BRUTTO

Brut-kasten, -ofen, -schrank, m. incubator. Briit-ofen, -schrank, m. incubator, brutto, a. adv. gross over-all. 

Brutto-formel, /. a formula indicating merely the number of atoms of each kind, and not their mode of union, an empirical molecular formula (e.g., CsHa). -gewicht, n. gross weight, -wert, m. gross value. 

The energies, geometries and electron distribution of the reaction partners can be used to describe the characteristic motions of the atoms and electrons during the reaction. The difference of the total energy of the educts and products AE — the reaction energy — can be linked to the thermochemistry of the reaction. That is valid for the brutto reaction... 

The acceptor ability of the cation is increased by electron-attracting substituents. The task was to seperate the substituent influences on the reactivity of the monomer from that on the cation and to find a relationship between these influences and the brutto rate constant of the cationic polymerization 76). 

When one compares the brutto polymerization rate constants, a measure of the reactivity of monomers during cationic homopolymerizations is obtained. It was found for p-substituted styrenes that lg kBr increased parallel to the reactivity, which the monomers show versus a constant acceptor 93). The reactivity graduation of the cationic chain ends is apparently overcomed by the structural influence on the monomers during the entire process of the cationic polymerization. The quantitative treatment of the substituent influences with the assistance of the LFE principle leads to the following Hammett-type equations for the brutto polymerization rate constants ... 

In electrode processes, the overall ( brutto ) reaction must be distinguished from the actual mechanism of the electrode process. For example, by a cathodic reaction at a number of metal electrodes, molecular hydrogen is formed, leading to the overall reaction... 

Name Brutto- forrael Mol- Gewicht Erstmals isoUert von... 

Name Struktur des Ringes D ( Brutto- formel Mol.- Gewicht erstmals isolicrt von... 

A second possible mathematical approach is to consider the equilibria via complexation or aggregation (21,22). Assuming that a drug compound can bind several tenside molecules in steps (concentration gradient), the brutto equilibria constants or stability constants KA can be given as follows. Normally the aggregation constant is calculated for 1 1 reactions or other known stoichiometric ratios (z) ... 

KP and v can, in contrast to kp, not be determined via the concentration gradient for binary and ternary mixed micelles, because for the calculation of the Nemstian distribution a constant CMC and an almost constant partial molar volume must be assumed. The calculation of aggregation constants of simple bile salt systems based on Eq. (4) yields similar results (Fig. 8b). Assuming the formation of several concurrent complexes, a brutto stability constant can be calculated. For each application of any tenside, suitable markers have to be found. The completeness of dissolution in the micellar phase is, among other parameters, dependent on the pH value and the ionic strength of the counterions. Therefore, the displacement method should be used, which is not dependent on the chemical solubilization properties of markers. For electrophoretic MACE studies, it is advantageous for the micellar constitution (structure of micelle, type of phase micellar or lamellar) to be known for the relevant range of concentrations (surfactant, lipids). 

Mit dieser Bezeichnung sind die Bindungen gemeint, die wahrend der Brutto-reaktion transformiert werden, was nicht notwendigerweise in einem konzer-tierten Reaktionsschritt geschehen muB. 

Abb. 19. Temperaturabhangigkeit der Obertragungskonstante des Monomeren so wie der thermischen Brutto-geschwindigkeit von Methylmethacrylat. O thermische Polymerisation in Substanz (61) katalysierte Polymerisation in Substanz (s. Abb. 20 und 21)... 

Alle in der Arbeit reproduzierten Spektren wurden mit einem Atlas-CH-4-Gerat bei einer Elektronenenergie von 70 eV aufgenommen. Die Proben wurden direkt in die Ionenquelle eingefiihrt und je nach der Fliichtigkeit der Verbindung zwischen 100° und 200° verdampft. Brutto-formeln wurden im Bedarfsfall mit einem Atlas-SM-IB-Massenspektro-meter bestimmt. 

To obtain stoichiometric equations for the reaction steps (brutto-equa-tions) that do not involve intermediates, one must add the steps of the detailed mechanism, first multiplying them by the numbers specified. For the simple mechanism of eqns. (44) these numbers equal unity and are placed on the right-hand side of the equations of the reaction steps. Horiuti specified these numbers as stoichiometric numbers (not to confuse them with stoichiometric coefficients, which indicate the number of molecules of a reacting substance). Stoichiometric numbers must fit the equation... 

Let us analyze the structure of eqn. (70). Its numerator can be written as K+ [A] - K [B], where K+ = Aq 2 3 and K = k 1k 2k 3. In this form, it corresponds to the brutto-equation of the reaction A = B obtained by adding all the steps of the detailed mechanism with unit stoichiometric numbers. The numerator is a kinetic equation for the brutto-reaction A = B considered to be elementary and fitting the mass action law. The denominator accounts for the "non-elementary character due to the inhibition of the complex catalytic reaction rate by the initial substances and products. 

It means that we consider only mono-, bi- and (rarely) termolecular reactions. The coefficients stoichiometric coefficients and stoichiometric numbers observed in the Horiuti-Temkin theory of steady-state reactions. The latter indicate the number by which the elementary step must be multiplied so that the addition of steps involved in one mechanism will provide a stoichiometric (brutto) equation containing no intermediates (they have been discussed in Chap. 2). 

The stoichiometric (brutto) equations for the conversion of gas-phase substances are considered. According to them, linear kinetic equations can be obtained, apparently, if only the time scale is changed. These reactions are pseudo-monomolecular and comprehensively treated by Wei and Prater [11]. An example is the familiar reaction of butene isomerization. 

The equation A = B corresponds to the stoichiometric (brutto) reaction. Here Z, AZ and BZ are the three intermediates through which a complex... 

Due to the fulfilment of this law of conservation, the number of linearly independent intermediates is not three but one fewer, i.e. it amounts to two. To the right of mechanism (1) we gave a column of numerals. Steps of the detailed mechanism must be multiplied by these numerals so that, after the subsequent addition of the equations, a stoichiometric equation for a complex reaction (a brutto equation) is obtained that contains no intermediates. The Japanese physical chemist Horiuti suggested that these numerals should be called "stoichiometric numerals. We believe this term is not too suitable, since it is often confused with stoichiometric coefficients, indicating the number of reactant molecules taking part in the reaction. In our opinion it would be more correct to call them Horiuti numerals. For our simplest mechanism, eqn. (1), these numerals amount to unity. 

This can also be said about the Horiuti number (or, as Horiuti called it himself, the stoichiometric number) discussed previously. The Horiuti numbers are the numbers chosen such that, after multiplying the chemical equation for every step by the appropriate Horiuti number and subsequent adding, all intermediates are cancelled. The equation thus obtained is the stoichiometric (brutto) equation. Each set of stoichiometric numbers leading to the elimination of intermediates is called a reaction route. In the general case, the Horiuti numbers form a matrix and its vector columns are the routes. 

A set of quasi-steady-state equations for a linear mechanism is of the form 6(e)tf = 0, where x and c are the vector-columns of the concentrations for the intermediates and observed substances (those participating in the brutto-reaction, i.e. initial substances and products) and b(c) is the matrix of the reaction weights... 

The sense of the cyclic characteristic is simple. It is a kinetic equation of our brutto-reaction as if it were a step and consists of elementary reactions obeying the law of mass action. For the cycle with the brutto-equation 0 = 0, the cyclic characteristic is C = 0. If all cycles have the same "natural brutto-equations, their cyclic characteristics are represented as... 

Thus cyclic characteristics of various cycles will differ only in values of the factors (n ). Cyclic characteristics for two different cycles with the same"natural brutto-equations are proportional to each other... 

After multiplying all steps of eqn. (49) by the vector vT we obtain a set of brutto-reaction equations... 

We have already said that, in principle, the "natural brutto-equation can... 

Mechanism I accounts for the "natural brutto-equation A = B obtained by adding steps of the detailed mechanism, whereas mechanisms II and III correspond to the equation 2 A = 2 B. Cyclic characteristics will, apparently, differ. In the former case C = K+ CA - K CB, in the latter C = K+Cl -K-Cl... 

As has been shown above, the cyclic characteristics is a kinetic equation for the brutto-reaction as if it were a simple step. But the denominator SjD, accounts for the "non-elementary character of this reaction and indicates the rate retardation by catalyst surface intermediates. 

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