Salts isothermal compressibility

Here, V refers to the molar volume of the nonelectrolyte, V and Vs° are the intrinsic3 and apparent molar volume of the salt, respectively, and /3 is the isothermic compressibility coefficient of the solution. Although this equation is strictly valid in the limit of Vi - 0 and ca - 0, it works quite satisfactorily for small nonpolar solutes. The equation shows that the effect is greatest for nonelectrolytes of large molar volume Vi, and for salts that cause the largest electrostriction, Vs - Vs°. A difficulty with this expression is that it is not always easy to evaluate the intrinsic volume of a salt (the mere volume, without... 

Variables 2 and Zj are charges of ions i and j Ay is the Pauling factor defined as Ay = (1 + zjnx + z-Jn i, where nK and nj represent the numbers of electrons in the outermost shell of ions i and j, respectively Cy = (3/2) aiajEiEj/(Ei + Ej) and dy = (9/4e2)Cy(a, 1/Ar1 + atjE/Nj), where a denotes the polarizability of ions, N is the number of the total electrons of an ion, and E is the first ionization potential, evaluated from the Equation Ef = Nle2h2I Tr2mai for ion i, where h and m are the Planck constant and the mass of the ion, respectively. Values of p, b, and cr are estimated from isothermal compressibilities and thermal expansion coefficients of 17 rock-salt-type crystals of alkali halides by Fumi and Tosi (15). 

Abstract - The recently obtained analytical solution of the mean spherical approximation has been used to calculate thermodynamic and structural properties of aqueous solutions of asymmetric electrolytes. The same approximation has also been used to calculate structure functions of pure and mixed molten salts. The agreement between experimental or quasi-experimental structure functions and those obtained within the framework of the MSA is quite good especially when the ionic radii are obtained by fitting the long wavelength limit of the structure functions to the isothermal compressibility of the system, under the condition that the diameter ratio is the same as in the crystal. 

FIGURE 7.3 The hydration numbers h(c) of aqueous salts at 25°C obtained from isothermal compressibility data for LiCl (-0-) and NaOH (- -). At the right-hand side are shown the BET parameters r (number of water-binding sites per formula unit of the salt) of these salts (large filled symbols) (From Ref. 21 with permission from the pubhsher, ACS). 

Activity Coefficients of Neutral Ion Pairs Neutral ion pairs can be treated as if they were nonelectrolytes being salted-out by the free ions of the electrolyte. For the salting-out of nonelectrolytes (Section 7.3) according to McDevit and Long [31] (see Section 7.3.2), the treatment requires the isothermal compressibility of the solvent Kj, the intrinsic volume of the electrolyte V(,.,. its standard partial molar volume y , and the latter quantity of the nonelectrolyte (ion pair) V . The value of can be estimated from values for the ions tabulated by Marcus et al. [32] and in Table 2.8 and are independent of the solvent, and values are known for many salts in many solvents (Table 4.6). The value of 17 must be estimated from the dimensions of the ions and may be assumed to be equal to for the symmetrical ion pair. Then its activity coefficient becomes according to Marcus [30] ... 

Expressions are also provided for the surface tension and the isothermal compressibility along the saturation (Uquid-vapor coexistence) line. The average melting temperature is taken to be = 1.03 7 (except for the lithium salts) and the critical temperature is 7) = 3.29 r [141]. 

The adiabatic compressibilities of molten salts are obtained from measurements of the ultrasound velocities in them, u, with a probable uncertainty of 1 %, and of their densities, p Ks = The isothermal compressibilities can be obtained... 

Other molten salts have somewhat different correlation expressions [221]. Isothermal compressibilities of molten salts may be estimated from the scaled particle theory if no experimental data are available [222] ... 

Table 3.15 The adiabatic compressibility, jts/GPa isothermal compressibility, jtx/GPa and internal pressure Pim/MPa of molten univalent metal salts at the corresponding temperatures r=i.i(r /K)...

The products of the surface tensions of molten salts and their isothermal compressibilities, aKj, show interesting regularities. These products for liquids in general follow the expression ... 

Cleaver B, Spencer PN (1955) Isothermal compressibilities and thermal pressure coefficients of molten salts. High Temp High Press 7 539-547... 

Cleaver B, Zani P (1978) Adiabatic thermal pressure coefficients of molten salts an indirect method for the measurement of isothermal compressibility. High Temp High Press 10 437... 

Hardly any compressibility data for hydrated molten salts have been found. StUl, for calcium nitrate hexahydrate (more precisely, Ca(N03)2 5.98H20) the isothermal compressibility Kt at 0.1 MPa is 0.195 0.016 GPa at 298 K diminishing to 0.188 0.015 GPa at 423 K spanning the melting point, 315 K and the corresponding temperature, l.lTm [78] (but note the wrong tmits in the publication). 

RTILs with BF4, PFs, and OCSO4 anions up to 373 K and 200 MPa. The resulting isothermal compressibilities Kt increased in this order of salts from 0.4 to 0.5 GPa at ambient pressure and diminished at increasing pressures. The free, compressible, volumes at 313 K and ambient pressure were 7.4 %, 6.7 %, and 7.6 % respectively. 

Table 6.6 The density, isobaric expansibility, molar volume, isothermal compressibility, and internal pressure at 25 °C of l-alkyl-3-methylimidazolium (C mim) salts, from Farahani et al. [238] unless otherwise noted...

Salts of fatty acids are classic objects of LB technique. Being placed at the air/water interface, these molecules arrange themselves in such a way that its hydrophilic part (COOH) penetrates water due to its electrostatic interactions with water molecnles, which can be considered electric dipoles. The hydrophobic part (aliphatic chain) orients itself to air, because it cannot penetrate water for entropy reasons. Therefore, if a few molecnles of snch type were placed at the water surface, they would form a two-dimensional system at the air/water interface. A compression isotherm of the stearic acid monolayer is presented in Figure 1. This curve shows the dependence of surface pressure upon area per molecnle, obtained at constant temperature. Usually, this dependence is called a rr-A isotherm. 

The quantity (HV2 — HV1) is the negative of the enthalpy change on compressing (isothermally) the vapor above the sea salt solution from pressure P2 to pressure P1 ... 

It is possible to control the pressures at which the phase transitions occur by fine tuning the strength of intermolecular interactions between the amphiphilic molecules. The interactions between the hydrophobic tails depend on temperature [37], while the interactions between the hydrophilic heads depend on the chemical composition of the subphase, namely its pH and ionic strength [4], For example, the fatty acid molecules in films prepared on subphase with high pH and high concentration of divalent salt, such as CaCl2 or CdCl2, are normal to the surface, i.e. are in solid state, even at low pressures. Pressure-area isotherms of such films are featureless compressed films are stable and easy to transfer [38]. 

Anionic at the Air/Water Interface. In Figure 2 we show II—1/A isotherms obtained by one of us (38) for Ci8 sulfate on several salt solutions at 20°C. We also show a few points where the A values overlap with the results on 0.01 M NaCl reported in our paper on entropies of compression (33). The favorable agreement between both sets of data at lower A is discussed in Ref. 33. The most likely explanation of the slight discrepancies is trace residual alcohol in the older experiments. No other data are available for comparison at these large A values. 

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