(Integrates with Chapter \(3 .)\) The standard free energy change \(\left(\Delta G^{\circ \prime}\right)\) for hydrolysis of phosphoenolpyruvate (PEP) is \(-61.9 \mathrm{kJ} / \mathrm{mol}\) The standard free energy change \(\left(\Delta G^{\circ \prime}\right)\) for ATP hydrolysis is \(-30.5 \mathrm{kJ} / \mathrm{mol}\) a. What is the standard free energy change for the pyruvate kinase reaction: ADP \(+\) phosphoenolpyruvate \(\longrightarrow\) ATP \(+\) pyruvate b. What is the equilibrium constant for this reaction? c. Assuming the intracellular concentrations of [ATP] and [ADP] remain fixed at \(8 \mathrm{m} M\) and \(1 \mathrm{m} M\), respectively, what will be the ratio of [pyruvate]/[phosphoenolpyruvate] when the pyruvate kinase reaction reaches equilibrium?

The concept of standard free energy change, represented as \( \Delta G^{\circ \prime} \) in biochemistry, is crucial for understanding the energetics of reactions in living organisms. It measures the amount of energy change that occurs during a reaction under standard conditions, which include a temperature of 25°C, 1 atmosphere of pressure, and all reactants and products at 1 M concentration, except for protons whose concentration is set at pH 7. A negative value of \( \Delta G^{\circ \prime} \) indicates that the reaction releases energy and can occur spontaneously, while a positive value would require energy input.

In biochemical pathways, the hydrolysis of compounds like phosphoenolpyruvate (PEP) and ATP is a common source of this energy. The magnitude of \( \Delta G^{\circ \prime} \) informs us about the potential of these compounds to drive biochemical reactions, with larger negative values indicating a higher energy release upon hydrolysis. Therefore, by analyzing \( \Delta G^{\circ \prime} \) values, students can predict the direction and spontaneity of reactions in metabolism.

The equilibrium constant, \( K_{eq} \) is a ratio that reflects the relative concentrations of products and reactants in a chemical reaction at equilibrium. It's a dimensionless number that gives us a sense of how far a reaction will go to completion before reaching a state where the forward and reverse reactions occur at the same rate. A large \( K_{eq} \) (much greater than 1) indicates that, at equilibrium, the reaction favors the formation of products; whereas a small \( K_{eq} \) (much less than 1) implies that the reactants are favored.

In the context of the pyruvate kinase reaction, knowing \( K_{eq} \) allows us to predict the extent to which phosphoenolpyruvate will be converted to pyruvate and ATP during cellular respiration. It informs researchers and students about how efficient this enzymatic step is under standard biological conditions and how different conditions might alter the reaction's equilibrium.

ATP hydrolysis is a fundamental reaction in biochemistry where the molecule adenosine triphosphate (ATP) is broken down into adenosine diphosphate (ADP) and an inorganic phosphate (Pi). This reaction is known for releasing a significant amount of energy, which is then used by the cell to perform various functions, including muscle contraction, nerve impulse propagation, and chemical synthesis.

The standard free energy change for ATP hydrolysis is about \( -30.5 \text{ kJ/mol} \). Given its central role in cellular energy transfer, ATP is commonly referred to as the 'energy currency' of the cell. Understanding the energetics of ATP hydrolysis not only clarifies how cells harness energy for physiological processes but also ties into broader concepts like energy coupling and enzyme kinetics.

Phosphoenolpyruvate (PEP) hydrolysis is another biochemical reaction that releases energy and is used by cells to drive endergonic processes. During glycolysis, PEP is converted to pyruvate by the enzyme pyruvate kinase, and this step involves the transfer of a phosphate group from PEP to ADP, forming ATP.

The standard free energy change for the hydrolysis of PEP is significantly negative (\( -61.9 \text{ kJ/mol} \) ), making it an even more potent source of energy than ATP hydrolysis. The comparison of these energy changes is beneficial in understanding the energy dynamics within the cell. It provides insight into why PEP is such an effective phosphate donor and plays a pivotal role in the final steps of glycolytic ATP production.