Initial product concentration

Consider the shape of the E vs. t relation for the cathodic reaction Ox + ne — Red, and assume that the initial product concentration = 0. Assume further that the share of nonfaradcaic current is small and that all the applied current can be regarded as faradaic. In reversible reactions the electrode potential is determined by the values of c. and Prior to current flow the potential is highly positive since Ci, red = v,xsi 0- When the current has been turned on, the changes in surface concentrations are determined by Eqs. (11.10). Substituting these values into theNemst equation and taking into account that in our case = 0, we obtain... 

We start with the case when chemical conversion at the active site is reversible. By assuming the initial product concentration to be negligible we may neglect the reversibility of product binding ... 

Since a reaction product catalyses the reaction, the initial concentration of product also has a strong effect on the TMRad. In the case illustrated in (Figure 12.6), an initial conversion of 10% leads to a reduction of the TMRad by a factor of 2. This also has direct implications for process safety the thermal history of the substance, that is, its exposure to temperature for a certain time increases initial product concentration, leading to effects comparable to those illustrated in Figure 12.5. Hence it becomes obvious that substances showing an autocatalytic decomposition are very sensitive to external effects, such as contaminations and previous thermal treatments. This is important for industrial applications as well as during the experimental characterization of such decompositions the sample chosen must be representative of the industrial situation, or several samples must be analysed. 

The dimensionless variable is introduced by normalizing the corresponding concentration Q to the initial product concentration C, il. The other dimensionless groups are defined as... 

On the other hand, the S (or rather the N) shape of the product nullcline implies the existence of a phenomenon of bistability when the substrate concentration is held constant in the course of time. Three steady states can indeed be obtained when the horizontal corresponding to the fixed value of a intersects the product nullcline in the region where the latter possesses a region of negative slope. The numerical integration of eqns (2.7) in these conditions reveals the evolution to either one of two simultaneously stable steady states the choice of the final state depends on the initial product concentration, y (fig. 3.3). Each of the two stable states possesses its own basin of attraction, which is the set of all initial conditions in the phase plane from which the system evolves to reach eventually that particular state. 

Fig. 3.9. Excitability with multiple thresholds. The response of the system to four increasing stimuli is shown the initial product concentration is y, = 1.6,1.8, 11 and 12, respectively. Amplification of an instantaneous increase in product occurs beyond two distinct thresholds. The curves are established by numerical integration of eqns (3.1) for v = 0.04 s"

Fig. 3.10. Dose-response curve for excitability in the conditions of fig. 3.9. Two abrupt thresholds are apparent, corresponding to distinct initial product concentrations, 71 (Moran Goldbeter, 1985).

Fig. S.17. Absorbance-time diagram of the photoreaction of 2-chloro-anthraquinone in neutral methanolic solution, irradiated at 313 nm with /q= 1.26 x KT Einstein cm s", initial product concentration oq = 8.24 x 10 mol T. ...

In the above E] and E2 are activation energies for the forward and reverse reactions, respectively, ( °)j and k°)2 the corresponding Arrhenius preexponential factors, and M the ratio of initial concentrations, (Cbo/Cao)- In this analysis the initial product concentrations are taken to be zero. 

X is a convenient quantity for summarizing experimental results as it represents the value of substrate concentration at which 50% of the maximum velocity V ) under the specified experimental condition is reached. Considering the initial rates in the case where initial product concentration is smalt, the rate equation may be written as ... 

Assuming that the initial product concentration Cro is not zero, i.e., R = Substituting it into Equation 14.38 and integrating between 0 and Xa, considering Xa < Xac where Xab is the equilibrium conversion ... 

Next, we wil use (B) to make an estimate of the rate constant. As we do not have experimental data for Rq and Pq. we will combine the known information with assumptions. We know the reaction time, t = 1.59xl0 s, and we know that it takes two H2O to make one O2. Next we will set the initial product concentration to one, Pq = 1. and assume that the reaction course is approximately linear during 10 time periods. We write for (B) ... 

Figure 8.1 le presents simplified (probable) system of the temperature gradients forming near the cold walls of the ICE working cylinder. The working process of a combustion chamber or a LPE gas generator occurs in the combustion zone having a temperature (T) profile along the x direction (Fig. 8.1 If). An imagined field of initial products concentration (combustion semi-products and burned-out gases) superimposes the temperature field.

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