Coefficients in Liquids at Infinite Dilution

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 ... 

In this case the equations are greatly simplified and the ratio of the slopes of the two phase boundaries at xA =1 is given by the activity coefficients of B at infinite dilution in the liquid and solid phases [11] ... 

The gas-phase diffusion coefficients are calculated using the equation given in Ref. [40]. The liquid-phase diffusion coefficients of components at infinite dilution in... 

Using a similar experimental set-up as for the determination of Abraham s solvation parameters, the activity coefficient of solutes at infinite dilution y" cm be determined from their retention times using gas-liquid chromatography [12, 67-72], Alternatively, the diluter technique is applied [67, 73] for which an inert gas transports the solute from the headspace (which is in equilibrium with the ionic liquid matrix) to a GC-column. The continuous decrease of the concentration in the headspace is measured as a function of time, generating an exponential function from which y°° is calculated. 

A wastewater stream of 0.038 m3/s, containing 10 ppm (by weight) of benzene, is to be stripped with air in a packed column operating at 298 K and 2 atm to reduce the benzene concentration to 0.005 ppm. The packing specified is 50-mm plastic Pall rings. The airflow rate to be used is five times the minimum. Henry s law constant for benzene in water at this temperature is 0.6 kPa-m3/mol (Davis and Cornwell, 1998). Calculate the tower diameter if the gas-pressure drop is not to exceed 500 Pa/m of packed height. Estimate the corresponding mass-transfer coefficients. The diffusivity of benzene vapor in air at 298 K and 1 atm is 0.096 cm2/s the diffusivity of liquid benzene in water at infinite dilution at 298 K is 1.02 x 10 5 cm2/s (Cussler, 1997). 

Kikuti has carefully studied the viscosities of sodium-ammonia solutions with concentrations ranging from infinite dilution to about 7.5M (supersaturated) at temperatures between —30 and -1-30°C. At all temperatures the coefficient of viscosity decreased with increase in concentration, the decrease being quite steep up to AM and then slowing down. At the highest concentrations, the coefficient of viscosity seemed to approach a constant value characteristic of the temperature. At — 30° C, close to the boiling point of liquid ammonia, the coefficient of viscosity at infinite dilution was 0.25 centipoises and at 7.5M it was 0.16 centipoises. At all concentrations, the viscosity decreased with increase in temperature similar to the behavior observed for pure ammonia. 

The activity coefficient of chromium in iron at infinite dilution relative to pure solid chromium as the standard state is unity. Calculate the change in free energy when solid chromium is dissolved in iron so as to form an infinitely dilute, weight percent solution of chromium in liquid iron at 1800 C (2073K) from the following data ... 

Vanadium melts at 1720°C (1993 K). The Raoultian activity coefficient of vanadium at infinite dilution in liquid iron at 1620°C (1893 K) is 0.068. Calculate the free energy change accompanying the transfer of the standard state from pure solid vanadium to the infinitely dilute, weight percent solution of vanadium in pure iron at 1620°C. 

This equation is simply Pick s first law of diffusion. Note that Ui — 0, but Ui is nonzero. Furthermore, for this binary system of solute i in a liquid s, the ideal solution binary diffusion coefficient D (valid at infinite dilution) is... 

Many more correlations are available for diffusion coefficients in the liquid phase than for the gas phase. Most, however, are restiicied to binary diffusion at infinite dilution D°s of lo self-diffusivity D -. This reflects the much greater complexity of liquids on a molecular level. For example, gas-phase diffusion exhibits neghgible composition effects and deviations from thermodynamic ideahty. Conversely, liquid-phase diffusion almost always involves volumetiic and thermodynamic effects due to composition variations. For concentrations greater than a few mole percent of A and B, corrections are needed to obtain the true diffusivity. Furthermore, there are many conditions that do not fit any of the correlations presented here. Thus, careful consideration is needed to produce a reasonable estimate. Again, if diffusivity data are available at the conditions of interest, then they are strongly preferred over the predictions of any correlations. 

The net retention volume and the specific retention volume, defined in Table 1.1, are important parameters for determining physicochemical constants from gas chromatographic data [9,10,32]. The free energy, enthalpy, and. entropy of nixing or solution, and the infinite dilution solute activity coefficients can be determined from retention measurements. Measurements are usually made at infinite dilution (Henry s law region) in which the value of the activity coefficient (also the gas-liquid partition coefficient) can be assumed to have a constant value. At infinite dilution the solute molecules are not sufficiently close to exert any mutual attractions, and the environment of each may be considered to consist entirely of solvent molecules. The activity... 

Here /g,hq and y ,ss are the activity coefficients of component B in the liquid and solid solutions at infinite dilution with pure solid and liquid taken as reference states. A fus A" is the standard molar entropy of fusion of component A at its fusion temperature Tfus A and AfusGg is the standard molar Gibbs energy of fusion of component B with the same crystal structure as component A at the melting temperature of component A. 

Heintz, A., Kulikov, D.V., and Verevkin, S.R, Thermodynamic properties of mixtures containing ionic liquids. 1. Activity coefficients at infinite dilution of alkanes, alkenes, and alkylbenzenes in 4-methyl-M-butylpyridinium tetrafluo-roborate using gas-liquid chromatography, /. Chem. Eng. Data, 46,1526,2001. 

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