Molar area increment

The adsorption model described above assumes the existence of different discrete states of protein molecules in the surface layer, with neighbouring states differing from one another by the molar area increment Aco. From the viewpoint of scaling analysis, (Aco) has to be close to the size of an electrostatic blob [132]. In adsorption layers of proteins the flexibility of chains increases due to the high concentration of both protein and inorganic electrolyte [133]. This allows to consider, instead of discrete states, an infinitesimal change do in the molar area. To perform the transition from the discrete to the continuous model one has to replace formally the summations in Eqs. (2.126)-(2.128) by an integration [86]. 

On the other hand, the number of possible states for adsorbed molecules, corresponding to different partial molar areas cOj, can be quite large. Theoretically one can assume a continuous change of co between cOmin and cOmax, and successive values varying from each other by an infinitesimal increment of the molar area Aco. The transition from a discrete to a continuous reorientation model can be performed formally, replacing the summation in Eqs. (2.78) and (2.89) by an integration. 

Here a is a constant which determines the variation in surface activity of the protein molecule in the i state with respect to the state 1 characterised by a minimum partial molar area C0[ = co j , bj = b,i . The value i can be either integer or fractional and the increment is defined by Ai = Aco/coi. For a = 0 one obtains b = bj = const, while for a > 0 the bj increase with increasing coj. 

The van der Waals parameters for carbon dioxide area = 3.640L2-atnvmol-2and b = 0.042 67L-mol 1. For carbon dioxide confined in a 1.00-L vessel at a constant temperature of 27°C, calculate the pressure of the gas by using the ideal gas law and the van der Waals equation for 0.100 to 0.500 mol C02 at 0.100-mol increments. Calculate the percentage deviation of the ideal value from the real value at each point. Under these conditions, which term has the larger effect on the real pressure of C02, the intermolecular attractions or the molar volume ... 

The reason why SIA is higher in urban areas is less obvious as these are secondary aerosols. The observed increment is predominantly caused by more nitrate and sulphate. The reaction of nitric acid and sulphuric acid with the sea-salt aerosol in a marine urbanised environment follows an irreversible reaction scheme. In essence, the chloride depletion stabilises part of the nitrate and sulphate in the coarse mode and may partly explain part of the observed increment. However, it also raises the question how to assign the coarse mode nitrate in the mass closure. The sea salt and nitrate contributions cannot simply be added any more as nitrate replaces chloride. Reduction of NOx emissions may cause a reduction of coarse mode nitrate, which is partly compensated by the fact that chloride is not lost anymore. A reduction would yield a net result of ((N03-C1)/N03 = (62-35)/62=) 27/62 times the nitrate reduction (where the numbers are molar weights of the respective components), and this factor could be used to scale back the coarse nitrate fraction in the chemical mass balance. A similar reasoning may be valid for the anthropogenic sulphate in the coarse fraction. Corrections like these are uncommon in current mass closure studies, and consequences will have to be explored in more detail. 

B, C, and D are constants, the electrostatic term is expressed by A = Dfi/RT in which fl is the dipole moment of the protein, and the hydrophobic term is expressed by Q, = [N + 4.8N1 3V2/3(Ke -1)]/RT, where N is Avogadro s number, is the non-polar surface area of the protein, V the molar volume of the solvent, and <7 is the surface tension increment, i.e., the difference between the surface tensions with and without salt x6 is a correction factor for the surface tension to take account of the curvature of the protein surface at molecular dimensions. 

The ratio of 6.8 for the two peak areas from stochastic TDFRS is close to the value of 5.9 as expected from the concentration ratio and the refractive index increments of the two PS, which depends on molar mass due to end-group effects. The thermal diffusion coefficient DT= 1.12 x 10 7 cm2 (sK) l is in excellent agreement with the value found previously in our laboratory [36]. 

FIGURE 10.14 Variation of molar increment per gram atom of aromatic carbon with aromatic surface area. 

The heat that is measured at each injection step after reaching equilibrium is proportional to the increment of complex formation at each step (Figure 11). As the reaction in the cell approaches saturation, the increment diminishes until eventually only the heat of dilution is measured (used for baseline correction in data analysis). At the end of the titration, an isotherm is constructed by plotting the net heat after equilibrium (peak area) versus the calculated molar ratio of the two reactants in the cell at the end of each titration step. The equilibrium constant K, the reaction stoichiometry, and the enthalpy AH can then be determined by fitting an appropriate model to the isotherm (see Figure 11). 

After the solution for Mj for each component has converged, the residue gas molar flow, Ni.j, for each component is calculated by subtracting Mj, the permeate flow, from the feed flow N j. This residue flow then becomes the feed flow to the next small increment of membrane area. 

Wher y and yi are the dispersive components of the solid surface and the interactive solutes phase, respectively. N is Avogadro s number and a is the area of the adsorbed molecules (solutes). In IGC experiments a series of interactive solutes, such as alkanes, can be injected into the chromatographic column in order to determine the dispersive surface energy, ys. A plot of AGi or (RT In Vg°) versus the number of carbons in the alkane chain can be meaningful, since such a plot is linear and the slope of the straight line will account for the incremental contribution of AGi. The molar enthalpy of adsorption can also be calculated from AGi as follows ... 

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