Surface excess concentration solute

The surface tension of an aqueous solution varies with the concentration of solute according to the equation y = 72 - 350C (provided that C is less than 0.05Af). Calculate the value of the constant k for the variation of surface excess of solute with concentration, where k is defined by the equation V = kC. The temperature is 25°C. 

Equation 9 states that the surface excess of solute, F, is proportional to the concentration of solute, C, multipHed by the rate of change of surface tension, with respect to solute concentration, d /dC. The concentration of a surfactant ia a G—L iaterface can be calculated from the linear segment of a plot of surface tension versus concentration and similarly for the concentration ia an L—L iaterface from a plot of iaterfacial teasioa. la typical appHcatioas, the approximate form of the Gibbs equatioa was employed to calculate the area occupied by a series of sulfosucciaic ester molecules at the air—water iaterface (8) and the energies of adsorption at the air-water iaterface for a series of commercial aonionic surfactants (9). 

If the supply of surfactant to and from the interface is very fast compared to surface convection, then adsorption equilibrium is attained along the entire bubble. In this case the bubble achieves a constant surface tension, and the formal results of Bretherton apply, only now for a bubble with an equilibrium surface excess concentration of surfactant. The net mass-transfer rate of surfactant to the interface is controlled by the slower of the adsorption-desorption kinetics and the diffusion of surfactant from the bulk solution. The characteris-... 

It has been reported that the sonochemical reduction of Au(III) reduction in an aqueous solution is strongly affected by the types and concentration of organic additives. Nagata et al. reported that organic additives with an appropriate hydro-phobic property enhance the rate of Au(III) reduction. For example, alcohols, ketones, surfactants and water-soluble polymers act as accelerators for the reduction of Au(III) under ultrasonic irradiation [24]. Grieser and coworkers [25] also reported the effects of alcohol additives on the reduction of Au(III). They suggested that the rate of the sonochemical reduction of Au(III) is related to the Gibbs surface excess concentration of the alcohol additives. 

Let us consider the interface between two phases, say between a liquid and a vapour, where a solute (i) is dissolved in the liquid phase. The real concentration gradient of solute near the interface may look like Figure 3.1. When the solute increases in concentration near the surface (e.g. a surfactant) there must be a surface excess of solute nf, compared with the bulk value continued right up to the interface. We can define a surface excess concentration (in units of moles per unit area) as ... 

Molecular weight of a solute from tt versus A isotherms Use of the van t Hoff equation for monolayers Suppression of evaporation by monolayers Surface excess concentration from surface tension data... 

In Fig. 3.3 the concentration profiles for solute 2 dissolved in liquid 1 are illustrated. We assume that the solute is enriched at the surface. The area of the dotted region corresponds to the surface excess of solute. 

As explained above, surface excess concentrations are defined relative to an arbitrarily chosen dividing surface. A convenient (and seemingly realistic) choice of location of this surface for a binary solution is that at which the surface excess concentration of the solvent (rA) is zero. The above expression then simplifies to... 

This is an important stabilising effect in foams which are formed from solutions of soaps, detergents, etc. If a film is subjected to local stretching as a result of some external disturbance, the consequent increase in surface area will be accompanied by a decrease in the surface excess concentration of foaming agent and, therefore, a local increase in surface tension (Gibbs effect). Since a certain time is... 

For a two-component solution, because z0 has been positioned to make the surface excess concentration of solvent zero, Eq. (48) becomes... 

With type 1 solutes, surface tension in aqueous solution mildly increases with concentration. Because activities generally increase with concentration, from Eq. (50), these solutes have a negative surface excess concentration (i.e., they are depleted in the surface layer). Inorganic electrolytes show this behavior. In the bulk solution, these ions are stabilized by interacting with the extended ionic environment of the solution. In the surface layer, this environment is limited in extent in one direction. 

Type 2 solutes moderately decrease surface tension in aqueous solution and, thus, have positive surface excess concentrations. This class of solutes includes organic molecules with polar groups that give them some water solubility. Short-chain organic acids, amines, and alcohols are of this type. 

Just as for gas adsorption, we can define a partial differential enthalpy of adsorption of a component, A ads/i(, which would correspond to the adsorption, from a solution of molality b, of an infinitesimal amount of component i, dn, on a solid surface already covered with solute at a reduced surface excess concentration J (n) ... 

The basic information in the study of sorption processes is the quantity of substances on the interfaces. In order to measure the sorbed quantity accurately, very sensitive analytical methods have to be applied because the typical amount of particles (atoms, ions, and molecules) on the interfaces is about I0-5 mol/m2. In the case of monolayer sorption, the sorbed quantity is within this range. As the sorbed quantity is defined as the difference between quantities of a given substance in the solution and/or in the solid before and after sorption processes (surface excess concentration, Chapter 1, Section 1.3.1), all methods suitable for the analysis of solid and liquid phases can be applied here, too. These methods have been discussed in Sections 4.1 and 4.2. In addition, radioisotopic tracer method can also be applied for the accurate measurement of the sorbed quantities. On the basis of the radiation properties of the available isotopes, gamma and beta spectroscopy can be used as an analytical method. Alpha spectroscopy may also be used, if needed however, it necessitates more complicated techniques and sample preparation due to the significant absorption of alpha radiation. The sensitivity of radioisotopic labeling depends on the half-life of the isotopes. With isotopes having medium half-time (days-years), 10 14-10-10 mol can be measured easily. 

For the liquid vapor interface, the surface tension is easUy measured as a function of the concentration as shown in Figure 9.10. The preceding equation can he used to determine the surface excess concentration of surfactant as a function of the sur ctant concentration if the sur ce tension of the solution as a fimction of surfactant concentration is known. For dilute aqueous solutions of organic substrates, the semi-empirical equation for the surface tension, y, of a solution of concentration C2,... 

We see that the shear- (i.e., tangential-) stress components are discontinuous across the interface whenever gradv y is nonzero. Now, the interfacial tension for a two-fluid system, made up of two pure bulk fluids, is a function of the local thermodynamic state - namely, the temperature and pressure. However, it is much more sensitive to the temperature than to the pressure, and it is generally assumed to be a function of temperature only. If the two-fluid system is a multicomponent system, it is often the case that there may be a preferential concentration of one or more of the components at the interface (for example, we may consider a system of pure A and pure B, which are immiscible, with a third solute component C that is soluble in A and/or B but that is preferentially attracted to the interface), and then the interfacial tension will also be a function of the (surface-excess) concentration of these solute components. Both the temperature and the concentrations of adsorbed species can be functions of position on the interface, thus leading to spatial gradients of y. 

For surface-active solutes the surface excess concentration, p can be considered to be equal to the actual surface concentration without significant error. The concentration of surfactant at the interface may therefore be calculated from surface or interfacial tension data by use of the appropriate Gibbs equation. Thus, for dilute solutions of a nonionic surfactant, or for a 1 1 ionic surfactant in the presence of a... 

This expression implies, as expected, that E increases as the thickness of the bulk solution in the lamella or the bulk concentration of the surfactant in the lamella decreases. It also implies a very great dependence on the surface excess concentration of the surfactant, T, and indicates that if T is zero, there is no film elasticity. 

The surface elasticity, therefore, decreases when either the thickness of the lamella or the bulk concentration of surfactant in it increases. Moreover, since T is proportional (equation 2.25) to (8y/81og C)T, the elasticity is very sensitive to change in the surface tension of the solution with change in the bulk phase concentration of the surfactant. Surface excess concentrations F for surfactants usually fall in the range 1-4 x 10-1° mol/cm2. Thus at 27°C (300 K), since R = 83 x 107 ergs moF1 deg-1,... 

The effect of surface-active materials in altering surface tension is expressed quantitatively through the Gibbs equation, which relates the change in surface tension to the concentration of surface-active materials. The relation takes a particularly simple form for a two-component dilute solution consisting of a solvent and a single solute. If the surface excess concentration (mol rn ) of the adsorbed solute is denoted by F and c is the bulk molar concentration, then... 

There is large body of data on the surface and interfacial tensions of aqueous surfactant solutions. This data show that the structure of the surfactant molecule has a pronounced effect on its ability to reduce these tensions. As the length of the alkyl or fluorinated alkyl chain increases, the CMC decreases and the surface excess concentration increases, causing a drop in the interfacial tension at a fixed surfactant concentration. At low surfactant concentrations the reduction in surface tension (or increase in surface pressure O = yo - y) is linear with the molar bulk solute concentration c (in the case of the dilute solution)... 

According to Eq. (28), at a constant solution composition, the smaller the absolute value of Fw, the smaller is the absolute value of the difference between surface excess concentrations and (relative) surface excesses. Since the extent of the reference phase can be selected arbitrarily, and the value of AF, depends directly on this choice, the latter is ill defined from a thermodynamic point of view. However, by introducing some nonthermodynamic assumptions, the value of AF can be estimated for several special cases. If the above-mentioned monolayer model can be considered as a reKable description of the interphase, the value of Fw is small, and the concentration of the species i in the solution (x, ) is also low, therefore AF,- is negligible, and Eq. (22) is always true. 

Adsorption is an entropically driven process by which molecules diffuse preferentially from a bulk phase to an interface. Due to the affinity that a surfactant molecule encounters towards both polar and non-polar phases, thermodynamic stability (i.e. a minimum in free energy or maximum in entropy of the system) occurs when these surfactants are adsorbed at a polar/non-polar (e.g. oil/water or air/water) interface. The difference between solute concentration in the bulk and that at the interface is the surface excess concentration. The latter... 

For a two-component Uquid-vapor system where the Gibbs dividing surface is defined so that the surface excess concentration of the solvent is zero (F = 0), the summation in Equation (9.12) is no longer necessary and a simple relationship between the surface tension of the liquid phase, o, and the surface excess concentration of solute i, F is obtained. It is therefore possible to employ experimentally accessible quantities such as surface tension and chemical potential to calculate the surface excess concentration of a solute species and to use that information to make other indirect observations about the system and its components. 

It is well known that the air/solution interface of an amphiphile solution is well populated (Clint, 1992) by the adsorbed molecules. Accordingly, it has been shown that the concentration of the surfactant is always greater at the surface due to adsorption over and above the concentration of surfactant in the bulk. For calculation of Gibbs free energy changes, required different surface properties (e.g., the surface excess concentration, Tmax, minimum area per surfactant molecule at the air/water interface, Amin etc.). The surface excess concentration is an effective measure of the Gibbs adsorption at liquid/air interface, which was calculated by applying equation (Chattoraj Birdi, 1984)... 

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