Langmuir isotherm, determination adsorption constant values

A Langmuir isotherm for an adsorption experiment shows that X, the amount of solute sorbed per weight sorbate, is 0.085 when the solute concentration in the fluid phase is 0.05. If the Langmuir constant K for the experimental conditions is 1.3, apply the concept of a unit operation to determine the value of X when the solute concentration is 0.1. Plot the Langmuir isotherm for C values of 2,4, 6, 8, and 10. What does the plot tell you about the amount of solute absorbed vs the fluid phase concentration ... 

In Section 4-1, it was shown that isotherm linearity is determined by 6, the fractional coverage of the surface by sample. The maximum value of 0 for isotherm linearity (the linear capacity 0o.i) in turn depends upon adsorbent heterogeneity specifically, the types of adsorbent sites (as defined by their Ki values) and their relative concentrations (iV,). Nowhere have we considered the variation of linear capacity with the extent of sample adsorption, i.e., the dependence of 60.1 on A . For a Langmuir isotherm Eq. (4-1) shows that linear capacity corresponds to 10% surface coverage, regardless of the value of X . Similarly, for a surface which contains several different site types (differing in values), it may easily be shown that if the Kf values of all sites are increased by a constant factor Q, K° is... 

Figures 13.18-13.22 display results of Langmuir analyses of adsorption isotherm data from steel-steel and steel-starch friction and hexadecane-water interfacial-tension measurements. As can be seen in figs. 13.18-13.22, in all cases plots of [veg oil] vs. 9 gave a straight line with an intercept close to 1. From linear regression analyses of the data, the exact values of the intercepts and slopes are obtained. From the slope, the equilibrium constant Kq is determined and used to calculate the free energy of adsorption using eq. (13.10).

Hoeft [44] also studied the cooperative and competitive adsorption of ionic surfactant mixtures onto hydrophobic surfaces. When shorter alkyl chain surfactants (sodium octyl sulfonate and sodium decyl sulfonate) are adsorbed, the decyl will displace the octyl surfactant. For mixtures of sodium dodecyi sulfonate and sodium octyl sulfonate, however, there appears to be an association between the surfactant molecules leading to enhanced adsorption of the sodium dodecyi sulfonate with no depletion of the octyl sulfonate adsorption. This is shown in Fig, 2, where the lines indicate the expected adsorption determined using a two-component Langmuir adsorption isotherm with the adsorption parameters determined analyzing the data from adsorption of each species individually. Also shown in Fig. 2 is the concentration of surface-active materials in the aqueous phase at equilibrium. In each of these experiments the total molar concentration and amount of surfactant solution added to the latex was a constant, as was the amount of latex. Thus a lower value for the bulk concentration corresponds to greater adsorption. 

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