Question

Finding gibbs energy change from fractional molar conversion

Answer 1

As a consequence of the second law of thermodynamics, at constant pressure and temperature, a reaction will spontaneously take place if the Gibbs free energy (free enthalpy) difference between the final state and the initial state is negative, i.e. if ΔG < 0. During the approach to equilibrium, the free enthalpy decreases, reaching a minimum at equilibrium where ΔG = 0. As a reminder, the definition of the Gibbs free energy is:


(8.9)

where H is the enthalpy, T is the absolute temperature and S is the entropy. In solutions, the standard free enthalpy, G°, is defined for a standard state in which the concentration of each component is 1 M. With respect to this reference value, the free enthalpy of the system of a solution of molecule A can be expressed in the form:


(8.10)

where a is the activity (effective concentration), R is the universal gas constant, which has the value 8.31447 J·K-1·mol-1. In dilute solutions, aapproximately equals the molar concentration of molecule A ([A]). Therefore:


(8.11)

In solution phase, in the case of a reaction with several components, the free enthalpy change of the reaction can be expressed as:

(8.12)

where, in the fraction, the products of the concentrations appear. In equilibrium, ΔG= 0 and the concentrations in the fraction are the equilibrium concentrations. Thus, the fraction gives exactly the equilibrium association constant. Therefore, the standard free enthalpy change can be determined directly from the equilibrium constant:


(8.13)

It is worth noting that, in biochemical systems, we use aqueous solutions in which the standard state is defined at neutral pH (pH 7.0).

ΔG° describes the stability of the products in a reaction, or the stability of the complex in a protein-ligand interaction in the equilibrium, relative to the reactants. Figure 8.2 shows the relationship between the dissociation constant and ΔG° for different binding affinities, compared to the case at KD = 100 nM (second line).

Answer 2

Answer:

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