Gibbs Free Energy and ATP Hydrolysis Quiz

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Questions and Answers

The Gibbs free energy change ($, riangle G$) for the reaction ATP → ADP + Pi is equal to $-30.5$ kJ mol−1.

True

The enthalpy change ($ riangle H$) for the reaction ATP → ADP + Pi is $+20.1$ kJ mol−1.

False

A positive change in entropy ($ riangle S$) indicates a decrease in disorder in the system.

False

For the unfolding of a protein to occur spontaneously, the Gibbs free energy ($ riangle G$) must be greater than zero.

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The change in entropy for the reaction ATP → ADP + Pi at 37 °C is calculated to be $34.0$ J K−1 mol−1.

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If $ riangle S°$ for a reaction is negative, it promotes spontaneity at higher temperatures.

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For the unfolding of a protein where $ riangle H° = 250.8$ kJ mol−1 and $ riangle S° = 752$ J K−1 mol−1, the process becomes spontaneous above a certain temperature.

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A reaction with a negative enthalpy change ($ riangle H$) always has a negative Gibbs free energy change ($ riangle G$).

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The temperature at which the reaction transitioning from ATP to ADP becomes spontaneous can be found using the equation $ riangle G = riangle H - T riangle S$.

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The values $ riangle H° = 250.8$ kJ mol−1 and $ riangle S° = 752$ J K−1 mol−1 indicates that unfolding a protein is always spontaneous.

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The change in Gibbs free energy ($\Delta G$) for the reaction ATP → ADP + Pi is positive at 37 °C.

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A reaction with a negative change in enthalpy ($\Delta H$) and a positive change in entropy ($\Delta S$) always has a negative Gibbs free energy ($\Delta G$) at all temperatures.

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For the unfolding of the protein to be spontaneous, the temperature must be lower than 250.8 °C.

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A positive change in entropy ($\Delta S$) for a reaction indicates a decrease in disorder of the system.

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The calculated change in entropy ($\Delta S$) for the reaction ATP → ADP + Pi is 34.0 kJ mol−1.

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The unfolding of a protein occurs spontaneously when the system's Gibbs free energy ($\Delta G$) is less than zero.

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If a reaction has a positive change in Gibbs free energy ($\Delta G$), it can still proceed if energy is supplied.

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The reaction ATP → ADP + Pi is an example of a process that increases the number of molecules in the system, hence increasing disorder.

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The threshold temperature for protein unfolding, calculated from given thermodynamic values, is influenced directly by changes in enthalpy ($\Delta H$) and entropy ($\Delta S$).

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An increase in temperature always leads to an increase in the Gibbs free energy ($\Delta G$) of a reaction.

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Study Notes

Gibbs Free Energy Equation Explanation

The Gibbs Free Energy equation is written as: G = H − TS
G : Gibbs free energy, a measure of the spontaneity of a reaction. A negative G indicates a spontaneous reaction, while a positive G indicates a non-spontaneous reaction.
H : Enthalpy change, a measure of the heat flow during a reaction.
T : Temperature in Kelvin.
S : Entropy change, a measure of the disorder of a system; a positive S indicates increased disorder, while a negative S indicates decreased disorder.

Calculating Entropy Change (S) in ATP Hydrolysis

The hydrolysis of ATP (adenosine triphosphate) to ADP (adenosine diphosphate) and inorganic phosphate (Pi) is a key energy-releasing process in biological systems.
Given:
- G° (standard Gibbs free energy) = -30.5 kJ mol-1
- H° (standard enthalpy change) = -20.1 kJ mol-1
- Temperature = 37°C (which should be converted to Kelvin, 37 + 273 = 310 K)
Calculate S° using the equation G = H − TS
Rearrange the equation to solve for S°:
- S° = (H° - G°) / T
- S° = (-20.1 kJ mol-1 - (-30.5 kJ mol-1)) / 310 K
- S° = 10.4 kJ mol-1 / 310 K
- S° = 0.034 kJ mol-1 K (or 34 J mol-1 K)

Significance of Enthalpy (H), Entropy (S) and Gibbs Free Energy (G) in ATP Hydrolysis

- Enthalpy (H): The enthalpy change is negative (-20.1 kJ mol-1), indicating an exothermic process (heat is released). This is likely due to the formation of new bonds, such as the P-O bond in inorganic phosphate (Pi).
Entropy (S): The entropy change is positive (+34 J mol-1 K), indicating an increase in disorder or randomness. This is expected as one molecule (ATP) is broken down into two molecules (ADP and Pi).
Gibbs Free Energy (G): The Gibbs free energy change is negative (-30.5 kJ mol-1), indicating a spontaneous reaction under these conditions. This means at 37 °C, the hydrolysis of ATP is favorable and will tend to proceed towards the formation of ADP and Pi. The negative value of G also indicates that the ATP hydrolysis is an exergonic process, releasing free energy that can be used to drive other cellular processes.

Spontaneous Protein Unfolding: Effect of Temperature on G

The unfolding of a protein is described as a process where a folded, active protein transitions to an unfolded, inactive state.
The enthalpy change (H°) for protein unfolding is positive (+250.8 kJ mol-1), meaning the process requires energy input (endothermic). This is because breaking the interactions that maintain the folded structure requires energy.
The entropy change (S°) for protein unfolding is also positive (+752 J K−1 mol −1), indicating an increase in disorder as the protein unfolds and becomes less structured.
The temperature at which the protein unfolding becomes spontaneous (i.e., G becomes negative) is determined by the balance between enthalpy and entropy.

Determining the Temperature for Spontaneous Protein Unfolding

For unfolding to be spontaneous (favorable), the G must be negative:
To find the critical temperature where the reaction switches to spontaneity, we need to find the temperature at which G = 0.
Using the equation G = H − TS, and setting G to 0:
- 0 = H - TS
- 0 = 250.8 kJ mol-1 - T (0.752 kJ K-1 mol-1)
- T = 250.8 kJ mol-1 / 0.752 kJ K-1 mol-1
- T = 333.6 K
Converting this temperature back to Celsius:
- T = 333.6 K - 273.15 K = 60.45 °C
Therefore, protein unfolding becomes spontaneous (favorable) above 60.45 °C.

Commentary on the Significance of the Values of H, S, and G

The positive enthalpy of protein unfolding (H°) reflects that unfolding requires energy input and is an endothermic process.
The positive entropy change (S°) reflects that unfolding leads to an increase in disorder within the protein structure.
The temperature at which unfolding becomes spontaneous is dependent on the interplay between the thermodynamic parameters of the reaction (enthalpy and entropy). At temperatures below 60.45°C, the enthalpy term (favorable for folded state) dominates, keeping the protein folded. However, at temperatures above 60.45 °C, the entropic term (favorable for unfolded state) dominates, promoting unfolding.