Infinite dilution equilibrium ratio

Gmehhng and Onken (op. cit.) give the activity coefficient of acetone in water at infinite dilution as 6.74 at 25 C, depending on which set of vapor-liquid equilibrium data is correlated. From Eqs. (15-1) and (15-7) the partition ratio at infinite dilution of solute can he calculated as follows ... 

The simplest mode of IGC is the infinite dilution mode , effected when the adsorbing species is present at very low concentration in a non-adsorbing carrier gas. Under such conditions, the adsorption may be assumed to be sub-monolayer, and if one assumes in addition that the surface is energetically homogeneous with respect to the adsorption (often an acceptable assumption for dispersion-force-only adsorbates), the isotherm will be linear (Henry s Law), i.e. the amount adsorbed will be linearly dependent on the partial saturation of the gas. The proportionality factor is the adsorption equilibrium constant, which is the ratio of the volume of gas adsorbed per unit area of solid to its relative saturation in the carrier. The quantity measured experimentally is the relative retention volume, Vn, for a gas sample injected into the column. It is the volume of carrier gas required to completely elute the sample, relative to the amount required to elute a non-adsorbing probe, i.e. 

This means that, with increasing length of chain, the equilibrium constants K1 and K2 (the first and second dissociation constants at infinite dilution of the acid) should not tend to equality rather their ratio K1/K2 should tend toward the value 4, as recognized by Adams.1... 

The substituent constant of the Hammett equation has been related successfully to the logarithm of the activity coefficient ratio at infinite dilution for a series of meta and para isomers of phenol. Hammett stated that a free energy relationship should exist between the equilibrium or rate behavior of a benzene derivative and a series of corresponding meta and para monosubstitut-ed benzene derivatives. The Hammett equation may be written... 

Once the composition of each equilibrium phase is known, infinite dilution activity coefficients for a third component in each phase can then be calculated. The octanol—water partition coefficient is direcdy proportional to the ratio of the infinite dilution activity coefficients for a third component distributed between the water-rich and octanol-rich phases (5,24). The primary drawback to the activity coefficient approach to Kqw estimation is the difficulty of the calculations involved, particulady when the activity coefficient model is complex. 

Calculation of Liquid-to-Gas Ratio The minimum possible liquid rate is readily calculated from the composition of the entering gas and the solubility of the solute in the exit liquor, with equilibrium being assumed. It may be necessary to estimate the temperature of the exit liquid based upon the heat of solution of the solute gas. Values of latent heat and specific heat and values of heats of solution (at infinite dilution) are given in Sec. 2. 

Binary interaction parameters (Ay) and infinite dilution activity coefficients are available for a wide variety of binary pairs. Therefore the ratio of the solute infinite dilution coefficient in solvent-rich phase to that of the second phase ( ) will provide an estimate of the equilibrium distribution coefficient. The method can provide a reasonable estimate of the distribution coefficient for dilute cases. 

Here F is the phase ratio (Vs/Vm) and a is the equilibrium constant at infinite dilution which coincides with the initial slope of the isotherm. For a heterogeneous surface with two types of adsorption sites the retention factor k is the sum of two contributions, originating from type-I and type-II sites, and a general expression of the retention factors of the two enantiomers under linear conditions can be expressed as ... 

Compilations of infinite-dilution activity coefficients, when available for the solute of interest, may be used to rank candidate solvents. Partition ratios at finite concentrations can be estimated from these data by extrapolation from infinite dilution using a suitable correlation equation such as NRTL [Eq. (15-25)]. Examples of these lands of calculations are given by Walas [Phase EquU ria in Chemical Engineering (Butterworth-Heinemann, 1985)]. Most activity coefficients available in the literature are for small organic molecules and are derived from vapor-liquid equilibrium measurements or azeotropic composition data. 

R is the gas constant, Bn is the second virial coefficient for the probe, B13 is the mixed virial coefficient of the solute vapor and carrier gas, V is the partial molar volume of 1 at infinite dilution, P is the total pressure, and K is the equilibrium partition coefficient, defined as the ratio of concentration of solute in the stationary phase, q, to that in the gas phase, c, that is, K s q/c. 

Zero Coverage. The peaks at Infinite dilution were slightly skewed (skew ratio 0.8), with virtually no dependence of retention volume on Injection size. Instead of the peak maximum method, retention volumes were measured by the method proposed by Conder and Young (32). To ensure that the adsorption of n-alkanes on carbon fibers was taking place under equilibrium conditions, the flow rate was varied In the range 20 to 32 cm3 min-1. The net retention volumes were essentially Independent of flow rate. 

Tc, numbers of adsorbent sites occupied by the solute and solvent, respectively, and V and van der Waals molar volumes of solute and solvent, respectively Kf is the ratio of the equilibrium concentrations of the solute in the stationary and mobile phases at infinite dilution of the solute ... 

The model of Chang and Rochelle (16) was used in this work with appropriate equilibrium constants and diffusivities to represent operation at 55°C in 0.3 M NaCl or 0.1 M CaCl2 (Tables III and W). Because the model uses only diffusivity ratios, the diffusivities in NaCl solution were taken to be the same as those at infinite dilution and 25°C (16), assuming that the diffusivity ratios were independent of temperature and NaCl concentration. 

Since the concentration of the TSC is vanishingly small, its activity coefficient may be assumed to be constant, corresponding to its value at infinite dilution. Thus, even though the rate of reaction on a catalyst is assumed to be proportional to the surface concentration of the transition-state complex (TSC), this in turn becomes related to the species activities in the bulk fluid due to the assumed pseudo-equilibrium between TSC. Further, the ratio of the forward and reverse rate constants... 

Figure 6 Partitioning of LiCl between water and 1-octanol at 25°C, as taken from ref. [2l6]. The lithium distribution ratios Du were determined at 1 1 initial phase ratio by use of ion chromatography (IC), inductively coupled plasma (ICP) atomic emission spectrometry, and Li NMR spectrometry. A correction was made for the slight volume changes due to the mutual solubility of 1-octanol and water. Error bars are indicated only for the ICP data, which were the least precise data obtained by the three techniques. The solid curved line represents the equilibrium model calculated by SXLSQl using the values of log/Cs= = —6.85 and logX, = — 2.74 (Table 12). The dashed curved line is an extrapolation of the model to indicate the approach to the calculated asymptotic value of the distribution ratio at infinite dilution (3.76 X 10...

SA2 Sato, Y., Tsuboi, A., Sorakubo, A., Takishima, S., Masuoka, H., and Ishikawa, T., Vapor-liquid equilibrium ratios for hexane at infinite dilution in ethylene + impact polypropylene copolymer and propylene + impact polypropylene copolymer. Fluid... 

Octanol is quite insoluble in water and vice versa hence the partition coefficients are not strongly temperature dependent, being mostly in the order of 0.001 to 0.01 log units per K (Lyman, 1990b). Even the low mutual solubility - at equilibrium the aqueous phase contains 4.5 x 10" mol/11-octanol and the organic phase contains 2.3 mol/1 water (Lyman, 1990b) - reveals so that the 1-octanol/water partition coefficient does not equal the ratio of the compounds solubilities in the individual solvents. This miscibility of the solvent phases, as well as ionization and association phenomena, limits the stringent validity of the presumed Nemst distribution, which, moreover, requires infinite dilution. Hence, at concentrations > 0.01 mol/1, is frequently observed to be dependent on the solute concentration. 

Due to the difficulty measuring ion activities, stability constants (fii) are typically determined at constant ionic strength and temperature. Such conditional values are valid thermodynamic parameters describing ion interactions in a specific standard state (different from infinite dilution, which condition defines Ihe true thermodynamic equilibrium). The ratio of activity coefficients (y,) is constant to a first approximation at a constant ionic strength and temperature. This ratio can therefore be combined into... 

For the data used, the ratio of solubility to (total) chloride concentration varied only slowly with concentration. Thus, conversion from one concentration scale to another left the functional form virtually unchanged. It should be observed that the change of concentration units has only a trivial effect on the thermodynamic equilibrium constants. Their determination requires only that the expressions provide suitable functions for extrapolation to infinite dilution."... 

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