Chapter 19, Problem 40RE

Interpretation Introduction

Interpretation:

The overall exergonic reaction of the citric cycle is to be shown despite the fact that some of the reactions in the citric acid cycle are endergonic in nature.

Concept introduction:

 The citric acid cycle, also known as the tricarboxylic acid cycle, is an important part of the aerobic respiration that takes place inside the mitochondria.

 Gibbs free energy change or standard free energy change is the amount of energy released after a chemical reaction, which is available to do work. The change in standard energy is represented by the symbol $\Delta$, and hence, the Gibbs free energy is represented by ${\text{ΔG}}^{\text{0}}$.

 An endergonic chemical reaction is one that absorbs energy in the form of heat and an exergonic reaction is one that releases energy.

Answer to Problem 40RE

Solution: Though one reaction in the citric acid cycle is endergonic in nature, the overall citric acid cycle is exergonic, because the overall standard free change is $-44.3\text{kJ}/\text{mol}$.

Explanation of Solution

Given information:

The table for individual reactions of the citric acid cycle is as follows:

$\begin{array}{ccc}\text{Step}& \text{Reaction}& \begin{array}{l} \Delta \text{G}°\\ \left(\text{kJ/mol}\right)\end{array}\\ & \text{Pyruvate}+\text{CoA-SH}+{\text{NAD}}^{+}\to \text{Acetyl-CoA}+\text{NADH}+{\text{CO}}_2& -33.4\\ 1& \text{Acetyl-CoA}+\text{Oxaloacetate}+{\text{H}}_2\text{O}\to \text{Citrate}+\text{CoA-SH}+{\text{H}}^{+}& -32.2\\ 2& \text{Citrate}\to \text{Isocitrate}& +6.3\\ 3& \text{Isocitrate}+{\text{NAD}}^{+}\to \text{α Ketoglutarate}+\text{NADH}+{\text{CO}}_2+{\text{H}}^{+}& -7.1\\ 4& \text{α Ketoglutarate}+{\text{NAD}}^{+}+\text{CoA-SH}\to \text{Succinyl CoA}+\text{NADH }+{\text{CO}}_2+{\text{H}}^{+}& -33.4\\ 5& \text{Succinyl CoA}+\text{GDP}+{\text{P}}_{\text{i}}\to \text{Succinate}+\text{GTP}+\text{CoA-SH}& -3.3\\ 6& \text{Succinate}+\text{FAD}\to \text{Fumarate}+{\text{FADH}}_2& -0\\ 7& \text{Fumarate}+{\text{H}}_2\text{O}\to \text{L-Malate}& -3.8\\ 8& \text{L-Malate}+{\text{NAD}}^{+}\to \text{Oxaloacetate}+\text{NADH}+{\text{H}}^{+}& +29.2\\ \text{Overall}& \text{Pyruvate}+4{\text{NAD}}^{+}+\text{FAD}+\text{GDP}+{\text{P}}_{\text{i}}+2{\text{H}}_2\text{O}\to {\text{CO}}_2+4\text{NADH}+{\text{FADH}}_2+\text{GTP}+{\text{H}}^{+}& -77.7\end{array}$

Any given metabolic reaction is a favorable reaction only when the value of Gibbs free energy $\left({\text{ΔG}}^{\text{o}}\right)$ is negative. A negative value of ${\text{ΔG}}^{\text{o}}$ indicates an exergonic process. If a process is endergonic or has a positive ${\text{ΔG}}^{\text{o}}$, then it is immediately followed by another set of reactions in which the value ${\text{ΔG}}^{\text{o}}$ is more negative. For example, in the citric acid cycle, there is only one reaction in which the energy is absorbed as a result of which the standard free energy change is positive. The endergonic reaction that takes place during the citric acid cycle is the oxidation of malate to OAA (oxaloacetate).

As observed from the table, the value of standard free energy change for the oxidation of malate into OAA is $+29.2$ kilojoules per mole (kJ/mol). This endergonic reaction is immediately coupled to the exergonic reaction in which citrate and CoA are produced as a result of condensation between OAA and acetyl CoA. The overall citric acid cycle is exergonic, even though the conversion of malate to OAA in the cycle is endergonic. The citric acid cycle is exergonic with an overall standard free energy change value of $-44.3\text{kJ}/\text{mol}$.

The overall value of standard free energy change for a citric acid cycle is obtained by subtracting the ${\text{ΔG}}^{\text{o}}$ for pyruvate as follows:

$\begin{array}{c}{\text{ΔG}}^{\text{0}}=-\text{77}\text{.7kJ/mol}-\left(-\text{33}\text{.4}\right)\text{kJ/mol}\\ =-\left(\text{77}\text{.7}+\text{33}\text{.4}\right)\text{ kJ/mol}\\ =-\text{44}\text{.3 kJ/mol}\end{array}$

Conclusion

There is an endergonic reaction in the citric acid cycle in which malate is converted into OAA; however, the overall citric acid cycle is exergonic in nature because the overall free energy change of the cycle is $-44.3\text{kJ}/\text{mol}$. A negative value of standard free energy change indicates a spontaneous and favorable reaction.