Molar cross section

Am molar cross-sectional area of the diffusing particle 6.4.1... 

This unit for the atomic cross section is very convenient because the molar cross section becomes... 

But Che molar flux of species r per unit cross-sectional area is given by... 

The cross-sectional average molar fluxes are defined by... 

Now consider Che cross-sectional average N of the total molar flux and the cross-sectional average diffusion fluxes J, defined by... 

At very low densities It Is quite easy Co give a theoretical description of thermal transpiration, alnce the classical theory of Knudsen screaming 9] can be extended to account for Che Influence of temperature gradients. For Isothermal flow through a straight capillary of circular cross-section, a well known calculation [9] gives the molar flux per unit cross-sectional area, N, In the form... 

Given the boundary condition (A.1.6) it is a straightforward matter to integrate the Navier Scokes equations in a cylindrical tube, and hence to find the molar flux N per unit cross-sectional area. The result, which was also obtained by Maxwell, is... 

Ideally, the sample should be injected onto the column as an infinitely thin disc, which covers the total cross section of the column. Because this is impossible, PSS has injected finite volumes onto the columns. In theory, these injection volumes should be as low as possible. In order to be able to detect the sample with significance, a certain (high) concentration of the sample has to be injected. This concept works well for low molar mass compounds, which do not generate much sample viscosity. However, when working with samples... 

Normally a calibration curve—molar mass against the total retention volume—exists for every GPC column or column combination. As a measure of the separation efficiency of a given column (set) the difference in the retention of two molar masses can be determined from this calibration curve. The same eluent and the same type of calibration standards have to be used for the comparison of different columns or sets. However, this volume difference is not in itself sufficient. In a first approximation the cross section area does not contribute to the separation. Dividing the retention difference by the cross section area normalizes the retention volume for different diameters of columns. The ISO standard method (3) contains such an equation... 

In the model equations, A represents the cross sectional area of reactor, a is the mole fraction of combustor fuel gas, C is the molar concentration of component gas, Cp the heat capacity of insulation and F is the molar flow rate of feed. The AH denotes the heat of reaction, L is the reactor length, P is the reactor pressure, R is the gas constant, T represents the temperature of gas, U is the overall heat transfer coefficient, v represents velocity of gas, W is the reactor width, and z denotes the reactor distance from the inlet. The Greek letters, e is the void fraction of catalyst bed, p the molar density of gas, and rj is the stoichiometric coefficient of reaction. The subscript, c, cat, r, b and a represent the combustor, catalyst, reformer, the insulation, and ambient, respectively. The obtained PDE model is solved using Finite Difference Method (FDM). 

Cross-sectional area Volumetric flow rate Reaction rate Stoichiometric constant Molar flow rate Molar feed flow rate A Molar feed flow rate B Molar inert flow rate Pressure Gas constant Temperature Fraction conversion Mole fraction Length... 

Lm = molar liquid flow-rate per unit cross-sectional area, a = interfacial surface area per unit volume,... 

Since we don t usually know enough about pore structure and other matters to assess the relative importance of these modes, we fall back on the phenomenological description of the rate of diffusion in terms of Fick s (first) law. According to this, for steady-state diffusion in one dimension (coordinate x) of species A, the molar flux, NA, in, say, mol m-2 (cross-sectional area of diffusion medium) s-1, through a particle is... 

The relationship between the molecular absorption cross-section and the molar absorption coefficient is described in Box 2.1. 

The specific conductance (k) of a solution is defined as the conductance (S) per centimetre of a solution that has a cross-sectional area of 1 cm2, and is measured in S cm-1 (or in non-SI units as fl-1 cm-1). The molar conductance (A) is the specific conductance of a solution corrected for the concentration of ions in the solution. A = k X volume of solution which contains 1 gram mole. 

G and L are the molar rates of flow of vapour and liquid, respectively, per unit cross-section of column. 

G Molar flowrate of vapour per unit time and unit cross-section kmol/m2s NL 2T 1... 

Gm Molar rate of flow of inert gas per unit cross-section kmol/m2s nl-2t- ... 

In copper there are two conduction electrons per atom and n = 8.5 X 10 electrons per cubic meter. For a wire with a cross section of 1 mm carrying a current of 1 A, a value of v = 25 X 10 m/h is obtained. For the sake of comparison, it is interesting to note that in a molar copper sulfate solution, the absolute mobility (mobility in a potential gradient of 1 V/cm) of copper ions is 2.5 X lO mTh. 

Fig. 2. Kriged cross-section of C02/CaO molar ratio along A - A on McIntyre grid line 3500E through the HMC deposit has been modified by hand to reflect section geology. White dots indicate sample locations.

Compounds were quantified by comparing the computer calculated area for the brominated compound with the integrated response for a known amount of octachlo-ronaphthalene. Differences in ionization cross-section, which affect the sensitivity of the mass spectrometer to a given compound, were compensated for by determining the relative molar response (RMR) of authentic compounds to octachloronaphthalene. 

Table I. Absorption Cross Sections (cJin) and Molar Extinction Coefficients (e) of Transition of ZnTPP...

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