Effect of temperature on compressibility properties of 0.1, 0.5 and 1.0 molal solutions of alkali metal nitrates. Part 2. Aqueous solutions of lithium nitrate, sodium nitrate and potassium nitrate in the 278.15 K to 353.15 K temperature range

Accepted Manuscript Effect of temperature on compressibility properties of 0.1, 0.5 and 1.0 molal solutions of alkali metal nitrates. Part 2. Aqueous solutions of lithium nitrate, sodium nitrate and potassium nitrate in the 278.15K to 353.15K temperature range

Alexander Apelblat PII: DOI: Reference:

S0167-7322(17)32809-X doi: 10.1016/j.molliq.2017.07.111 MOLLIQ 7690

To appear in:

Journal of Molecular Liquids

Received date: Revised date: Accepted date:

26 June 2017 20 July 2017 25 July 2017

Please cite this article as: Alexander Apelblat , Effect of temperature on compressibility properties of 0.1, 0.5 and 1.0 molal solutions of alkali metal nitrates. Part 2. Aqueous solutions of lithium nitrate, sodium nitrate and potassium nitrate in the 278.15K to 353.15K temperature range, Journal of Molecular Liquids (2017), doi: 10.1016/ j.molliq.2017.07.111

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ACCEPTED MANUSCRIPT 1

Effect of Temperature on Compressibility Properties of 0.1, 0.5 and 1.0 Molal Solutions of Alkali Metal Nitrates. Part 2. Aqueous Solutions of Lithium Nitrate, Sodium Nitrate and Potassium Nitrate

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in the 278.15 K to 353.15 K Temperature Range. Alexander Apelblat*

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Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel

Abstract

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Sound velocities in aqueous solutions of LiNO3, NaNO3 and KNO3 were measured at 1 K intervals from T = (278.15 to 353.15) K, in the 0.1 mol.kg-1 0.5 mol.kg-1 and 1.0 mol.kg-1 solutions. Determined sound velocities and densities served to determine the isentropic isothermal compressibilities, the apparent molar compressibilities, the apparent molar volumes, the isochoric thermal pressure coefficients, cubic expansion coefficients, changes of heat capacities with volume and with pressure, and the hydration numbers. In addition were evaluated the ultrasonic relaxation times and corresponding thermodynamic functions of the activation of the viscous process. Determined parameters are qualitatively correlated with changes in the structure of water when alkali metal nitrates are dissolved in it. Keywords: Alkali metal nitrates. Sound velocities. Densities. Isothermal and isentropic

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compressibilities. The apparent molar compressibilities and the apparent molar volumes. Isochoric thermal pressure coefficients. Cubic expansion coefficients. Changes of in heat

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capacities with volume and pressure. Thermodynamic functions of the activation of the

viscous process. Structure of aqueous solutions of alkali metal nitrates.

*Corresponding author, E-mail: [email protected]

ACCEPTED MANUSCRIPT 2 1. Introduction Changes in the structure of water caused by dissolved inorganic salts wetre extensively investigated over a long period of time by determining compressibility properties of electrolyte solutions. Measurements of sound velocities and densities permitted to evaluate a number of important parameters such as compressibility coefficients, the apparent molar compressibilities and hydration numbers of

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electrolytes. As expected, halides of alkali metals received highest interest in the literature being major components of natural and synthetically prepared aqueous solutions. On contrary, compressibility properties of alkali metal nitrate solutions is

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considerably less known in spite that sodium nitrate and potassium nitrate are

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produced on large industrial scale. They are used as various fertilizers, solid rocket propellants, food additives and preservatives, heat storage materials, additives to

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toothpastes, and constituents of many other chemical products. Recently, a number of potential applications was found also for lithium nitrate as oxidizing agent in productions of fireworks, as component of store heat and building materials.

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Starting from 1943, there is only few investigations where sound velocities in aqueous solutions of alkali metal nitrates are reported [1-15]. Usually, measurements

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were performed as a function of concentration at one temperature, but there are also more detailed investigations like that of Mikhailov with coworkers [2,3].

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Unfortunately, part of results is given only in graphical form. Rather fragmentary physicochemical properties of solutions (densities, viscosities and heat capacities) of lithium, sodium and potassium nitrates are dispersed between a number of

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investigations [16-39] and they are summarized in [40-32]. Determined in the literature sound velocities u(m;T) served to evaluate isothermal

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isentropic

compressibilities

S(T,m)

and

the

apparent

molar

compressibilities (T;m), but not other thermodynamic quantities, because as pointed above, the experiments were performed only at few temperatures with large 5-10 K gaps between them. And, this prevents to perform numerical differentiations of experimental data with regard to temperature T at constant molality m. Similarly as in Part 1, in which are discussed aqueous solutions with alkali metal halides, also in this investigation densities (T;m) and sound velocities u(m;T) were measured at 1 K intervals. Measurements were performed in the temperature range from 278.15 K to 353.15 K, and at fixed 0.1, 0.5 and 1.0 mol.kg-1

ACCEPTED MANUSCRIPT 3 concentrations. The experimental results expressed as polynomials of temperature, permited to evaluate beside S(T,m) and (T;m) values, a number of compressibility properties such as the isothermal compressibilities T(T,m), the isochoric thermal pressure coefficients (∂P/∂T)V,m, and changes of the heat capacities CV with volume (∂CV/∂V)T,m. As a by-product, the ultrasonic (viscous) relaxation times (T;m) and the corresponding thermodynamic functions of activation of the viscous process

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G*(T;m), H*(T;m) and S*(T;m) were also determined. From the knowledge of compressibility coefficients, it was possible by applying the Passynski method [43], to

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estimate values of hydration numbers h(T;m) as a function of temperature and concentration. Using densities (T;m), volumetric properties of solutions such as the

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apparent molar volumes V2,(T;m), the cubic expansion coefficients (T;m), and changes of heat capacities CP with pressure (∂CP/∂P)T,m were evaluated. When it is

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possible, the reported here volumetric and compressibility properties of alkali metal nitrate solutions are compared with the literature results. The changes in heat

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capacities with regard to pressure and volume are related to second derivatives with regard to temperature, .(∂2V/∂T2)P,m and (∂2P/∂T2)V,m. Behaviour of these derivatives is discussed in a some detail, because they qualitatively correlate changes in the

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structure of water caused by dissolved alkali metal nitrates. These changes are

2. Experimental

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compared with those produced by alkali metal halides.

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ACS reagents LiNO3, NaNO3 and KNO3 (mass fraction ≥ 0.99) all from Sigma-Aldrich, were used without further purification. Solutions were prepared by

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mass by dissolving alkali metal nitrates in double distilled water. Essentially, experimental procedure in the case of alkali metal nitrates was the same as reported in Part 1 for alkali metal halides. Ultrasound measurements were performed from 278 K to about 358 K, using the velocimeter acquired from Optel Company. (Wroclaw, Poland). Parallel determinations were carried out by using a Sing-Around Meter (SAM) constructed in the University of Silesia (Poland). SAM apparatus permitted measurements in the temperature range from 278 K to 323 K, but it served only for control purposes. The sample cells with prepared solutions were immersed in a thermostat (± 0.05 K) to reach thermal equilibrium and temperatures were changed in 1 K intervals.

ACCEPTED MANUSCRIPT 4 The ultrasonic velocimeters were frequently calibrated with water by fixing the value of u1(T) = 1496.73 ms-1 at T = 298.15 K and by determining deviations at other temperatures from the Marczak equation [44]

u1(T ) / m  s-1  1.402385 103  5.038813100  5.799136 102 2  3.287156 104 3 1.398845106 4  2.78786 109 5   T / K  273.15

(1)

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This equation is based on a critical analysis of known in the literature sound velocities in pure water. Precision of our measurements was established by determination of differences between measured velocities of sound in pure water and those derived

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from the Marczak equation, u1(T). Over studied temperature intervals, the mean

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value of deviation from the above equation was for the Optel instrument about ± 0.2 ms-1 and for the SAM apparatus about ± 0.4 ms-1. A more detailed discussion about

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accuracy of determined quantities is given in Part 1.

Simultaneously with measurements of sound velocities, also densities (T;m)

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of degassed solutions alkali metal nitrates solutions were determined at 1 K temperature intervals. They were measured by using a Metler-Toledo DA 310 M densimeter. The estimated thermal control and stability was better than ± 0.01 K and

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the over-all uncertainty of our density measurements is about ± 0.00001 g.cm-3.

3. Results and Discussion

3.1 Thermodynamic quantities derived from measured sound velocities and densities.

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Using experimental densities (T;m = const.) and velocities of sound u(T; m = const.) at fixed concentration m, the isentropic (adiabatic) compressibility coefficient

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can be evaluated from the Newton-Laplace equation

1 V S (T; m)    

V  P T ,m



1  (T; m)  1    2 (T; m)  P T ,m u(T; m) (T; m)

(2)

For mathematical convenience (to derive the first and second derivatives with respect to temperature T), all quantities under consideration were smoothed by fitting them to polynomials in the form

Y ( )/[unit]  A  B  C 2  D 3  E 4  F 5   T / K  273.15

(3)

ACCEPTED MANUSCRIPT 5 where the dimensionless coefficients A, B, C, D, E and F were evaluated by an unweighted least-squares method. Deviations between experimental and calculated quantities were randomly distributed within the estimated accuracy of our experiments. Using polynomials of density, the cubic expansion coefficients, (T;m),

  ln (T; m)  1 V )P,m     V T T  P,m

 (T; m)  (

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(isobaric thermal expansibilities) were evaluated from

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and if the isobaric heat capacities of solution per unit volume exist in the literature, the isothermal compressibility coefficient can be determined

V  P T ,m

 S (T ; m) 

T 2 (T ; m) CP (T ; m)

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1 V T (T ; m)    

(5)

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where CP(T;m) = cP(T;m(T;m) where cP(T;m) is the isobaric specific heat capacity. From knowledge of (T;m) and T(T, m) values, it is possible to calculate the

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isochoric thermal pressure coefficients

P   (T; m)    T V ,m T (T; m)

V (T; m)  

(6)

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From measured densities (T;m), the apparent molar volumes are

V (T; m) VH2O (T ) M2 1000  1 1       m (T, m) m  (T; m) H2O (T ) 

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V2, (T; m) 

(7)

where M2 is the molar mass of dissolved in water alkali metal nitrate and densities of

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pure water H2O (T ) , were calculated from [45]

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H2O (T )/ g  cm-3  0.9999727  4.035198105  7.090436106 2 

3.554779 108 3 1.00270981010 4   T / K  273.15

(8)

The apparent molar compressibilities are derived by differentiation of Eq. (7) with regard to pressure P

 V (T; m)  S (T; m)M2 1000  S (T; m) S,H2O (T )  K2, (T; m)   2,       P (T; m) m  (T; m) H2O (T )   T ,m

(9)

Applying the Maxwell relation to differentials of the internal energy and enthalpy the volumetric and thermal properties of solutions are interrelated in the following form

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 2V   CP    T  2    f (T; m)  P   T  T   2 P   CV     T  2  T  V  V   T  T  T 

   g(T ; m) 

(10)

These functions, as will be seen later, give an indication about changes in the structure of water caused by dissolved solute.

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Basing on isothermal compressibility coefficients, the hydration numbers of electrolytes h(T;m) according to Passynski are [43]

1000  T (T; m)  H2O (T )  1   mMH2O  T ,H2O (T )  (T; m) 

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h(T; m) 

(11)

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This expression is based on the assumptions that the ions and the primary hydration shell are incompressible while the water in the secondary hydration shell has the same

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compressibility as the bulk water and finally that solutions are sufficiently dilute to ignore ion-ion interactions. The comparison of hydration numbers derived from

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compressibility properties with those obtained by other methods is dubious since they depend on chosen model and their definition.

If viscosities (T;m) of investigated solutions are available in the literature,

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then by using the isentropic compressibility coefficients, the ultrasonic (viscous)

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relaxation times  (T; m)  S (T; m) (T; m) and the thermodynamic functions of activation of the viscous process can be determined.

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  h G (T ; m)  RT ln    kT (T ; m)  G (T ; m)  S (T ; m)   T   G (T ; m)  H (T ; m)  T S (T; m)

(12)

where h and k denote the Planck and the Boltzmann constants.. There is a number of empirical relationships to correlate sound velocities and isentropic compressibility coefficients [46-50]

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R1(m)  M12u1/3 (T; m)/ (T; m) 7 R2 (m)  1/ S (T ; m) (T ; m) M12 R3 (m)  1/ 7 S (T; m)(T; m) M12  x1M1+ x2M2

(13)

These expressions are useful for electrolyte solutions, because they are nearly independent of temperature and linearly depend on concentration.

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Detailed error analysis of experimental and calculated quantities is given in Part 1. For lowest concentration 0.1 mol.kg-1 (highest errors), the expected error in

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S(T;m) are about 0.1 percent, but in case of isobaric thermal expansibilities and

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isothermal compressibility coefficients the uncertainty limits increase to few percent. Errors in the apparent molar volumes are about 3 percent and in the apparent molar

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compressibilities are large, 10 percent, but they decreases rapidly with increasing concentration m. The uncertainty associated with hydration numbers is about 5

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percent.

3.2 Aqueous solutions of lithium nitrate.

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Investigation of compressibilities in lithium nitrate solutions started in 1943 by Corey[1] who measured sound velocity in a single solution m = 0.305 mol.kg-1 at

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25 0C. Rao and Rao [5] presented graphically sound velocities at 30 0C, in the 0 - 3.0 mol.kg-1 range, and they estimated that the hydration number of LiNO3 is about h = 2.2. In similar concentration range, also in graphical form, but at 27

0

C,

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Subrahmanyam [6] presented isentropic compressibility coefficients of alkali metal nitrates and concluded that the lowering compressibility will be in the following order

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S(LiNO3) > S(NaNO3) > S (KNO3). He estimated that the hydration number of lithium nitrate is h = 4.3. Sivakumar and Subrahmanyam [10] performed measurements at 25 0C, but in dilute solutions of LiNO3, m < 0.1 mol.kg-1 and have difficulty to establish whether LiNO3 acts as the structure-promoting or structurebreaking electrolyte. Densities and viscosities of lithium nitrate solutions, from 30 0C to 50 0C, and in the 0.01 - 1.0 mol.kg-1 concentration range were determined by Roy et al. [14], but sound velocities were measured only at 30 0C. From determination of volumetric properties they deduced that hydration of cations in nitrate solutions follow the order Li+ > K+ > Na+ and that alkali metal nitrates are structure-breaking

ACCEPTED MANUSCRIPT 8 solutes. Extensive determinations of sound velocities of lithium salts in water and in some organic solvents were performed from 30 0C to 80 0C, in the 0.2 - 1.0 mol.kg-1 concentration range by Ramabrahmam and Suryanarayan [8] They observed that isentropic compressibility decreases with increasing concentration and for a given concentration as a function of temperature it has a minimum. A more detailed study of lithium nitrate solutions, from 0.0181 mol.kg-1 to 21.82 mol.kg-1 and in the 0 0C - 50 C temperature range was performed by Rohman and Mahiuddin [13]. Basing on data

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in concentrated solutions of LiNO3, and using the Onori approach [51-53], they reported that the hydration number is h = 15. Also from measurements of sound

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velocities in concentrated solutions, from 15 0C to 25 0C, Chekunova and Afanasiev

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[15] postulated much larger hydration numbers in the range h = 17 - 25. Such large values are coming from the Afanasiev and coworkers theory of hydration of

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electrolytes [54-57], but usually reported in the literature hydration numbers of electrolytes are considerably lower [43, 58-65].

Determined sound velocities in lithium nitrate solutions u(T:m), the isentropic

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compressibility coefficients S(T;m) and the changes in heat capacities with volume (∂CV/∂V)T,m are presented in Table 1. Used physical properties of LiNO3 solutions and

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evaluated thermodynamic quantities are reported in Supplementary Content (Tables S1 and S2). Reported in the literature sound velocities were compared with those

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determined here (Table1), by plotting changes in sound velocity, u(T:m) = [u(T:m) u1(T)]. As can be observed in Figure S1, with an exception of the Rohman and

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Mahiuddin results [13], the agreement is quite satisfactory. Considering temperature dependence of sound velocities u(T:m) in the case of lithium salts, they can be arranged in the following series u(Li2SO4) > u(LiBr) > u(LiCl) > u(LiNO3) > u(H2O)

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> u(LiI) [3,66,67]. As expected, the isentropic compressibility coefficients S(T;m) and the isothermal compressibility coefficients T(T;m) of lithium nitrate solutions are lower than those of pure water (Figure 1). For temperatures lower than about 40 0C the absolute value of the apparent molar compressibility (T;m) decreases with concentration m, and about this temperature the reverse order for (T;m) is observed. The isochoric thermal pressure coefficients of pure water V(T) are smaller than those of lithium nitrate solutions. They increase with concentration m, and temperature T , and the curvature of curves changes from concave downward to concave upward. Values of the apparent molar volumes of lithium nitrate solutions

ACCEPTED MANUSCRIPT 9 V2,(T;m) are close to those of sodium nitrate solutions. There is an agreement between reported here and existed in the literature densities [19-21,23,28,32,37-42], with one exception of the Roy et al. [14], their values are clearly incorrect. An indication about water changes in lithium nitrate solutions can be predicted by an examination of the following functions for finite but low value of m [68]

f (T ; m)   f (T ; m)  f (T ;0) g(T ; m)   g(T ; m)  g(T ;0)

(14)

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 2V  f (T ; m)  T  2   T   2 P  g(T ; m)  T  2   T 

The less ordered structure of water is expected if f(T;m) < 0 or if g(T;m) < 0 and

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the more ordered structure if f(T;m) > 0 or if g(T;m) > 0. As can be observed in Figure 3, at lowest concentration 0.1 mol.kg-1, both functions for less than 60 0C are

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nearly zero, and after this they are positive. At room temperatures, this fact is not surprising by considering a some kind of compensation between existed in aqueous solution ions. Since Li+ cation is structure-making ion and NO3- anion is structure-

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breaking ion [69], the over-all effect on water structure is probably small. At high

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temperatures, similarly as for alkali metal halides, lithium nitrate produces more structured water. With increasing concentration, these effects in both temperature regions are stronger (Figure 2).

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Basing on the Passynski approach [43], determined hydration numbers of alkali metal nitrates decrease with increasing temperature and concentration, but these

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changes are relatively small (Figure 3). As can be observed, hydration numbers can be arranged in the following order h(KNO3) > h(NaNO3) > h(LiNO3). For lithium nitrate, known in the literature h(LiNO3) are systematically lower than values reported here (see for example Tamura and Sasaki [61] h(LiNO3) = 3.0 - 3.4). At 25 0C, the hydration numbers of chlorides have similar values as nitrates, but this is not true for lithium salts (h(LiCl) = 4.7, h(LiNO3) = 6.0 ; h(NaCl) = 7.6, h(NaNO3) = 7.5 ; h(KCl) = 7.5, h(KNO3) = 7.8). Differences between nitrates and halides are more evident in the case of bromides and especially with iodides. In Eyring’s theory of viscous flow, the presence of the ions will affect the movement of solvent molecules and advance of themselves. In terms of the ultrasonic

ACCEPTED MANUSCRIPT 10 (viscous) relaxation times (T;m), it is observed that they decrease strongly with increasing temperature, but effect of concentration is rather small. Concentration dependence is better expressed by differences in the ultrasonic (viscous) relaxation times (T;m) as compared to that of pure water (T;m) = [(T;0) - (T;m)]. In Figure 4 are plotted (T;m) values of lithium nitrate solutions and contrary to other investigated salts they are negative and their negative values increase with increase of

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concentration m. Calculated from ultrasonic (viscous) relaxation times (T;m) the corresponding thermodynamic functions (Eqs 12 ) are similar to those of halides. The

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Gibbs free energy of activation G*(T;m) have small positive values and H*(T;m) > TS*(T;m) >> G*(T;m) > 0 (Figure 5). The enthalpy and entropy terms as a function

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of T change curvatures from concave downward to concave upward having minima near 60 0C and their concentration dependence is small. investigated

temperature

range,

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Over

R3(m)

function

reproduces

compressibility parameters in lithium nitrate solutions with the standard deviation of

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about ± 5.5 10-6 Pa1/7.m3.mol-1 (with less than 1.4 percent error)

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 x M +x M  R3 (m) / Pa1/7  m3  mol-1  106  1/ 71 1 2 2  S (T ; m)(T ; m)  R3 (LiNO3 ,m)  395.72  9.680 m*

(15)

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m*  m /1 mol  kg-1

3.3 Aqueous solutions of sodium nitrate.

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Compressibility and volumetric properties of sodium nitrate solutions have been investigated more times than other nitrates. Considering sound velocities, first

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measurements were performed in 1957 by Mikhailov et al. [3] in a wide range of temperatures and concentrations, from 0 to 90 0C, and from 0.1 to 10.0 mol.kg-1. Rohman and Mahiuddin [13] studied sodium nitrate solutions in a similar concentration range, but in a shorter temperature interval, from 5 to 50 0C. All other investigation were performed at one temperature only. At 25 0C, in different concentration ranges, sound velocities were reported by Millero et al. [9], Sivakumar and Subrahmanyam [10] and Maret and Yeager [70]. Two investigations are known at 30 0C, that of Subrahmanyam and Bhimasenachar [4] in moderately concentrated solutions of sodium nitrate, and that of Roy et al. [14] in dilute solutions. Following the Passynski procedure [43], Maret and Yeager [70] reported that hydration number

ACCEPTED MANUSCRIPT 11 of NaNO3 is h = 5.0, when Allam and Lee [7] gave a higher value of h = 6.9. However, using Onori approach [51-53], Rohman and Mahiuddin [13] obtained for concentrated solution of sodium nitrate hydration numbers about twenty. Measured sound velocities in sodium nitrate solutions u(T:m), the isentropic compressibility coefficients S(T;m) and the changes in heat capacities with volume (∂CV/∂V)T,m are presented in Table 2. Used physical properties of NaNO3 solutions

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and evaluated thermodynamic quantities are reported in Supplementary Content (Tables S3 and S4). Scattering of sound velocities by coming from different

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investigations and expressed by u(T:m) = [u(T:m) - u1(T)] values is acceptable and their consistency is confirmed by an excellent agreement between the Optel and SAM

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results (Figure S2). Sound velocities values of alkali metal chlorides are always larger than corresponding nitrates u(MeCl) > u(MeNO3) > u(H2O) and they can be arranged

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in the following series u(NaCl) > u(KCl) ≈ u(LiCl) > u(NaNO3) ≈ u(LiNO3) > u(KNO3) > u(H2O). The isentropic compressibility coefficients S(T;m) and the

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isothermal compressibility coefficients T(T;m) of sodium nitrate solutions are lowest between alkali metal nitrates (H2O) > (LiNO3) > (KNO3) > (NaNO3) (Figure 1). Absolute values of the apparent molar compressibilities (T;m) decrease

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with concentration m and temperature T (Figure S3). Values of the apparent molar

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volumes of sodium nitrate solutions V2,(T;m) are in an agreement with the literature values [23,29,35,40], but reported here V2,(T;m) of 0.1 mol.kg-1 solutions are systematically lower, by about 2.0 cm3.mol-1. The isochoric thermal pressure

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coefficients V(T;m) of sodium nitrate solutions are larger than those of pure water and they increase with temperature and concentration.

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An examination of f(T;m) and g(T;m) functions in sodium nitrate solutions (Figure 6 and 7) clearly indicates that over large temperature range, NaNO3 behaves as structure-breaking solute and this effect increases with increase of concentration. This is not surprising considering that according to the Marcus classification of ions at room temperatures [69] sodium cation is borderline ion, and nitrate anion is strong structure-breaking ion. However, at high temperatures than 50 0C, an enhancement of water structure can not be entirely be ignored. From knowledge of isentropic compressibility coefficients S(T;m) and viscosities of solutions, it is possible to evaluate the ultrasonic (viscous) relaxation times (T;m). They are comparable with those determined by Syrnikov and Penkina

ACCEPTED MANUSCRIPT 12 [71] from viscosity experiments. Similarly as with other investigated electrolytes,

(T;m) decrease strongly with increasing temperature, but very weakly with concentration. Differences in the ultrasonic (viscous) relaxation times (T;m) as compared to that of pure water (T;m) = [(T;0) - (T;m)] (Figure 8) differ from those observed for lithium nitrate solutions (Figure 4). They are nearly always positive, increase with concentration of sodium nitrate, and have at all times concave

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upward curvature. Since the ultrasonic (viscous) relaxation times (T;m) are similar for both nitrates, also changes in curvature of thermodynamic functions of activation

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are similar. However, (T;m) are different, and this has considerable influence on the form of H*(T;m) and TS*(T;m) as a function of temperature (see Figure 5 and 9).

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The function R3(m)

(16)

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m*  m /1 mol  kg-1

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 x M +x M  R3 (m) / Pa1/7  m3  mol-1  106  1/ 71 1 2 2  S (T ; m)(T ; m)  R3 (NaNO3,m)  395.36 10.722 m*

reproduces the compressibility parameters in sodium nitrate solutions with the

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standard deviation of about ± 5.6 10-6 Pa1/7.m3.mol-1 (with about 1.4 percent error)

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3.4 Aqueous solutions of potassium nitrate. Properties of sodium and potassium nitrate solutions were frequently determined together, but those of KNO3 are less known. Sound velocities

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measurements in solutions from 0 to 90 0C, and from 0.1 to 4.0 mol.kg-1 were performed by Mikhailov et al. [3]. In dilute solutions, Roy et al. [14] determined

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u(T;m) values from 30 0C to 50 0C. At 25 0C, in different concentration ranges, sound velocities were reported by Millero et al. [9], Sivakumar and Subrahmanyam [10] and Maret and Yeager [70] and at 30 0C Subrahmanyam and Bhimasenachar [4] and Sivaramakrishnalyer and Abdulkhadarb [11]. Reported by Maret and Yeager [70] hydration number of KNO3 is h = 6.0, close the Allam and Lee [7] result h = 6.1. With an exception of sound velocities at high temperatures going from [3], reasonable low scattering of u(T:m) = [u(T:m) - u1(T)] values in potassium nitrate solutions is observed (Figure S4). Determined sound velocities in potassium nitrate solutions u(T:m), the isentropic compressibility coefficients S(T;m) and the changes in heat capacities with

ACCEPTED MANUSCRIPT 13 volume (∂CV/∂V)T,m are presented in Table 3. Evaluated thermodynamic quantities and physical properties of potassium nitrate solutions are reported in Supplementary Content (Tables S5 and S6). Since sets of densities of KNO3 solutions as a function of temperature were incomplete, densities (T;m) were evaluated from the author equation [72]

(T;w) 

H2O (T )

1 H2O (T )[Aw  Bw2 ]

(17)

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A=0.61564 ; B=  0.1390

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where w is mass fraction of potassium nitrate in aqueous solution, and H2O (T ) are densities of pure water (see Eq. 8).

SC

With an exception of KI, sound velocities in potassium salt solutions are always larger than those in pure water, for example at 25 0C in dilute solutions

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u(K2CO3) > u(K2SO4) > u(KF) > u(KHCO3) > u(K2Cr2O7) > u(KCl) > u(KNO3) > u(KClO3) > u(KCN) > u(KBr) > u(H2O) > u(KI) [1,9,70]. Recently Singh et al. [73]

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showed for other potassium salts that at 20 0C, for m < 0.1 mol.kg-1, u(KH2PO4) > u(K2HPO4) > u(KOH) > u(K2Cr2O7) > u(KCl) > u(KMnO4) > u(H2O). The isentropic compressibility coefficients S(T;m) of alkali metal nitrates can

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be arranged in the following series S(NaNO3) < S(LiNO3) < S(KNO3) < S(H2O)

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(Figure 1). The opposite series V(NaNO3) > V(LiNO3) > V(KNO3) > V(H2O) exists for the isochoric thermal pressure coefficients V(T;m) = (∂P/∂T)V,m (Figure S5). Signs of f(T;m) = [f(T;m) - f(T;m = 0)] and g(T;m) = [g(T;m) - g(T;m = 0)] functions are

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only consistent in the case of aqueous potassium nitrate solutions for temperatures lower than about 55 0C. At higher temperatures they have opposite signs. As can be

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observed in Figure 10, at low temperatures both f(T;m) and g(T;m) are negative (structure-breaking solute), and over a large temperature range they are positive (structure-making solute). At higher temperatures it is not clear whether dissolved potassium nitrate reduces a number of hydrogen bonds in water. Considering that both K+ and NO3- ions are destroying the water structure [69], the results based on f(T;m) and g(T;m) functions are rather surprising. Hydration numbers based on the Passynski approach [43] of potassium nitrate are close to those of sodium nitrate and they decrease with increase of temperature (Figure 3).

ACCEPTED MANUSCRIPT 14 The ultrasonic (viscous) relaxation times of alkali metal nitrates (T;m) have similar behaviour with regard to temperature (see also [71]). However, they differ if differences between relaxation times in solution and in pure water (T;m) = [(T;0) - (T;m)] are considered (Figures 4, 8 and 11). As can be seen, in case of potassium nitrate solutions, (T;m) is positive, but at high temperatures, contrary to other nitrates, the form of (T;m) function has a strong asymmetry. Calculated from

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(T;m) values of the enthalpy and entropy of activation are presented in Figure 12. And, the asymmetry in (T;m) is also evident in the form of thermodynamic

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functions. As for other nitrates we have H*(T;m) > TS*(T;m) >> G*(T;m) > 0 with G*(LiNO3) > G*(H2O) > G*(NaNO3) > G*(KNO3) > 0.

SC

Compressibility parameters in potassium nitrate solutions can be represented by the function R3(m)

m*  m /1 mol  kg

MA

NU

 x M +x M  R3 (m) / Pa1/7  m3  mol-1  106  1/ 71 1 2 2  S (T ; m)(T ; m)  R3 (KNO3,m)  395.48 14.179 m*

(18)

-1

with the standard deviation of about ± 5.6 10-6 Pa1/7.m3.mol-1 (with about 1.4 percent

4. Conclusions

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error)

Sound velocities in 0.1, 0.5 and 1.0 mol.kg-1 solutions of alkali metal nitrates

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were determined the temperature range from 278.15 K to 363.15 K, at 1 K intervals. A number of compressibility and volumetric properties were determined by using

AC

sound velocities, densities, heat capacities and viscosities of these solutions. Basing on them, the isentropic compressibilities S(T;m), the isothermal compressibilities T(T;m), the apparent molar compressibilities (T;m)the isochoric thermal pressure coefficients (∂P/∂T)V,m, the apparent molar volumes V2,(T;m), the cubic expansion coefficients (T;m), the changes of heat capacities CV with volume (∂CV/∂V)T,m and the changes of heat capacities CP with pressure (∂CP/∂P)T,m, the hydration numbers h(T;m), the ultrasonic (viscous) relaxation times (T;m), the Gibbs free energy G*(T;m), entropy TS*(T;m) and enthalpy H*(T;m) of activation of the viscous process were evaluated. It was found that measured sound velocities and other

ACCEPTED MANUSCRIPT 15 evaluated quantities are consistent with the literature results. Reported here compressibility and volumetric properties were qualitatively correlated with changes in the structure of water. Comparison between different salts gives not always monotonic change in properties with regard to cations and anions. However, it was always observed that at low and at room temperatures, alkali metal nitrates behave as the structure-breaking solutes, but with increasing temperature, they become in

PT

aqueous solutions, the structure-making solutes. This conclusion is supported by looking on independent changes in heats capacities with regard to volume and

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pressure.

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Acknowledgments

The author is indebted to Professor Marija Bešter-Rogač, Ljubljana University,

NU

Slovenia, who helped to obtain a number of papers dealing with the subject. I am also grateful to Professor Emanuel Manzurola from Ben Gurion University of the Negev, Beer Sheva, who over a long period of time was engaged in mutual research and

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construction of equipment used in this investigation and to Zoya Orekhova and

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Paulina Veinner for their excellent technical assistance.

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Arabian J. Chem. 9 (2016) S373-S378

ACCEPTED MANUSCRIPT 22

TABLE 1 Experimental sound velocities uexp, isentropic compressibility coefficients S and (∂CV/∂V)T values in lithium nitrate solutions. uexp

0.1 mol.kg-1 LiNO3

4.63 4.61 4.59 4.56 4.54 4.52 4.50 4.48 4.46 4.45 4.43 4.41 4.39 4.38 4.36 4.35 4.33 4.32 4.31 4.29 4.28 4.27 4.26 4.25 4.24 4.23 4.22 4.21 4.20 4.19 4.18 4.18 4.17 4.16 4.16 4.15 4.15 4.14 4.14 4.13 4.13 4.12

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1482.9 1486.2 1489.9 1493.0 1496.1 1499.5 1502.6 1505.5 1508.6 1511.5 1514.4 1517.4 1520.1 1522.5 1525.2 1527.6 1529.7 1532.1 1534.5 1536.6 1538.8 1540.9 1542.7 1544.6 1546.4 1548.3 1550.1 1552.0 1553.5 1555.1 1556.3 1557.9 1559.2 1560.4 1561.6 1562.7 1563.9 1565.4 1566.7 1567.6 1568.5 1569.5

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82.65 82.22 81.74 81.23 80.67 80.08 79.46 78.80 78.11 77.39 76.65 75.88 75.09 74.28 73.45 72.60 71.73 70.85 69.96 69.06 68.15 67.23 66.31 65.38 64.44 63.51 62.58 61.65 60.72 59.79 58.87 57.96 57.06 56.16 55.28 54.40 53.54 52.69 51.86 51.04 50.24 49.46

(∂CV/∂V)T

0.5 mol.kg-1 LiNO3

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4.85 4.82 4.80 4.77 4.74 4.72 4.69 4.67 4.65 4.63 4.61 4.59 4.57 4.55 4.53 4.51 4.50 4.48 4.46 4.45 4.44 4.42 4.41 4.40 4.38 4.37 4.36 4.35 4.34 4.33 4.32 4.31 4.30 4.30 4.29 4.28 4.27 4.27 4.26 4.26 4.25 4.25

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1480.7 1483.6 1487.2 1490.4 1493.8 1496.8 1500.0 1503.1 1506.0 1508.9 1511.7 1514.4 1517.1 1519.5 1522.0 1524.5 1526.8 1529.2 1531.4 1533.6 1535.6 1537.6 1539.6 1541.7 1543.5 1545.3 1547.0 1548.8 1550.4 1552.1 1553.4 1555.0 1556.4 1557.8 1559.3 1560.2 1561.7 1562.8 1564.0 1565.2 1566.3 1567.1

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5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

S

93.84 92.07 90.25 88.40 86.51 84.60 82.67 80.72 78.78 76.83 74.89 72.97 71.07 69.19 67.35 65.54 63.78 62.06 60.40 58.79 57.25 55.77 54.36 53.03 51.77 50.60 49.51 48.50 47.59 46.76 46.04 45.40 44.87 44.44 44.11 43.88 43.75 43.72 43.80 43.98 44.26 44.64

uexp

S

(∂CV/∂V)T

1.0 mol.kg-1 LiNO3 1470.9 1473.8 1477.0 1481.2 1484.2 1487.5 1491.2 1494.3 1497.0 1500.1 1503.2 1505.7 1508.8 1511.3 1513.6 1516.4 1518.8 1521.2 1523.5 1525.7 1528.0 1530.3 1532.2 1534.0 1536.3 1538.1 1539.8 1541.5 1543.3 1545.0 1546.6 1548.0 1549.7 1550.9 1552.3 1553.6 1554.9 1556.2 1557.5 1558.7 1559.6 1560.7

4.39 4.37 4.35 4.34 4.32 4.30 4.29 4.27 4.25 4.24 4.22 4.21 4.20 4.18 4.17 4.16 4.14 4.13 4.12 4.11 4.10 4.09 4.08 4.07 4.07 4.06 4.05 4.04 4.04 4.03 4.02 4.02 4.01 4.01 4.00 4.00 3.99 3.99 3.98 3.98 3.98 3.97

PT

(∂CV/∂V)T

RI

S

SC

uexp

NU



97.72 94.93 92.09 89.20 86.29 83.35 80.40 77.45 74.52 71.62 68.75 65.93 63.17 60.47 57.85 55.31 52.87 50.52 48.29 46.18 44.18 42.32 40.60 39.02 37.59 36.31 35.19 34.23 33.44 32.82 32.37 32.09 31.99 32.07 32.33 32.76 33.37 34.16 35.13 36.27 37.58 39.06

ACCEPTED MANUSCRIPT 23

SC

NU

MA

D

PT E

CE

AC

uexp./m.s-1 ; S = 105 /bar-1; (∂CV/∂V)T /bar.K-1.

3.97 3.97 3.96 3.96 3.96 3.96 3.96 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.96 3.96 3.96 3.97 3.97 3.97 3.98 3.98 3.99 4.00 4.01 4.01

PT

1561.7 1562.6 1563.6 1564.5 1565.3 1565.9 1566.8 1567.5 1568.1 1568.7 1569.3 1570.0 1570.3 1570.6 1570.9 1571.2 1571.8 1572.2 1572.5 1572.8 1572.8 1572.8 1573.1 1573.4 1573.4 1573.4 1573.7 1573.4 1573.4 1573.4 1573.1 1573.1 1572.8 1572.5

RI

47 1568.0 4.24 48.69 1570.4 4.12 45.13 48 1568.9 4.24 47.94 1571.4 4.12 45.71 49 1569.9 4.23 47.22 1572.4 4.11 46.39 50 1570.7 4.23 46.51 1573.0 4.11 47.16 51 1571.3 4.22 45.82 1573.6 4.11 48.03 52 1572.3 4.22 45.15 1574.3 4.10 48.99 53 1572.9 4.22 44.51 1574.9 4.10 50.03 54 1573.6 4.21 43.88 1575.2 4.10 51.16 55 1574.2 4.21 43.28 1576.2 4.10 52.37 56 1574.5 4.21 42.70 1576.8 4.10 53.65 57 1574.8 4.21 42.15 1577.4 4.09 55.01 58 1575.5 4.21 41.62 1577.7 4.09 56.43 59 1576.1 4.21 41.11 1578.1 4.09 57.92 60 1576.4 4.20 40.62 1578.4 4.09 59.46 61 1576.7 4.20 40.16 1578.7 4.09 61.06 62 1577.3 4.20 39.72 1579.0 4.09 62.70 63 1577.6 4.20 39.31 1579.3 4.09 64.37 64 1577.6 4.20 38.91 1579.6 4.09 66.08 65 1578.0 4.20 38.54 1580.0 4.09 67.82 66 1578.0 4.20 38.20 1580.0 4.09 69.57 67 1578.3 4.20 37.87 1580.3 4.09 71.33 68 1578.3 4.21 37.57 1580.3 4.09 73.09 69 1578.3 4.21 37.29 1580.3 4.09 74.84 70 1578.6 4.21 37.03 1580.6 4.10 76.58 71 1578.6 4.21 36.79 1580.9 4.10 78.29 72 1578.9 4.21 36.57 1580.6 4.10 79.96 73 1578.6 4.21 36.36 1580.3 4.11 81.58 74 1578.6 4.22 36.18 1580.3 4.11 83.15 75 1578.3 4.22 36.01 1580.0 4.11 84.64 76 1578.3 4.22 35.86 1579.6 4.12 86.06 77 1578.0 4.22 35.72 1579.3 4.12 87.38 78 1578.0 4.23 35.60 1579.0 4.13 88.60 79 1577.6 4.23 35.49 1578.7 4.14 89.70 80 1577.3 4.23 35.39 1578.4 4.15 90.67 5 Notation and units: 1 bar = 10 PaK - 273.15

40.71 42.52 44.48 46.60 48.86 51.26 53.80 56.45 59.23 62.11 65.09 68.15 71.29 74.50 77.76 81.06 84.38 87.71 91.05 94.36 97.63 100.9 104.0 107.1 110.0 112.8 115.5 118.0 120.3 122.4 124.2 125.8 127.1 128.0

ACCEPTED MANUSCRIPT 24

TABLE 2 Experimental sound velocities uexp, isentropic compressibility coefficients S and (∂CV/∂V)T values in sodium nitrate solutions. uexp

0.1 mol.kg-1 NaNO3

4.58 4.56 4.54 4.52 4.50 4.48 4.46 4.44 4.42 4.40 4.38 4.37 4.35 4.33 4.32 4.30 4.29 4.27 4.26 4.25 4.24 4.22 4.21 4.20 4.19 4.18 4.17 4.16 4.15 4.15 4.14 4.13 4.13 4.12 4.11 4.11 4.10 4.10 4.09 4.09 4.09 4.08

MA

1455.0 1458.5 1462.3 1466.7 1470.0 1473.7 1477.2 1480.6 1483.7 1487.1 1490.5 1493.3 1496.5 1499.5 1502.2 1505.0 1507.6 1510.2 1512.8 1515.4 1517.7 1519.9 1522.3 1524.4 1526.6 1528.5 1530.7 1532.6 1534.4 1536.2 1537.9 1539.6 1541.2 1542.9 1544.3 1545.8 1547.2 1548.4 1549.9 1551.1 1552.4 1553.5

D

80.5 80.0 79.6 79.1 78.6 78.0 77.4 76.8 76.1 75.4 74.7 74.0 73.3 72.5 71.7 71.0 70.1 69.3 68.5 67.7 66.8 65.9 65.1 64.2 63.3 62.5 61.6 60.7 59.9 59.0 58.1 57.3 56.4 55.6 54.8 53.9 53.1 52.3 51.5 50.8 50.0 49.3

(∂CV/∂V)T

0.5 mol.kg-1 NaNO3

PT E

4.84 4.81 4.79 4.76 4.73 4.71 4.69 4.66 4.64 4.62 4.60 4.58 4.56 4.54 4.52 4.50 4.49 4.47 4.46 4.44 4.43 4.41 4.40 4.39 4.37 4.36 4.35 4.34 4.33 4.32 4.31 4.30 4.29 4.28 4.28 4.27 4.26 4.26 4.25 4.24 4.24 4.23

CE

1433.1 1436.6 1441.0 1445.0 1449.1 1453.0 1456.8 1460.5 1464.2 1467.7 1471.0 1474.5 1477.7 1481.2 1484.1 1487.1 1489.9 1492.8 1495.8 1498.2 1500.9 1503.4 1505.9 1508.5 1510.8 1513.0 1515.2 1517.3 1519.4 1521.4 1523.3 1525.4 1527.0 1528.8 1530.4 1532.1 1533.7 1535.3 1536.7 1538.0 1539.3 1540.7

AC

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

S

74.6 74.3 73.8 73.2 72.7 72.0 71.3 70.5 69.8 68.9 68.1 67.2 66.2 65.3 64.3 63.4 62.4 61.4 60.4 59.4 58.4 57.4 56.4 55.5 54.5 53.6 52.7 51.8 50.9 50.1 49.2 48.4 47.7 47.0 46.3 45.6 45.0 44.4 43.8 43.3 42.8 42.3

uexp

S

(∂CV/∂V)T

1.0 mol.kg-1 NaNO3 1482.9 1486.2 1489.9 1493.0 1496.1 1499.5 1502.6 1505.5 1508.6 1511.5 1514.4 1517.4 1520.1 1522.5 1525.2 1527.6 1529.7 1532.1 1534.5 1536.6 1538.8 1540.9 1542.7 1544.6 1546.4 1548.3 1550.1 1552.0 1553.5 1555.1 1556.3 1557.9 1559.2 1560.4 1561.6 1562.7 1563.9 1565.4 1566.7 1567.6 1568.5 1569.5

4.30 4.28 4.27 4.25 4.23 4.22 4.20 4.18 4.17 4.15 4.14 4.13 4.11 4.10 4.09 4.07 4.06 4.05 4.04 4.03 4.02 4.01 4.00 3.99 3.98 3.98 3.97 3.96 3.96 3.95 3.95 3.94 3.94 3.93 3.93 3.92 3.92 3.92 3.91 3.91 3.91 3.90

PT

(∂CV/∂V)T

RI

S

SC

uexp

NU



54.2 54.8 55.3 55.7 56.0 56.3 56.4 56.5 56.5 56.4 56.3 56.1 55.8 55.5 55.1 54.7 54.2 53.7 53.1 52.5 51.8 51.1 50.4 49.7 48.9 48.1 47.3 46.4 45.5 44.6 43.7 42.8 41.8 40.9 39.9 38.9 37.9 36.8 35.8 34.7 33.7 32.6

ACCEPTED MANUSCRIPT 25

SC

NU

MA

D

PT E

CE

AC

uexp./m.s-1 ; S = 105 /bar-1; (∂CV/∂V)T /bar.K-1.

3.90 3.90 3.90 3.90 3.89 3.89 3.89 3.89 3.89 3.89 3.89 3.88 3.88 3.88 3.88 3.88 3.88 3.88 3.88 3.88 3.88 3.89 3.89 3.89 3.89 3.90 3.90 3.91 3.91 3.92 3.93 3.94 3.95 3.96

PT

1570.4 1571.4 1572.4 1573.0 1573.6 1574.3 1574.9 1575.2 1576.2 1576.8 1577.4 1577.7 1578.1 1578.4 1578.7 1579.0 1579.3 1579.6 1580.0 1580.0 1580.3 1580.3 1580.3 1580.6 1580.9 1580.6 1580.3 1580.3 1580.0 1579.6 1579.3 1579.0 1578.7 1578.4

RI

47 1541.9 4.23 48.5 1554.4 4.08 41.9 48 1543.0 4.22 47.8 1555.6 4.07 41.5 49 1544.3 4.22 47.1 1556.7 4.07 41.2 50 1545.4 4.21 46.4 1557.5 4.07 40.9 51 1547.1 4.21 45.8 1558.8 4.07 40.6 52 1548.0 4.21 45.1 1559.4 4.06 40.3 53 1548.6 4.20 44.5 1560.3 4.06 40.1 54 1549.5 4.20 43.9 1560.9 4.06 39.9 55 1550.5 4.20 43.3 1561.6 4.06 39.7 56 1551.1 4.20 42.8 1562.5 4.05 39.6 57 1552.0 4.19 42.2 1563.1 4.05 39.5 58 1552.6 4.19 41.7 1563.8 4.05 39.4 59 1553.2 4.19 41.2 1564.1 4.05 39.3 60 1553.9 4.19 40.8 1564.4 4.05 39.2 61 1554.5 4.19 40.3 1564.7 4.05 39.1 62 1554.8 4.19 39.9 1565.0 4.05 39.0 63 1555.4 4.19 39.5 1565.3 4.05 39.0 64 1555.7 4.19 39.1 1565.7 4.05 38.9 65 1556.0 4.19 38.7 1566.0 4.05 38.8 66 1556.3 4.19 38.4 1566.3 4.05 38.8 67 1556.6 4.19 38.1 1566.6 4.05 38.7 68 1557.0 4.19 37.8 1566.9 4.05 38.5 69 1557.0 4.19 37.5 1567.2 4.05 38.4 70 1557.0 4.19 37.2 1567.5 4.05 38.2 71 1557.0 4.20 37.0 1567.5 4.06 38.0 72 1557.3 4.20 36.8 1567.9 4.06 37.8 73 1557.3 4.20 36.6 1567.5 4.06 37.5 74 1557.6 4.20 36.4 1567.5 4.07 37.1 75 1557.9 4.21 36.3 1567.2 4.07 36.7 76 1557.6 4.21 36.1 1566.9 4.08 36.2 77 1557.3 4.21 36.0 1566.6 4.09 35.7 78 1557.3 4.22 35.9 1566.3 4.09 35.0 79 1557.3 4.22 35.8 1566.0 4.10 34.3 80 1557.0 4.22 35.7 1565.7 4.11 33.5 5 Notation and units: 1 bar = 10 PaK - 273.15

31.5 30.4 29.2 28.1 26.9 25.7 24.5 23.3 22.1 20.8 19.5 18.1 16.7 15.3 13.9 12.4 10.8 9.2 7.6 5.9 4.1 2.2 0.3 -1.7 -3.8 -5.9 -8.2 -10.5 -13.0 -15.6 -18.3 -21.1 -24.0 -27.1

ACCEPTED MANUSCRIPT 26

TABLE 3 Experimental sound velocities uexp, isentropic compressibility coefficients S and (∂CV/∂V)T values in potassium nitrate solutions. uexp

0.1 mol.kg-1 KNO3

4.61 4.59 4.56 4.54 4.52 4.50 4.48 4.46 4.44 4.42 4.40 4.38 4.37 4.35 4.33 4.32 4.30 4.29 4.28 4.26 4.25 4.24 4.23 4.21 4.20 4.19 4.18 4.17 4.17 4.16 4.15 4.14 4.13 4.13 4.12 4.11 4.11 4.10 4.10 4.09 4.09 4.08

MA

1451.0 1454.4 1458.2 1462.0 1466.1 1469.6 1472.9 1475.9 1479.8 1482.9 1486.0 1488.0 1492.1 1495.0 1497.8 1500.7 1503.6 1506.2 1508.5 1510.9 1513.5 1515.9 1518.6 1520.7 1522.6 1524.6 1526.5 1528.5 1530.2 1531.6 1533.3 1535.3 1537.0 1538.9 1540.8 1542.5 1544.0 1545.2 1546.4 1548.0 1549.2 1550.1

D

75.48 75.94 76.33 76.67 76.95 77.17 77.34 77.45 77.51 77.51 77.47 77.37 77.23 77.03 76.79 76.50 76.17 75.79 75.37 74.91 74.41 73.86 73.28 72.66 72.00 71.31 70.58 69.81 69.02 68.19 67.33 66.44 65.53 64.58 63.61 62.61 61.59 60.55 59.48 58.39 57.28 56.15

(∂CV/∂V)T

0.5 mol.kg-1 KNO3

PT E

4.85 4.82 4.79 4.77 4.74 4.71 4.69 4.67 4.65 4.62 4.60 4.58 4.56 4.54 4.53 4.51 4.49 4.48 4.46 4.44 4.43 4.42 4.40 4.39 4.38 4.37 4.35 4.34 4.33 4.32 4.31 4.31 4.30 4.29 4.28 4.27 4.27 4.26 4.25 4.25 4.24 4.24

CE

1432.1 1435.8 1439.7 1443.6 1447.8 1451.8 1455.7 1459.6 1463.0 1466.7 1470.1 1473.4 1476.5 1480.0 1483.1 1486.2 1489.0 1491.8 1494.7 1497.3 1500.0 1502.6 1505.0 1507.4 1510.0 1512.0 1514.2 1516.5 1518.5 1520.2 1522.2 1524.2 1526.1 1527.9 1529.7 1531.2 1532.6 1534.2 1535.6 1537.1 1538.3 1539.7

AC

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

S

uexp

S

(∂CV/∂V)T

1.0 mol.kg-1 KNO3

80.71 80.58 80.40 80.15 79.84 79.47 79.06 78.59 78.07 77.51 76.91 76.27 75.59 74.88 74.15 73.38 72.59 71.77 70.94 70.08 69.21 68.33 67.44 66.54 65.63 64.71 63.79 62.87 61.95 61.03 60.12 59.21 58.30 57.41 56.52 55.64 54.77 53.91 53.06 52.23 51.41 50.60

1470.9 1473.8 1477.0 1481.2 1484.2 1487.5 1491.2 1494.3 1497.0 1500.1 1503.2 1505.7 1508.8 1511.3 1513.6 1516.4 1518.8 1521.2 1523.5 1525.7 1528.0 1530.3 1532.2 1534.0 1536.3 1538.1 1539.8 1541.5 1543.3 1545.0 1546.6 1548.0 1549.7 1550.9 1552.3 1553.6 1554.9 1556.2 1557.5 1558.7 1559.6 1560.7

4.37 4.35 4.33 4.31 4.29 4.27 4.25 4.23 4.22 4.20 4.19 4.17 4.16 4.14 4.13 4.12 4.10 4.09 4.08 4.07 4.06 4.05 4.04 4.03 4.02 4.01 4.00 4.00 3.99 3.98 3.97 3.97 3.96 3.96 3.95 3.95 3.94 3.94 3.93 3.93 3.92 3.92

PT

(∂CV/∂V)T

RI

S

SC

uexp

NU



80.19 80.52 80.78 80.99 81.13 81.22 81.25 81.23 81.15 81.02 80.84 80.61 80.34 80.01 79.64 79.23 78.77 78.27 77.73 77.14 76.53 75.87 75.18 74.45 73.69 72.90 72.07 71.22 70.33 69.42 68.48 67.52 66.53 65.52 64.48 63.42 62.34 61.25 60.13 59.00 57.85 56.68

ACCEPTED MANUSCRIPT 27

SC

NU

MA

D

PT E

CE

AC

uexp./m.s-1 ; S = 105 /bar-1; (∂CV/∂V)T /bar.K-1.

3.92 3.91 3.91 3.91 3.91 3.91 3.90 3.90 3.90 3.90 3.90 3.90 3.90 3.90 3.90 3.90 3.90 3.90 3.90 3.90 3.90 3.90 3.91 3.91 3.91 3.91 3.91 3.92 3.92 3.92 3.93 3.93 3.93 3.94

PT

1561.7 1562.6 1563.6 1564.5 1565.3 1565.9 1566.8 1567.5 1568.1 1568.7 1569.3 1570.0 1570.3 1570.6 1570.9 1571.2 1571.8 1572.2 1572.5 1572.8 1572.8 1572.8 1573.1 1573.4 1573.4 1573.4 1573.7 1573.4 1573.4 1573.4 1573.1 1573.1 1572.8 1572.5

RI

47 1540.9 4.23 55.00 1551.4 4.08 49.81 48 1542.2 4.23 53.84 1552.3 4.08 49.03 49 1543.3 4.22 52.65 1553.2 4.07 48.27 50 1544.2 4.22 51.45 1554.5 4.07 47.52 51 1545.3 4.22 50.24 1555.4 4.07 46.78 52 1546.2 4.21 49.02 1556.0 4.06 46.06 53 1546.8 4.21 47.78 1557.0 4.06 45.35 54 1547.4 4.21 46.52 1557.6 4.06 44.66 55 1548.0 4.21 45.26 1558.2 4.06 43.98 56 1549.3 4.20 43.99 1559.1 4.06 43.31 57 1550.2 4.20 42.71 1559.8 4.05 42.66 58 1550.8 4.20 41.42 1560.1 4.05 42.01 59 1551.4 4.20 40.12 1560.7 4.05 41.37 60 1551.7 4.20 38.82 1561.3 4.05 40.75 61 1552.4 4.20 37.51 1562.3 4.05 40.13 62 1553.0 4.20 36.20 1562.6 4.05 39.51 63 1553.3 4.20 34.89 1562.9 4.05 38.90 64 1553.6 4.20 33.57 1563.2 4.05 38.29 65 1553.9 4.20 32.25 1563.5 4.05 37.68 66 1554.5 4.20 30.92 1563.8 4.05 37.07 67 1554.8 4.20 29.60 1564.1 4.05 36.46 68 1555.2 4.20 28.28 1564.4 4.05 35.84 69 1555.5 4.20 26.96 1564.4 4.05 35.21 70 1555.5 4.20 25.64 1564.7 4.05 34.58 71 1555.5 4.20 24.32 1564.7 4.06 33.93 72 1555.5 4.21 23.01 1565.1 4.06 33.26 73 1555.8 4.21 21.70 1564.7 4.06 32.57 74 1555.8 4.21 20.40 1564.7 4.07 31.86 75 1556.1 4.21 19.11 1564.7 4.07 31.13 76 1555.8 4.22 17.81 1564.4 4.08 30.37 77 1555.8 4.22 16.53 1564.4 4.08 29.57 78 1555.8 4.22 15.26 1564.1 4.09 28.74 79 1555.5 4.23 13.99 1563.8 4.09 27.86 80 1555.5 4.23 12.73 1563.5 4.10 26.95 5 Notation and units: 1 bar = 10 PaK - 273.15

55.50 54.30 53.09 51.87 50.63 49.39 48.13 46.87 45.59 44.31 43.02 41.72 40.42 39.11 37.79 36.47 35.15 33.82 32.49 31.15 29.82 28.48 27.13 25.79 24.44 23.10 21.75 20.40 19.04 17.69 16.34 14.98 13.62 12.27

ACCEPTED MANUSCRIPT 28

4.8

T

4.4

LiNO3

PT

S

RI

10

T , S 10 /Pa

-1

H2O

NaNO3

KNO3

25

50

NU

0

SC

4.0

75



MA

Figure 1. The isothermal compressibility coefficients T(T;m). and the isentropic compressibility coefficients S.(T;m) of pure water and 1.0 mol.kg-1 lithium nitrate,

D

sodium nitrate and potassium nitrate solutions (T(T;m). > S.(T;m)) as a function of

AC

CE

PT E

dimensionless temperature  = T/K - 273.15.

ACCEPTED MANUSCRIPT 29

LiNO3

3

40

20

-1

PT

g(T;m)/barK , f(T;m)/cm K

-1

60

SC

RI

0

NU

-20 40

20

60

80

MA



Figure 2. Differences in the change of molar heat capacities with volume g(T;m) = [(∂CV/∂V)T,m] and differences in the change of molar heat capacities with pressure

D

f(T;m) = [-(∂CP/∂P)T,m] of lithium nitrate solutions as a function of dimensionless

PT E

temperature  = T/K - 273.15. 0.1 mol.kg-1;

0.5 mol.kg-1;

1.0 mol.kg-1.

f(T;m) :

0.1 mol.kg-1;

0.5 mol.kg-1;

1.0 mol.kg-1.

AC

CE

g(T;m) :

ACCEPTED MANUSCRIPT 30

12

8

PT

h(T;m)

KNO3

NaNO3

RI

LiNO3

25

0

NU

SC

4

50

75

MA



Figure 3 Hydration numbers h(T;m) of 0.5 mol.kg-1 and 1.0 mol.kg-1 solutions of lithium nitrate, sodium nitrate and potassium nitrate as a function of dimensionless

AC

CE

PT E

D

temperature  = T/K - 273.15.

ACCEPTED MANUSCRIPT 31

0.1

LiNO3

13

(T;m) 10 /s

0.0

PT

0.1 m -0.1

RI

0.5 m

SC

-0.2

-0.3 0

25

NU

1.0 m

50

75

MA



Figure 4. Differences between the ultrasonic relaxation times of water and those of

D

0.1 mol.kg-1, 0.5 mol.kg-1 and 1.0 mol.kg-1 lithium nitrate solutions (T;m) = [(T;0) -

PT E

(T;m)]. as a function of concentration m and dimensionless temperature  = T/K -

AC

CE

273.15.

ACCEPTED MANUSCRIPT 32

RI

PT

15

SC

10

0

NU

 H*(T;m),T S*(T;m) / kJmol

-1

20

25

50

75

MA



D

Figure 5. The change of enthalpy of activation H*(T;m) (upper curves) and entropy of activation TS*(T;m) (lower curves) in 0.1 mol.kg-1, 0.5 mol.kg-1 and 1.0 mol.kg-1

273.15.

0.5 mol.kg-1;

AC

CE

0.1 mol.kg-1;

PT E

solutions of lithium nitrate as a function of dimensionless temperature  = T/K -

1.0 mol.kg-1.

ACCEPTED MANUSCRIPT 33

1

NaNO3

PT

0

RI

3

f(T;m)/cm K

-1

0.1 m

SC

0.5 m -1

-2 0

MA

25

NU

1.0 m

50

75

D



Figure 6. Differences in the change of molar heat capacities with pressure f(T;m) =

PT E

[(∂CP/∂P)T,m] of sodium nitrate 0.1 mol.kg-1, 0.5 mol.kg-1 and 1.0 mol.kg-1 solutions

AC

CE

as a function of dimensionless temperature  = T/K - 273.15.

ACCEPTED MANUSCRIPT 34

60

1.0 m

PT

30

RI

0.5 m

SC

0

-30 25

0

NU

g(T;m)/barK

-1

NaNO3

0.1 m

50

75

Figure 7.

MA



Differences in the change of molar heat capacities with volume g(T;m) =

D

[(∂CV/∂V)T,m] of sodium nitrate 0.1 mol.kg-1, 0.5 mol.kg-1 and 1.0 mol.kg-1 solutions

AC

CE

PT E

as a function of dimensionless temperature  = T/K - 273.15.

ACCEPTED MANUSCRIPT 35

0.50

PT

0.25

1.0 m 0.5 m

RI

10

 (T;m)10 /s

NaNO3

SC

0.00

0.1 m 25

50

NU

0

75

MA



Figure 8. Differences between the ultrasonic relaxation times of water and those of

D

0.1 mol.kg-1, 0.5 mol.kg-1 and 1.0 mol.kg-1 sodium nitrate solutions (T;m) = [(T;0) -

PT E

(T;m)] as a function of concentration m and dimensionless temperature  = T/K -

AC

CE

273.15.

ACCEPTED MANUSCRIPT 36

PT

NaNO3

SC

RI

20

10

NU

 H*(T;m),T S*(T;m) / kJmol

-1

30

50

25

0

75

MA



Figure 9. The change of enthalpy of activation H*(T;m) (upper curves) and entropy

D

of activation TS*(T;m) (lower curves) in 0.1 mol.kg-1, 0.5 mol.kg-1 and 1.0 mol.kg-1

273.15.

0.5 mol.kg-1;

AC

CE

0.1 mol.kg-1;

PT E

solutions of sodium nitrate as a function of dimensionless temperature  = T/K -

1.0 mol.kg-1.

ACCEPTED MANUSCRIPT 37

10

PT

3

g(T;m)/barK , f(T;m)/cm K

-1

KNO3

RI

5

SC

-1

0

MA

NU

-5

-10 0

25

50

75

D



PT E

Figure 10. Differences in the change of molar heat capacities with volume g(T;m) = [(∂CV/∂V)T,m] and differences in the change of molar heat capacities with pressure f(T;m) = [-(∂CP/∂P)T,m] of potassium nitrate solutions as a function of

CE

dimensionless temperature  = T/K - 273.15. 0.1 mol.kg-1;

0.5 mol.kg-1;

1.0 mol.kg-1.

f(T;m) :

0.1 mol.kg-1;

0.5 mol.kg-1;

1.0 mol.kg-1.

AC

g(T;m) :

ACCEPTED MANUSCRIPT 38

0.50

1.0 m KNO3

PT RI

0.25

0.1 m

SC

10

 (T;m)10 /s

0.5 m

0

25

NU

0.00

50

75

MA



Figure 11. Differences between the ultrasonic relaxation times of water and those of

D

0.1 mol.kg-1, 0.5 mol.kg-1 and 1.0 mol.kg-1 potassium nitrate solutions (T;m) =

AC

CE

= T/K - 273.15.

PT E

[(T;0) - (T;m)]. as a function of concentration m and dimensionless temperature 

ACCEPTED MANUSCRIPT 39

PT

KNO3

SC

RI

20

10

0

NU

 H*(T;m),T S*(T;m) / kJmol

-1

30

25

50

75

MA



Figure 12. The change of enthalpy of activation H*(T;m) (upper curves) and entropy of activation TS*(T;m) (lower curves) in 0.1 mol.kg-1, 0.5 mol.kg-1 and 1.0

= T/K - 273.15.

0.5 mol.kg-1;

AC

CE

0.1 mol.kg-1;

PT E

D

mol.kg-1 solutions of potassium nitrate as a function of dimensionless temperature 

1.0 mol.kg-1.

ACCEPTED MANUSCRIPT 40

Graphical Abstract 12

PT

8

RI

h(T;m)

KNO3

NaNO3

SC

LiNO3

0

25

NU

4

AC

CE

PT E

D

MA



50

75

ACCEPTED MANUSCRIPT 41

Highlights 

Compressibilities of alkali metal nitrate solutions at fixed m were determined in a wide T range.



From sound velocities and densities, a number of thermodynamic parameters were evaluated. First and second derivatives of V and P with respect to T indicated changes in

PT



structure of water.

RI

Lithium and sodium nitrates behave as halides, but the case of potassium

CE

PT E

D

MA

NU

SC

nitrate is more complex.

AC

