Question

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

Short answer

The reaction has \Delta G^{\text{os}} of -260.36 \text{ kJ mol}^{-1} and is exergonic because \Delta G^{\text{os}} is negative.

Step-by-step solution

Identify Given Values

Determine the given values from the exercise. We have two given $\mathrm{\Delta }G$ values: $\mathrm{\Delta }{G}_1^{\text{os}}=+6.64{\text{ kJ mol}}^{-1}$ for the reaction Citrate \rightarrow Isocitrate, and $\mathrm{\Delta }{G}_2^{\text{os}}=-267{\text{ kJ mol}}^{-1}$ for the reaction Isocitrate \rightarrow \alpha-Ketoglutarate.

Find Overall \Delta G^{\text{os}}

Add the two given $\mathrm{\Delta }G$ values to find the overall $$\mathrm{\Delta }{G}^{\text{os}}=\mathrm{\Delta }{G}_1^{\text{os}}+\mathrm{\Delta }{G}_2^{\text{os}}$$. Substituting in the values, we have: $$\mathrm{\Delta }{G}^{\text{os}}=(+6.64{\text{ kJ mol}}^{-1})+(-267{\text{ kJ mol}}^{-1})=-260.36{\text{ kJ mol}}^{-1}$$

Determine Exergonic or Endergonic Reaction

Evaluate whether the reaction is exergonic or endergonic. A reaction is exergonic if $\mathrm{\Delta }{G}^{\text{os}}$ is negative and endergonic if $\mathrm{\Delta }{G}^{\text{os}}$ is positive. Since $\mathrm{\Delta }{G}^{\text{os}}=-260.36{\text{ kJ mol}}^{-1}$ is negative, the reaction is exergonic.

Key concepts

Bioenergetics

Bioenergetics is the study of how energy is transferred and transformed within living organisms. It explains how cells manage their energy resources to perform different functions.
The two main types of reactions in bioenergetics are exergonic and endergonic reactions.
Exergonic reactions release energy, while endergonic reactions absorb energy.
Bioenergetics is crucial for understanding how cells carry out processes like synthesis, movement, and signaling. This involves complex molecular interactions and understanding the balance between energy input and output.
One key factor in bioenergetics is the concept of Gibbs Free Energy, denoted as $\text{G}$. This value helps predict whether a reaction will occur spontaneously.
For a given reaction, if $\text{G}$ is negative, the reaction is favorable and releases energy (exergonic). Conversely, if $\text{G}$ is positive, the reaction requires energy input to proceed (endergonic).
Understanding bioenergetics is fundamental in fields like biochemistry and molecular biology, providing the basis for comprehending how life sustains itself through energy transformations.

Metabolic Pathways

Metabolic pathways are series of chemical reactions occurring within a cell. These pathways convert molecules into other forms, facilitating energy extraction and use.
Two main types of metabolic pathways exist: anabolic and catabolic pathways.
Anabolic pathways build complex molecules from simpler ones and are usually endergonic, requiring energy.
Catabolic pathways, on the other hand, break down complex molecules into simpler forms and typically release energy, making them exergonic.
Each step in a metabolic pathway involves a specific enzyme that accelerates the reaction.
Coordination and regulation of these enzymes are fundamental to maintaining cellular function and homeostasis.
Metabolic pathways interconnect, forming a complex network ensuring that the cell meets its energy and material needs.
Understanding these pathways is vital for appreciating how cells grow, develop, and respond to environmental changes.

Thermodynamics

Thermodynamics is the study of energy transfer and its impact on matter. In biological systems, thermodynamics principles apply to understand energy transformation in cells.
The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed.
The second law of thermodynamics states that energy transfer will always lead to an increase in the system's entropy, or disorder.
Gibbs Free Energy ($\text{G}$) is a crucial concept derived from these laws. It quantifies the useful work obtainable from a reaction at constant temperature and pressure.
The change in Gibbs Free Energy (\