Amount of a component

In its broad sense, an adsorption isotherm is an experimental or theoretical functional relationship between the adsorbed amount of a component and its amount in the bulk phase adjacent to the interface. Usually, the adsorption isotherm of a component i has the form... 

Column and detector properties determine the minimum amount of a component that can be reliably distinguished from the background noise. If we arbitrarily select a signal to noise ratio of 4 as the minimum value for the confident determination of a peak in a chromatogram then for a mass sensitive detector the minimum detectable amount is given by... 

The sample capacity Q, arbitrarily defined as the maximum amount of a component that can be injected on a column giving a limited (10%) increase in peak width, is given by... 

The amount of a component absorbed or stripped in a column is dependent on the column design (the number of stages), the component solubility, and the gas and liquid rates. The fraction absorbed can be estimated using the absorption factor method, attributed to Kremser (1930) (see Volume 2, Chapter 12). If the concentration of solute in the solvent feed to the column is zero, or can be neglected, then for the solute component the fraction absorbed =... 

Choosing the basis in this manner sometimes leads to some initial confusion, because we select species present in the system to serve as components. There is a risk of confusing the amount of a component, which describes bulk composition but not the actual state of the system, with the amount of a species or mineral that exists in reality. 

As a final note, a variant of the calculation is useful in many cases. Suppose a chemical analysis of a groundwater is available, giving the amount of a component in solution, and we wish to compute how much of the component is sorbed to the sediment. We can solve this problem by eliminating the summations over the sorbed species (the over q terms) from each of the mass balance equations,... 

One of the questions that arises in soil analysis is whether a determination of the total amount of a component in soil is desired or if just the biologically available amount is more relevant. Related to this is the question of which species of the component is present. In some cases, speciation is of utmost importance. For instance, chromium can be present as Cr(III) or Cr(VI). Cr(VI) is more toxic and thus of greater concern [15], This concern is also related to the biological availability of a specific species. In this case, while knowing the total chromium content (i.e., the sum of Cr(III) and Cr(IV)... 

In a back titration, an excess amount of standardized reagent is reacted with an unknown amount of a component of interest. When the reaction is complete, the remaining unused reagent is titrated and the amount of component of interest is determined by difference. In the Kjeldahl procedures described next, ammonia is distilled into an add of known concentration. When all of the ammonia has been distilled, the remaining unreacted add is titrated. The... 

For those scientists who had to perform quantitation, the linearity of the A/D was also critical. Linearity is the condition in which the detector s response is directly proportional to the concentration or amount of a component over a specified range of component concentrations or amounts. It is imperative that the A/D not add any additional error or variability to the performance of the detector. The resulting calibration curve now becomes dependent on the combined linearity of the detector and the /VD. Accurate quantitation requires that the system is linear over the range of actual sample concentrations or amounts. Many pharmaceutical assays, like degradation and stability studies, require that the system be able to identify and quantitate very disparate levels of peaks. In many cases, this translates into a 3 to 4 order of magnitude difference between the main active component and the impurities that need to be quantitated. 

Mole fraction, often symbolized by x or X followed by a subscript denoting the entity, represents the amount of a component divided by the total amount of all components. Thus, the mole fraction of component B of a solution, xb, is equal to hb/Xhi where Hb is the amount of substance B and Sni is the total amount of all substances in solution. In biochemical systems, usually the solvent is disregarded in determining mole fractions. The mole fraction, a dimensionless number expressed in decimal fractions or percentages, is temperature-independent and is a useful description for solutions in theoretical studies and in physical biochemistry. 

Many recent workers have contributed to the development of iteration solutions, especially in the method of solving the mass balance equations. Amundson and Pontinen (Al) have proposed a general method of solution through matrices. Edmister (El) has solved the equations through development of a series expression relating the amount of a component at a stage to the amount in a product. Matching relations at... 

The chemical potential is defined as the increase in free energy of a system on adding an infinitesimal amount of a component (per unit number of molecules of that component added) when T, p and the composition of all other components are held constant. Clearly, from this definition, if a component i in phase A has a higher chemical potential than in phase B (that is, xf > pf) then the total free energy will be lowered if molecules are transferred from phase A to B and this will occur in a spontaneous process until the chemical potentials equalize, at equilibrium. It is easy to see from this why the chemical potential is... 

Distribution coefficients. The amount of a component in a specified amount of stationary phase, or in an amount of stationary phase of specified surface area, divided by the analytical concentration in the mobile phase. 

Usually statements of problems on chemical equilibrium include the initial amounts of several species, but this doesn t really indicate the number of components. The initial amounts of all species can be used to calculate the initial amounts of components. The choice of components is arbitrary because /xA or fiB could have been eliminated from the fundamental equation at chemical equilibrium, rather than fiAB. However, the number C of components is unique. Note that in equation 3.3-2 the components have the chemical potentials of species. This is an example of the theorems of Beattie and Oppenheim (1979) that (1) the chemical potential of a component of a phase is independent of the choice of components, and (2) the chemical potential of a constituent of a phase when considered to be a species is equal to its chemical potential when considered to be a component. The amount of a component in a species can be negative. 

The prime on the amount of a component indicates that these are the components other than the hydrogen component. The corresponding Gibbs-Duhem equation... 

The partial derivative of the Gibbs energy with respect to the amount of a component yields the chemical potential of a species (Beattie and Oppenheim, 1979). 

Raoult s law is obeyed when the components in the mixture are closely related. With dissimilar components, deviations from Equation (6.5) can be marked. If, however, small amounts of a component are present (for example, if the component in excess is thought of as the solvent and the component present in small amounts as the solute ) then at low Xsoiute values, Henry s law, Equation (6.7) is obeyed ... 

Figure 6.9 shows typical control structures for two special types of columns. Figure 6.9a is for a column whose feed contains a small amount of a component that is much more volatile than the main component. The distillate product is a small fraction of the feed stream. It is removed from the reflux drum as a vapor to hold column pressure. Reflux flow is fixed, and reflux drum level is controlled by manipulating condenser coolant. In the petroleum industry, this type of column is called a stabilizer. The first column in the HDA process is this type. 

The effectiveness factor r of a reaction is defined as the ratio of the amount of a component (participating in that reaction) converted inside a catalyst pellet to the amount that would have been converted if the conditions on the outer surface were to prevail everywhere inside the catalyst pellet. Hence ... 

If the amount of a component that is available to migrate is so small that even if everything were to migrate to the food the migration limit cannot be exceeded, it is clear that the SML carniot be exceeded. This calculation can... 

Restrictions for the residual amount of a component instead of a specific migration limit are set by the legislator in cases where specific migration of a component is difficult to obtain (for example, because the component is very volatile) or impossible to determine directly (for example, if the component is very reactive and would react with the food simulant). There are two ways to determine the residual content, by worst-case calculation or by analytical determination. The generic approach is shown in Eig. 5.3. 

If the amount of a component is already known to be so small that the residual content limit is not exceeded, this is sufficient. This can be calculated using already available information like ingredient specification, the amount of chemical added, etc. One consequence is that this worst-case calculation is not possible for monomers, but only for additives and processing aids. In real-life this approach could be used in rare cases only and an analytical determination is the method most commonly used. 

Turner et al. used this technique to prove that the unresolved peak in the gas chromatograms of Toxicant A consisted of the two components B8-806 (P-42a) and B8-809 (P-42b) [79], The second approach is quantitative NMR. This technique can be used to calculate the amount of a component in a solution since the integrals of proton resonances are in the first order independent of the component structure and proton position. Nikiforov et al. studied the composition of toxaphene in this way. Toxaphene components with geminal chlorine atoms on primary carbons have proton signals in the range of 6-7 ppm. Monitoring this ppm range allows the determination of the number of components in a mixture [69]. 

Molecular diffusion in emulsions can be effectively slowed down by including in the dispersed phase a small amount of a component with lesser water solubility, in the case of a PFC emulsion, a secondary, higher MW ( heavier ) PFC.t This is the role of 7 in Fluosol and of 8 in Perftoran, however, at the cost of longer organ half-lives of 65 and 90 days, respectively. 

The amount of a component in each of the pyrolysis products is given by the following equations ... 

The Limit of Detection is the smallest concentration/amount of a component of interest that can be measured by a single measurement with a stated level of confidence. This subject is discussed in detail elsewhere (22). 

Consider now a solution containing no moles, with mole fractions and Xg of solute and solvent, respectively. After this solution has been equilibrated with a mass m of adsorbent, there are n and n ° molecules (of either solute or solvent) in the adsorbed layer and in the solution, respectively. The amount of a component adsorbed by a sohd adsorbent in a closed system corresponds to the change in the solution concentration. Ax a = Since the solution contains at least... 

All cases of practical importance in liquid chromatography deal with the separation of multicomponent feed mixtures. As shown in Chapter 2, the combination of the mass balance equations for the components of the feed, their isotherm equations, and a chromatography model that accounts for the kinetics of mass transfer between the two phases of the system permits the calculation of the individual band profiles of these compounds. To address this problem, we need first to understand, measure, and model the equilibrium isotherms of multicomponent mixtures. These equilibria are more complex than single-component ones, due to the competition between the different components for interaction with the stationary phase, a phenomenon that is imderstood but not yet predictable. We observe that the adsorption isotherms of the different compounds that are simultaneously present in a solution are almost always neither linear nor independent. In a finite-concentration solution, the amount of a component adsorbed at equilib-... 

Saturation capacity of the stationary phase, qy. Amount of a component needed to saturate the stationary phase in the column. In adsorption, amount needed to make a monolayer on the adsorbent surface. In ion exchange, amount required to exchange all the ion sites on the resin. 

In order to distinguish the total amount of a component B from the amounts in each column, we call the columns BBB. where l indicates the column number. 

---