Osmotic coefficient pressures

The themiodynamic properties calculated by different routes are different, since the MS solution is an approximation. The osmotic coefficient from the virial pressure, compressibility and energy equations are not the same. Of these, the energy equation is the most accurate by comparison with computer simulations of Card and Valleau [ ]. The osmotic coefficients from the virial and compressibility equations are... 

Rard (1992) reported the results of isopiestic vapor-pressure measurements for the aqueous solution of high-purity NiCl2 solution form 1.4382 to 5.7199 mol/kg at 298.1510.005 K. Based on these measurements he calculated the osmotic coefficient of aqueous NiCb solutions. He also evaluated other data from the literature and finally presented a set of smoothed osmotic coefficient and activity of water data (see Table IV in original reference). 

The activity coefficient of the solvent remains close to unity up to quite high electrolyte concentrations e.g. the activity coefficient for water in an aqueous solution of 2 m KC1 at 25°C equals y0x = 1.004, while the value for potassium chloride in this solution is y tX = 0.614, indicating a quite large deviation from the ideal behaviour. Thus, the activity coefficient of the solvent is not a suitable characteristic of the real behaviour of solutions of electrolytes. If the deviation from ideal behaviour is to be expressed in terms of quantities connected with the solvent, then the osmotic coefficient is employed. The osmotic pressure of the system is denoted as jz and the hypothetical osmotic pressure of a solution with the same composition that would behave ideally as jt. The equations for the osmotic pressures jt and jt are obtained from the equilibrium condition of the pure solvent and of the solution. Under equilibrium conditions the chemical potential of the pure solvent, which is equal to the standard chemical potential at the pressure p, is equal to the chemical potential of the solvent in the solution under the osmotic pressure jt,... 

The osmotic pressure of an electrolyte solution jt can be considered as the ideal osmotic pressure jt decreased by the pressure jrel resulting from electric cohesion between ions. The work connected with a change in the concentration of the solution is n dV = jt dV — jrel dV. The electric part of this work is then JteldV = dWcl, and thus jzc] = (dWei/dV)T,n. The osmotic coefficient 0 is given by the ratio jt/jt, from which it follows that... 

Helgeson, H. C., D. H. Kirkham and G. C. Flowers, 1981, Theoretical prediction of the thermodynamic behavior of aqueous electrolytes at high temperatures and pressures, IV. Calculation of activity coefficients, osmotic coefficients, and apparent molal and standard and relative partial molal properties to 600 °C and 5 kB. American Journal of Science 281, 1249-1516. 

As a means of verifying the model parameters of Table II, the osmotic coefficient was calculated from isopiestic vapor pressure measurement data (17) for the KCl-KBr-H20 system at 25°C (Table III). 

A wide variety of data for mean ionic activity coefficients, osmotic coefficients, vapor pressure depression, and vapor-liquid equilibrium of binary and ternary electrolyte systems have been correlated successfully by the local composition model. Some results are shown in Table 1 to Table 10 and Figure 3 to Figure 7. In each case, the chemical equilibrium between the species has been ignored. That is, complete dissociation of strong electrolytes has been assumed. This assumption is not required by the local composition model but has been made here in order to simplify the systems treated. 

It can be observed that g is the ratio between the observed osmotic pressure and the osmotic pressure that would be observed for a completely dissociated electrolyte that follows Henry s law [see Equation (15.47)], hence the name, osmotic coefficient. A similar result can be obtained for the boiling point elevation, the freezing point depression, and the vapor pressure lowering. 

The osmotic coefficient of water in NaCl solutions of varying concentration can be calculated from data in Ref. 15. From the resulting values of the osmotic coefficients, the effect of NaCl concentration on the equilibrium temperature for Equation (13.16) can be determined. The results of some calculations for a constant pressure of 1 atm are shown in Figure 20.5 (16). 

To calculate the osmotic pressure we used values of osmotic coefficients from ref. (lOj. Total organic carbon analysis (Beckman 914A] of samples from the water filled compartment verified that the membranes are impermeable to sucrose, so that the reflection coefficient a is equal to unity. 

Clegg, S. L, and P. Brinibleconibe, Equilibrium Partial Pressures and Mean Activity and Osmotic Coefficients of 0-100% Nitric Acid as a Function of Temperature, J. Phys. Chem., 94, 5369-5380 (1990), and references therein. 

Figure 18.6 Thermal properties of aqueous NaCl solutions as a function of temperature, pressure and concentration, (a) activity coefficient (b) osmotic coefficient (c) relative apparent molar enthalpy and (d) apparent molar heat capacity. The effect of pressure is shown as alternating grey and white isobaric surfaces of 7 , , L, and Cp at p = 0.1 or saturation, 20, 30, 40, 50, 70, and 100 MPa, that increase with increasing p in (a), (b), and (d), and decrease with increasing P in (c).

To our knowledge, no one has ever worked out the mathematics for directly estimating the pressure dependence of the osmotic coefficient (or aw) using the Pitzer approach. However, Monnin (1990) developed an alternative model based on the Pitzer approach that allows calculation of the pressure dependence for the activity of water (aw). The density of an aqueous solution (p) can be calculated with the equation... 

Table A.2 is model output for seawater freezing at 253.15 K. Beneath the title, the output includes temperature, ionic strength, density of the solution (p), osmotic coefficient amount of unfrozen water, amount of ice, and pressure on the system. Beneath this line are the solution and gaseous species in the system. The seven columns include species identification, initial concentration, final (equilibrium) concentration, activity coefficient, activity, moles in the solution phase, and mass balance. The mass balance column only contains those components for which a mass balance is maintained. The number of these components minus 1 is generally the number of independent components in the system (in this case, 8 — 1 = 7). The mass balances (col. 7) should equal the initial concentrations (col. 2). This mass balance comparison is a good check on the computational accuracy.

Clegg SL, Brimblecombe P (1990a) Equilibrium partial pressures and mean activity and osmotic coefficients of 0-100% nitric acid as a function of temperature. J Phys Chem 94 5369-5380 Clegg SL, Brimblecombe P (1990b) The solubility and activity coefficient of oxygen in salt solutions and brines. Geochim Cosmochim Acta 54 3315-3328... 

There are many measurement techniques for activity coefficients. These include measuring the colligative property (osmotic coefficients) relationship, the junction potentials, the freezing point depression, or deviations from ideal solution theory of only one electrolyte. The osmotic coefficient method presented here can be used to determine activity coefficients of a 1 1 electrolyte in water. A vapor pressure osmometer (i.e., dew point osmometer) measures vapor pressure depression. 

Heat capacity, molar Heat capacity at constant pressure Heat capacity at constant volume Helmholtz energy Internal energy Isothermal compressibility Joule-Thomson coefficient Pressure, osmotic Pressure coefficient Specific heat capacity Surface tension Temperature Celsius... 

Oral cavity, 125 Ordinate scale, 17 Ordinate value, 17 Organic composition of condensation nuclei, 240-241 Orr, C., 52, 172, 247 Osmotic coefficients, 243 Osmotic pressure, 134 Ottewill, R. H., 264 Oxidation process, 2, 331 Oxygen ... 

The value of osmotic coefficient 6 is the ratio of the osmotic pressure to the one at the ideal mixture condition... 

The model was shown to predict osmotic coefficients to within the experimental error for the determination of osmotic coefficients from saturated vapor pressure measurements. Activity coefficient calculations appeared to be consistent with the available data for mixed electrolyte solutions. 

On application of the van t Hoff equation to the dmg molecules in solution, consideration must be made of any ionisation of the molecules, since osmotic pressure, being a colligative property, will be dependent on the total number of particles in solution (including the free counterions). To allow for what was at the time considered to be anomalous behaviour of electrolyte solutions, van t Hoff introduced a correction factor, i. The value of this factor approaches a number equal to that of the number of ions, v, into which each molecule dissociates as the solution is progressively diluted. The ratio ijv is termed the practical osmotic coefficient, [Pg.69]

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