AG at equilibrium

It can be difficult to judge the solubility of a substance from its solubility product. For example, silver chloride, AgCl, has a K o = 1 x 10 °, and silver chromate has a K o = 2.5 x 10 . Which silver salt will allow the greater solution concentration of silver ion, Ag , at equilibrium This is equivalent to asking the question, which salt has the greater solubility ... 

First, we calculate the initial concentrations of Ag and CN. Then, because Kf is so large, we assume that the reaction goes to completion. This assumption will allow us to solve for the concentration of Ag at equilibrium. The initial concentrations of Ag and CN are ... 

The free energy of activation for the anodic (forward) and cathodic (reverse) reactions are located at the same level (Fig. 3.2). The dissolution and discharge reactions need the same energy of activation (AG ). At equilibrium there is no net current, as i — i = 0. The electrode potential assumes its equilibrium value rev Here, rf = r = io> 0 is called Exchange Current Density It is the current density associated with an electrode at equilibrium. Every reversible electrode has a characteristic exchange current density. 

If a reaction has gone to completion, a certain amount of energy has been released. The eqnilibrium constant can be related directly to the thermodynamic function called the Gibbs standard free enei change, AG°. At equilibrium. 

However, the concentration of uncomplexed silver ion, though very small, is not zero. To determine the value of [Ag+], let s start with [[Ag(NH3)2] ] and [NH3] in solution and establish [Ag ] at equilibrium. 

When the e.m.f. of a cell is measured by balancing it against an external voltage, so that no current flows, the maximum e.m.f. is obtained since the cell is at equilibrium. The maximum work obtainable from the cell is then nFE J, where n is the number of electrons transferred, F is the Faraday unit and E is the maximum cell e.m.f. We saw in Chapter 3 that the maximum amount of work obtainable from a reaction is given by the free energy change, i.e. - AG. Hence... 

We have seen that the energetic feasibility of a reaction can be deduced from redox potential data. It is also possible to deduce the theoretical equilibrium position for a reaction. In Chapter 3 we saw that when AG = 0 the system is at equilibrium. Since AG = — nFE. this means that the potential of the cell must be zero. Consider once again the reaction... 

FIGURE 3 19 Distribution of two products at equilibrium at 25 C as a function of the standard free energy difference (AG ) between them... 

The sign of AG can be used to predict the direction in which a reaction moves to reach its equilibrium position. A reaction is always thermodynamically favored when enthalpy decreases and entropy increases. Substituting the inequalities AH < 0 and AS > 0 into equation 6.2 shows that AG is negative when a reaction is thermodynamically favored. When AG is positive, the reaction is unfavorable as written (although the reverse reaction is favorable). Systems at equilibrium have a AG of zero. 

A thermodynamic function for systems at constant temperature and pressure that indicates whether or not a reaction is favorable (AG < 0), unfavorable (AG > 0), or at equilibrium (AG = 0). 

The standard-state electrochemical potential, E°, provides an alternative way of expressing the equilibrium constant for a redox reaction. Since a reaction at equilibrium has a AG of zero, the electrochemical potential, E, also must be zero. Substituting into equation 6.24 and rearranging shows that... 

Estimation of the free-energy change associated with a reaction permits the calcula-aon of the equilibrium position for a reaction and indicates the feasibility of a given chemical process. A positive AG° imposes a limit on the extent to which a reaction can x cur. For example, as can be calculated using Eq. (4.2), a AG° of 1.0 kcal/mol limits conversion to product at equilibrium to 15%. An appreciably negative AG° indicates that e reaction is thermodynamically favorable. 

Steps 1 and 2 require thermodynamic data. Eigure 2-1 shows the equilibrium constants of some reactions as a function of temperature. The Appendix at the end of this chapter gives a tabulation of the standard change of free energy AG° at 298 K. 

If AG is equal to 0, the process is at equilibrium, and there is no net flow either in the forward or reverse direction. When AG = 0, A.S = H/T, and the enthalpic and entropic changes are exactly balanced. Any process with a nonzero AG proceeds spontaneously to a final state of lower free energy. If AG is negative, the process proceeds spontaneously in the direction written. If AG is positive, the reaction or process proceeds spontaneously in the reverse direction. (The sign and value of AG do not allow us to determine how fast the process will go.) If the process has a negative AG, it is said to be exergonic, whereas processes with positive AG values are endergonic. 

To this point, the pathway has generated a pool of pentose phosphates. The AG° for each of the last two reactions is small, and the three pentose-5-phosphates coexist at equilibrium. The pathway has also produced two molecules of N/ DPH for each glucose-6-P converted to pentose-5-phosphate. The next three steps rearrange the five-carbon skeletons of the pentoses to produce three-, four-, six-, and seven-carbon units, which can be used for various metabolic purposes. Why should the cell do this Very often, the cellular need for... 

The free-energy change of the glycogen phosphorylase reaction is AG° = +3.1 kj/mol. If [P ] = 1 mM, what is the concentration of glncose-1-P when this reaction is at equilibrium ... 

Table 1. Parameters of the interatomic potentials. Distances are given in as, densities in flg, charges in e and energies in Ry. ri4s and Vc have been set to 0.57 and 8.33 ag for iron. The corresponding values for nickel are 0.85 and 8.78 ag ao denotes the equilibrium lattice constant of the elements po is the electron density at equilibrium for the perfect lattices, i.e. 0.002776 ag and 0.003543 ag for iron and nickel respectively.

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 ... 

Fig. 1.20 Cell consisting of two reversible Ag /Ag electrodes (Ag in AgN03 solution). The rate and direction of charge transfer is indicated by the length and arrow-head as follows gain of electrons by Ag -he- Ag—> loss of electrons by Ag - Ag + e- —. (o) Both electrodes at equilibrium and (f>) electrodes polarised by an external source of e.m.f. the position of the electrodes in the vertical direction indicates the potential change. (K, high-impedance voltmeter A, ammeter R, variable resistance)...

For simplicity a cell consisting of two identical electrodes of silver immersed in silver nitrate solution will be considered first (Fig. 1.20a), i.e. Agi/AgNOj/Ag,. On open circuit each electrode will be at equilibrium, and the rate of transfer of silver ions from the metal lattice to the solution and from the solution to the metal lattice will be equal, i.e. the electrodes will be in a state of dynamic equilibrium. The rate of charge transfer, which may be regarded as either the rate of transfer of silver cations (positive charge) in one direction, or the transfer of electrons (negative charge) in the opposite direction, in an electrochemical reaction is the current I, so that for the equilibrium at electrode I... 

It is apparent from this that since the rates of the cathodic and anodic processes at each electrode are equal, there will be no net transfer of charge in fact, with this particular cell, consisting of two identical electrodes in the same electrolyte solution, a similar situation would prevail even if the electrodes were short-circuited, since there is no tendency for a spontaneous reaction to occur, i.e. the system is at equilibrium and AG = 0. 

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