Question

In the Citric Acid Cycle (also known as the Krebs Cycle), citrate is converted to isocitrate. From the algebraic sign of \(\Delta \mathrm{G}^{\circ}\) for the isomerization, what is the favored or spontaneous direction of the reaction? Calculate \(\Delta \mathrm{G}^{\circ}\) for the following reaction and explain what bearing this reaction will have on the isomerization of citrate and the operation of the Krebs Cycle: Isocitrate \(^{3-}+(1 / 2) \mathrm{O}_{2}(\mathrm{~g})+\mathrm{H}^{\mathrm{f}} \rightleftarrows\) a ketoglutarate \(^{2-}+\mathrm{H}_{2} \mathrm{O}(\ell)+\) (g) \(\Delta \mathrm{G}_{\mathrm{f}}\) in \((\mathrm{Kcal} / \mathrm{mole})\) are for citrate \({ }^{3-}=-279.24\); \(\mathrm{CO}_{2}(\mathrm{~g}\) isocitrate \(^{3-}=-277.65 ; \mathrm{H}^{\mathrm{f}}=0, \mathrm{O}_{2}=0\) \(\alpha\) -ketoglutarate \(^{2-}=-190.62 ; \mathrm{H}_{2} \mathrm{O}(\ell)=-56.69\) \(\mathrm{CO}_{2}(\mathrm{~g})=-94.26\)

Short answer

The Gibbs Free Energy (\( \Delta G^\circ \)) for the given reaction is \( -341.57 \ Kcal/mole \). Since the calculated \( \Delta G^\circ \) is negative, the reaction is spontaneous and will proceed in the forward direction. This means that the isomerization of citrate to isocitrate and the further transformation of isocitrate to \(\alpha\)-ketoglutarate is a spontaneous process in the Citric Acid Cycle, thus favoring the operation of the Krebs Cycle in this direction.

Step-by-step solution

Determine the formula for calculating Gibbs Free Energy \( \Delta G^\circ \) for a reaction

It is crucial to start this exercise with the general formula for Gibbs Free Energy \( \Delta G^\circ \) for a reaction. It is computed as follows: \[ \Delta G^\circ = \Sigma n \Delta G_f^\circ(products) - \Sigma m \Delta G_f^\circ(reactants) \] On the left hand side, we have the sum of the Gibbs free energies of formation \(\Delta G_f^\circ \) of the products, each multiplied by its stoichiometric coefficient \(n\). On the right hand side is the sum of the Gibbs free energies of formation of the reactants, each multiplied by its stoichiometric coefficient \(m\). Here, the stoichiometric coefficients come from the balanced chemical equation for the reaction.

Substitute the given values into the formula

The next step is to substitute the \( \Delta G_f^\circ \) values given in the exercise into the Gibbs Free Energy formula. For the reaction given: Isocitrate \( ^{3-}+(1 / 2) O_{2}(g)+H^{f} \rightarrow \alpha -\)ketoglutarate \( ^{2-}+H_{2} O(l)+CO_{2}(g) \) We substitute the respective \( \Delta G_f^\circ \) values for each species in the reaction given as: Isocitrate \( ^{3-} = -277.65 Kcal/mole \) \( O_{2} = 0 Kcal/mole \) \( H^{f}=0 Kcal/mole \) \( \alpha -\)ketoglutarate \( ^{2-} = -190.62 Kcal/mole \) \( H_{2} O(l) = -56.69 Kcal/mole \) \( CO_{2}(g) = -94.26 Kcal/mole \) In the formula, substituting these values yields: \[ \Delta G^\circ = [ 1(-190.62) + 1(-56.69) +1(-94.26) ] - [ 1(-277.65) + (1/2)(0) + 1(0) ] \]

Calculate the Gibbs Free Energy \( \Delta G^\circ \) for the reaction

To get the \( \Delta G^\circ \) for the reaction, simply perform the addition and subtraction in the equation from Step 2. This gives \[ \Delta G^\circ = [ -190.62 - 56.69 - 94.26 ] - [ -277.65 ] \] Which simplifies to \[ \Delta G^\circ = -341.57 Kcal/mole \] Therefore, the Gibbs Free Energy \( \Delta G^\circ \) for this reaction is \( -341.57 Kcal/mole \).

Analyze the sign of \( \Delta G^\circ \) and explain the favored direction of the reaction

As the calculated \( \Delta G^\circ \) is negative, the reaction is spontaneous and will proceed in the forward direction. This implies that, in the Citric Acid Cycle, the isomerization of citrate to isocitrate and the further transformation of isocitrate to \(\alpha\)-ketoglutarate is a spontaneous process under standard conditions. As a result, the operation of the Krebs Cycle is favored in this direction. This is an important aspect of the cellular respiration in which energy is released from organic compounds.

Key concepts

Gibbs Free Energy

Gibbs Free Energy is a vital concept for understanding chemical reactions. It represents the energy available to do work in a system, under constant temperature and pressure. Gibbs Free Energy, denoted as \( \Delta G \), helps predict whether a reaction will occur spontaneously. The formula to calculate it is:

• \[ \Delta G = \Delta H - T \Delta S \]
• where \( \Delta H \) is enthalpy change, \( T \) is temperature, and \( \Delta S \) is entropy change.

In terms of determining reaction spontaneity, a negative \( \Delta G \) indicates that the reaction can proceed spontaneously. In this particular exercise, the calculated \( \Delta G\circ \) for the reaction was negative, meaning the process was spontaneous. This concept is crucial in the operation of cellular respiration, where biological cells convert biochemical energy to ATP, the body's energy currency.

isomerization

Isomerization is a specific type of chemical reaction where a molecule is transformed into another molecule with the same chemical formula but a different structure. This can involve the rearrangement of atoms and bonds. In the Citric Acid Cycle, this process occurs when citrate is isomerized to isocitrate. This transformation, despite its seemingly minor nature, is crucial for subsequent steps in energy extraction.The algebraic sign of \( \Delta G\circ \) helps to determine if this transformation occurs naturally. A negative \( \Delta G\circ \) signifies that the isomerization will likely happen spontaneously under standard conditions. This characteristic plays an imperative role in the Citric Acid Cycle, ensuring that the pathway proceeds efficiently, releasing energy that cells harness for various functions.

spontaneous reaction

A spontaneous reaction is a chemical process that occurs without being driven by an external source of energy. When a reaction is spontaneous, it signifies that it can progress with a decrease in free energy, reflecting a state of greater stability. When \( \Delta G\circ \) is negative, it indicates that reactants can convert to products without outside intervention. This characteristic is intrinsic to many biological systems to ensure efficiency and conservation of energy.Reactions that are spontaneous are key components of metabolic pathways, like the Citric Acid Cycle. In this cycle, spontaneous reactions ensure that energy is extracted and utilized efficiently within cells, contributing to an organism's survival and homeostasis.

Krebs Cycle

The Krebs Cycle, also called the Citric Acid Cycle, is a central part of cellular respiration. It is a series of chemical reactions that take place in the mitochondria. The cycle plays a pivotal role in converting biochemical energy from nutrients into Adenosine Triphosphate (ATP), which is then used as energy within cells. Within the cycle:

• Acetyl-CoA combines with oxaloacetate to form citrate.
• Citrate undergoes a series of transformations, including isomerization and decarboxylation.
• These transformations release energy stored in bonds, which is captured in ATP and electron carriers like NADH and FADH2.

The Krebs Cycle not only produces ATP but also provides essential precursors for many biosynthetic pathways, highlighting its importance in cellular metabolism.

cellular respiration

Cellular respiration is the process by which cells convert biochemical energy from nutrients into ATP, and release waste products. It involves multiple steps and pathways, of which the Citric Acid Cycle (Krebs Cycle) is a core component. The entire pathway includes:

• Glycolysis, where glucose is broken down to pyruvate.
• The transition cycle, where pyruvate is converted to acetyl-CoA.
• The Citric Acid Cycle, which further processes acetyl-CoA, releasing energy.
• The Electron Transport Chain, where the majority of ATP is generated.

Cellular respiration is incredibly efficient, enabling organisms to thrive and sustain various physiological processes. Understanding this system bridges numerous subfields of biology and biochemistry, emphasizing the importance of energy transformations in living organisms.