Area, molecular

Application of 150 MPa pressure increases the interfacial tension for w-hex-ane-water from 50.5 to 53.0 mN/m at 25°C. Calculate AV. What is AV for that area corresponding to a molecular size (take a representative molecular area to be 20 A ) Convert this to cm /cm mol. 

Neumann has adapted the pendant drop experiment (see Section II-7) to measure the surface pressure of insoluble monolayers [70]. By varying the droplet volume with a motor-driven syringe, they measure the surface pressure as a function of area in both expansion and compression. In tests with octadecanol monolayers, they found excellent agreement between axisymmetric drop shape analysis and a conventional film balance. Unlike the Wilhelmy plate and film balance, the pendant drop experiment can be readily adapted to studies in a pressure cell [70]. In studies of the rate dependence of the molecular area at collapse, Neumann and co-workers found more consistent and reproducible results with the actual area at collapse rather than that determined by conventional extrapolation to zero surface pressure [71]. The collapse pressure and shape of the pressure-area isotherm change with the compression rate [72]. 

Fig. rV-IS. A fluorescence micrograph showing the dural solid domains formed in a mixture of the two enantiomers of dipalmitoylpho hatidylcholine (DPPC) at a pressure of 9 dyn/cm and average molecular area of 70 A. (From Ref. 169.)... 

Barnes cautions about using the appropriate units (molecular area with mole fraction, or area per unit mass with mass fraction) when analyzing area data [244]. 

Assume that an aqueous solute adsorbs at the mercury-water interface according to the Langmuir equation x/xm = bc/( + be), where Xm is the maximum possible amount and x/x = 0.5 at C = 0.3Af. Neglecting activity coefficient effects, estimate the value of the mercury-solution interfacial tension when C is Q.IM. The limiting molecular area of the solute is 20 A per molecule. The temperature is 25°C. 

One hundred milliliters of an aqueous solution of methylene blue contains 3.0 mg dye per liter and has an optical density (or molar absorbancy) of 0.60 at a certain wavelength. After the solution is equilibrated with 25 mg of a charcoal the supernatant has an optical density of 0.20. Estimate the specific surface area of the charcoal assuming that the molecular area of methylene blue is 197 A. ... 

Dye adsorption from solution may be used to estimate the surface area of a powdered solid. Suppose that if 3.0 g of a bone charcoal is equilibrated with 100 ml of initially 10 Af methylene blue, the final dye concentration is 0.3 x 10 Af, while if 6.0 g of bone charcoal had been used, the final concentration would have been 0.1 x Qr M. Assuming that the dye adsorption obeys the Langmuir equation, calculate the specific surface area of the bone charcoal in square meters per gram. Assume that the molecular area of methylene blue is 197 A. ... 

The example of Section XI-5B may be completed as follows. It is found that 0 = 0.5 at a butanol concentration of 0.3 g/100 cm. The heat of solution of butanol is 25 cal/g. The molecular area of adsorbed butanol is 40 A. Show that the heat of adsorption of butanol at this concentration is about 50 ergs/cm. ... 

At what molecular area should a fatty-acid film spread on 0.05A/ NaOH have a film pressure of 4 dyn/cm, according to the Donnan treatment and to the Gouy treatment Assume the hydrocarbon part of the film to behave as an ideal gas. Assume 20°C. 

Davies [114] found that the rates of desorption of sodium laurate and of lauric acid films were in the ratio 6.70 1 at 21.5°C at molecular areas of 90 and 60 per molecule, respectively. Calculate o. the potential at the plane CD in Fig. XV-12. 

A variety of experimental data has been found to fit the Langmuir equation reasonably well. Data are generally plotted according to the linear form, Eq. XVn-9, to obtain the constants b and n from the best fitting straight line. The specific surface area, E, can then be obtained from Eq. XVII-10. A widely used practice is to take to be the molecular area of the adsorbate, estimated from liquid or solid adsorbate densities. On the other hand, the Langmuir model is cast around the concept of adsorption sites, whose spacing one would suppose to be characteristic of the adsorbent. See Section XVII-5B for an additional discussion of the problem. 

Finally, it is perfectly possible to choose a standard state for the surface phase. De Boer [14] makes a plea for taking that value of such that the average distance apart of the molecules is the same as in the gas phase at STP. This is a hypothetical standard state in that for an ideal two-dimensional gas with this molecular separation would be 0.338 dyn/cm at 0°C. The standard molecular area is then 4.08 x 10 T. The main advantage of this choice is that it simplifies the relationship between translational entropies of the two- and the three-dimensional standard states. 

The standard entropy of adsorption AS2 of benzene on a certain surface was found to be -25.2 EU at 323.1 K the standard states being the vapor at 1 atm and the film at an area of 22.5 x T per molecule. Discuss, with appropriate calculations, what the state of the adsorbed film might be, particularly as to whether it is mobile or localized. Take the molecular area of benzene to be 22 A. ... 

When plotted according to the linear form of the BET equation, data for the adsorption of N2 on Graphon at 77 K give an intercept of 0.004 and a slope of 1.7 (both in cubic centimeters STP per gram). Calculate E assuming a molecular area of 16 for N2. Calculate also the heat of adsorption for the first layer (the heat of condensation of N2 is 1.3 kcal/mol). Would your answer for Vm be much different if the intercept were taken to be zero (and the slope the same) Comment briefly on the practical significance of your conclusion. 

Anotlier metliod applicable to interfaces is tlie detennination of tlie partial molecular area (7 of a biopolynier partitioning into a lipid monolayer at tlie water-air interface using tlie Langmuir trough [28]. The first step is to record a series of pressure 71-area (A) isotlienns witli different amounts of an amphiphilic biopolynier spread at tlie interface. 

Values of molecular area a es used by Davis, DeWitt and Emmett ... 

In their pioneer work, Brunauer and Emmett adopted the value a (Ar) = 13-8 for the molecular area of argon, by insertion of the liquid density Pi in the standard equation (2.27). The same figure was recommended by McClellan and Harnsberger " as a result of their comprehensive survey of the literature, already referred to. These workers noted that the recorded values of a (based on a (N2) = 16 2 A ) extended over the wide range 10-19 A, and concluded that the area occupied per molecule of argon in the completed monolayer varied from one adsorbent to another. 

Molecular area, a (Ar) of argon at 77 K on graphitized carbon blacks (Argon BET plots constructed with p (liquid) surface areas determined by BET-nitrogen, with a (Na)... 

The idea of a constant value for the molecular area of argon on different solids would seem reasonable in view of the non-specific nature of argon... 

The molecular area, calculated from the density of the supercooled liquid at 77 K is a ,(Kr) = 15-2 A, but Beebe found it necessary to adopt the higher value 19-5 A to bring the krypton-based area into line with the area of Harkins reference sample of anatase. ... 

The survey in the present section shows quite clearly that it is not possible to assign a fixed value of a to a given adsorptive, which will remain valid for its adsorption on ail adsorbents. As demonstrated in Section 2.7, nitrogen and argon would seem to provide the best approximation to a constant effective molecular area, with = 16-2 A and a, (Ar) = 16-6 A. ... 

The BET method for calculation of specific surface A involves two steps evaluation of the monolayer capacity n from the isotherm, and conversion of n into A by means of the molecular area a . 

It will be noted that this method avoids any necessity to assume a value for the molecular area of the adsorbate, and it is not even necessary that the... 

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