Free energy reactant concentration

As a system moves from a nonequilibrium to an equilibrium position, AG must change from its initial value to zero. At the same time, the species involved in the reaction undergo a change in their concentrations. The Gibb s free energy, therefore, must be a function of the concentrations of reactants and products. 

But spontaneity depends on the concentrations of reactants and products. If the ratio [Bl YCA] is less than a certain value, the reaction is spontaneous in the forward direction if [Bl YCA] exceeds this value, the reaction is spontaneous in the reverse direction. Therefore, it is useful to define a standard free-energy change (AG°) which applies to a standard state where [A] = [B] = 1 M. 

Thus, AG tells us about the reaction with respect to the substances present and their concentrations. AG° focuses more clearly on the differences in free energy between the reactants and products by removing their concentrations from consideration. 

Equation (3.12) shows that the free energy change for a reaction can be very different from the standard-state value if the concentrations of reactants and products differ significantly from unit activity (1 Mfor solutions). The effects can often be dramatic. Consider the hydrolysis of phosphocreatine ... 

Under cellular conditions, this first reaction of glycolysis is even more favorable than at standard state. As pointed out in Chapter 3, the free energy change for any reaction depends on the concentrations of reactants and products. 

We have already noted that the standard free energy change for a reaction, AG°, does not reflect the actual conditions in a ceil, where reactants and products are not at standard-state concentrations (1 M). Equation 3.12 was introduced to permit calculations of actual free energy changes under non-standard-state conditions. Similarly, standard reduction potentials for redox couples must be modified to account for the actual concentrations of the oxidized and reduced species. For any redox couple. 

Equilibrium concentrations of reactants and products can be calculated from the equilibrium constant, K q, which is related to the free energy of reaction, AGrxn ... 

As an example of two reactions that are coupled, look at the phosphorylation reaction of glucose to yield glucose 6-phosphate plus water, an important step in the breakdown of dietary carbohydrates. The reaction of glucose with HOPO 2- does not occur spontaneously because it is energetically unfavorable, with AG° = + 13.8 kj/mol. (The standard free-energy change for a biological reaction is denoted AG0 and refers to a process in which reactants and products have a concentration of 1.0 M in a soiution with pH = 7.)... 

The value of AG at a particular stage of the reaction is the difference in the molar Gibbs free energies of the products and the reactants at the partial pressures or concentrations that they have at that stage, weighted by the stoichiometric coefficients interpreted as amounts in moles ... 

Example 9.4 deals with a system at equilibrium, but suppose the reaction mixture has arbitrary concentrations. How can we tell whether it will have a tendency to form more products or to decompose into reactants To answer this question, we first need the equilibrium constant. We may have to determine it experimentally or calculate it from standard Gibbs free energy data. Then we calculate the reaction quotient, Q, from the actual composition of the reaction mixture, as described in Section 9.3. To predict whether a particular mixture of reactants and products will rend to produce more products or more reactants, we compare Q with K ... 

That is, the equilibrium constant for a reaction is equal to the ratio of the rate constants for the forward and reverse elementary reactions that contribute to the overall reaction. We can now see in kinetic terms rather than thermodynamic (Gibbs free energy) terms when to expect a large equilibrium constant K 1 (and products are favored) when k for the forward direction is much larger than k for the reverse direction. In this case, the fast forward reaction builds up a high concentration of products before reaching equilibrium (Fig. 13.21). In contrast, K 1 (and reactants are favored) when k is much smaller than k. Now the reverse reaction destroys the products rapidly, and so their concentrations are very low. 

When the reactants are present in concentrations of 1.0 mol/L, AG is the standard free energy change. For biochemical reactions, a standard state is defined as having a pH of 7.0. The standard free energy change at this standard state is denoted by AG". ... 

In vivo, under steady-state conditions, there is a net flux from left to right because there is a continuous supply of A and removal of D. In practice, there are invariably one or more nonequilibrium reactions in a metabolic pathway, where the reactants are present in concentrations that are far from equilibrium. In attempting to reach equilibrium, large losses of free energy occur as heat, making this type of reaction essentially irreversible, eg. 

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... 

If k is expressed in liters per mole per second, the standard state for the free energy and entropy of activation is 1 mole/liter. If the units of k are cubic centimeters per molecule per second, the corresponding standard state concentration is 1 molecule/cm3. The magnitudes of AG and AS reflect changes in the standard state, so it is not useful to say that a particular reaction is characterized by specific numerical values of these parameters unless the standard states associated with them are clearly identified. These standard states are automatically determined by the units chosen to describe the reactant concentrations in the phenomenological rate expressions. 

The free energy of chemical reactions may be estimated both under the standard conditions and under real, or physiological, conditions. The standard free energy, AG°, of a biochemical reaction is defined as a free energy change under the standard conditions, i.e. at the concentration of reactants 1 mol/litre, temperature 25 °C <298 X), and pH 7. 

From changes in free energy in standard reference conditions it is possible to calculate equilibrium constants for reactions involving several reactants and products. Consider, for example, the chemical reaction aA + bB = cC + dD at equilibrium in solution. For this reaction we can define a stoichiometric equilibrium constant in terms of the concentrations of the reactants and products as... 

Fig. 18 Free energy profiles for the solvent extraction of copper, where L is Acorga P50. The profile shows the free energy of a site on the liquid/liquid interface. All higher-order rate constants are reduced to first-order rate constants by using the concentrations of reactants in either phase. The free energy lost in each cycle can be seen from the difference between 0 and the 10%, 50% and 80% extraction lines on the right of the diagram. The double-headed arrows indicate the rate-limiting free energy difference.

Just by looking at the value of AG, you can determine which way a reaction goes. If AG < 0, the reaction goes to the right. If AG > 0, the reaction goes to the left. And, if AG = 0, the products and reactants are of exactly the same free energy (note that this does not mean that the products and reactants are at the same concentration), and the reaction is at equilibrium. 

With a Keq of 2.3 X 105 M, the AG0 is -1.36 log10 (2.3 X 105) = -7.3 kcal/mol. This would be the AG if the products/reactants ratio were 1, but it s not. Let s assume that the local concentration of ATP in a cell is 5 mM, [ADP] is 60 pM, and [PJ is 5 mM (these are approximately right, but they will vary from cell to cell and at any given time in a cell). Keep in mind that this also means the amount of free energy available from ATP hydrolysis will vary from cell to cell and from time to time. 

It is easy to understand the lower reactivity of non-ionic nucleophiles in micelles as compared with water. Micelles have a lower polarity than water and reactions of non-ionic nucleophiles are typically inhibited by solvents of low polarity. Thus, micelles behave as a submicroscopic solvent which has less ability than water, or a polar organic solvent, to interact with a polar transition state. Micellar medium effects on reaction rate, like kinetic solvent effects, depend on differences in free energy between initial and transition states, and a favorable distribution of reactants from water into a micellar pseudophase means that reactants have a lower free energy in micelles than in water. This factor, of itself, will inhibit reaction, but it may be offset by favorable interactions with the transition state and, for bimolecular reactions, by the concentration of reactants into the small volume of the micellar pseudophase. 

Where possible we have used the free energies AG calculated from in vivo concentrations of metabolites rather than the standard free energies AG°, which do not take account of local concentrations of reactants and products. 

The main significance of being able to calculate or to measure AG values is that we are then able to make predictions about reactions and in particular identify which reactions are likely to be control points in pathways. The absolute numerical value of the actual change in free energy (AG ) is dependant upon the actual concentrations of the reactant(s) and product(s) involved in the reaction. Comparisons of values for different reactions are meaningless unless they have been determined under identical and standardized experimental conditions. The term standard free energy (symbol AG°) is used to specify just such conditions. 

The standard free energy change is the value obtained when the reactants and products (including H+) are at molar concentration and gasses (if present) are at 1 atmosphere of pressure. Such conditions are quite unphysiological, especially the proton concentration, as 1 molar H+ concentration gives a pH 0 biochemical reactions occur at a pH of between 5 and 8, mostly around pH 7. So a third term, AG°, is introduced to indicate that the reaction is occurring at pH 7. 

Valuable information on mechanisms has been obtained from data on solvent exchange (4.4).The rate law, one of the most used mechanistic tools, is not useful in this instance, unfortunately, since the concentration of one of the reactants, the solvent, is invariant. Sometimes the exchange can be examined in a neutral solvent, although this is difficult to find. The reactants and products are however identical in (4.4), there is no free energy of reaction to overcome, and the activation parameters have been used exclusively, with great effect, to assign mechanism. This applies particularly to volumes of activation, since solvation differences are approximately zero and the observed volume of activation can be equated with the intrinsic one (Sec. 2.3.3). 

The free energy is calculated from the stability constant, which can be determined by a number of experimental methods that measure some quantity sensitive to a change in concentration of one of the reactants. Measurement of pH, spectroscopic absorption, redox potential, and distribution coefficient in a solvent extraction system are all common techniques. 

Equation 2. The free-energy change as a function of concentration (activity) of the reactants... 

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