Adding Free-Energy Changes

Free-energy changes for chemical reactions can he added and subtracted to give free-energy changes for other chemical reactions. 

If you want to prove to yourself that free energies sum, you can write the equilibrium expressions for the first and second reactions and multiply them together, and you ll get the equilibrium expression for the hydrolysis of ATP. Multiplication is equivalent to the addition of logarithms, so that when you multiply equilibrium constants, you re actually adding free energies (or vice versa). 

The free energy of a favorable chemical reaction can be used to make an unfavorable reaction happen. 

The formation of a peptide bond (as in proteins) is not a favorable reaction. Hydrolysis of the peptide bond would be the spontaneous reaction  

If we guess that the intracellular concentrations of the amino acids are 1 mM each for AAi and AA2, and the dipeptide concentration is also 1 mM, the AG would actually he +4.6 kcal/mol. This tells you that peptide bonds cannot be made under these conditions. 

---

The conditions utilized in the above development of minimum energy are not sufficient to describe electrodialysis. In addition to the desalination of water, salt is moved from a saline feed to a more concentrated compartment. That free-energy change must be added to the free energy given in Eq. (20-107), which describes the movement... 

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... 

In this, to the free energy change for the reaction involving the interaction of chlorine and the metal oxide, is added the large value of the free energy of formation of carbon dioxide from its constituent elements. 

Although the reactions themselves can be added to obtain the desired equation, the E° for this equation is not the sum of the E° values for the above three reactions. The E° for the desired equation is actually the weighted average of the E° values for reactions (1) to (3). It can be obtained by summing up the free energy changes for the three reactions. (For reactions of the same type, standard voltages are not additive AG° values are additive, however). When (1) and (2) (each multiplied by two) are added to (3) we obtain ... 

The concept of substance activity was derived by Gilbert N. Lewis in 1907 from the laws of equilibrium thermodynamics and is described in detail in the text entitled Thermodynamics and the Free Energy of Chemical Substances by Lewis and Randell (1923). In a homogeneous mixture, each component has a chemical potential (jjl), which describes how much the free energy changes per mole of substance added to the system. The chemical potential of water (pw) in a solution is given by... 

Another key feature of redox thermodynamic cycles is that the free energy change in solution is still defined to involve a gas-phase electron, that is, the solvation free energy of the electron is happily not an issue. And, once again, redox potentials in soludon typically assume 1 M standard states for ad species (but not always in this chapter s case study, for instance, all redox potentials were measured and computed for chloride ion concentrations buffered to 0.001 M). So, free energy changes associated with concentration adjustments must also be properly taken into account. 

Suppose that a process occurred by which dnP moles of species z (component) were taken from phase 1 and added to phase 2. Then the free energy change, AG, in G becomes... 

The standard free energy change per electron transferred, ArG°(W )/n, of reaction Eq. 14-29 can now be simply derived from Table 14.2 by adding the ArG°(W) value of reaction (12) (+41.0 kJ mor1) and reversed reaction (1) (+78.3 kJ-mor1) ArG°(W)/ n = +119.3 kJ-mol-1. Thus, on a per-electron basis, under standard conditions (pH 7), we have to invest 119.3 kJ-mol-1 to (photo)synthesize glucose from C02 and H20. In our standard redox potential picture using h(W) values, this is equivalent... 

The overall standard free-energy change is obtained by adding the AG ° values for individual reactions ... 

For the reaction aA + bB cC + t/D, the equilibrium constant is K = [C]l[D], /[A]"(B), Solute concentrations should be expressed in moles per liter gas concentrations should be in bars and the concentrations of pure solids, liquids, and solvents are omitted. If the direction of a reaction is changed. K = UK. If two reactions are added. A", = K, K-,. The equilibrium constant can be calculated from the free-energy change for a chemical reaction K = e AcrlRT. The equation AG = AH — TAS summarizes the observations that a reaction is favored if it liberates heat (exothermic, negative AH) or increases disorder (positive AS). Le Chatelier s principle predicts the effect on a chemical reaction when reactants or products are added or temperature is changed. The reaction quotient, Q, tells how a system must change to reach equilibrium. 

Because half-reactions (1) and (2) contain a different number of electrons, the net reaction (3) is another half-reaction, and E°3 can t be obtained simply by adding E° and E°2. The free-energy changes, however, are additive because G is a state function ... 

The quantity A/ /L does not involve the translational free energy change of a surfactant molecule since the latter was included in the mixing entropy contribution. The change from an LC crystallized solid to a disordered liquid is considered to occur in two steps the first is from the LC crystallized solid (called below LC solid) to a liquid (called LC liquid), in which the molecules become somewhat disordered but occupy the same surface area Ac and the second step is from the LC liquid to the LE liquid, in which the molecular surface area varies from Ac to Ad- The former is a kind of melting process and has a melting free energy... 

---