Problem 83 - Chemistry The Molecular Science

Question

Another step in the metabolism of glucose, which occurs after the formation of glucose 6 -phosphate, is the conversion of fructose 6 -phosphate to fructose 1,6 -bisphosphate ("bis" means two): $$ \begin{aligned} \text { Fructose } 6 \text { -phosphate }(\mathrm{aq})+\mathrm{H}_{2} \mathrm{PO}_{4}^{-}(\mathrm{aq}) & \longrightarrow \\ & \text { fructose } 1,6 \text { -bisphosphate(aq) }+\mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{H}^{+}(\text {aq }) \end{aligned} $$ (a) This reaction has a Gibbs free energy change of \(+16.7 \mathrm{~kJ} / \mathrm{mol}\) of fructose 6 -phosphate. Is it endergonic or exergonic? (b) Write the equation for the formation of \(1 \mathrm{~mol}\) ADP from ATP, for which \(\Delta_{\mathrm{r}} G^{\circ}=-30.5 \mathrm{~kJ} / \mathrm{mol}\) (c) Couple these two reactions to get an exergonic process; write its overall chemical equation, and calculate the Gibbs free energy change.

Step-by-Step Solution

Answer

(a) Endergonic; (b) ATP(aq) → ADP(aq) + Pi(aq); (c) Overall: ATP + Fructose 6-phosphate → Fructose 1,6-bisphosphate + ADP + H2O, \(\Delta G = -13.8 \text{kJ/mol}\).

Step 1: Determine if reaction is Endergonic or Exergonic

The Gibbs free energy change for the reaction converting fructose 6-phosphate to fructose 1,6-bisphosphate is given as \(+16.7 \text{ kJ/mol}\). Since the \(\Delta G\) is positive, this indicates that the reaction is **endergonic**, requiring energy input to proceed.

Step 2: Write Equation for ADP Formation

The formation of 1 mol of ADP from ATP can be represented by the equation: ATP(aq) \( \rightarrow \) ADP(aq) + \( \mathrm{P_{i}} \)(aq) This reaction has a standard Gibbs free energy change \(\Delta G^{\circ} = -30.5 \text{ kJ/mol}\), indicating an **exergonic** reaction, releasing energy.

Step 3: Couple the Two Reactions

To couple the reactions, we add them together to create a single overall reaction: 1. Fructose 6-phosphate(aq) + H\(_2\)PO\(_4^-\)(aq) \( \rightarrow \) Fructose 1,6-bisphosphate(aq) + H\(_2\)O(\ell) + H\(^+\)(aq), \(+16.7 \text{ kJ/mol}\) 2. ATP(aq) \( \rightarrow \) ADP(aq) + \(\mathrm{P_{i}}\)(aq), \(-30.5 \text{ kJ/mol}\) The net Gibbs free energy change for the coupled reaction is the sum of the individual \(\Delta G\) values: \(16.7 + (-30.5) = -13.8 \text{ kJ/mol}\). The overall reaction is: ATP(aq) + Fructose 6-phosphate(aq) \( \rightarrow \) Fructose 1,6-bisphosphate(aq) + ADP(aq) + H\(_2\)O(\ell)

Step 4: Confirm Overall Reaction is Exergonic

Check the overall Gibbs free energy change which is \(-13.8 \text{ kJ/mol}\). Since this \(\Delta G\) is negative, it confirms that the coupled process is **exergonic**, meaning it can proceed spontaneously.

Key Concepts

Metabolism

Metabolism is the sum of all chemical processes that occur in a living organism to maintain life. It involves pathways that break down nutrients to generate energy and simple precursors, as well as the pathways that construct vital biological molecules from these precursors.

Metabolism is divided into two main types:

• Catabolism: The breakdown of complex molecules into simpler ones, releasing energy.
• Anabolism: The building up of complex molecules from simpler ones, requiring energy.

The conversion of fructose 6-phosphate to fructose 1,6-bisphosphate in glycolysis is a key metabolic step.

It plays a role in regulating energy production and consumption.

Gibbs Free Energy

Gibbs free energy, represented as \(\Delta G\), is a thermodynamic quantity that indicates the spontaneity of a reaction. A negative \(\Delta G\) value denotes a spontaneous reaction, while a positive one requires energy input.

In our exercise, the conversion of fructose 6-phosphate to fructose 1,6-bisphosphate has a \(\Delta G = +16.7\) kJ/mol, indicating it is not spontaneous.

• A positive \(\Delta G\) implies energy is needed from the environment for the reaction to proceed.

This is crucial for understanding how cells manage biochemical pathways to ensure energy efficiency and reactant conversion.

ATP and ADP Conversion

The conversion of ATP (adenosine triphosphate) to ADP (adenosine diphosphate) is a central process in cellular energy transduction. ATP acts as an energy currency in cells, storing energy within its high-energy phosphate bonds.

When ATP is converted to ADP, one phosphate group is released, along with energy, described by the reaction:
ATP(aq) \(\rightarrow\) ADP(aq) + \(\mathrm{P_{i}}\)(aq)

This process is exergonic, with \(\Delta G^{\circ} = -30.5\) kJ/mol, meaning it releases energy that can be used to drive endergonic reactions in the cell.

• This conversion helps in balancing energy needs, acting as a mediator between energy-demanding and energy-releasing processes.

Endergonic and Exergonic Reactions

Understanding endergonic and exergonic reactions helps explain how cells manage their energy. An endergonic reaction requires an input of energy and has a positive \(\Delta G\), like the conversion of fructose 6-phosphate to fructose 1,6-bisphosphate.

In contrast, exergonic reactions release energy and have a negative \(\Delta G\), such as the conversion of ATP to ADP.

• Coupling endergonic and exergonic reactions is essential in biological systems to ensure that energy-intensive processes can occur.
• The net \(\Delta G\) of \(-13.8\) kJ/mol in our coupled reaction example shows it is exergonic, allowing the overall process to occur spontaneously in cells.

This balance is what enables organisms to efficiently regulate and optimize energy usage across various biochemical pathways.