Formation curve

The extent of tht formation of a complex, denoted by the symbol n, is defined as being the average number of ligands bound to the metallic ion. It is equal to the ratio of the difference between the total ligand concentration and that remaining free, on the one hand, and the analytical concentration of the metallic ion on the other. In the case of the cadmium complexes, it is written as 

It is easy to check, according to the preceding considerations, that 

The diagram n as a function of the decimal antilogarithm of the ligand activity (concentration) of the free ligand after complexation (here pCl) is known as the formation curve. The mathematical study of the formation curve permits us to determine the equilibrium constants, A l, K2, K3, K4, etc. (see Sect. 24.3). The formation curve concept is due to J. Bjerrum. It can be extended to other phenomena in solution. 

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Ignition temperature estimated by extrapolating the steeply ascending portion of the CO2 formation curve to zero CO2 concentration Temperature which shows the maximum CO2 concentration... 

Irving, H. M. Rossotti, H. S., The calculation of formation curves of metal complexes from pH titration curves in mixed solvents, J. Chem. Soc. 2904-2910 (1954). 

FIGURE 14.1 Oxidation of cyclohexanone kinetic curves of 1-naphtol decay (curves without primes) and hydroperoxide formation (curves with primes) at T — 413K(1, l ),403K(2, 2 ), and 393 K (3, 3 ). 

Such calculations can be done for a series of free ligand concentrations to generate a family of formation curves of concentration or mole fraction of metal complex species as a function of the concentration of the free ligand. Such curves are shown in Figs. 3.1 and 3.2. These calculations are particularly useful for trace level values of metal as they require only knowledge of the free ligand concentrations and the P . Values of stability constants can be found in Refs. [1,2]. 

After 4 or 5 hours the reaction is complete and a sigmoidal living ends formation curve is observed (1 ). The degree of polymerization of the oligoisoprenyllithium equals about ten. By addition of catalytic amounts of complexing agent (TMEDA or PMDT) the remarkable increase of the initiation rate is not measurable by ultra violet spectroscopy. Also, only the propagation step was studied. 

Figure 3 also shows that the prenol formation curve goes through a sharp maximum. After a certain reaction time, (conversion 70%), the C=C bond of the prenol is preferentially hydrogenated with regard to the C=0 bond of the isovaleraldehyde. 

Figure 7.18 A phase diagram showing the three common hydrate dissociation techniques, relative to the initial sample condition (intersection of horizontal and vertical arrows). Depressurization is shown as AT = 0 thermal stimulation as AP = 0 inhibitor injection is represented by displacing the solid hydrate formation curve to the dashed curve, via injection of 10 wt% methanol in the free water phase.

The ocean cools the fluids as they flow, including both produced water (here assumed to be salt-free) and condensed water that is always salt-free. At about 9 miles the flowing hydrocarbons and water enter the hydrate region (to the left of the line marked hydrate formation curve ), remaining in the uninhibited hydrate envelope until mile 45. Such a distance may represent several days of residence time for the water phase (which flows slower than the hydrocarbon phases) so that hydrates would undoubtedly form, were no inhibition steps taken. 

The pipeline pressure and temperature, calculated using PIPEPHASE , were superimposed on the hydrate formation curve shown in Figure 8.3. Gas leaves... 

Figure 8.2 Dog Lake gas hydrate formation curves with methanol in free water phase. (From Todd, J.L., et al., Reliabilty Engineering—Gas Freezing and Hydrates, Texaco Company Hydrate Handbook (1996). With permission.)...

In Figure 8.7, the curves determine the restriction downstream pressure at which hydrate blockages will form for a given upstream pressure and temperature. Gas A expands from 2000 psia and 110°F until it strikes the hydrate formation curve at 700 psia (and 54°F), so 700 psia represents the limit to hydrate-free expansion. Gas B expands from 1800 psia (120°F) to intersect the hydrate formation curve at a limiting pressure of 270 psia (39°F). In expansion processes while the upstream temperature and pressure are known, the discharge temperature is almost never known, but the discharge pressure is normally set by a downstream vessel or pressure drop. 

The TG curves in Figure 6 indicate that the phosphorus presence in the grafted fabrics increase the thermal decomposition rate (curves 2,3,4 and 5 have different slopes in comparison with curve 1) facilitating the char formation (curve 4) and decreases the flammable volatile content. 

From observation of the first parts of the butane formation curves (initial time), it appears that the dissociation rate of thiophene is the highest one. 

Jn corroboration of these arguments, the plots on Fig. 4 illustrate profiles of the main reaction rate inside the catalyst grain on assuming different mechanisms of coke formation. Curve 1 corresponds to the rate... 

Figure 4.7 Comparison of glass formation (curve abef ) and crystallization (curve abed). The point T, is the glass transition temperature and Tm is the melting temperature. (After J. West, Solid State Chemistry and Its Applications. Copyright 1985 John Wiley Sons, Inc. Reproduced with permission.)...

The pL values at various h values were evaluated and log K determined by pointwise calculations. Typical formation curves of h vs. pL are shown in Fig. 3.4. log K obtained from the curves by noting the pL values at h = 0.5. Pointwise calculations were used to obtain accurate values of log K. The formation function used in these calculations is given by equation (3.24)... 

Another method used to combat hydrates is the use of heat. In this scheme we alter the temperature such that a hydrate will not form. From an earlier example, this means that the temperature must be such that it moves the conditions to the right of the hydrate formation curve. 

The remaining spectra in Figure 6 show evidence of similar formation of SiO for the different passivation treatments. The extent of oxide formation as judged from the intensity of the peak at 1070 cm" depended on the particular passivation treatment as did stability to an additional 10 min. "standard" RIE. For example, SME resulted in a much greater extent of oxide formation (curve 2d) than high-bias (curves 3d and 4d) or barrel etching (curve 5d). 

Type B diagrams are observed when complexes of limited solubility are formed. In Fig. 5, the segment xy in curve Bg shows the formation of a complex that increases the total solubility of the compound. This is similar to a Type A diagram. At point y, however, the solubility of the complex is reached and as additional compound goes into solution, some solid complex precipitates. At point z, all of the excess solid compound added to the vials has been consumed by this process. Further addition of complexing agent beyond point z results in depletion of the compound from solution by complex formation. Curve Bj is interpreted in a similar manner except that the complex formed is so insoluble that no increase in solubility is observed. 

The inflexion of the carbonyl formation curve for LDPE oxidised during processing illustrated in Figure 2 always occurs at about the same time of photo-oxidation (see Figure 6). In heavily thermally oxidised polyethylene the carbonyl index actually decreases initially before increasing again. Ketone carbonyl is the main product formed in the... 

The aldehyde formation curve gave evidence that the cleavage of one mole of side-chain double bond yielded one mole of aldehyde, the other end of the double bond being converted to something else. This was in agreement with the results observed by Criegee (1). 

The ozonolysis was therefore repeated under a variety of conditions and new curves were constructed for each. The results were best at low temperature (—78° C. was better than —53° C.), at a high olefin concentration (as high as the solubility limitations would permit), in nonpolar solvents, and with a small amount of pyridine present in the solvent. The dramatic effect of the inclusion of approximately 1% pyridine is shown in Figure 3. The selectivity was greatly improved, the nuclear double bond remaining intact until the side-cham double bond had almost completely reacted. The aldehyde formation curve indicates that approximately two molecules of aldehyde were formed from the cleavage of each double bond. These curves represent optimal conditions and were selected from runs at various pyridine concentrations. 

The maximum rate ever observed, during this study, for COj production was 300 pmol kg s while the maxima for formaldehyde and carbon monoxide were 1300 pmol kg s and 3400 pmol kg s respectively. Hence, combination of the rates for HCHO and CO was the important factor in determining the overall shapes of the total product formation curves and CO2 will not be discussed further here. 

Absolute rate constants have been determined for aromatic triplet formation in acetone solutions of several aromatic compounds (5, 30). The formation curves were observed directly for anthracene and naphthalene triplet (5) and for diphenyl triplet. These rate curves were found to fit a first order rate law, and were interpreted as a bimolecular energy transfer process from a state of the solvent molecule which is probably the triplet, that is, by Reaction 11. These rate constants, as well as the triplet yields, are listed in Table VI. The rate constants for anthracene and naphthalene triplet formation appear to correspond to diffusion controlled rate constants. Two further points are of interest, which are in contrast with observations in other systems which will be discussed. In acetone, most of the yield of aromatic triplet (at concentrations of the aromatic compound of 5 X 10"3M or lower) is formed in diffusional processes such as collisional energy transfer. Any fast formation appears... 

Similar transient formation curves were obtained when other organic molecules, listed in Table I, were used instead of benzene. The rate constants obtained are given in Table I along with that obtained for benzene. The values for benzene and toluene are in good agreement with the relative rate constants given by Cvetanovic (3). 

If the formation curve for Ab" is observed, the analysis may be carried out by considering the analogous equation for d[Ab"]/dt. This was done for only the ra-terphenyl-p-terphenyl system, in which case the m-ter-phenylide band is obscured by a strong absorption of the p-terphenylide. 

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