**2. Methodology and kinetics studies**

Kinetics of the reduction of ferricyphen, and or, ferricypyr (oxidizing agent) was studied in an aqueous medium under the pseudo-first-order condition. The concentration of ferrocyanide (reducing agent) was always in excess of the oxidizing agents. The reactions were probed at room temperature i.e., 25 °C, and at constant ionic strength i.e., 0.06 M. The concentration ratio between the oxidizing agents and the reducing agent was always maintained at 1:2.5, 1:5, 1:7.5, and 1:10, respectively. The reactions were probed spectrophotometrically under ordinary experimental conditions. No specific or extraordinary experimental setup was required such as an inert atmosphere, dark room, and/or a catalyst. However, the fresh solutions of the reactants were prepared and wrapped in aluminum foil soon after preparation because ferricyphen and or ferricypyr get reduced when their aqueous solutions are exposed to light. The reactions were started upon mixing the reactants and a rise in the absorbance was monitored as a function of time (**Figure 2A**). The instrumental setup consisted of a home-built assembly as mentioned earlier [27]. The molar absorptivity of the reduced ferricyphen i.e., ferrocyphen, and reduced ferricypyr i.e., ferrocypyr are several folds higher than the oxidized ferrocyphen (ferricyphen) and ferrocypyr (ferricypyr). The spectra of the reactants and products are shown in **Figure 2B** and compared to the literature [21–29] that supports the electron transfer mechanism. The integration method was implemented to figure out the rate constant. Each experiment was repeated three to six times for accuracy and the rate constant is an average value. The reactions were kinetically examined, and it was determined that each one among them was completed in two phases.

The rate of both reactions was found independent of the concentration of the oxidizing agents i.e., sensitizers, and the reducing agent i.e., mediator during the first phase of the reaction. The rate of the second phase of both reactions, on the other hand, was shown to be first order and dependent on the concentrations of the sensitizers and mediator. The linear rate equations (integration method) of zero and first

**Figure 2.**

*(A) Time course graphs at a varying concentration of ferrocyanide and fixed ferricyphen/ferricypyr. (B) UV-visible absorption spectral analysis of the sensitizer-mediator redox reactions.*

order were best fitted with the highest linear fit R2 value on the time course data in the first and the second phases of the reactions. The slope of each plot yielded the observed zero order rate constant (*k*obs) and the observed pseudo-first-order rate constant (*k*<sup>0</sup> obs), respectively. The effect of variation in the concentration of each of the sensitizers and the mediator on each of the rate constant was studied. It is assumed that if the concentration of the reactant is low and is varied, the rate constant should not be varied rather the rate of the reaction is varied according to the Eqs. (1)–(5) considering the pseudo-first-order condition. However, the rate constant is varied

*Catalytic Behavior of Extended π-Conjugation in the Kinetics of Sensitizer-Mediator… DOI: http://dx.doi.org/10.5772/intechopen.106511*

when the concentration of the reactant that has been taken in excess is varied rather than the rate of the reaction in case of the first order dependence on the mediator. Similarly, if it is zero order, the rate constant will have no effect by variation in the concentration of the mediator. **Figure 3** depicts the outcomes.

$$Rate = k\_{obs} [\text{Sensitivity}]^0 \text{ first phase of the reaction} \tag{1}$$

$$Rate = k\_{obs} \tag{2}$$

Since sensitizer < < mediator

$$\mathbf{k} \colon \mathbf{k}\_{obs} = k\_1 [\mathbf{M} \mathbf{d} \mathbf{d} \mathbf{d} \mathbf{t} \mathbf{t} \mathbf{r}]^0 \mathbf{f} \mathbf{r} \mathbf{t} \mathbf{t} \text{ phase of the reaction} \tag{3}$$

$$k\_{obs} = k\_1 \tag{4}$$

$$Rate = k\_{obs}'[\text{Sensitivity}] \text{ second phase of the reaction} \tag{5}$$

Since sensitizer < < mediator

$$\mathbf{k}' \mathbf{k}'\_{obs} = k\_2 [\mathbf{M} \text{dialator}] \text{ second phase of the reaction} \tag{6}$$

Eqs. (4) and (6) reveal *k*<sup>1</sup> as the overall zero order rate constant of the first phase of the reactions and *k*<sup>2</sup> as the overall second order rate constant of the second phase of the reactions. A first order is observed corresponding to the concentration of the mediator in each case i.e., ferricyphen/ferrocyanide phase-II and ferricypyr/ferrocyanide phase-II (**Figure 3**). The plots have intercepts that interpret the initial zero order reaction phase corresponding to the concentration of the mediator. However, the rest of the plots (**Figure 3**) reveal the results according to the Eqs. (1)–(5). The rate constants either observed zero order rate constant (*k*obs) and the observed pseudofirst order rate constant (*k*<sup>0</sup> obs) were independent of the concentration of the sensitizers in both phases and the mediator in the first phase of the reaction. Because of the low concentration that was maintained to follow the pseudo-first order condition, the rate constants corresponding to the sensitizers were independent of the concentration terms of the sensitizers in both phases. As a result, the findings show that the

**Figure 3.** *Kinetic analysis of the sensitizer-mediator reactions.*

**Figure 4.** *Effect of pH on the rate constants of the first and second phases of each sensitizer-mediator reaction.*

pseudo-first order criterion was successfully implemented. It is worth noting that the first phase of both reactions was long enough to get the reactions to about 70% completion. In the first phase of both of the reactions, the zero order rate constant (*k*obs) is the multiplication product with the molar absorptivity (ɛ) of either of ferrocyphen or ferrocypyr, respectively. The zero order integrated rate equation (linear-fit) was implemented on the absorbance data rather concentration data of the time course graphs. Therefore, the slope of the plot was the multiplication product of ɛ∙*k*obs at the pathlength of the quartz cuvette equal to 1 cm. This multiplication of the constant value to the rate constant just adds a constant mathematical figure to the rate constant and does not affect the rate constant and overall findings of the data and the results.

For further rectification of the results, the effect of pH was monitored on the rate constants in each phase of the reactions under the pseudo-first order condition. The concentration of the mediator was always in excess over the sensitizers and the concentration of the nitric acid was always in excess over the mediator at room temperature and constant ionic strength 0.12 M. The results are revealed in **Figure 4** by plotting the graphs between pH and the rate constants on x-y coordinates respectively for each of the sensitizer-mediator interaction. The first phase of each reaction was observed unaffected of pH that declares and confirms the zero order reaction in this phase of each reaction. However, the second phase of the reaction shows curvatures (**Figure 4**). The value of the pseudo-first order rate constant (*k*<sup>0</sup> obs) decreased with decreasing pH and became constant at the low values of the pH as has been shown in the **Figure 4**. These results indicate the formation of the monoprotonated ferrocyanide upon increasing the acidity of the reaction medium via conversion of free ferrocyanide species to the rate-inhibiting monoprotonated ferrocyanide and though the value of the rate constant decreased in each case. The protonation of the sensitizers under the pH employed have not been mentioned in the literature [22]. However, ferrocyanide may form mono- to tetra-protonated species considering the charge on the free ferrocyanide and depending on the acidity of the reaction medium [30].
