Isopiestic measurement

From a thermodynamic standpoint, freezing point measurements and isopiestic measurements are similar since both yield directly the activity of the solvent. When done carefully, freezing point data can generate activity coefficient values at concentrations down to 0.001 molal. During the first half of this century, much activity coefficient data was obtained from freezing point measurements. However, the popularity of this technique has decreased and is seldom used for aqueous solutions at the present time. 

Equilibrium constants have been measured for (41)-(45) using a variety of techniques spectrophotometry 49), conductivity, 170-NMR line broadening (50), isopiestic measurements, potentiometry, and others 51). From these data, speciation distribution estimates have been calculated 52). As the equilibrium constants for (41)—(45) are quite sensitive to ionic strength, so are the speciation distributions. Thus, for pH = 1, Cr(VI)T = 10-2 M and T = 25°C, the [H2Cr04] is calculated to be 29%at/ = 0 and 1% at I = 1.0M(52). Nevertheless, a considerable proportion ( 50%) of Cr(VI) in the pH range 1-6 is estimated to be in the HCr04 form. 

The homogeneous region of the ternary system is limited by the solubility curve (12). The area with isopiestic measured points is dashed in Figures 3 and 4. 

The osmotic coefficient of the binary nonelectrolyte solution was obtained from isopiestic measurements... 

Primary and secondary hydration shells around DNA. The hydration of DNA is not homogeneous. It can be described in terms of two shells, as suggested by sedimentation equilibrium studies [857-859, 861], isopiestic measurements [860], gravimetric and infrared spectroscopic investigations [853-855, 862]. 

Isopiestic measurements showed that the water activity in H20/ NMA solvent mixture of x2 = 0.5 is the same, within experimental error, as that predicted by Raoult s Law. Hence, the emf was corrected to 1 atm partial pressure of hydrogen on the assumption that NMA is involatile and that all of the solutions obey Raoult s Law. The observed emf for each HBr solution at each solvent composition and temperature, corrected as described above, is listed in Table II. 

Baes et al. (19) have investigated this trimer formation in n-hexane through isopiestic measurements and have found little indication of the trimer species. In subsequent investigations Baes (20) and Baes and Baker (21) suggested HDEHP partial trimerization as an explanation for... 

In the foregoing method the mean ionic activity coefficient of the solute has been calculated from actual vapor pressure data. If the osmotic coefficients for a reference substance are known over a range of concentrations, the activity coefficients of another electrolyte can be derived from isopiestic measurements, without actually determining the vapor pressures. If w, and p refer to an experimental electrolyte and wr, 0r and vr apply to a reference electrolyte which is isopiestic (isotonic) with the former, then by equation (39.46)... 

The mean activity coefficients of the sulphates of Cd, Cu, Mg, Mn, Ni, and Zn are quite similar [50HAR/OWE]. The variation at a concentration of 0.5 m is less than 10%. Ojkova and Staneva [890JK/STA] made isopiestic measurement on aqueous solutions of the selenates of Co, Cu, Mg, Ni, and Zn. The mean activity coefficients obtained from these measurements also show a moderate variation between the salts. The value of for MgSe04, = 0.12, will be used to extrapolate the conditional solubility product to / = 0. The selected result is ... 

The osmotic coefficient of Li2Se04 solutions in the concentration range 0.927 to 3.708 mol kg was determined by isopiestic measurements at 298.15 K. Sodium chloride solutions were employed as reference standards. An equilibration period of 20 days yielded an agreement within 0.2% between duplicates. 

The paper also contains a calculation of the Pitzer coefficients of nickel selenate solutions from isopiestic measurements by Ojkova and Staneva [890JK/STA]. The results contained in Table A-122 also appear in [98CHR/OJK], [2001BAR/CHR],... 

Several years ago, an extended experimental program was carried out by G. M. Sletmoe (Shell Development Co.) geared towards helping the coatings formulator and pressmen to utilize solvent blends effectively. These studies involved determination of solvent evaporation rates for both neat solvent blends and alkyd resin solutions. Sletmoe also determined isotherms showing solvent activity in resin solutions through isopiestic measurements to relate evaporation rates to equilibrium solvent partial pressures. Some of these data have been published (2, 3, 4) with guideline observations and rules for their application. 

The mean value of the entirely independent investigations (emf measurements [99MAL/CAR] and isopiestic measurements [69LIB/SAD]) is selected ... 

BLO/RAZ], [85DRA/MAD] and isopiestic measurements [80LIB/SAD], [83HOL/MES]. There is a broad consensus, primarily based on the spectroscopic evidence, that, for temperatures below 100°C, association of these ions in dilute solutions... 

The authors carried out isopiestic measurements on aqueous solutions of nickel sulphate at 383.14 K and 413.22 K for nickel sulphate molalities between 1.52 and 5.66. The results were interpreted using a modified Pitzer equation without invoking formation of NiS04(aq) as discrete species. The results at these high ionic strengths were not used in the present assessment. 

Fig. 17.7. Two experimental techniques for measuring stoichiometric ion activity coefficients in hydrothermal solutions, (a) Determination by measuring difference in vapor pressures between solutions of known total salt concentration and pure water, (b) Isopiestic measurement in which sample solutions containing known weights of salts are equilibrated with a standard solution for which activity coefficients have been independently measured. In a sealed system water activity is everywhere the same at equilibrium measured salt concentrations in each sample container give the desired activity coefficients from the known activity of water in the standard salt solution.

From isopiestic measurements to determine the osmotic coefficient in 0.1 and 0.2 molal potassium nitrate and to estimate its activity coefficient at 0.1 molality. 

To calculate the dissociation constant of dimerized benzoic acid in benzene solution from isopiestic measurements. 

The chemistry of U02 extraction by organophosphate anions is complicated by solvent association reactions. Thus while HDEHP is monomeric in polar diluents of high dielectric constant, such as methanol, it is dimeric in nonpolar solvents such as benzene or n-hexane. In the case of mono-2-ethylhexyl phosphoric acid (HjMEHP), association was found to occur to an even greater extent and isopiestic measurements indicated an average of 6.2 molecules were associated in benzene, rising to 14.5 in n-hexane. On the basis of the known solid state structure of the dimer of (PhCH20)2P(0)0H, (1) was presumed to represent the solution structure of (HDEHP)2. 

Figure 4.4.6. Schematic of the experimental arrangement for an isopiestic measurements. [Reprinted with permission from Ref 77, Copyright 1995, Elsevier Science].

SA4 Sadeghi, R. and Ziamajidi, F., Thermodynamic properties of aqueous polypropylene oxide 400 solutions from isopiestic measurements over a range of temperatures. Fluid Phase Equil, 249, 165, 2006. 

SA1 Sadeghi, R. and Shahebrahimi, Y., Vapor-liquid equilibria of aqueous polymer solutions from vapor-pressure osmometry and isopiestic measurements, J. Chem. Eng. Data, 56, 789, 2011. 

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