A critical reaction in the production of energy to do work...

A critical reaction in the production of energy to do work or drive chemical reactions in biological systems is the hydrolysis of adenosine triphosphate, ATP, to adenosine diphosphate, ADP, as described by $$ \mathrm{ATP}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \leftrightharpoons \mathrm{ADP}(a q)+\mathrm{HPO}_{4}^{2-}(a q) $$ for which $\Delta G_{\mathrm{rxn}}^{\circ}=-30.5 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$ at $37.0^{\circ} \mathrm{C}$ and $\mathrm{pH}$ 7.0. Calculate the value of $\Delta G_{\mathrm{rxn}}$ in a biological cell in which $[\mathrm{ATP}]=5.0 \mathrm{mM},[\mathrm{ADP}]=0.50 \mathrm{mM}$, and $\left[\mathrm{HPO}_{4}^{2-}\right]=5.0 \mathrm{mM}$. Is the hydrolysis of ATP spontaneous under these conditions?

A critical reaction in the production of energy to do work or drive chemical reactions in biological systems is the hydrolysis of adenosine triphosphate, ATP, to adenosine diphosphate, ADP, as described by
$$
\mathrm{ATP}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \leftrightharpoons \mathrm{ADP}(a q)+\mathrm{HPO}_{4}^{2-}(a q)
$$
for which $\Delta G_{\mathrm{rxn}}^{\circ}=-30.5 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$ at $37.0^{\circ} \mathrm{C}$ and $\mathrm{pH}$
7.0. Calculate the value of $\Delta G_{\mathrm{rxn}}$ in a biological cell in which $[\mathrm{ATP}]=5.0 \mathrm{mM},[\mathrm{ADP}]=0.50 \mathrm{mM}$, and
$\left[\mathrm{HPO}_{4}^{2-}\right]=5.0 \mathrm{mM}$. Is the hydrolysis of ATP spontaneous under these conditions?

Key Concepts

Gibbs Free Energy (?G)

Gibbs free energy is a thermodynamic quantity that determines whether a chemical reaction will occur spontaneously under a given set of conditions. A negative ?G indicates that the reaction can proceed spontaneously, releasing energy that can be harnessed to perform work in biological systems.

Standard Free Energy Change (?G°)

The standard free energy change is defined under standard conditions—often including defined temperature, pH, and concentrations—providing a reference point for the reaction's inherent energy change. In biological systems, these conditions may differ, so ?G° serves as the basis for calculating the actual free energy change under cellular conditions.

Reaction Quotient (Q) and the Equation ?G = ?G° + RT ln Q

The reaction quotient, Q, represents the ratio of the concentrations (or activities) of products to reactants at any point in a reaction. In the equation ?G = ?G° + RT ln Q, Q accounts for deviations from standard conditions, allowing us to determine the actual Gibbs free energy change by incorporating concentration differences observed in cellular environments.

Biochemical Energy Currency and Reaction Spontaneity

In biological contexts, molecules such as ATP serve as the primary energy currency, where their hydrolysis releases energy useful for driving various cellular processes. The concepts of Gibbs free energy and the reaction quotient help determine whether reactions like ATP hydrolysis are spontaneous under the specific conditions inside a cell.

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