In order to estimate the quantity of adsorbate in the monolayer, the density of the liquid adsorbate and the volume of the molecule must be used. If the liquid is assumed to consist of a close-packed fee structure, the minimum surface area for [Pg.123]

1 mol of adsorbate in a monolayer on a substrate can be calculated from the density of the liquid pHq and the molecular mass of the adsorbate M ds- [Pg.123]

To study adsorption, in practice, the relationship between the amount adsorbed, a, and the equilibrium pressure, / , at constant temperature, T, is measured in order to get an adsorption isotherm [1] [Pg.276]

For separation by adsorption, adsorption capacity is often the most important parameter because it determines how much adsorbent is required to accomplish a certain task. For the adsorption of a variety of antibiotics, steroids, and hormons, the adsorption isotherm relating the amount of solute bound to solid and that in solvent can be described by the empirical Freundlich equation. [Pg.276]

Another correlation often employed to correlate adsorption data for proteins is the Langmuir isotherm, [Pg.276]

1 Since the concentration in the adsorbent phase Y is expressed as a solute-free basis, the concentration in the diluent phase X is also expressed on a solute-free basis for uniformity. However, for dilute solutions, the difference between X (mass fraction on a solute-free basis) and x (mass fraction in solution including solute) is negligible. [Pg.276]

The data of v. Szyszkowski have been employed for determining FA. [Pg.48]

There are three forms of the Langmuir-Szyszkowski equation, Eq. III-57, Eq. Ill-107, and a third form that expresses ir as a function of F. (n) Derive Eq. III-57 from Eq. Ill-107 and (b) derive the third form. [Pg.93]

These two equations represent the generalized Szyszkowski-Langmuir adsorption model. [Pg.31]

Equations 21 and 22 present the useful extension of the Szyszkowski-Langmuir model to the adsorption with two orientational states at the interface. If the molecular interactions are considered, a similar simphfied model with P = 2 = P and b = b2 = b can be obtained from Eqs. 10 and 11, giving [Pg.32]

The Frumkin theory with Eqs. 17-18 presents the first improvement of the Szyszkowski-Langmuir theory and is shown in Pig. 1 by the thick line. The Frumkin theory requires input for the surfactant interaction parameter [Pg.38]

In the following table are given the limiting values of A calculated from Milner s and v. Szyszkowski s equations by Langmuir and Harkins. [Pg.45]

Very careful measurements by the method of capillary rise have been carried out by Volkmann, v. Szyszkowski, Richards and Harkins. [Pg.11]

Finally, assuming the ideality of both the enthalpic and entropic mixing gives p = 0 and Eqs. 17 and 18 simplify to the well-known Szyszkowski-Langmuir equation given by [Pg.31]

Bianco and Marmur [143] have developed a means to measure the surface elasticity of soap bubbles. Their results are well modeled by the von Szyszkowski equation (Eq. III-57) and Eq. Ill-118. They find that the elasticity increases with the size of the bubble for small bubbles but that it may go through a maximum for larger bubbles. Li and Neumann [144] have shown the effects of surface elasticity on wetting and capillary rise phenomena, with important implications for measurement of surface tension. [Pg.90]

Fig.l Surface tension versus solution concentration of nonionic surfactant CnEs as measured at r = 298.15 K (data points) [45], and as predicted by the Szyszkowski-Langmuir adsorption model (thin line) described by Eq. 20 and by the Frumkin adsorption model (thick line) described by Eqs. 17-18 [Pg.39]

Similar conclusions as to the attainment of a finite maximum value of r as pointed out by Langmuir J.A.G.S. xxxix. 1883, 1917) can be obtained from an empiric equation put forward by V. Szyszkowski Zeit Phys. Qhem. LXiv. 385,1908) in the following form [Pg.42]

Where T is the excess surface concentration and R and T have their usual meanings. In order to evaluate the slopes, dyint/dCp, the experimental data of dyint versus Qc and Cpeo can be adjusted to the empirical equation of Szyszkowski [30], [Pg.213]

Fig. 3 Comparison of the surface tension for nonionic surfactant CnEg as measured at T = 298.15 K, data points [45], with improved models considering orientational states of surfactant molecules at the surface. The data shown are obtained by regression analysis minimizing the revised chi-square The calculation with fi = 0 represents the best fit of the improved Szyszkowski-Langmuir model described by Eqs. 21 and 22. The other calculated curve with =- 3.921 shows the best fit of the improved Frumkin adsorption model described by Eqs. 23 and 24 |

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