In glycolysis, the hydrolysis of ATP to ADP drives the...

In glycolysis, the hydrolysis of ATP to ADP drives the phosphorylation of glucose: $$\begin{array}{l}\text { Glucose }+\mathrm{ATP} \rightleftharpoons \mathrm{ADP}+\text { glucose } 6 \text { -phosphate } \\\qquad \Delta G_{\mathrm{rm}}^{\circ}=-17.7 \mathrm{kJ}\end{array}$$ What is the value of $K_{c}$ for this reaction at $298 \mathrm{K} ?$

In glycolysis, the hydrolysis of ATP to ADP drives the phosphorylation of glucose:
$$\begin{array}{l}\text { Glucose }+\mathrm{ATP} \rightleftharpoons \mathrm{ADP}+\text { glucose } 6 \text { -phosphate } \\\qquad \Delta G_{\mathrm{rm}}^{\circ}=-17.7 \mathrm{kJ}\end{array}$$
What is the value of $K_{c}$ for this reaction at $298 \mathrm{K} ?$

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Key Concepts

Gibbs Free Energy (?G)

Gibbs free energy is a thermodynamic quantity that indicates the maximum reversible work obtainable from a system at constant temperature and pressure. It is a key determinant of reaction spontaneity, where a negative ?G signifies that a reaction can proceed spontaneously under the given conditions. Understanding ?G is central to analyzing biochemical reactions and their energetics.

Equilibrium Constant (K)

The equilibrium constant (K) quantifies the ratio of product concentrations to reactant concentrations when a reaction has reached equilibrium. It provides insight into the position of equilibrium for a given reaction and is used to predict the extent to which reactants are converted to products under standard conditions.

Relationship between ?G and K

The thermodynamic relationship ?G° = –RT ln K connects the standard free energy change of a reaction to its equilibrium constant. This equation shows that even a relatively small free energy change can correspond to a large equilibrium constant, highlighting the sensitivity of equilibrium positions to changes in reaction energetics. It is fundamental in linking thermodynamic properties with measurable equilibrium behavior.

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