Zero-free energy conditions

By assuming local equilibrium of the dissociation reactions, a zero free energy condition results which relates the local chemical potential of the neutral species to the charged species actually present. Thus, local equilibrium of reaction(21) implies the following generalized free energy equality... 

Potentiometric transducers measure the potential under conditions of constant current. This device can be used to determine the analytical quantity of interest, generally the concentration of a certain analyte. The potential that develops in the electrochemical cell is the result of the free-energy change that would occur if the chemical phenomena were to proceed until the equilibrium condition is satisfied. For electrochemical cells containing an anode and a cathode, the potential difference between the cathode electrode potential and the anode electrode potential is the potential of the electrochemical cell. If the reaction is conducted under standard-state conditions, then this equation allows the calculation of the standard cell potential. When the reaction conditions are not standard state, however, one must use the Nernst equation to determine the cell potential. Physical phenomena that do not involve explicit redox reactions, but whose initial conditions have a non-zero free energy, also will generate a potential. An example of this would be ion-concentration gradients across a semi-permeable membrane this can also be a potentiometric phenomenon and is the basis of measurements that use ion-selective electrodes (ISEs). 

There is really no limit to the possible initial conditions. If the system had featured 2.00 moles of pure A, then twice the work would have become available. If the chemist initiates matters by injecting (separately) 0.30 moles of A and 0.70 moles of B, then almost zero free energy would be offered. Note that the reaction switches two ways. If the initial conditions corresponded to A and B samples of 0.10 and 0.90 moles, respectively, then free energy would be obtained at the expense of the B population. For equilibrium conditions to exist and maintain, the reaction must be able to operate in forward and reverse directions. It is for this reason that the terms reactant and product are spoken largely for convenience. The reality is that B is the product of reactant A A is the product of reactant B. 

The production of ammonia is of historical interest because it represents the first important application of thermodynamics to an industrial process. Considering the synthesis reaction of ammonia from its elements, the calculated reaction heat (AH) and free energy change (AG) at room temperature are approximately -46 and -16.5 KJ/mol, respectively. Although the calculated equilibrium constant = 3.6 X 108 at room temperature is substantially high, no reaction occurs under these conditions, and the rate is practically zero. The ammonia synthesis reaction could be represented as follows ... 

Consider, for example, the saturated solution of a sparingly soluble crystal. Let AII>a, and AS, t denote the heat of solution and the entropy of solution when a few additional pairs are taken into the saturated solution. The condition for equilibrium between the solid and the solution. is, of course, that there shall be no change in the free energy in this process a saturated solution is one for which AF is zero. Hence we may write at once... 

The second law also describes the equilibrium state of a system as one of maximum entropy and minimum free energy. For a system at constant temperature and pressure the equilibrium condition requires that the change in free energy is zero ... 

Electrolyte solutions ordinarily do not contain free electrons. The concept of electrochemical potential of the electrons in solution, ft , can stiU be used for those among the bound electrons that will participate in redox reactions in the solution. Consider the equilibrium Ox + ne Red in the solution. In equilibrium, the total change in Gibbs energy in the reaction is zero hence the condition for equilibrium can be formulated as... 

Here, the a s refer to the activities in the chosen arbitrary state. The concept of activity is presented separately in a later section. For the present, the activity of a species in a system may just be considered to be a function of its concentration in the system, and when the species is in a pure form (or in its standard state), its activity is taken to be unity. The activities ac, aD, aA, aB given above correspond to the actual conditions of the reaction, and these may or may not correspond to the state of equilibrium. Two special situations can be considered. In the first, the arbitrary states are taken to correspond to those for the system at equilibrium. Q would then become identical to the equilibrium constant K and, according to the Van t Hoff isotherm, AG would then be zero. In the second situation, all the reactants and the products are considered to be present as pure species or in their standard states, and aA, aB, ac, and aD are all equal to 1. Then (7=1 and the free energy change is given by... 

AG° is the free-energy change for a reaction under conditions where the product/reactant ratio is l.1 Don t get confused on this point—AG° is not the free-energy change at equilibrium (that s zero), it s the free energy change when the products/reactants ratio is 1. AG° is a way to compare different reactions to decide which one is intrinsically more favorable. The comparison is made, by convention, at a product/reactant ratio of 1. Just because a reaction has a negative AG° doesn t mean that it can t be made... 

We teach our students that the infinite zero-point energy that arises when a free relativistic scalar (or Dirac-) field theory is canonically quantized can be subtracted (discarded) by a suitable redefinition of the energy-origin in other words, by normal ordering. However, the energy-origin can be re-defined only once, and only in homogenous space (i.e. without boundary conditions) and... 

In contrast, the O diffusion constant drops to zero at 75 GPa (2.6 g/cc) for both L and S initial configurations. The surprisingly small hysteresis in the fluid to superionic transition allows us to place the transition point between 70 GPa (2.5 g/cc) and 77 GPa (2.6 g/cc). The small hysteresis is most likely caused by the weak O-H bonds at the conditions studied, which have free energy barriers to dissociation comparable with kBT (see below). Simulations that start from the L initial configurations are found to quench to an amorphous solid upon compression to 2.6 g/cc. 

The combined first and second laws state that, at constant T and V, a system seeks to minimize A until dA for any subsequent change is zero (Equation 4.14), and likewise, at constant T and P, the Gibbs free energy decreases until dG for any subsequent change equals zero (Equation 4.20). One then recognizes that the condition for equilibrium is exactly the same at constant T and V as it is at constant T, P. 

AG° is the free-energy change for a reaction under conditions where the product/reactant ratio is 1. Don t get confused on this point—ACf is not the free-energy change at equilibrium (that s zero), it s the free energy... 

Given that quantum chemistry calculations directly provide electronic energies, which formally correspond to zero temperature and pressure, ways for connecting to finite, realistic temperature and pressure are needed. One method is first-principles thermodynamics (FPT), the basic concept of which is that the thermodynamically prevailing state of a surface is the one that minimizes the surface free energy, y, subject to external conditions such as temperature and the chemical potentials of the various components of the system ... 

---