Surface area per adsorbate molecule

The adsorption isotherm can then be plotted in terms of Tj as a function of C. The surface area per adsorbate molecule on the adsorbent a in square angstroms is... 

Calculate the surface energies of each of these liquids and plot a graph of y for the CTAB solutions as a function of logio(conc.). Use your results and the Gibbs adsorption equation (see later) to estimate the minimum surface area per CTAB molecule adsorbed at the air-water interface. 

When adsorption follows the Langmuir equation, determination of the values of rm and a permits calculation of the area per adsorbed molecule at surface saturation and the free energy of adsorption at infinite dilution. To determine whether adsorption is following the Langmuir equation and to permit calculation of the values of rm and a, the equation is usually transformed into linear form by inverting it. Thus,... 

According to Equation 3.25, the surface excess in a tightly packed monolayer is related to the slope of the linear portion of a plot of surface tension versus the logarithm of solution concentration. From this, the area per adsorbed molecule (Aj) can be calculated from ... 

It is a rule rather than an exception that adsorption-induced adaptation leads to an increased area per adsorbed molecule the molecule more or less spreads at the interface as shown in Figure 15.5. The area per adsorbed molecule in the n-state is and in the p-state A. The ratio A /A = a>. The maximum number of molecules in the n-state per unit surface area is and that in the p-state N. Hence, Nq = aN and NqA = 1. Furthermore, 9 = nJNo and 0p = h Nq. Note that both 0 and 0p are expressed in the number of adsorbate molecules per fixed number of sites per unit surface area. This implies that (0 + 0p) scales with the adsorbed mass per unit surface area. It follows that... 

Adsorbate r, "C J5bet Surface area per o molecule, A- Specific surface area ... 

If Type I adsorption behavior is obeyed, a plot of PA/v versus PA should be linear with slope l/vm. Once the volume corresponding to a mono-layer has been determined, it can be converted to the number of molecules adsorbed by dividing by the molal volume at the reference conditions and multiplying by Avogadro s number (N0). When this number of molecules is multiplied in turn by the area covered per adsorbed molecule (a), the total surface area of the catalyst (S) is obtained. Thus,... 

Fibers with high-aspect ratios have very large surface areas in relation to unit mass. The higher the aspect ratio, the greater is the surface area per unit mass. The number of ions, molecules of water, or other liquids or gases adsorbed on a fiber, can be used to estimate the surface area. The nature of the adhering species is affected by the kind and distribution of charges on the fiber surface, which, in turn, is directly related to the composition and structure of the surface and ultimately of the material itself. 

The competition model of Snyder assumes that the adso tion surface is completely covered by adsorbed eluent molecules forming a mono-layer. When solute molecules are adsorbed they displace olvent molecules. Due to the size differences one or more eluent mofecules are displaced by the solute molecules. The adsorbent surface is ijissumed to be homogeneous and each molecule tends to interact totally wRh the surface, i.e., it is adsorbed flatwise. Thus, the adsorbent surface area that the molecules require can be calculated from their molecular dimensions. Neglecting the interactions between solute and eluent molecules in the liquid and the adsorbed phase, the retention of an adsorbed molecule (expressed as net retention volume per unit weight of adsorbent K) can be related to the properties of the stationary phase, the eluent, and the sample by... 

The number of polymer molecules adsorbed per unit area was calculated from adsorption isotherm data and the surface area per unit mass of the sample. 

The surface tension data given in Figure 3.5 was obtained for aqueous solutions of a trivalent cationic surfactant (C0RCI3) in both water and in 150 mM NaCl solution. Use the data and the Gibbs adsorption isotherm to obtain estimates of the minimum surface area per molecule adsorbed at the air/water interface. 

Calculate the number of acetic acid molecules adsorbed per gram of charcoal (N) and the corresponding equilibrium acid concentration (C). Plot N against C and C/N against C. Determine the surface area per gram of charcoal assuming that one adsorbed acetic acid molecule occupies an area of 21A. Estimate the value of the equilibrium constant K with the correct units. 

In order to obtain a measure for the density 6 of an adsorbed film on the metal film (in numbers of foreign molecules per atom of metal surface) the number of the surface atoms must be estimated, assuming that certain lattice planes are predominant. The average surface area per metal atom can be calculated from the middle density of these lattice planes, and the number of the surface atoms follows from the area of the macrosurface. This number is a lower limit, and the number 0 calculated from this and from the number of adsorbed molecules is an upper limiting value. 

A promising aspect of RS for probing surface chemistry involves its ability to evaluate the molecular orientation of monolayer coverages via polarization measurements (146). The orientation of a surface active dye, Suminol Milling Brilliant Red BS, has been studied at a water-carbon tetrachloride interface (147). As the surface area per molecule was reduced the spectra showed a transition which was interpreted as a change from a mixture of orientations to one predominantly perpendicular with respect to the surface. A thorough theoretical analysis of the use of depolarization ratios for the prediction of primary surface orientations of adsorbed molecules has also been reported (148). Similar developments are occurring in IR spectrscopy and a determination of the molecular orientations in a series of polymers has been reported (149). 

The electrostatic contribution to the energy when the only ions present in the solution are those of the counterions of the surfactant molecules, hence in the absence of an added electrolyte, is calculated by integrating the electrostatic pressure from infinity to the distance xi. Denoting the surface charge o, = a, e/A, where a, is the degree of dissociation and A is the area per surfactant molecule adsorbed on the interface, the electrostatic energy per unit area is given by (see Appendix B)... 

The estimate of the surface area of chromatographic silica support is a complicated issue. It is usually performed via the BET method using low temperature nitrogen adsorption (N2.- sorptometry). The total surface area of the adsorbent is the product of the number of adsorbed molecules and the surface area per molecule. However, if the pore size distribution is not very narrow, an estimate of bonding density on the basis of carbon load and surface area may yield a large error because the smallest pores are not available for derivatization and the calculated bonding density is lower than the actual one. 

Adsorbed molecules will also return to the gas because of thermal agitation. If denotes the number of moles of adsorbed molecules of species i per unit area per second which would return to the gas from a surface completely covered by molecules of species i, then the number of moles of species i per unit surface area per second returning to the gas is... 

---