Total rate of formation

Note this equation is identical to the corresponding equation for the mechanism without inhibition. This is as it should be since addition of the steady state equations should generate the algebraic statement that the total rate of formation of the chain carriers should be balanced by the total rate of removal of the chain carriers . 

Highly reactive intermediates, such as atoms and free radicals, occur at small concentrations in many reaction systems. Their net rates of production, Rj, are normally small relative to their total rates of formation and consumption, except for small regions near the start and end of the reaction interval of space or time. This behavior prompted the assumption... 

To write the reactions above in more compact notation we could let Aj = A, A2 = B, and so on, to arrive at the generic sequence of q reactions shown in Table 6-2. The letter Aj represents a chemical species (e.g., A, = HCl, A2 = NaOH). The first subscript, i, in the stoichiometric coefficient Vy and in the reaction rate ry refers to the reaction number while the second subscript, j, refers to the particular species in the reaction. We are now in a position to evaluate the total rate of formation of each species from all reac-... 

The total rate of formation of species j ftom all reactions... 

Although Np can be determined directly from the rate transient of P, and the transient for the step change in inert flow normalised to the total rate of formation of P(r), it is easier to normalise all the transients to their maximum flow rate and integrate to get Tp first. Like other rate constants, k and hence Tp is a function of temperature. However, it may also be a function of partial pressure.So A is a form of TOF and a measure of site activity, and like all TOFs,[ l it gives a measure of site activity at a set of reaction conditions. 

If one examines the entries in Table 113.1-2 for the total quantities of substrate and biomass present as functions of time, it is evident that the total amount of substrate declines continuously while the total biomass increases as the reaction proceeds. Note that on a mass basis the total rate of consumption of substrate always significantly exceeds the total rate of formation of biomass. Moreover, the magnitudes of both of these rates increase as time elapses, an indication that this reaction is indeed autocatalytic. 

The first parameter investigated was the reaction temperature. Figure 4 show the rates of formation of CH3COOH, CH3COOCH3, and the total rate of formation of the carbonylated products (CH3COOH + CH3COOCH3) at different temperatures. 

Therefore, a time-invariant population of droplets is established when J becomes independent of n, that is to say, when the total rate of formation of n-molecule droplets by single molecule addition to fn-7>molecule droplets plus single-molecule subtraction from f/H 7)-molecule droplets equals the total /i-molecule droplet rate of dis pearance by single-molecule addition to, and subtraction from, n-molecule droplets. The theory assumes that such a steady state is rapidly established. Rearranging Equation (3) but with J now independent of n,... 

The operator (.) selects only the positive terms in the summation, and the operator (.) selects only the negative terms and makes them positive. Equation (7.10) calculates the ratio of the sum of the rates belonging to the pair of species (i, j) to the total rate of formation or destruction of species i. Note that aU forward and backward rates must be considered separately as a single reaction when using the connection weights (7.10), or else partial equilibrium reactions could result in artificially low connection weights. 

If more than one reaction takes place, the rate of each reaction must be known in order to calculate the total rate of formation or consumption of a species. Thus,... 

Total rate of formation of i when multiple reactions take place... 

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