Reading Energy Diagrams

As we begin to study reactions in the next chapter, we will rely heavily on the use of energy diagrams. Let s quickly review some of the features of energy diagrams. 

Energy diagrams showing the difference between kinetics and thermodynamics. 

An energy diagram showing two possible pathways for the reaction between A and B. 

An energy diagram showing two possible pathways for the reaction between A and B. In this case, C and D are the thermodynamic products, while E and F are the kinetic products. 

In an energy diagrann, all peaks are transition states, and all valleys are intermediates. 

---

Gibbs Free Energy (Section 6.3) Reading Energy Diagrams (Section 6.6)... 

Symmetry prevents interaction between the ai(t2g) and a2(ir) orbitals. The metal-ligand n acceptor interaction will thus stabilize the e-component of the t2g shell, while leaving the a i-orbital in place, as shown in the simple orbital-energy diagram in the left panel of Fig. 6.6. We can now calculate the transfer term for the e and U2 orbital transitions. In each case only one component needs to be calculated. The interaction element in this case is obtained from Iiq. (6.96) and the transfer fraction reads ... 

Remember the sign convention 2 H — H—H, A//° = —104 kcal/mol. The minus sign tells us that this reaction is exothermic as read from left to right. An exothermic reaction will have products that are more stable than the starting materials. The products will be lower than the reactants on the energy diagram. 

The calculation of this term requires the vibration frequency vf of the activated complex. The mechanics of small movements allows us to calculate the vibration frequency from the potential energy diagram (see Appendix 3). Plotting the diagram of the potential energies will allow us to calculate all the characteristics of the activated complex. The activation energy value can also be read directly from the plot. 

Prior to a discussion on the impact of processing air dew point and temperature on the drying rate behavior of a product, it is necessary to consider heat and mass transfer. Water will move from the granule to air in an attempt to reach an equilibrium, or saturated condition, determined by thermodynamics, which can be read from a phase diagram or psychrometric chart. The rate at which water will move from liquid in the granule to vapor in the air increases the further away the system is from equilibrium. When the water evaporates, it requires an amount of energy, the heat of vaporization, in order to change from liquid to vapor. Because of this, we must also consider transfer of heat as well as movement of material. These concepts can be described by equations shown in Table 5. 

The problem is now reduced to one of evaluating the matrix elements. We shall not discuss the details of this process the reading list, Appendix IX, cites several such calculations. Figure 8.20 shows the energy level diagram for ferrocene produced by one of them. 

Fig. 16 Schematic energy level diagram for the species involved in the write-lock-read-unlock-erase cycle in the case of the 4 -methoxyflavilium ionJ39 ...

The equations described earlier contain two unknown functions, h(r) and c(r). Therefore, they are not closed without another equation that relates the two functions. Several approximations have been proposed for the closure relations HNC, PY, MSA, etc. [12]. The HNC closure can be obtained from the diagramatic expansion of the pair correlation functions in terms of density by discarding a set of diagrams called bridge diagrams, which have multifold integrals. It should be noted that the terms kept in the HNC closure relation still include those up to the infinite orders of the density. Alternatively, the relation has been derived from the linear response of a free energy functional to the density fluctuation created by a molecule fixed in the space within the Percus trick. The HNC closure relation reads... 

Thus those accounts of the Indicator Diagram that assimilate Watt s use of it to its later conceptualization as a measure of work or energy in mid-nineteenth-century thermodynamics are misleading. They read Watt s understanding of the steam engine and the indicator diagram through the historical fog of both the chemical and the thermodynamic revolutions. 

---