The standard free energy change for the hydrolysis of ATP was given in Problem 91. In a particular cell, the concentrations of ATP, ADP, and Pi are 0.0031 M, 0.0014 M, and 0.0048 M, respectively. Calculate the free energy change for the hydrolysis of ATP under these conditions, assuming a temperature of 298 K.

Verified step by step guidance

1. Identify the reaction for the hydrolysis of ATP: \[ \text{ATP} + \text{H}_2\text{O} \rightarrow \text{ADP} + \text{P}_i \]
2. Use the equation for the free energy change under non-standard conditions: \[ \Delta G = \Delta G^\circ + RT \ln Q \]
3. Calculate the reaction quotient \( Q \) using the concentrations: \[ Q = \frac{[\text{ADP}][\text{P}_i]}{[\text{ATP}]} \]
4. Substitute the given concentrations into the expression for \( Q \): \[ Q = \frac{0.0014 \times 0.0048}{0.0031} \]
5. Substitute \( \Delta G^\circ \), \( R = 8.314 \text{ J/mol K} \), \( T = 298 \text{ K} \), and the calculated \( Q \) into the equation for \( \Delta G \) to find the free energy change.

Key Concepts

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. The change in Gibbs Free Energy (ΔG) during a reaction indicates whether the process is spontaneous (ΔG < 0) or non-spontaneous (ΔG > 0). It is crucial for understanding energy changes in biochemical reactions, such as ATP hydrolysis.

Reaction Quotient (Q)

The reaction quotient (Q) is a ratio that compares the concentrations of products to reactants at any point in a reaction. It is used to determine the direction of the reaction and is calculated using the formula Q = [products]/[reactants]. In the context of ATP hydrolysis, Q helps assess how the actual concentrations of ATP, ADP, and inorganic phosphate (Pi) affect the free energy change.

Standard Free Energy Change (ΔG°)

The standard free energy change (ΔG°) is the change in Gibbs Free Energy under standard conditions (1 M concentration, 1 atm pressure, and 25°C). It provides a baseline for comparing the free energy changes of reactions. For ATP hydrolysis, ΔG° is typically negative, indicating that the reaction is energetically favorable under standard conditions, but actual conditions can alter this value.