Initial concentration ratios

One set of experiments was done with both Q and B present at initial concentrations much higher than that of A. With k, kx, and k-j known from other work, the value of k was then estimated, because under these conditions the steady-state approximation for [I] held. To check theory against experiment, one can also determine the products. In the case at hand, meaningful data could be obtained only when concentrations were used for which no valid approximation applies for the concentration of the intermediate. With kinsim, the final amount of each product was calculated for several concentrations. Figure 5-3 shows a plot of [P]o<4R] for different ratios of [B]o/[Q]o the product ratio changes 38-fold for a 51-fold variation in the initial concentration ratio. Had the same ratios of [B]o/tQ]o been taken, but with different absolute values, the indicated product ratios would not have stayed the same. Thus, this plot is for purposes of display only and should not be taken to imply a functional relationship between the quantities in the two axes. 

Since Fj = Z[Ac< ]/Z[I ,j] the value of the induction factor depends on the rate ratio of competing reactions (5) and (6). Thus, on increasing the initial concentration ratio of Ac to I over any limit, the rate ratio increases to infinity. In this case the coupling intermediate Aj is entirely consumed in reaction (6) in the oxidation of Ac d, i-e- P == 0, and Fj reaches its limiting value. The limiting... 

Knowing the initial concentrations of substrate and ligand and the fraction of unbound substrate in the reaction mixture, the association constant can be calculated. The binding isotherm needs the measurement of five to ten reaction mixtures of different initial concentration ratios, but with commercial instruments this is easily automated, and the higher consumption of sample volume (about 80 nL) doesn t matter. 

Changes in solution concentration of Ni(ll) and rongalite for an initial concentration ratio rongalite/Ni(ll) of 1.5/0.5 as a function of time containing (1) only Ni(ll) and rongalite, (2) thermofixated PAN fibre and (3) freshly formed PAN fibre. 

Fig. 2.13 Influence of the c /cq ratio on the anodic-cathodic waves when species R is soluble in the electrolytic solution (solid curves) (Eq. (2.137) considering the upper sign) and when it is amalgamated in the electrode (dotted curves) (Eq. (2.137) considering the lower sign), jsphe.ss pAsDoC 0/rs (see Eq. 2.148). Three electrode sphericity values ( JD-g t/rs) are considered 0.071 (green curves), 0.214 (blue curves), and 0.451 (red curves), and two different initial concentration ratios Cq = 1 mM, = 0 (a), co = cr = 1 mM (b). Do = 10-5 cm2 s 1, y = 0.7. Reproduced with permission [52]...

The initial sum of concentrations of the two strong eluents for ternary elution strength gradients , Aj, or their initial concentration ratio, for ternary selectivity gradients can be optimised using a similar approach to that for binary gradient elution. 

This equation defines the initial rate of formation of product for a reaction proceeding at constant volume in which the initial concentration ratio / is identical with the stoichiometric ratio r. It follows from eqn. (15) by writing a = 1 and da = [A]o d[A], or more directly from eqn. (11) and the definition of r. Clearly the product concentration-time curve is almost linear in the very early stages of the reaction (say from a = 1.0 to 0.95) and, therefore, provided it can be accurately defined by making a series of accurate determinations of [P] and t in this region, the measurement of initial rate presents no problem. A series of such measurements at differing values of [A]o (and [BJo to keep I — r) enables the value of (fl+6) to be found on the basis of the analogous equation to (27), viz. 

Fig. 1.8. Main B species reaction with water vapor, the initial concentration ratio of B/Si = 1CF4. The total pressure is 1 bar [11]...

Another example is the work of Perrier et al. [202] that proposes first to remove the terminal thioester group (after RAFT) and second to recover the CTA. To achieve the bifunctionality and the recovery of the CTA, the monofunctional oligomer is placed in solution with a high extent of initiator (polymer-to-initiator concentration ratio 1 20). The radical provided by the initiator will react on the reactive C = S bond of the terminal thioester. By using an excess of initiator radical, the fragmentation will occur and free the new leaving thioester group, directly replaced by a radical provided by the excess of initiator (Scheme 34). 

Consider two substances, A and B, present in a solution. Initially, the concentration ratio is CJCb, after extraction, the concentration ratio in the organic phase will be CaFaIC Fb, where Fa and Fb are the corresponding fractions extracted. The ratio Fa/Fb (the factor by which the initial concentration ratio is changed by the separation) is a measure of the separation of the two substances. A corollary measure... 

How this result could arise when the initial concentration ratio Ti C2H4was 1.0 0.7 Fig. 9 Oligomer distribution after 3 h polymerization time at 258 K... 

Let us now consider how this result could arise when the initial concentration ratio Ti/C2H4 was 1.0 0.7. If all the initial added Ti had been active, then at the end of the reaction on average less than one ethylene per Ti-CH3 would have undergone insertion. In this case we would find mostly Ti-propyl chains and possibly a small quantity of Ti-pentyl chains. It is assumed that all the ethylene has been consumed and, as can be seen in Fig. 9, there are much longer oligomer chains present even though there is a considerable amount of imreacted ethylene left. 

The chains propagate proportionally to the yield, u = ([3/]o — [ ])/[A ]o, and to the initial concentration ratio in such living polymerizations. The number-average molar mass is also given by... 

The value of/i can be determined from the position of the DA concentration maximum as a function of the initial concentration ratios of D and A. A simple method proceeds from solutions of equal molar concentrations of A and D, which are then mixed for various volume fractions, d>D = 1 - . For ideal solutions, with [Af]o = ([A] + [D])o ... 

The main parameters of the reaction rate are reaction order, initial concentrations (ratio M), and the factor of expansion or contraction (sa). The space time and consequently the reactor volume depend on these parameters. 

When the ROMP of a monomer M is initiated by a metal carbene complex I it is frequently found that when all the monomer has been consumed there is still some residual initiator present. This is either because the propagation rate constant kp is larger than the initiation rate constant ki and/or because the initial monomer to initiator concentration ratio [M]q/[I]q is not very large. From the observed ratio of the initial initiator to final initiator concentrations [I]oo/[I]o is possible to determine the value of kp l from eqn. (5), obtained by integrating the appropriate rate expressions for the consumption of M and I. [43]. This relationship may be expressed in graphical form, plotting kp i against [I]oo/[I]o different values of [M]q/[I]q [44]. 

This technique offers two distinct advantages when working with long-lived nuclides (1) the initial concentration ratio of the parent nuclide relative to a reference isotope need not be known and (2) the in-growth of the daughter activity is roughly linear with age. 

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