One reaction that occurs in human metabolism is For this...

One reaction that occurs in human metabolism is For this reaction $\Delta G^{\circ}=14 \mathrm{~kJ}$ at $25^{\circ} \mathrm{C}$. a. Calculate $K$ for this reaction at $25^{\circ} \mathrm{C}$. b. In a living cell this reaction is coupled with the hydrolysis of ATP. (See Exercise 79.) Calculate $\Delta G^{\circ}$ and $K$ at $25^{\circ} \mathrm{C}$ for the following reaction: Glutamic acid $(a q)+\mathrm{ATP}(a q)+\mathrm{NH}_{3}(a q) \rightleftharpoons$ Glutamine $(a q)+\mathrm{ADP}(a q)+\mathrm{H}_{2} \mathrm{PO}_{4}^{-}(a q)$

One reaction that occurs in human metabolism is
For this reaction $\Delta G^{\circ}=14 \mathrm{~kJ}$ at $25^{\circ} \mathrm{C}$.
a. Calculate $K$ for this reaction at $25^{\circ} \mathrm{C}$.
b. In a living cell this reaction is coupled with the hydrolysis of ATP. (See Exercise 79.) Calculate $\Delta G^{\circ}$ and $K$ at $25^{\circ} \mathrm{C}$ for the following reaction:
Glutamic acid $(a q)+\mathrm{ATP}(a q)+\mathrm{NH}_{3}(a q) \rightleftharpoons$
Glutamine $(a q)+\mathrm{ADP}(a q)+\mathrm{H}_{2} \mathrm{PO}_{4}^{-}(a q)$

Key Concepts

ATP Hydrolysis

ATP hydrolysis is the process by which adenosine triphosphate (ATP) is converted into adenosine diphosphate (ADP) and inorganic phosphate, releasing energy. This energy release (characterized by a large negative ?G°) is widely used in biochemistry to drive non-spontaneous reactions through reaction coupling, making ATP a primary energy currency in the cell.

Standard Gibbs Free Energy

Standard Gibbs free energy (?G°) is a thermodynamic quantity that indicates the spontaneity of a reaction under standard conditions (usually 1 atm pressure and 1 M concentration for all reactants and products). It is related to the position of equilibrium, and a negative ?G° suggests that the reaction is spontaneous while a positive ?G° indicates non-spontaneity under standard conditions.

Equilibrium Constant

The equilibrium constant (K) is a dimensionless quantity that describes the ratio of the concentrations of products to reactants at equilibrium. It is directly related to the standard Gibbs free energy change of the reaction through the equation ?G° = -RT ln K, where R is the gas constant and T is the temperature in Kelvin.

Reaction Coupling

Reaction coupling is a critical concept in biochemical processes where an energetically unfavorable reaction (with a positive ?G°) is driven forward by coupling it to an energetically favorable reaction (with a negative ?G°), such as the hydrolysis of ATP. This mechanism allows cells to drive endergonic reactions that are essential for biological function.

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