A Bordwell thermodynamic cycle use experimentally determined and reasonable estimates of

Gibbs free energy In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and pr ...

(ΔG˚) values to determine unknown and experimentally inaccessible values.

Overview

Analogous to Hess's Law which deal with the summation of

enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...

(ΔH) values, Bordwell thermodynamic cycles deal with the summation of

(ΔG) values. Free energies used in these systems are most often determined from equilibriums and

redox potential Redox potential (also known as oxidation / reduction potential, ''ORP'', ''pe'', ''E_'', or E_) is a measure of the tendency of a chemical species to acquire electrons from or lose electrons to an electrode and thereby be reduced or oxidised respe ...

s, both of which correlate with free energy. This is with the caveat that redox scales are not absolute and thus it is important that all electrons are evaluated in redox pairs. This removes the offset of a given reference potential, otherwise the values are reported as potentials (V) against that reference. It is also worth recognizing that the values of the pK_a system are just moderately transformed K_eq values. When working with equilibrium energy values such as ΔG˚ and E˚_1/2 values it common to employ a naught (˚) symbol. The naught has a two component definition. The first more common component is that it refers to the physical conditions being at standard state. The second more significant component is that energy refers to an equilibrium energy even if there is a conditionally defined standard state. Just as

activation energy In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (''E''a) of a reaction is measured in joules per mole (J/mol), kilojoules pe ...

with the double dagger ΔG^‡ refers the energy difference between reactants and the

transition state In chemistry, the transition state of a chemical reaction is a particular configuration along the reaction coordinate. It is defined as the state corresponding to the highest potential energy along this reaction coordinate. It is often marked wi ...

, ΔG˚ refers to the energy difference between reactants and products. The nought is assumed when working with equilibrium values such as K_eq and pK_a. The example below contains four reactions that can be related through their associated free energies. [ An example of the former is the dissolution of ammonium nitrate. This process is spontaneous even though it is endothermic. It occurs because the favored increase in disorder that accompanies dissolution outweighs the unfavored increase in energy.] Given any three values and the fourth can be calculated. Its important to note that the fourth reaction in the series is an inverted homolytic bond cleavage stated in terms of free energy. The chemical transformation for the associated -ΔG˚ is the same it would be for a

bond dissociation energy The bond-dissociation energy (BDE, ''D''0, or ''DH°'') is one measure of the strength of a chemical bond . It can be defined as the standard enthalpy change when is cleaved by homolysis to give fragments A and B, which are usually radical s ...

(BDE). However, the -ΔG˚ is not a BDE, since BDE are by definition stated in terms of enthalpy (ΔH˚). The two values are of course related by ΔG˚ = ΔH˚ - TΔS˚ and as a result educated comparisons can be made between ΔG˚ and ΔH˚. :R- ⇌ e- + R^. (Reaction 1) ::ΔG = -nFE˚_1/2 :H⁺ + e- ⇌ H^. (Reaction 2) ::ΔG = -nFE˚_1/2 :RH ⇌ H⁺ + R- (Reaction 3) ::ΔG = RT(2.303)pK_a :R^. + H^. ⇌ RH (Reaction 4) ::ΔG = -RTln(K_eq)

Conversions

Relationships between K_eq, pK_eq, E˚_1/2, and ΔG˚. :ΔG˚ = -RTln(K_eq) :ΔG˚ = (2.303)RT(pK_eq) :ΔG˚ = -nFE˚_1/2 Useful conversion factors: :-23.06 (kcal/mol)(e⁻)⁻¹(V)⁻¹ :1.37(pK_eq) kcal/mol :1.37 log(K_eq)kcal/mol

References

{{Reflist Thermodynamic cycles