Biochemistry - The Chemical Reactions of Living Cells, Volume 1 - D. Metzler 1980

Energetics of Biochemical Reactions
Thermodynamics
Reactions in Solution

Biochemists are typically interested in The properties of compounds in relatively dilute aqueous solutions (such as the Cytoplasm), although in certain cases they must also deal with non-aqueous solutions. In each of these scenarios, it is necessary to define the standard state of a solute. For a substance in an aqueous solution, the standard state is conventionally taken as its state in a hypothetical molal solution (1 mole of solute per 1 kg of Water) whose properties are identical to those of the solute at infinite dilution. In this case, we can write an equation analogous to equation (3-22), expressing the Free energy of 1 mole of solute, , in terms of the free energy in the hypothetical standard state at unit activity and in terms of the solute activity¹:

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Equation (3-23) and the equations derived from it incorporate molal activities. However, for very dilute solutions, where the Properties of the solute molecules closely approximate those in a hypothetical ideal solution (the standard state), concentrations may be used in place of activities. For any real solution, activity is equal to the product of the activity coefficient and the concentration

   а = ус,       (2-24)

where $a$ is the activity, $y$ is the activity coefficient, and $c$ is the molal concentration. Thus, to predict The behavior of substances in moderately concentrated solutions using tables of thermodynamic Functions for solutes, one must multiply the concentration of each component by its corresponding activity coefficient. For rough estimates, which often fully suffice for biochemical purposes, it is common practice to set activities equal to concentrations. Furthermore, for dilute solutions, the more familiar molar concentrations (moles of solute per liter of solution) are virtually equal to molal concentrations².

It follows from equation (3-23) that The change in free energy upon diluting a solution from an initial state with activity a₁ to a final state with activity a₂ is given by