Energy cycles

MgCl(s), however, is not energetically stable with respect to disproportionation. The following energy cycle enables the enthalpy of disproportionation to be calculated, i.e. 

After diagonalization of the EHT matrix, the lowest 4 orbitals have an energy sum of about —70 eV. The electronic energy for these doubly occupied orbitals is 2(—70) = — 140 eV. The energy gain of the molecule relative to its atoms is —140 — ( — 110) = —30eV = —690 kcal mol (1 eV = 23 kcal mol ) therefore, the molecule is stable relative to its atoms. We can envision an energy cycle with three steps (Eig. 7-5) ... 

Fig. 1. The energy cycle of a thermal electric generating station having two alternative cooling systems (—) the open-circuit or once-through system and (-------------------------------------) a representative closed-cycle, cooling-tower system. Reproduced by permission (3).

It is instructive to draw up a free-energy cycle for the cell reaction (3) so as to illustrate the dominant energy terms in the single electrode reaction (1) ... 

Finally, we look at indirect ways of measuring these energies. Both internal energy and enthalpy are state functions, so energy cycles may be constructed according to Hess s law we look also at Bom-Haber cycles for systems in which ionization processes occur. 

But what is the magnitude of the lattice enthalpy We cannot measure it directly experimentally, so we measure it indirectly, with a Hess s law energy cycle. The first scientists to determine lattice enthalpies this way were the German scientists Bom and Haber we construct a Born-Haber cycle, which is a form of Hess s-law cycle. 

Strategy. (1) We start by compiling data from tables. (2) We construct an energy cycle. (3) Conceptually, we equate two energies we say the lattice enthalpy is the same as the sum of a series of enthalpies that describe our converting solid NaCl first to the respective elements and thence the respective gas-phase ions. 

We construct the appropriate energy cycle see Figure 3.8. For simplicity, it is usual to draw the cycle with positive enthalpies going up and negative enthalpies going down. 

The proton dissociation constants, of two series of 3,7-bis(arylazo)-2,6-diphenyl-1 //-irnidazo[l,2-7]pyrazoles, in the ground state and the excited state were determined by the spectrophotometric method and utilizing the Forster energy cycle, respectively. These constants were correlated by the Hammett equation and the results of such correlations with spectral data indicated that both series of compounds exist in solution almost exclusively in the l//-bis-(arylazo) tautomeric form A <2002T2875> (Scheme 3). 

Changes in society have always been of creative interest for artists. The Russian sculptor and bionics specialist Vadim Kosmatschof creates visionary works that deal with one of the most topical subjects of our time ecological balance. For many years now, the artist has devoted himself to the visualization of an emission-free energy cycle, raising public awareness of ecological contexts with his kinetic sculptures in the constructivist tradition. 

Doctor, R. D., Molburg, J. C. and Brockmeier, N. F. (2000). Carbon dioxide recovered from fossil-energy cycles. GHGT5, pp. 567-571. 

Phosphate ion is a major participant in the biological energy cycle through the reactions of mono-, di-, and triphosphates, including one of the most important of these reactions, producing adenosine diphosphate from adenosine triphosphate (see structures in Section 2.3.1, Table 2.2) ... 

An attempt has also been made to derive the binding energy of atoms in clusters from a measurement of the critical energy deficit of cluster ions. For n+ cluster ions of m atom size, from consideration of Born-Haber energy cycle, the critical ion energy deficit can be easily shown to be given by100... 

Fig. 2. Energy cycle for electron transfer under Franck-Condon conditions (<> ) in relation to electron transfer at thermal equilibrium (°E) for redox species in solution...

Figure 11.9 Free energy cycle for computation of p/f, values (where n is an integer). This cycle is...

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