Indian Journal of Chemistry
Vol. 48A, January 2009, pp. 57-62
A comparative study of partial molar volumes
of some hydrated and anhydrous salts of
transition metal sulphates and magnesium
sulphate in water at different temperatures
M L Parmar*, Praveen Sharma & M K Guleria
Department of Chemistry, Himachal Pradesh University,
Summer Hill, Shimla 171 005, India
Received 28 July 2008; accepted 14 December 2008
Partial molar volumes of some hydrated and anhydrous salts of
transition metal sulphates, viz., cobalt sulphate, nickel sulphate
copper sulphate, zinc sulphate and magnesium sulphate have been
determined in water at five equidistant temperatures (298.15,
303.15, 308.15, 313.15 and 318.15 K). The density data have been
analysed by means of Mason’s equation. The partial molar
o
volumes ( φ v ) and experimental slopes ( Sv* ) have been
interpreted in terms of ion-solvent and ion-ion interactions,
respectively. The partial molar volumes vary with temperature as
a power series of temperature. Structure-making/breaking
capacities of hydrated and anhydrous salts have been inferred
[
from the sign of ∂ 2φv0 / ∂T 2
]
p
, i.e., the second derivative of
partial molar volume with respect to temperature at constant
pressure. The hydrated salts act as structure makers while
anhydrous salts act as structure breakers in water, i.e., the
behaviour is reversed on removal of water of crystallization.
Keywords: Solution chemistry, Electrolytes, Partial molar
volume, Cobalt, Nickel, Copper, Zinc, Manganese
Partial molar volumes of electrolytes provide valuable
information about the ion-ion and ion-solvent
interactions1-16. This information is of fundamental
importance for the understanding of reaction rates and
chemical equilibria involving dissolved electrolytes.
These studies are of great help in characterizing the
structure and properties of solutions. Survey of
literature shows that although many studies on
thermodynamic properties of various electrolytes have
been carried out in aqueous and aquo-organic solvent
mixtures, no attention has been paid to the
comparative behaviour of hydrated and anhydrous
salts in the same medium.
As the partial molar volume of a electrolyte reflects
the cumulative effects of ion-ion and ion-solvent
interactions, it would be of interest to study the partial
molar volumes of hydrated and anhydrous salts of
some transition metal sulphates viz., cobalt sulphate,
nickel sulphate, copper sulphate, zinc sulphate and
magnesium sulphate in water. Such data are expected
to highlight the role of water of crystallization in
influencing the partial molar volumes in water. These
considerations prompted us to undertake the
present study.
Experimental
Hydrated salts of transition metal sulphates, viz.,
cobalt sulphate (CoSO4·7H2O), nickel sulphate
(NiSO4·6H2O), copper sulphate (CuSO4·5H2O), zinc
sulphate (ZnSO4·7H2O), and magnesium sulphate
(MgSO4·7H2O) and anhydrous salts of transition
metal sulphates viz., cobalt sulphate (CoSO4), nickel
sulphate (NiSO4), copper sulphate (CuSO4), zinc
sulphate (ZnSO4), and magnesium sulphate (MgSO4),
were all of AR grade. The water of crystallization, in
both the hydrated and anhydrous salts, was estimated
by the standard method17. The anhydrous salts were
prepared after repeated heating and cooling in a
desiccator, until constant weight of the salt was
obtained17. After complete dehydration, these salts
were always placed over P2O5 in a desiccator to keep
them in dry atmosphere. Freshly distilled conductivity
water (Sp. cond. ~10-6Ω-1cm-1) was used for preparing
electrolyte solutions as well as standard liquid.
Aqueous solutions of hydrated and anhydrous salts
(conc. range 0.005-0.100 mol kg-1) were made by
weight and molalities, m, were converted into
molarities, c, using the standard expression18,
c = 1000 dm/(1000 + mM2), where d is the solution
density and M2 the molecular weight of the hydrated
or anhydrous salt. The density was measured with the
help of an apparatus similar to the one reported by
Ward and Millero19, and described below.
The glass sample cell had a bakelite top with a hole
in the centre and was placed in a temperature bath
thermostatically controlled to ± 0.01 K. The glass
float used weighed 37.5464 g and had a volume of
24.8754 ± 0.001 cm3. Densities of the solutions were
calculated from the expression: d – do = [Wo - W]/Vf,
where d and do are the densities of the sample solution
and pure water, respectively; W and Wo are the
weights of the float in the sample solution and pure
water respectively and Vf is the volume of the float.
INDIAN J CHEM, SEC A, JANUARY 2009
58
The accuracy was checked by measuring the density
of pure dioxane at 298.15 K, The obtained value of
d = 1.0268 g cm-3 is in excellent agreement with the
literature20 value of d = 1.0269 g cm-3. The accuracy
in density measurement was ±1 × 10-4 g cm-3.
The apparent molar volumes (φv) were calculated
from the density data using the following standard
expression21:
φv =
M2
10 3  d − d o 
−


do
c  do 
…(1)
where do is the density of solvent (water). The density
measurements were carried out in a well-stirred
water-bath with a temperature control of ± 0.01 K.
303.15, 308.15 and 318.15 K), have been used to
calculate the apparent molar volumes ( v) of the salts.
The plots of v against the square root of molar
concentration (c½) are linear with positive slopes for
hydrated salts and negative slopes for anhydrous salts.
The sample plots are shown in Figs 1 and 2 for
hydrated and anhydrous cobalt sulphate, respectively,
in water at different temperatures.
The limiting apparent molar volumes ( φ vo ) and
experimental slopes (Sv) were calculated using the
least-square treatment to the linear plots of φv versus
c½, using Masson’s equation22:
φv = φ vo + S v* ·c½
…(2)
where φ vo = V20 is the partial molar volume of salt
Results and discussion
The densities measured for the solutions of
hydrated and anhydrous salts of transition metal
sulphates, viz., cobalt sulphate, nickel sulphate,
copper sulphate, zinc sulphate and magnesium
sulphate in water at different temperatures (298.15,
and Sv the experimental slope. The values of φ vo and
Sv, along with standard errors, are listed in Table 1. It
is evident from the data that Sv is positive for hydrated
salts while it is negative for anhydrous salts of
transition metal sulphates and magnesium sulphate in
Fig. 1—Plots of фv versus c1/2 for hydrated cobalt sulphate in
water at different temperatures. [1, 298.15; 2, 303.15; 3, 308.15;
4, 313.15; 5, 318.15 K].
Fig. 2—Plots of фv versus c1/2 for anhydrous cobalt sulphate in
water at different temperatures. [1, 298.15; 2, 303.15; 3, 308.15;
4, 313.15; 5, 318.15 K].
NOTES
water at all temperatures, i.e., the values of Sv become
negative as the hydrated salts are changed to
anhydrous salts. In other words, the removal of water
of crystallization from the hydrated salts of transition
metal sulphates and magnesium sulphate changes the
sign of Sv from positive to negative i.e., the behaviour
is altogether changed.
It is evident from the data (cf. Table 1) that Sv is
positive but very small in magnitude for the hydrated
59
salts of transition metal sulphates and magnesium
sulphate in water at different temperatures. Since Sv is
a measure of ion-ion interactions, the results indicate
the existence of specific ion-ion interactions. These
interactions, however, increase with the increase in
temperature in the case of hydrated salts of transition
metal sulphates and magnesium sulphate, which may
be attributed to the decrease in solvation of ions with
the rise in temperature.
o
Table 1—Partial molar volumes ( φ v ) and experimental slopes (Sv) for hydrated and anhydrous salts of transition metal sulphates and
magnesium sulphate in water at different temperatures. Standard errors are given in parentheses
Temp.(K)
φvo
× 10-6
(m3 mol-1)
Sv × 10-6
Temp.(K)
(m3 dm3/2 mol-3/2)
φvo
× 10-6
Sv × 10-6
(m3 mol-1)
(m3 dm3/2 mol-3/2)
Hydrated salts
Anhydrous salts
CoSO4·7H2O
298.15
303.15
308.15
313.15
318.15
0.325 (± 0.005)
0.338 (± 0.007)
0.341 (± 0.013)
0.346 (± 0.003)
0.355 (± 0.004)
CoSO4
298.15
303.15
308.15
313.15
318.15
103.70 (± 0.14)
106.50 (± 0.05)
109.02 (± 0.08)
111.27 (± 0.06)
113.28 (± 0.07)
-0.343 (± 0.007)
-0.346 (± 0.003)
-0.354 (± 0.004)
-0.359 (± 0.003)
-0.372 (± 0.003)
0.714 (± 0.003)
0.784 (± 0.005)
0.791 (± 0.006)
0.875 (± 0.012)
0.906 (± 0.009)
NiSO4
298.15
303.15
308.15
313.15
318.15
74.89 (± 0.09)
79.54 (± 0.15)
83.96 (± 0.19)
88.23 (± 0.08)
92.16 (± 0.28)
-0.744 (± 0.004)
-0.769 (± 0.007)
-0.793 (± 0.009)
-0.798 (± 0.004)
-0.820 (± 0.010)
0.704 (± 0.009)
0.765 (± 0.014)
0.813 (± 0.006)
0.845 (± 0.006)
0.857 (± 0.007)
CuSO4
298.15
303.15
308.15
313.15
318.15
64.02 (± 0.18)
66.43 (± 0.18)
68.61 (± 0.11)
70.66 (± 0.05)
72.55 (± 0.10)
-0.628 (± 0.009)
-0.636 (± 0.009)
-0.647 (± 0.006)
-0.658 (± 0.003)
-0.664 (± 0.005)
ZnSO4
298.15
303.15
308.15
313.15
318.15
99.57 (± 0.25)
104.05 (± 0.09)
108.08 (± 0.22)
111.67 (± 0.18)
114.85 (± 0.16)
-0.901 (± 0.013)
-0.931 (± 0.005)
-0.960 (± 0.011)
-0.996 (± 0.009)
-1.109 (± 0.008)
MgSO4
298.15
303.15
308.15
313.15
318.15
79.79 (± 0.14)
89.93 (± 0.15)
96.71 (± 0.14)
102.43 (± 0.17)
107.40 (± 0.15)
-0.887 (± 0.007)
-0.921 (± 0.008)
-0.973 (± 0.007)
-1.067 (± 0.009)
-1.313 (± 0.008)
NiSO4·6H2O
298.15
303.15
308.15
313.15
318.15
CuSO4·5H2O
298.15
303.15
308.15
313.15
318.15
102.56 (± 0.10)
100.07 (± 0.13)
97.70 (± 0.25)
95.37 (± 0.05)
93.33 (± 0.07)
67.34 (± 0.06)
61.57 (± 0.10)
56.73 (± 0.11)
52.72 (± 0.24)
49.19 (± 0.19)
55.90 (± 0.18)
52.21 (± 0.28)
48.76 (± 0.12)
45.75 (± 0.11)
43.84 (± 0.13)
ZnSO4·7H2O
298.15
303.15
308.15
313.15
318.15
88.90 (± 0.10)
83.13 (± 0.10)
78.07 (± 0.40)
73.44 (± 0.27)
69.23 (± 0.16)
0.903 (± 0.005)
0.982 (± 0.005)
0.990 (± 0.021)
1.061 (± 0.014)
1.107 (± 0.008)
MgSO4·7H2O
298.15
303.15
308.15
313.15
318.15
130.16 (± 0.08)
108.19 (± 0.07)
88.27 (± 0.18)
71.86 (± 0.20)
57.86 (± 0.81)
0.340 (± 0.004)
0.381 (± 0.003)
0.766 (± 0.009)
1.196 (± 0.010)
1.494 (± 0.042)
60
INDIAN J CHEM, SEC A, JANUARY 2009
These results of hydrated salts of transition metal
sulphates and magnesium sulphate at different
temperatures suggest a possible explanation for the
absence of the negative Sv values for all the hydrated
salts in water. Although at infinite dilution all of these
salts are completely dissociated in water at different
temperatures, the situation would be different at
higher concentrations. These salts are not completely
ionized such that interionic penetration does not occur
which may give rise to positive slopes in the φv versus
c½ curves.
It is also clear from Table 1 that Sv is negative for
anhydrous salts of transition metal sulphates and
magnesium sulphate in water at different temperatures.
The results indicate the presence of weak ion-ion
interactions. These interactions, however, decrease
with the increase of temperature, which may be
attributed to the increase in solvation of ions with the
rise in temperature. Further, in water, these salts may
be completely ionized at fairly high concentrations.
Therefore, appreciable interionic penetration occurs
and this gives rise to negative slopes in the φv versus c½
curves for these anhydrous salts.
Since φ vo is a measure of ion-solvent interactions
(as ion-ion interactions vanish at infinite dilution),
therefore, it is evident from Table 1 that the values of
φvo are positive and large for both the hydrated and
anhydrous salts of transition metal sulphates and
magnesium sulphate in water at different
temperatures, indicating the presence of strong ionsolvent interactions. These interactions are, however,
weakened with the rise in temperature for the
hydrated salts of transition metal sulphates and
magnesium sulphate, which may be attributed to the
decrease in ion-solvation in water. However, in the
case of anhydrous salts of transition metal sulphates
and magnesium sulphate, the ion-solvent interactions
are further strengthened with rise in temperature. The
increase in φ vo with the increase in temperature, for
individual anhydrous salt, may be attributed to
increase in solvation.
Since, the sulphate ion is the common ion in the
case of these hydrated and anhydrous salts, from the
values of φ vo at a particular temperature, it may be
concluded that the solvation of cations follows the
order: Mg2+ > Co2+ > Zn2+ > Ni2+ > Cu2+ for hydrated
salts, and for anhydrous salts: Co2+ > Zn2+ > Mg2+ >
Ni2+ > Cu2+.
The temperature dependence of φ vo for hydrated
and anhydrous salts of transition metal sulphates and
magnesium sulphate studied here in water, can be
expressed by the general equation (Eq. 3).
φvo = a + bT + cT2
…(3)
Various coefficients of Eq. (3) for both hydrated and
anhydrous salts of transition metal sulphates and
magnesium sulphate are given in Table 2.
The partial molar volume expansibilities,
o
φ E = ∂φ vo / ∂T 2 P calculated from Eq. (3) are given
in Table 3. It is evident from Table 3 that the values
of φ Eo , for hydrated salts of transition metal sulphates
and magnesium sulphate at different temperatures are
of course negative but increase in magnitude with the
increase in temperature, indicating that the behaviour
of these hydrated salts is just like symmetrical
tetraalkyl ammonium salts23. The positive increase in
φ Eo may be ascribed to the presence of “caging
effect”23. In other words, all the hydrated salts of
transition metal sulphates and magnesium sulphate
occupy the interstitial spaces in the solvent, i.e., water,
resulting in structure-making hydrophobic character.
[
]
Table 2—Various coefficients of Eq. (3) for hydrated and
anhydrous salts of transition metal sulphates and magnesium
sulphate in water. Standard errors are given in parentheses
Salt
a
b
c
521.58
(± 3.24)
1778.05
(± 5.32)
909.45
(± 4.27)
1232.20
(± 2.13)
5931.68
(± 6.59)
- 2.36
(± 0.32)
- 10.21
(± 1.15)
- 4.95
(± 0.93)
- 6.52
(± 1.63)
- 34.37
(± 1.93)
+ 0.003
(± 0.001)
+ 0.015
(± 0.002)
+ 0.007
(± 0.001)
+ 0.009
(± 0.002)
+ 0.050
(± 0.010)
- 434.42 (±
1.87)
- 202.32 (±
2.97)
- 223.63 (±
3.94)
- 631.71 (±
2.20)
- 2856.42 (±
5.68)
+ 2.60
(± 0.97)
+ 1.62
(± 0.63)
+ 1.43
(± 0.16)
+ 4.17
(± 1.13)
+ 19.45
(± 2.31)
- 0.005
(± 0.002)
- 0.004
(± 0.001)
- 0.003
(± 0.001)
- 0.008
(± 0.001)
- 0.034
(± 0.001)
Hydrated salts
CoSO4·7H2O
NiSO4·6H2O
CuSO4·5H2O
ZnSO4·7H2O
MgSO4·7H2O
Anhydrous salts
CoSO4
NiSO4
CuSO4
ZnSO4
MgSO4
NOTES
61
o
Table 3—Partial molar volume expansibilities ( φ E ) for hydrated and anhydrous salts of transition metal sulphates and
magnesium sulphate in water at different temperatures
Salt
Partial molar volume expansibilties
φ oE × 10-6 (m3 mol-1 K-1) at temp. (K) =
298.15
303.15
308.15
313.15
318.15
Hydrated salts
CoSO4
NiSO4
CuSO4
ZnSO4
MgSO4
-0.571
-1.266
-0.776
-1.153
-4.555
-0.541
-1.116
-0.706
-1.063
-4.055
-0.511
-0.966
-0.636
-0.973
-3.555
-0.481
-0.816
-0.566
-0.883
-3.055
-0.451
-0.666
-0.496
-0.793
-2.555
Anhydrous salts
CoSO4
NiSO4
CuSO4
ZnSO4
MgSO4
-0.382
-0.765
-0.359
-0.600
-14.594
-0.432
-0.805
-0.389
-0.680
-14.934
-0.482
-0.845
-0.419
-0.760
-15.274
-0.532
-0.885
-0.449
-0.840
-15.614
-0.582
-0.925
-0.479
-0.920
-15.954
On the other hand, the values of φ Eo , of course
negative, further decrease in magnitude with the rise
in temperature, for all the anhydrous salts of transition
metal sulphates and magnesium sulphate in water,
suggesting that the behaviour of these anhydrous salts
is just like common salts, because in the case of
common salts the molar volume expansibility should
decrease with the increase in temperature24,25. The
decrease in φ Eo with the increase in temperature, for
all the anhydrous salts of transition metal sulphates
and magnesium sulphate in water, shows the absence
of caging or packing effect23,25.
The variation of φ Eo with temperature, for all the
hydrated and anhydrous salts of transition metal
sulphates and magnesium sulphate, has been found to
be linear in water. A sample plot for anhydrous salts
of transition metal sulphates is shown in Fig. 3.
It has been emphasized by different workers that Sv
is not the sole criterion for determining the structuremaking or breaking nature of any solute. Hepler26
developed a technique of examining the sign of
∂ 2φ vo / ∂T 2 P for various solutes in terms of long
range structure-making and breaking capacity of the
solutes in aqueous solutions using the general
thermodynamic expression:
[
[∂C
]
p
]
/ ∂P T
[∂ φ
2
=—
o
v
/ ∂T 2
]
P
…(4)
On the basis of this expression it has been deduced
that structure-making solute should have positive
Fig. 3—Variation of фE° with temperature for anhydrous cobalt
sulphate, nickel sulphate, copper sulphate and zinc sulphate in
water. [1, CoSO4; 2, NiSO4; 3, CuSO4; 4, ZnSO4].
INDIAN J CHEM, SEC A, JANUARY 2009
62
value, whereas structure-breaking solute should have
negative value. In the present system, it is observed
from Eq. (3) that ∂ 2φ vo / ∂T 2 P is positive for
hydrated salts of transition metal sulphates and
magnesium sulphate in water, thereby showing that
all the hydrated salts of transition metal sulphates and
magnesium
sulphate
act
as
structuremakers/promoters in water. In other words, it may be
said that the addition of hydrated salts of cobalt
sulphate, nickel sulphate, copper sulphate, zinc
sulphate and magnesium sulphate to water causes an
increase in the structure of water.
On the other hand, the value of ∂ 2φ vo / ∂T 2 P is
negative for the solutions of anhydrous salts of
transition metal sulphates and magnesium sulphate in
water, suggesting that the anhydrous salts of the
transition metal sulphates and magnesium sulphate act
as structure-breakers in water. In other words the
addition of anhydrous salts of cobalt sulphate, nickel
sulphate, copper sulphate, zinc sulphate and
magnesium sulphate to water causes a decrease in the
structure of water.
If the results of hydrated and anhydrous salts of
transition metal sulphates and magnesium sulphate in
water are compared, there is a drastic change in the
behaviour of these salts. The hydrated salts act as
structure-makers while the anhydrous salts act as
structure-breakers in water. In other words, the
addition of hydrated salts causes an increase in the
structure of water and there is a presence of “caging
effect”, while the addition of anhydrous salts causes a
decrease in the structure of water, i.e., these salts
modify the structure of water and there is an absence
of “caging effect”.
From these results it may be concluded that just the
removal of water of crystallization changes the
behaviour of these salts altogether.
[
]
[
]
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