The Power Exchange Function

It has been found that for binary exchange, a mass action expression in which the ratio of sorbed cation mole fractions is raised to the nth power (n 1), can fit a wider range of empirical sorption data than when n = 1. Thus, for the homovalent exchange reaction. 

In the simplest case, = n = 1 in Eq. (10.25). For such conditions the reaction is called Don-nan exchange. Donnan exchange behavior has several implications  

the exchange reaction is controlled by valence differences of the ions only, not size differences. Sorption occurs between sorbate ions and a surface of opposite sign and the bonding is strictly electrostatic  

the activity coefficients of both dissolved and sorbed ions have equal ratios and those ratios are constant and equal unity. 

Donnan exchange best applies to the sorption of major dissolved cations ( 1 O to 10 mol/kg) such as Na, Ca, and Mg + by minerals of practically constant surface charge, such as the smectite and vermiculite clays and zeolitic minerals. 

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Simple ion exchange describes the competitive adsorption onto clays of most metal cations present in solution at concentrations from about 10 to 10 mol/kg. It has most often been used.to describe the sorption of alkaline earth and alkali metal cations onto clays. In the case of minerals having pH-dependent surface charge (e.g., kaolinite, metal oxyhydroxides) simple ion exchange or the power-exchange function (see below) may also fit the adsorption data mea.sured in systems at constant pH. 

What is the power-exchange function and how is it related to ion exchange and Donnan exchange Give examples of the applicability of each of these approaches to competitive cation adsorption. How are activity coefficients dealt with in ion-exchange reactions ... 

Langmuir, D. 1981, The power exchange function A general model for metal adsorption onto geological materials. In Adsorption from aqueous solutions, ed D. H, Tewari, pp. 1-17. New York Plenum Press. 

When an empirical fit of exchange data can be accomplished with a power exchange function in which n = 1, but 1, the reaction can be termed simple ion exchange. That a sorption reaction obeys simple ion exchange implies that... 

The general power-exchange function applies when n I and 1. The exchange reaction... 

The sorption equilibrium obeys a power-exchange function... 

OzsvATH, D. 1979. Modeling heavy metal sorption from subsurface waters with the n-power exchange function. M.S. thesis. The Pennsylvania State Univ, University Park, PA. 

In ion-exchange chromatography (lEC), the mobile phase modulator is typically a salt in aqueous solution, and the stationary phase is an ion-exchanger. For ddnte conditions, the solute retention faclor is commonly found to be a power-law function of the salt uormahty [cf. Eq. (16-27) for ion-exchange equilibrium]. 

This study presents kinetic data obtained with a microreactor set-up both at atmospheric pressure and at high pressures up to 50 bar as a function of temperature and of the partial pressures from which power-law expressions and apparent activation energies are derived. An additional microreactor set-up equipped with a calibrated mass spectrometer was used for the isotopic exchange reaction (DER) N2 + N2 = 2 N2 and the transient kinetic experiments. The transient experiments comprised the temperature-programmed desorption (TPD) of N2 and H2. Furthermore, the interaction of N2 with Ru surfaces was monitored by means of temperature-programmed adsorption (TPA) using a dilute mixture of N2 in He. The kinetic data set is intended to serve as basis for a detailed microkinetic analysis of NH3 synthesis kinetics [10] following the concepts by Dumesic et al. [11]. 

Once the plate starts to corrode, many problems appear to affect performance and durability, even serious failure, of fhe fuel cells. For example, fhe interface contact resistance between the corroded metal plates and GDL will increase to reduce the power output. The corrosion products (mainly various cations) will contaminate the catalyst and membrane and affect eir normal functions because the polymer membrane essentially is a strong cation exchanger and the catalyst is susceptible to the ion impurity. Hence, adding a corrosion-resistant coating to the metal plate will almost inevitably assure the performance and long-term durability of a sfack. 

The ratio of symmetry numbers s s° in equation 11.40 merely represents the relative probabilities of forming symmetrical and unsymmetrical molecules, and ni and nf are the masses of exchanging molecules (the translational contribution to the partition function ratio is at all T equal to the power ratio of the inverse molecular weight). Denoting as AX, the vibrational frequency shift from isotopically heavy to light molecules (i.e., AX, = X° — X ) and assuming AX, to be intrinsically positive, equation 11.40 can be transated into... 

Taking the specific net power output (net output power per unit total heat exchanger surface area) as the design objective function, optimize the warm-side (heater or high-temperature side heat exchanger) and cold-side (cooler or low-temperature side heat exchanger) working fluid temperatures. 

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