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

Energetics of Biochemical Reactions
Thermodynamics
Summation of Free Energy Changes

An important feature of thermodynamic calculations is that $\Delta G$ for a set of multiple Chemical Reactions is simply equal to the sum of the $\Delta G$ values for the individual reactions [see equations (3-16) through (3-19)]. The same applies to $\Delta H$ and $\Delta S$.

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In this example, equation (3-16) for the decomposition of acetic acid into its elements is added to equations (3-17) and (3-18), which describe The formation of the required number of $\text{CO}_2$ and $\text{H}_2\text{O}$ molecules. Summing these three equations yields the overall equation for the combustion of acetic acid to form $\text{CO}_2$ and Water, and the sum of the $\Delta G$ values for each of the three equations gives the $\Delta G$ of combustion for acetic acid. Note that the resulting $\Delta G$ value corresponds to the combustion of pure liquid acetic acid in oxygen at a pressure of 1 atm, yielding $\text{CO}_2$ at 1 atm and pure liquid water as products—with both reactants and products in their Standard States.

The Procedure described above can be represented by equation (3-20), a general equation that allows the calculation of $\Delta G^0$ for any reaction when the $\Delta G$ values of the products and reactants are known:

How does The change in Free energy vary when a compound transitions from its standard state to some other state? Let us consider the case where the gas pressure changes. It is easy to demonstrate (consult any Thermodynamics textbook) that

(dG/dP)_T = V.       (3-21)

Combining equation (3-21) with the ideal gas law yields the relationship between the free energy of 1 mole of a substance¹ at pressure P and the Standard Free Energy at pressure P⁰:

Since P⁰ is defined as 1 atm, the change in Free energy of 1 mole of a substance when the pressure changes from P⁰ to P is simply equal to $RT\ln P$. In thermodynamics, the derivation of the most important thermodynamic equations is typically illustrated using ideal gases; however, when applied to biochemical systems, solutions serve as a more relevant analogue.

¹ The bar over the symbols G or $\Delta G$ always indicates that the free energy or its change refers to 1 mole of the substance.