Molar distribution

Figure I 6.34 Degree of polymerization distribution molar distribution ( ) with number average degree of polymerization (dp = 140 glucose unimers) mass distribution ( ) with weight average degree of polymerization dp = 1242 glucose unimers.

Heats of Adsorption. Temperature effects were determined by measuring adsorption at three temperatures. As seen from TABLE IV, the K values vary with temperature such that for butylate, K increases with temperature, while for alachlor and metolachlor, K decreases with temperature. These results indicate that butylate becomes more adsorbed to Keeton soil as the temperature increases while alachlor and metolachlor become less adsorbed as temperature increases. In order to obtain a quantitative measure of these effects, heats of adsorption (AH) were calculated as described previously in the Materials and Methods section (equation 3). TABLE IV contains values for the average molar distribution constants (Kd) for butylate, alachlor, and metolachlor which were plotted vs the inverse temperatures (1/°K) to obtain the AH s shown in Figure 3. 

Fig. 7. Relative molar distribution of amino acids in humic substances (data were collected from Ghosh and Schnitzer [37] and Schnitzer [38])...

Still more recently, Giggenbach (1980) proposed simple linear equations relating the molar distribution constants of the main reactive gases to T expressed in Celsius ... 

To understand fully the relationship between Henry s constant and the molar distribution constant of a given species between a gas and a liquid phase, we must recall the concept of the compressibility factor of a gas (see section 9.3) ... 

Figure 9J8 Molar distribution constants of various gaseous species as a function of T. Reprinted from W. F. Giggenbach, Geochimica et Cosmochimica Acta, 44, 2021-2032, copyright 1980, with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK.

Analogously, assuming the carrier component to obey Raoult s law in the solid, we obtain the following equation for normalized molar distribution D,/f... 

The fact that X for both salts lies in the range 0.20-0.25 shows that water in the membrane is a less effective solvent for ions than is bulk water i.e. the low-dielectric-constant matrix polymer lies well within the range of the electrostatic fields around the ions. Our value of Xg, the molar distribution coefficient of sodium chloride between polymer and solution, is in good agreement with values obtained by direct measurement (1,5,10, 11,12). This is further evidence in favour of our theories and assumptions. 

Analysis of resins described by Poisson distributions shows the validity of this constraint for standards. A cumulative, molar distribution of macromolecules is determined from the normalized... 

Degree of polymerization is n. Molar distributions are interpolated to specific degrees of polymerization. 

The polystyrene data were collected from a steady state, continuous, well-mixed reactor. The initiator was n-butylli-thlum for data of Figure 2 and was azobisisobutylnitrile for data of Figure 3. Toluene was used as a solvent. The former polymerizatl n y ields an exponential population density distribution ( ), M /M = 1.5 the latter yields a molar distribution defined as th product of degree of polymerization and an exponential ( ), M /M = 2.0. Standards utilized in calibration of both instrumen s ftere polystyrene supplied by Pressure Chemical Company. 

For a polymerization comprised of propagation kinetics only, a Poisson molar distribution exists for a batch polymerization initially seeded with a polymeric species Ai(0). Rate of propagation is defined by... 

The argument of the exponential is x. Therefore, molar distributions of oligomeric species leached from cured resins will be presented on semilogarlthmlc graphs. 

For batch polymerizations initially void of polymeric species, the molar distribution of polymeric species is expressed by... 

AtoT =, , cumulative molar distribution j 0 J moles/volume... 

From these simple gas products, which correspond to a very large portion of the reacted feed stock, two basic cracking patterns are postulated the first is applicable to aliphatics and alicyclics (I) (thus including paraffins, olefins, and naphthenes), the second to substituted aromatics (II). These two basic patterns are best illustrated by Figures 1 and 2, which show the molar distribution of the principal cracked products according to the number of carbon atoms in the fragments, per 100 moles of feed stock cracked, for selected representatives of the four major hydrocarbon classes, all at 500° C. (see Table II for experimental conditions and product analyses). 

Results of chemical analysis showed that the glucosamine and total fatty acid contents of the KDO depleted, toxic lipid A and the nontoxic lipid A were essentially the same but that the nontoxic lipid A was significantly lower in the phosphorus content (Table V). The molar ratio of glucosamine phosphorus fatty acids was 2 2 4 for the toxic lipid A and 2 1 4 for the nontoxic lipid A. The relative molar distribution of normal fatty acids (lauric, myristic, and palmitic acids) and the 3-hydroxymyristic acid did not indicate a correlation between the content of these components and toxicity. The nontoxic lipid A possessed as high a tumor regression activity when combined with CWS as did the purified... 

The mechanism of the unprecedented chromium-catalysed selective tetramerization of ethylene to oct-1-ene has been investigated. The unusually high oct-1-ene selectivity of this reaction apparently results from the unique extended metallacyclic mechanism in operation. Both oct-1-ene and higher alk-l-enes were formed by further ethylene insertion into a metallacycloheptane intermediate, whereas hex-1-ene was formed by elimination from this species as in other trimerization reactions. Further mechanistic support was obtained by deuterium labelling studies, analysis of the molar distribution of alk-l-ene products, and identification of secondary co-oligomerization reaction products. A bimetallic disproportionation mechanism was proposed to account for the available data.120... 

Table 10.6 compares the average size (DPn) and size distributions of six laboratory-purified amyloses and one commercial sample of potato amylose, which were determined by classic colorimetric and fluorescent-labeling techniques using 2-ami-nopyridine. The data by the two techniques are consistent and show that wheat and other cereal amyloses are smaller in size than those from root and tuber starches. The molar distribution technique indicated that wheat amylose contained two molecular species, compared with one for rice and com amyloses.209,210 Moreover, the molar size distributions for the cereal amyloses are much narrower than those of the tuber amyloses, and the cereal amyloses contain a preponderance of molecules of DPn < 1000 whereas the tuber amyloses contain 78-95% of molecules with DPn > 1000, and even 3-5% above DPn 10000. None of the amylose samples in Table 10.6 showed molecules with less than DPn 200, possibly because they had been purified as alcohol-inclusion complexes.209... 

Figure 15. Molar distribution of cracked product from hexadecane at 1000 psig, 3.1 WHSV, 30 H2/HC and 94% conversion [177],...

The organic modifier concentration stationary phase and the mobile phase, leading to log fe=0, has also been proposed as a measure to rank lipophilicity. [Pg.195]

Heterogeneity is a generic quality of polysaccharides All characteristics occur as distributions and may be handled as distributions of molar fractions, referring to the number of distributed components, or distributions of mass fractions, referring to mass contributions of distributed components. In particular, for broad distributions, the difference between mass and molar distribution becomes significant and sometimes crucial. Molar mass distribution is a central piece in this puzzle of correlating molecular characteristics with polysaccharide performance. Additionally, optional branching characteristics, substitution patterns, and responses of aqueous polysaccharide systems to different kinds of applied stress need to be determined. 

TABLE 4. Mean Relative Molar Distribution of Amino Acids in Acid Hydrolyzates of Humic Acids and Fulvic Acids Extracted from Soils Formed Under Cool Temperature Climates"... 

TABLE 6. Relative Molar Distribution of Amino Acids in Humic Substances (a-Amino Acid Nitrogen of Each Amino Acid x 100/Total Amino Acid Nitrogen)... 

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