Equilibrium, chemical osmotic

A close analogy exists between swelling equilibrium and osmotic equilibrium. The elastic reaction of the network structure may be interpreted as a pressure acting on the solution, or swollen gel. In the equilibrium state this pressure is sufficient to increase the chemical potential of the solvent in the solution so that it equals that of the excess solvent surrounding the swollen gel. Thus the network structure performs the multiple role of solute, osmotic membrane, and pressure-generating device. 

Jacobus Hendricus van t Hoff (1852-1911) was born in Rotterdam, Netherlands, and studied at Delft, Leyden, Bonn, Paris, and Utrecht. Widely educated, he served as professor of chemistry, mineralogy, and geology at the University of Amsterdam from 1878 to 1896, and later became professor at Berlin. He received the first Nobel Prize in chemistry in 1901 for hts work on chemical equilibrium and osmotic pressure. 

From a difference in chemical potential it is easy to calculate a clear quantity, the osmotic pressure. Flory has drawn the analogy between swelling equilibrium and osmotic equilibrium (Flory 1953). The difference between the osmotic pressure and the elastic response 71 / of the network chains in the swollen network is named swelling pressure Ures- H can be calculated as following ... 

Systems for extracting, transforming, and using energy from the environment (Fig. 1-lb), enabling organisms to build and maintain their intricate structures and to do mechanical, chemical, osmotic, and electrical work. Inanimate matter tends, rather, to decay toward a more disordered state, to come to equilibrium with its surroundings. 

In chemical thermodynamics, osmotic pressure should be determined as follows [8]. Consider the equilibrium between a solution whose chemical potential is jji and a solvent whose chemical potential is fi". The solution and the solvent are separated by a semi-permeable membrane. The chemical (osmotic) equilibrium between them occurs under the condition... 

The criterion for phase equilibrium is given by Eq. (8.14) to be the equality of chemical potential in the phases in question for each of the components in the mixture. In Sec. 8.8 we shall use this idea to discuss the osmotic pressure of a... 

To conclude, the introduction of species-selective membranes into the simulation box results in the osmotic equilibrium between a part of the system containing the products of association and a part in which only a one-component Lennard-Jones fluid is present. The density of the fluid in the nonreactive part of the system is lower than in the reactive part, at osmotic equilibrium. This makes the calculations of the chemical potential efficient. The quahty of the results is similar to those from the grand canonical Monte Carlo simulation. The method is neither restricted to dimerization nor to spherically symmetric associative interactions. Even in the presence of higher-order complexes in large amounts, the proposed approach remains successful. 

The chemical potential of associating systems has also been studied more recently by Bryk et al. [2]. They have extended the usual GEMC method for studying osmotic equihbrium by including four simulation cells in series, rather than the usual two compartments, but with osmotic equilibrium established between only two adjacent compartments (e.g. I and II, II and III, or IV and I). Each semi-permeable membrane was made permeable to only one species as shown and described below ... 

The deduction adopted is due to M. Planck (Thermodynamik, 3 Aufl., Kap. 5), and depends fundamentally on the separation of the gas mixture, resulting from continuous evaporation of the solution, into its constituents by means of semipermeable membranes. Another method, depending on such a separation applied directly to the solution, i.e., an osmotic process, is due to van t Hoff, who arrived at the laws of equilibrium in dilute solution from the standpoint of osmotic pressure. The applications of the law of mass-action belong to treatises on chemical statics (cf. Mel lor, Chemical Statics and Dynamics) we shall here consider only one or two cases which serve to illustrate some fundamental aspects of the theory. 

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

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,... 

Osmosis is the passage of a pure solvent into a solution separated from it by a semipermeable membrane, which is permeable to the solvent but not to the polymeric solute. The osmotic pressure n is the pressure that must be applied to the solution in order to stop the flow. Equilibrium is reached when the chemical potential of the solvent is identical on either side of the membrane. The principle of a membrane osmometer is sketched in Figure 2. 

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. 

Under fuel cell operation, a finite proton current density, 0, and the associated electro-osmotic drag effect will further affect the distribution and fluxes of water in the PEM. After relaxation to steady-state operation, mechanical equilibrium prevails locally to fix the water distribution, while chemical equilibrium is rescinded by the finite flux of water across the membrane surfaces. External conditions defined by temperature, vapor pressures, total gas pressures, and proton current density are sufficient to determine the stationary distribution and the flux of water. 

It should be noted that the condition of a dilute solution was introduced into the considerations for two reasons primarily, in order that it would be possible to replace the activities by concentrations and thus determine the equilibrium concentrations on the basis of (2.3.3) and, secondarily, in order for it to be possible to neglect the effect of pressure on the chemical potentials of the components whose electrochemical potentials appear in (2.3.2). Because of the differing ionic concentrations in solutions 1 and 2, the osmotic pressures in these solutions are not identical and this difference must be compensated by external pressure. A derivation considering the effect of pressure can be found, for example in [9] or p. 191 of [18]. 

Fugacity. Accdg to Hackh s (Ref 1), it is the escaping tendency in a heterogeneous mixture, by which. a chemical equilibrium responds to altered conditions. In a dilute soln obeying the gas laws, the fugacity equals the osmotic pressure. In other solns it is the value of the pressure for which these equations are still valid... 

For a binary polymer solution, the reciprocal of the osmotic compressibility 0n/0c at constant T and the solvent chemical potential p0 can be determined by sedimentation equilibrium through the relation [58,59] ... 

This relationship constitutes the basic definition of the activity. If the solution behaves ideally, a, =x, and Equation (18) define Raoult s law. Those four solution properties that we know as the colligative properties are all based on Equation (12) in each, solvent in solution is in equilibrium with pure solvent in another phase and has the same chemical potential in both phases. This can be solvent vapor in equilibrium with solvent in solution (as in vapor pressure lowering and boiling point elevation) or solvent in solution in equilibrium with pure, solid solvent (as in freezing point depression). Equation (12) also applies to osmotic equilibrium as shown in Figure 3.2. 

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