Reaction Species Graphs

The use of graphs in electrochemical reaction networks, specifically (1) reaction species graphs, (2) reaction mechanism graphs, and (3) reaction route graphs... 

The model components, including both the chemical species and the reactions, are represented by nodes in the graph. Each species can be a reactant, product, or modifier of one or more reactions. Each such relationship is represented by an edge in the graph. 

The information cited is enough for plotting the flow graph for the reaction under consideration (Figure 4.8). This graph enables the compiling of the corresponding kinetic equations for reaction species... 

Figure 8.23 During a reaction, the participating species approach, collide and then interact. A seamless transition exists between pure reactants and pure products. The rearrangement of electrons requires large amounts of energy, which is lost as product forms. The highest energy on the activation energy graph corresponds to the formation of the transition-state complex. The relative magnitudes of the bond orders are indicated by the heaviness of the lines...

Figure 14 displays the product formation of H20, N2, C02, and CO. The concentration C(t) is represented by the actual number of product molecules formed at time t. Each point on the graphs (open circles) represents an average over a 250-fs interval. The number molecules in the simulation were sufficient to capture clear trends in the chemical composition of the species involved. It is not surprising to find that the rate of H20 formation is much faster than that of N2. Fewer reaction steps are required to produce a triatomic species like water, whereas the formation of N2 involves a much more complicated mechanism.108 Furthermore, the formation of water starts around 0.5 ps and seems to have reached a steady state at 10 ps, with oscillatory behavior of decomposition and formation clearly visible. The formation of N2, on the other hand, starts around 1.5 ps and is still progressing (as the slope of the graph is slightly positive) after 55 ps of simulation time, albeit slowly. 

Although diagrams like Fig. 6.1 are especially convenient to illustrate the qualitative features of TST and VTST, the solution of the equations of motion in (rAB,rBc) coordinates is complicated due to cross terms coupling the motions of the different species. It is for that reason we introduced mass scaled Jacobi coordinates in order to simplify the equations of motion. So, one now asks what does the potential function for reaction between A and BC look like in these new mass scaled Jacobi coordinates. To illustrate we construct a graph with axes designated rAB and rBc within the (x,y) coordinate system. In the x,y space lines of constant y are parallel to the x axis while lines of constant x are parallel to the y axis. The rAB and rBc axes are constructed in similar fashion. Lines of constant rBc are parallel to the rAB axis while lines of constant rAB are parallel are parallel to the rBc axis. From the above transformation, Equations 6.10 to 6.13... 

Figure 2.3 shows how the chemistry of dissolved arsenious acid varies with pH. An analogous graph for arsenic acid is in Figure 2.4. As expected, protonated species of the acids are more common under low pH conditions were H+ is abundant. For both weak acids, dissociation constants (Ka values) may be derived to describe their gain or loss of H+ with changing pH conditions (Table 2.10 (Faure, 1998), 119-120). For example, the following reaction involving the dissociation of H3ASO3 in water at 25 °C and 1 bar pressure has a dissociation constant (K ) of HP9 2 (Wolthers et al., 2005), 3490 ...

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