Question

The \(\Delta G^{\circ}\) for the reaction Citrate \(\rightarrow\) Isocitrate is \(+6.64 \mathrm{kJ} \mathrm{mol}^{-1}=+1.59 \mathrm{kcal} \mathrm{mol}^{-1} .\) The \(\Delta G^{\mathrm{o}}\) for the reaction Isoci- trate \(\rightarrow \alpha\) -Ketoglutarate is \(-267 \mathrm{kJ} \mathrm{mol}^{-1}=-63.9 \mathrm{kcal} \mathrm{mol}^{-1} .\) What is the \(\Delta G^{\text {or }}\) for the conversion of citrate to \(\alpha\) -ketoglutarate? Is that reaction exergonic or endergonic, and why?

Short answer

\Delta G^{\text{or}} is -260.36 \ \mathrm{kJ} \ \mathrm{mol}^{-1}. The reaction is exergonic because \ \Delta G < 0.

Step-by-step solution

Identify Given Reactants and Products

We are given two reactions: (1) Citrate to Isocitrate with \(\Delta G^{\circ} = +6.64 \ \mathrm{kJ} \ \mathrm{mol}^{-1} \ \mathrm{or} \ +1.59 \ \mathrm{kcal} \ \mathrm{mol}^{-1}\), and (2) Isocitrate to \ \alpha\-Ketoglutarate with \(\ \Delta G^{\circ} = -267 \ \mathrm{kJ} \ \mathrm{mol}^{-1} \ \mathrm{or} \ -63.9 \ \ \mathrm{kcal} \ \mathrm{mol}^{-1}\). Next, determine the overall reaction: Citrate to \ \alpha\-Ketoglutarate.

Calculate Overall \Delta G^{\text{or}}

The overall \ \Delta G^{\text{or}} for the reaction from Citrate to \ \alpha\-Ketoglutarate is the sum of the \ \Delta G^{\text{or}} values for the two steps: \(\ \Delta G^{\text{or}}_{\text{overall}} = \ \Delta G^{\text{or}}_{\text{step 1}} + \ \Delta G^{\text{or}}_{\text{step 2}} \).

Sum the \Delta G^{\text{or}} Values

Combine the \ \Delta G^{\text{or}} values to get the total: \(\ \Delta G^{\text{or}}_{\text{overall}} = +6.64 \ \mathrm{kJ} \ \mathrm{mol}^{-1} + (-267 \ \mathrm{kJ} \ \mathrm{mol}^{-1}) = -260.36 \ \mathrm{kJ} \ \mathrm{mol}^{-1} \ \).

Determine Exergonic or Endergonic

A reaction is exergonic if \(\ \Delta G < 0\) and endergonic if \(\ \Delta G > 0\). Since \(\ \Delta G = -260.36 \ \mathrm{kJ} \ \mathrm{mol}^{-1}\), the reaction is exergonic.

Key concepts

Delta G

In biochemical thermodynamics, \( \Delta G \) stands for Gibbs free energy change. This is a crucial factor in determining whether a reaction will proceed spontaneously.
\[ \Delta G \] can be defined as the difference in free energy between the starting product (reactant) and the ending product. The equation to compute \( \Delta G \) is: \[ \Delta G = \Delta H - T \Delta S \] where \( \Delta H \) is the change in enthalpy, \( T \) is the temperature in Kelvin, and \( \Delta S \) is the change in entropy.

In our exercise, we encounter two reactions with given \( \Delta G^{\circ} \) values: - Citrate to Isocitrate: \( \Delta G^{\circ} = +6.64 \; kJ \; mol^{-1} \),- Isocitrate to \( \alpha \)-Ketoglutarate: \( \Delta G^{\circ} = -267 \; kJ \; mol^{-1} \). Adding these will give us the overall \( \Delta G^{\circ}_{overall} = -260.36 \; kJ \; mol^{-1} \).
This computed value will tell us much about the nature of this biochemical reaction, including its spontaneity.

Exergonic Reaction

An exergonic reaction is a type of chemical reaction where the change in Gibbs free energy \( \Delta G \) is negative. When \( \Delta G < 0 \, \) the reaction releases energy, making it exergonic.
Exergonic reactions are typically spontaneous, meaning they can occur without the input of additional energy.
In our problem, after calculating the overall \( \Delta G \) for the conversion of Citrate to \( \alpha \)-Ketoglutarate, we found it to be \( -260.36 \; kJ \; mol^{-1} \).
This large negative value indicates the reaction releases a significant amount of energy, classifying it as highly exergonic.
Such reactions are fundamental in biological systems as they often drive endergonic processes, supplying them with the necessary energy.

Endergonic Reaction

In contrast to exergonic reactions, endergonic reactions have a positive \( \Delta G \: \Delta G > 0 \).
These reactions require an input of energy to proceed since they are not spontaneous. Often, the energy required is obtained from exergonic reactions.
In biochemical pathways, these two types of reactions are frequently coupled, meaning the energy released by an exergonic process provides the necessary boost for an endergonic one.
Though our exercise highlighted an exergonic reaction, understanding endergonic reactions is vital in comprehending overall bioenergetics.
For instance, the synthesis of complex molecules like proteins or nucleic acids generally involves endergonic steps that depend on the exergonic breakdown of molecules like ATP.