(0.003)
0.339(0.00 I)
0.409(0.004 )
0.705(0.005)
0.767(0.003)
0.834(0.004 )
It is evident from Table 3 that the values of the
coefficient A are either negative or positive but very
small for the different mineral salts studied thereby
showing the existence of weak ion-ion interactions,
which of course further improve with the rise in
temperature for sodium sulphate, and potassium
sulphate while in case of ammoni um su lphate and
magnesium sulphate, the ion-ion interac tions are
further weakened with the rise in temperature.
The values of B-coefficient are positive and large,
as compared to that of A for all the mineral salts
studied in urea + water (Xl/rca = 0.02S) at all
temperatures, thereby showing the presence of strong
ion-solvent interactions. Further, the value of Bcoefficient for sodium sulphate and potassium
sulphate decreases with the rise in temperature which
suggests that ion-solvent interactions are weakened
with the rise in temperature, while reverse happens in
case of ammonium sulphate and magnesium sulphate.
The value of dB/dT is positive for ammonium
sulphate and magnesium sulphate thereby showing
that these two mineral salts behave as structure
PARMAR et al.: VISCOSITY B-COEFFICIENT OF MINERAL SALTS IN BINARY AQUEOUS SOLUTIONS
- 0
2035
-0
Table 2-Values of V I (dllr1mOr'). V 2 (dll/IIlOr'), ,1J.l/* (kJlllor') and ,1J.l/*(kJlllor') for sodium sulphate, potassi um sulphate.
ammonium sulphate and magnesium sulphate in various mole-fractions of urea (XI/r",,) at 308.15 K.
Urea + water
0.010
0.025
0.040
0.055
0.070
18.37
18.77
19.24
19.63
19.98
9.04
9.20
9.33
9.46
9.63
( Xllre<,)
- 0
VI
,1J.l ,o*
Sodium sulphate
- 0
V2
,1J.l/*
82.41
66.19
75.00
84.06
114. 12
123
87
125
140
143
Potassium sulphate
- ()
V2
,1J.ll 0'
50.95
46.87
53.42
61.30
159.08
31
20
31
36
61
Ammonium sulphate
- ()
V2
,1J.l/*
92 . 11
71.33
60.97
71.12
8 1.56
74
62
52
63
65
Magnesiu m sulphate
140.33
141.09
145.48
132.76
146.94
73
82
120
124
133
breakers in urea + water. On the other hand the value
of dBleLT is negative for sodium sulphate and
potassium sulphate which suggests that these two
mineral salts act as structure makers/pr<?moters .
The data of viscosity B-coefficient at different
temperatures have also been analysed by applying the
transition state theory . The values of ,1J..L'r and ,1J1 'r
have been calculated from Eqns. (3) and (4)
respectively, and are recorded in Table 4. The
corresponding values of V'; and V~ have also been
recorded in Table 4.
According to Feakin's model 22 , ,1J1~ . decreases
with temperature for solutes having negative values of
dB/dT. This is nicely shown in case of sodium
sulphate and potassium sulphate which act as
structure makers, while reverse is true in case of
ammonium sulphate and magnesium sulphate, which
act as structure breakers.
The activation entropy fo r different mineral salts
studied has also been calculated from the followinz
relation 22 (Eqn. 6):
~
180
170
130
120
110
Fig. 2-P!ots of
11 r - 1 ve rsus
.JC
for potassium sulphate in
(X III COI = 0.025) urea-water solution at different temperatures
d(,1J1 ~* J/dT = - 115/*
. .. (6)
INDIAN J CHEM, SEC A, OCTOBER 2002
2036
Table 3--Values of parameters A (dm 3/2 mol v,) and B(dm 3 mor l ) of Jones-Dole equation for sodium sulphate, potassium sulph ate,
ammonium sulphate and magnesium sulphate in urea + water (Xure" = 0.025) at different temperatures. Standard errors are given in
parentheses.
303.15
Temperature
308.15
313.15
318. 15
-0.034(±0.00 I)
0.503(±0.004 )
-0.013(±0.002)
0.460(±0.008)
(K)
Sodium sulphate
A
-0.053(±0.002)
0.544(±0.002)
B
-0.039(±0.00 I)
0.520(±0.002)
Potassium sulphate
A
0.112(±0.000)
0.087(±0.000)
B
0.136(±0.001)
0.053(±0.003)
0.146(±0.004)
, 0.035(±0.000)
0.160(±0.003)
0.024(±0.002)
Ammonium sulphate
A
-0.001 (±O.OOO)
0.287(±0.002)
B
-0.023(±0.00 I)
0.334(±0.004)
-0.035(±0.001)
0.359(±0.003)
-0.050(±0.002)
0.401 (±O.OO I)
Magnesium sulphate
A
0.142(±0.002)
0.392(±0.002)
B
-0
0.124(±0.002)
0.409(±0.004)
0.101(±0.001)
0.445(±0.003)
0.088(±0.002)
0.465(±0.003)
- 0
Table 4--Values of V 2 (dn/mor'), V2 (dI1l 3mor'), IJI1/*(kJmor') and IJI1/*( kJl/1or ' ) for sodium sulphate. potassium sulphate,
ammonium sulphate, and magnesium sulphate in urea + water (Xur<'ll = 0.025) at different temperatures.
Temperature (K)
-0
VI
0*
111
303.15
18.74
308. 15
18.77
313.15
18.81
3 18.15
18.86
9.28
9.20
9.08
9.01
Sodium sulphate
- 0
71.97
66.19
55.30
52.5 8
V2
J-l / *
89
86
83
78
Potassium sulphate
-()
V2
J-l/ *
53.71
46.87
43.22
41.72
26
20
17
15
Ammonium sulphate
-
(j
V2
112
o~
69.59
71.33
74.8 1
76.06
55
62
66
73
Magnesium sulphate
- 0
V2
IJ'
i:!.2
139.03
141.09
146.51
147 .8 1
78
82
88
92
2037
PARMAR el at.: VISCOSITY B-COEFFICIENT OF MINERAL SALTS IN BINARY AQU EOUS SOLUTIONS
Table 5--Entropy , T,1S/'(kJmot') and enthalpy, ,1H/ (kJlIl or ' ), of act ivat ion for viscous fl ow of sodium sulphate, potassium
sulphate, ammonium sulphate and magnesium sulph ate in urea + water (X" rca = 0.025) at differe nt temperatures.
Temperature
303. 15
308. 15
313. 15
3 18.15
233
3 16
236
315
212
229
215
230
(K )
Sodium sulphate
T,1S/ '
,1H/"
225
316
229
315
Potassium sulph ate
205
23 1
T,1S/ '
,1H/'
208
228
Ammonium sulphate
T,1S/J'
,1H/"
-365
-308
-372
-310
-378
-3 11
-384
-312
Magnesium sulphate
-296
-217
T,1S/"
,1H/ '
-30 1
-218
-305
-218
-310
-21 8
has been calculated with the help of fo ll owin g
22
relation (Eqn. 7):
10 0
80
. . . (7)
60
30
..
20
a
10
"..,
E
x
~~ 100
"-
4
80
60
::~~
303.15
30B .15
- - - T IK) -
Fi g. 3--Plots of
0*
L'. ~1 2
313 .15
31B.15
--_
ve rsus temperature for sodium sulphat e.
potassium sulphate. ammonium sulphate and magnesium sulphate
in (XlIre" = 0.025) urea- water soluti on.
The values of LlS2o· have been calculated from the
slopes of lin ear pl ots of LlJ..l/ * versus T, as shown in
Fig. 3. The values of TLlS/ * at different temperatures
are listed in Table 5. The activati on enthalpy (LlH/) *)
and the values are also recorded in Table 5.
It is evident from Table 5 that both enthalpy and
entropy of activation are positive in case of Na+ and
J
K+ ions (S042 - being common) and LlH/* > TLlS/ " ,
thereby suggesting that ion-solvent interactions for
these cations are nearly complete in the ground state.
Similar observations have been made by Feakins C/.
25
0/ .
in aqueous solutions of Lie!. Further th e positi ve
valu es of the activat io n enthalpy a nd entropy al so
suggest that the formation of transition state is
assoc iated with bond breaking and decrease in orde r
and the slip-plane is somewhere in th e region o f
centro-symmetric order. On the other hand in case of
NH/ and Mg2+ ions (SO} - being common) both
enthalpy and entropy of activation are negative, which
suggests that the transition state is associated with
bond breaking and increase in order. Altho ugh a
detailed mechanism for this cannot be easily
advanced, it may be suggested that the slip-plane is in
the disordered state.
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2
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INDIAN J CHEM, SEC A, OCTOBER 2002
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