Ultrasonic study of mixture, containing Aqueous solution of 'NaCl' and 'KCl' for different ratios of Sodium to Potassium about Vitality ratio and about Human body Temperature

Abstract

The Ultrasonic velocity, density and viscosity have been measured for different ratios of sodium (Na) to potassium (K) about vitality ratio and about normal body temperature. The ratios are analysed in terms of the thermodynamic parameters derived from the ultrasonic data.

Full text

Research Journal of Chemical Sciences ______________________________________________ ISSN 2231-606X
Vol. 5(6), 32-39, June (2015) Res. J. Chem. Sci.
International Science Congress Association 32
Ultrasonic study of mixture, containing Aqueous solution of ‘NaCl’ and
‘KCl’ for different ratios of Sodium to Potassium about Vitality ratio and
about Human body Temperature
Manoj Kumar Praharaj
*
and Sarmistha Mishra
Dept. of Physics, ABIT, CDA, Sector-1, Cuttack, India
Available online at: www.isca.in, www.isca.me
Received 5
th
May 2015, revised 1
st
June 2015, accepted 15
th
June 2015
Abstract
The Ultrasonic velocity, density and viscosity have been measured for different ratios of sodium (Na) to potassium (K) about
vitality ratio and about normal body temperature. The ratios are analysed in terms of the thermodynamic parameters derived
from the ultrasonic data.
Keywords: Thermodynamic parameters, ultrasonic velocity, vitality ratio.
Introduction
Ultrasonic method finds extensive application in investigating
various physicochemical parameters involving molecular
interactions in liquid mixtures
1-10
. This technique has also been
used in engineering, agriculture and medicine
11-13
. In
engineering it is used to study the structure of materials.
Ultrasonic pulses can speed up certain chemical reactions and
act as a catalytic agent in wheat germination.
We have applied the same to study the variation in the
thermodynamic parameters when the ratio of certain minerals
like Na to K, Ca to Mg etc are changed. Human body needs
many minerals known as essential minerals. These are further
divided in two major minerals (like Na, K …) and micro
minerals (like Fe, Si,…). The later is required in small amounts.
However the amounts needed are not an indicator of their
importance. It has been seen that mineral ratios are often more
important in studying nutritional deficiencies and excesses than
mineral levels alone. Mineral ratios are indicative of disease
trends. Ratios also predict future metabolic dysfunction or
hidden metabolic dysfunction.
The basic mineral ratios that are important are i. Na; K ii.
Ca:Mg iii. Na:Mg iv. Zn:Cu. Sodium to potassium ratio is
referred to as the life-death ratio. Sodium is normally extra
cellular and potassium is intracellular. An imbalanced sodium
potassium ratio is associated with heart, liver, kidney and
immune deficiency dieses. The Na:K ratio can be studied
through hair analysis or blood serum analysis. Previous analysis
pinpoints the development of metabolic dysfunction before
symptoms manifest, but the latter does it only when the
condition is advanced.
The thermodynamic parameters have been studied for Na:K
ratios obtained from hair analysis at different temperatures
14
. In
this paper we do similar analysis for Na:K ratio obtained from
blood serum analysis at the same temperatures. The ideal Na:K
ratio from hair analysis is 2.5 : 1 and from blood serum analysis
is 28.5 : 1.
Material and Methods
Experimental technique: The aqueous solution of sodium
chloride (NaCl) and potassium chloride (KCl) with different
concentrations in mole fraction were prepared. The alytical
reagent grade and spectroscopic reagent grade chemicals with
minimum assay of 99.9%, obtained from E-Merck Ltd (India)
are used for the solutions.
The density, viscosity, and ultrasonic velocity for all the
aqueous solutions were measured at temperatures 298K, 303 K
308 K, 310 K, 312 K and 323 K at constant frequency of 3
MHz.
Ultrasonic velocity of the mixtures were measured by using an
ultrasonic interferometer (Model M-84, supplied by M/S Mittal
Enterprises, New Delhi), with the accuracy of ±0.1m·s−1. The
densities of the mixture were measured using a 10-ml specific
gravity bottle by relative measurement method with an accuracy
of ±0.01 kg·m−3, and an Oswald viscometer (10 ml) with an
accuracy of ± 0.001 Ns· m−2 was used for the viscosity
measurement. To maintain the constancy of temperature, an
electronically operated digital constant temperature bath (Model
SSI-03 Spl, supplied by M/S Mittal Enterprises, New Delhi),
operating in the temperature range of−10°C to 85°C with an
accuracy of ±0.1°C had been used.
Theory: Following relations were used for calculating different
acoustic and thermodynamical parameters
Adiabatic compressibility:

Research Journal of Chemical Sciences ___________________________________________________________ ISSN 2231-606X
Vol. 5(6), 32-39, June (2015) Res. J. Chem. Sci.
International Science Congress Association 33
Free volume:
Where: ‘K’ is a dimensionless constant independent of
temperature and liquid. Its value is 4.281 x 10
9
.
Internal pressure: … … (N.m
-2
)
Where: ‘b’ stands for the cubic packing factor, which is
assumed to be ‘2’ for all liquids and solutions.
Acoustic impedance (Z): (Kg.m
2
.s
-1
)
Gibb’s free energy (∆G): (k.J.mol
-1
)
Where: ‘K’ is the Boltzmann’s constant and ‘h’ is the Plank’s
constant.
Molar volume (V
m
): …………… (m
3
mol
-1
)
Rao’s constant (R): (m
3
.mol
-1
.(m/s)
1/3
)
Surface tension (S): (N.m
-1
)
Where: the symbols have their usual meanings
Results and Discussion
Experimental values of density, viscosity are presented in table -
1, ultrasonic velocity is given in table-2. Calculated values of
adiabatic compressibility, Gibb’s free energy, internal pressure,
free volume, molar volume, acoustic impedance and surface
tension are reported in table - 3 to table - 9. Variation of some of
these parameter’s with mole fraction of NaCl are shown in
figures-1 to 8.
Sodium ions are largely hydrated and hence are less mobile than
potassium ions hence density increases as sodium potassium
ratios increases. As the temperature increases, the mobility of
ions increases, hence density decreases. Viscosity changes in the
same way as density.
Ultrasonic velocity increases and adiabatic compressibility
decreases as temperature increases. The same nature of change
also occurs when the ratio Na : K increases. This confirms that
in both the cases, the intermolecular force increases.
Table–1
Values of Density (ρ) and Viscosity (η) of mixtures at 293K, 303K, 308k, 310K, 312K and 323K
Mole fraction
Na/K
Density (ρ)
(Kg.m
-3
)
Viscosity (η)
(x10
-3
N.s.m
-2
)
NaCl KCl 293 K 303 K 308K 310 K 312 K 323 K
293
K
303
K 308K
310
K
312
K
323
K
0.0634
0.0022
22:1
1145.
9
1141.9
1138.8
1138.7
1137.9
1134.5
1.28
1.13
1.01
0.89
0.84
0.71
0.0767
0.0022
27:1
1175.8
1171.2
1169.8
1168.7
1167.8
1164.7
1.34
1.20
1.06
1.01
0.95
0.78
0.0793
0.0022
28:1
1179.9
1175.1
1173.5
1171.5
1170.6
1167.4
1.39
1.22
1.08
1.02
0.96
0.81
0.08
06
0.0022
28.5:1
1182.8
1179.1
1178.1
1177.5
1176.6
1173.3
1.41
1.26
1.11
1.04
0.98
0.84
0.0819
0.0022
29:1
1186.2
1184.7
1182.8
1180.8
1179.4
1176.9
1.45
1.27
1.12
1.05
0.98
0.78
0.0947
0.0022
34:1
1198.0
1196.9
1194.8
1192.7
1190.1
1187.5
1.49
1.34
1.1
7
1.01
0.93
0.84
Table–2
Values of Velocity (V) of mixtures at 293K, 303K, 308k, 310K, 312K and 323K
Mole fraction
Na/K
Velocity(V) ms
-
1
NaCl
KCl
293 K
303 K
308K
310 K
312 K
323 K
0.0634
0.0022
22:1
1713.0
1721.5
1725.7
1729.2
1730.7
1737.4
0.0767
0
.0022
27:1
1747.1
1752.1
1754.1
1755.5
1757.3
1764.2
0.0793
0.0022
28:1
1756.7
1762.4
1764.3
1766.9
1768.7
1776.9
0.0806
0.0022
28.5:1
1766.2
1773.8
1775.8
1777.9
1780.5
1786.2
0.0819
0.0022
29:1
1774.2
1776.9
1779.5
1782.0
1783.8
1788.7
0.0947
0.0022
34:1
1789.1
1795.6
1802.5
1814.7
1822.3
1828.5
Table–3
Values of Adiabatic compressibility (β) of mixtures at 293K, 303K, 308k, 310K, 312K and 323K
Mole fraction
Na/K
β = Inv( U
2
. ρ) x 10
-
10
NaCl
KCl
293 K
303 K
308K
310 K
312 K
323 K
0.0634
0.0022
22:1
2.974
2.954
2.948
2.937
2.934
2.920
0.0767
0.0022
27:1
2.786
2.781
2.778
2.776
2.773
2.758
0.0793
0.0022
28:1
2.746
2.74
2.737
2.734
2.731
2.713
0.0806
0.0022
28.5:1
2.710
2.695
2.691
2.687
2.681
2.671
0.0819
0.0022
29:1
2.678
2.673
2.670
2.667
2.
665
2.656
0.0947
0.0022
34:1
1.49
1.34
1.17
1.01
0.93
0.84

Research Journal of Chemical Sciences ___________________________________________________________ ISSN 2231-606X
Vol. 5(6), 32-39, June (2015) Res. J. Chem. Sci.
International Science Congress Association 34
Figure-1
Variation of Ultrasonic velocity with mole fraction of NaCl
Figure-2
Variation of Adiabatic compressibility with mole fraction of NaCl
Table–4
Values of Gibb’s free energy ( ∆G ) of mixtures at 293K, 303K, 308k, 310K, 312K and 323K
Mole fraction Na/K
Gibb’s free energy ( ∆G )
( x 10
- 20
k.J.mol
-1
)
NaCl KCl 293 K 303 K 308K 310 K 312 K 323 K
0.0634 0.0022 22:1 0.4573 0.4320 0.3958 0.3489 0.3272 0.2772
0.0767 0.0022 27:1 0.4509 0.4306 0.3932 0.3769 0.3554 0.2936
0.0793 0.0022 28:1 0.4581 0.4335 0.3953 0.3750 0.3517 0.3033
0.0806 0.0022 28.5:1 0.4601 0.4378 0.3972 0.3770 0.3525 0.3113
0.0819 0.0022 29:1 0.4662 0.4395 0.3988 0.3779 0.3540 0.2743
0.0947 0.0022 34:1 0.4671 0.4498 0.4032 0.3399 0.3072 0.2863

Research Journal of Chemical Sciences ___________________________________________________________ ISSN 2231-606X
Vol. 5(6), 32-39, June (2015) Res. J. Chem. Sci.
International Science Congress Association 35
Increase in Gibb’s free energy (∆G) suggests closer approach of
molecules in the mixture and vice versa
15
. ‘∆G’ in this case
decreases as temperature increases for a fixed Na : K ratio.
Temperature remaining constant, ‘∆G’ increases slowly with
increasing Na : K ratio. However at temperatures 310 K and 312
K, ‘∆G’ becomes minimum for the Na : K ratio equal to 28:1.
Minimum value of ‘∆G’ indicates good flow of the mixture.
Figure-3
Variation of Gibb’s free energy with mole fraction of NaCl
Table–5
Values of Internal pressure ( π
i
) of mixtures at 293K, 303K, 308k, 310K, 312K and 323K
Mole fraction Na/K Internal pressure ( π
i
) (x 10
6
N.m
-
2
)
NaCl KCl 293 K 303 K 308K 310 K 312 K 323 K
0.0634 0.0022 22:1 2780.5 2688.2 2570.9 2436.3 2376.6 2253.1
0.0767 0.0022 27:1 2786.8 2706.9 2587.9 2537.9 2475.4 2314.7
0.0793 0.0022 28:1 2814.4 2719.1 2596.4 2532.9 2465.4 2341.0
0.0806 0.0022 28.5:1 2828.9 2744.9 2615.3 2554.8 2483.7 2375.6
0.0819 0.0022 29:1 2858.1 2760.4 2627.3 2561.5 2490.0 2282.4
0.0947 0.0022 34:1 2827.5 2765.4 2616.4 2433.5 2343.0 2298.7
Figure-4
Variation of Internal pressure with mole fraction of NaCl

Research Journal of Chemical Sciences ___________________________________________________________ ISSN 2231-606X
Vol. 5(6), 32-39, June (2015) Res. J. Chem. Sci.
International Science Congress Association 36
Na: K ratio remaining constant, internal pressure (π
i
) decreases
as temperature increases. At any particular temperature, internal
pressure increases slowly as the Na : K ratio increases. However
‘π
i
’ becomes minimum for the ratio 28:1 at temperatures 310 K
and 312 K. Minimum internal pressure indicates minimum
cohesive force which is also observed while studying ‘∆G’.
Free volume is the average volume in which the center of a
molecule can move due to the repulsion of the surrounding
molecules
16
. For a particular ratio of Na : K , free volume
increases as temperature increases. This may be due to the fact
that, effective free volume changes due to the transmission of
collision effect through the molecules. At a fixed temperature,
free volume decreases as the ratio of Na : K increases. However
at temperatures 310 K and 312 K free volume becomes
maximum for the ratio 28:1. Free volume is maximum when
internal pressure is minimum.
Table–6
Values of Free volume (V
f
) of mixtures at 293K, 303K, 308k, 310K, 312K and 323K
Mole fraction Na/K Free volume (V
f
) (10
-
7
m
3
.mol
-
1
)
NaCl KCl 293 K 303 K 308K 310 K 312 K 323 K
0.0634 0.0022 22:1 0.1648 0.2003 0.2392 0.2865 0.3143 0.4067
0.0767 0.0022 27:1 0.1638 0.1961 0.2351 0.2537 0.2783 0.3757
0.0793 0.0022 28:1 0.1585 0.1928 0.2320 0.2539 0.2803 0.3612
0.0806 0.0022 28.5:1 0.1561 0.1878 0.2277 0.2487 0.2756 0.3475
0.0819 0.0022 29:1 0.1515 0.1855 0.2252 0.2470 0.2734 0.3923
0.0947 0.0022 34:1 0.1522 0.1796 0.2219 0.2803 0.3187 0.3728
Figure-5
Variation of Free volume with mole fraction of NaCl
Table–7
Values of Molar volume (V
m
) of mixtures at 293K, 303K, 308k, 310K, 312K and 323K
Mole fraction Na/K
Molar volume (V
m
)
(m
3
·mol
−1
)
NaCl KCl 293 K 303 K 308K 310 K 312 K 323 K
0.0634 0.0022 22:1 0.0181 0.0181 0.0182 0.0182 0.0182 0.0183
0.0767 0.0022 27:1 0.0181 0.0181 0.0182 0.0182 0.0182 0.0182
0.0793 0.0022 28:1 0.0181 0.0182 0.0182 0.0182 0.0182 0.0183
0.0806 0.0022 28.5:1 0.0181 0.0181 0.0182 0.0182 0.0182 0.0182
0.0819 0.0022 29:1 0.0181 0.0181 0.0181 0.0182 0.0182 0.0182
0.0947 0.0022 34:1 0.0183 0.0184 0.0184 0.0184 0.0185 0.0185

Research Journal of Chemical Sciences ___________________________________________________________ ISSN 2231-606X
Vol. 5(6), 32-39, June (2015) Res. J. Chem. Sci.
International Science Congress Association 37
Molar volume should increases with increase in temperature as
thermal energy facilitates increases in molecular separation. The
change is however slow as the effect due to thermal energy is
restricted by strong electrostatic force between molecules.
Molar volume appears to be practically constant for the Na: K
ratios 28:1, 28.5:1 and 29:1 at temperatures 308 K, 310 K,
312K, indicating no change in intermolecular interaction. This is
also confirmed by the constancy of the Rao;s constant at the
same temperatures and for the same ratios.
Figure-6
Variation of Molar volume with mole fraction of NaCl
Table–8
Values of Acoustic impedance (Z) of mixtures at 293K, 303K, 308k, 310K, 312K and 323K
Mole fraction Na/K Acoustic impedance (Z)
NaCl KCl 293 K 303 K 308K 310 K 312 K 323 K
0.0634 0.0022 22:1 1.963 1.966 1.965 1.969 1.970 1.971
0.0767 0.0022 27:1 2.054 2.052 2.052 2.052 2.052 2.055
0.0793 0.0022 28:1 2.073 2.071 2.070 2.070 2.070 2.074
0.0806 0.0022 28.5:1 2.089 2.091 2.092 2.093 2.095 2.096
0.0819 0.0022 29:1 2.105 2.105 2.105 2.104 2.104 2.105
0.0947 0.0022 34:1 2.143 2.149 2.154 2.164 2.169 2.171
Figure-7
Variation of Acoustic impedance with mole fraction of NaCl

Research Journal of Chemical Sciences ___________________________________________________________ ISSN 2231-606X
Vol. 5(6), 32-39, June (2015) Res. J. Chem. Sci.
International Science Congress Association 38
Acoustic impedance remains practically constant, as
temperature increases for a particular ratio of Na :K, but
increases as Na : K ratio increases when temperature remains
constant. The former is true as cohesive force remains
practically constant for a fixed Na : K ratio. Temperature
remaining constant when Na : K ratio increases cohesion force
increases, hence ‘Z’ increases.
With increase in temperature, surface tension increases very
slowly. This is also confirmed by the fact that the ultrasonic
velocity increases slowly with temperature. Surface tension also
increases with increasing Na : K ratio. However it practically
remains constant over the ratio range 27:1 to 29:1 which is near
the vitality ratio.
Conclusion
Results indicate that, ultrasonic velocity and other derived
parameters depend on the Na : K ratio as well as temperature.
The parameters do not show much variation about vitality ratio
and near body temperature. For very small and large ratios, the
change in the parameters is apparent indicating the deviation
from the vitality ratio or healthy ratio.
References
1. Shende Amardeep, Tabhane Priyanka, Chimankar OP
and Tabhane Vilas A, Prediction of Internal Pressure and
Surface Tension and their Correlation with Molecular
Interaction in Aqueous Amino Acids, Int. J. of Sci. and
Res., ISU, (2015)
2. Praharaj M.K., Satapathy A, Mishra P.R. and Mishra S.,
Ultrasonic studies of ternary liquid mixtures of N-N-
dimethylformamide, nitrobenzene and cyclohexane at
diff. frequencies at 318 K, J. of Theo. and Appl. Phy.,
7(23), 1-6 (2013)
3. Pradhan S.K., Dash S.K., Moharana L. and Swain B.B.,
Molecular interaction parameters of binary mixtures of
diethyl ether and apolar solvents using ultrasonic probe,
Indian Journal of Pure and Applied Physics, (48), 326-
333 (2010)
4. Praharaj M.K., Satapathy A, Mishra P.R. and Mishra S,
Thermodynamic Parameters and Their Excess Values for
Binary Mixtures of Cyclohexane Plus Benzene and
Substituted Benzenes at Different Ultrasonic
Frequencies, Int. J. of Eng. Res. and Tech., 3(11), 1060-
1065 (2014)
Table–9
Values of Surface tension (S) of mixtures at 293K, 303K, 308k, 310K, 312K and 323K
Mole fraction Na/K Surface tension (N.m
-
1
)
NaCl KCl 293 K 303 K 308K 310 K 312 K 323 K
0.0634 0.0022 22:1 51183 51385 51436 51584 51619 51761
0.0767 0.0022 27:1 54094 54115 54143 54157 54198 54373
0.0793 0.0022 28:1 54733 54772 54790 54819 54858 55088
0.0806 0.0022 28.5:1 55309 55494 55545 55612 55691 55803
0.0819 0.0022 29:1 55846 55906 55937 55962 55981 56093
0.0947 0.0022 34:1 57116 57377 57608 58089 58325 58493
Figure-8
Variation of Surface tension with mole fraction of NaCl

Research Journal of Chemical Sciences ___________________________________________________________ ISSN 2231-606X
Vol. 5(6), 32-39, June (2015) Res. J. Chem. Sci.
International Science Congress Association 39
5. Rajagopal K. and Chenthilnath S., Excess
thermodynamic studies of binary mixtures of 2-methyl 2-
propanol with ketones, Ind. J. of Pure and App. Phy.,
(48), 326-333 (2010)
6. Praharaj M.K., Satapathy A, Mishra P.R. and Mishra S,
Ultrasonic analysis of intermolecular interaction in the
mixtures of benzene with N, N-dimethylformamide and
cyclohexane at different temperatures, J. of Chem. and
Phar. Res., 5(1), 49-56 (2013)
7. Praharaj Manoj Kumar and Mishra Sarmistha,
Comparative Study of Molecular Interaction in Ternary
Liquid Mixtures of Polar and Non-PolarSolvents by
Ultrasonic Velocity Measurements, Int. J. of Sc. and
Res., 3(11), 642-646, (2014)
8. Nath G, Acharaya S and Paikaray, Ultrasonic study of
binary mixtures of acetone with Mono-Substituted
Benzene at Different Frequencies, J. Acous. Soc. of India,
34(4), 135-139 (2007)
9. Praharaj Manoj Kumar and Mishra Sarmistha, Study of
acoustic and thermodynamic parameters for binary
mixture containing cyclohexane and the substituted
benzenes at different temperatures, J. of Chem., Bio. and
Phy. Sc., Section C, 5(1), 686-699 (2014)
10. Dash Ashok Kumar1 and Paikaray Rita, Ultrasonic Study
on Ternary Mixture of Dimethyl Acetamide (DMAC) in
Diethyl ether and Acetone, Res. J. Physical Sci., 1(3), 12-
20 (2013)
11. Praharaj M.K., Satapathy A, Mishra P.R. and Mishra S,
Study of Acoustical and Thermodynamic Properties of
Aqueous Solution of NaCl at different Concentrations
and Temperatures through Ultrasonic Technique, Arch.
of Appl. Sc. Res., 4(2), 837-845 (2012)
12. Praharaj M.K., Satapathy A, Mishra P.R. and Mishra S,
Study of Acoustical and Thermodynamic Properties of
Aqueous Solution of NaCl at different Concentrations
and Frequencies through Ultrasonic Technique, Int. J. of
Res. in Pure and App. Phy., 2(1), 15-21 (2012)
13. Thirumaran S. and Rajeswari M., Acoustical studies on
binary liquid mixtures of some aromatic
hydrocarbonswith dimethylsulphooxide (DMSO) at
303.15K, Sch. Res. Lib., 2(2), 149-156 (2011)
14. Praharaj Manoj Kumar and Mishra Sarmistha, Study of
Acoustic and Thermodynamic Parameters for Different
Ratios of Aqueous Sodium Chloride and Potassium
Chloride Solution At and About the Normal Human
Body Temperature, Int. J. of Sc. and Res., ISU, 58-65
(2015)
15. Praharaj M.K., Satapathy A, Mishra P.R. and Mishra S,
Study of thermodynamic and transport properties of
ternary liquid mixture at different frequencies, Journal of
Chemical and Pharmaceutical Research, 4(4), 1910-
1920 (2012)
16. Praharaj M.K., Satapathy A, Mishra P.R. and Mishra S,
study of molecular interaction in mixture of n,n-
dimethylformamide, cyclohexane and pyridine at
different frequencies, Chemical Science Transactions,
2(4), 1395-1401 (2013)