Thermodynamics of Exergonic and Endergonic Reactions

1. Exergonic Reactions

An exergonic reaction is one in which the free energy of the products is lower than the free energy of the reactants, resulting in a negative $\Delta G$ ($\Delta G < 0$). Because energy is released, these reactions occur spontaneously without the need for an external energy input.

2. Endergonic Reactions

Conversely, an endergonic reaction is one where the products have more free energy than the reactants, resulting in a positive $\Delta G$ ($\Delta G > 0$). These reactions are non-spontaneous and require an input of energy to proceed.

Standard Free Energy and Concentration Effects

In laboratory settings, we often refer to the standard free energy change, denoted as $\Delta G^{\circ}$. In biochemistry, we specifically use $\Delta G^{\circ \prime}$ to represent the standard free energy change at a physiological pH of 7.

However, the actual free energy change ($\Delta G$) in a living cell is not always equal to the standard free energy change. $\Delta G$ fluctuates based on the actual concentrations of the reactants and products present in the environment. The relationship is defined by the following equation:

$$\begin{aligned} \Delta G = \Delta G^{\circ \prime} \\ + RT \ln \frac{[\text{Products}]}{[\text{Reactants}]} \end{aligned}$$

Where:

• $R$ is the gas constant.
• $T$ is the absolute temperature (in Kelvin).
• The brackets $[\dots]$ denote the molar concentration of the species.

Equilibrium and the Equilibrium Constant ($K_{\text{eq}}$)

As a reaction proceeds, the concentrations of reactants and products change, which in turn changes the $\Delta G$. Eventually, the system reaches a state of equilibrium, where there is no net change in the amount of reactant or product. At this specific point, the free energy change is zero: $\Delta G = 0$

The relationship between the standard free energy change ($\Delta G^{\circ \prime}$) and the equilibrium constant ($K_{\text{eq}}^{\prime}$) is a cornerstone of chemical thermodynamics. At equilibrium, the equation simplifies to:

$$\begin{aligned} \Delta G^{\circ \prime} = -RT \ln K_{\text{eq}}^{\prime} \end{aligned}$$

From this relationship, we can derive several critical insights regarding the direction of reactions:

• Highly Exergonic Reactions: If a reaction is very exergonic (large negative $\Delta G^{\circ \prime}$), the equilibrium constant $K_{\text{eq}}^{\prime}$ will be very large ($K_{\text{eq}}^{\prime} > 1$), meaning the reaction favors the formation of products.
• Highly Endergonic Reactions: If a reaction is very endergonic (large positive $\Delta G^{\circ \prime}$), the equilibrium constant $K_{\text{eq}}^{\prime}$ will be very small ($K_{\text{eq}}^{\prime} < 1$), meaning the reaction favors the reactants.

Summary Table: Relationship between $\Delta G^{\circ \prime}$ and $K_{\text{eq}}^{\prime}$

The following table illustrates how the magnitude of the equilibrium constant scales with the standard free energy change at $25^{\circ}\text{C}$:

Exam Tip: Remember that enzymes do not change the $\Delta G$ of a reaction. They only speed up the rate at which equilibrium is reached by lowering the activation energy. They cannot make a non-spontaneous reaction spontaneous!