Fructose-1-phosphate can be hydrolyzed into fructose + inorganic phosphate (Pi) with a ΔG° of –16.0 kJ/mol. If ATP can be hydrolyzed into ADP + Pi with a ΔG° of –30.5 kJ/mol, what is the free energy change for the reaction of fructose + ATP → fructose 1-phospate + ADP
The Correct Answer and Explanation is:
To calculate the free energy change (ΔG°) for the reaction ( \text{fructose} + \text{ATP} \rightarrow \text{fructose-1-phosphate} + \text{ADP} ), we can utilize the values of the standard free energy changes (ΔG°) for the reactions involved. The key reactions to consider are:
- Hydrolysis of ATP:
[
\text{ATP} \rightarrow \text{ADP} + \text{P}_i \quad \text{with } \Delta G° = -30.5 \, \text{kJ/mol}
] - Hydrolysis of fructose-1-phosphate:
[
\text{fructose-1-phosphate} \rightarrow \text{fructose} + \text{P}_i \quad \text{with } \Delta G° = -16.0 \, \text{kJ/mol}
]
In our target reaction, we can reverse the hydrolysis of fructose-1-phosphate because the fructose-1-phosphate is formed, leading to a change in sign of its ΔG°:
[
\text{fructose} + \text{P}_i \rightarrow \text{fructose-1-phosphate} \quad \Delta G° = +16.0 \, \text{kJ/mol}
]
Now, we can combine the two reactions to find the overall free energy change for the desired reaction:
[
\text{fructose} + \text{ATP} \rightarrow \text{fructose-1-phosphate} + \text{ADP}
]
Using the equation for ΔG°:
[
\Delta G°{\text{overall}} = \Delta G°{\text{ATP hydrolysis}} + \Delta G°_{\text{reverse fructose-1-phosphate}}
]
Substituting the values:
[
\Delta G°_{\text{overall}} = (-30.5 \, \text{kJ/mol}) + (+16.0 \, \text{kJ/mol}) = -14.5 \, \text{kJ/mol}
]
Conclusion
Thus, the free energy change for the reaction ( \text{fructose} + \text{ATP} \rightarrow \text{fructose-1-phosphate} + \text{ADP} ) is –14.5 kJ/mol.
This negative value indicates that the reaction is energetically favorable and can occur spontaneously under standard conditions. The hydrolysis of ATP provides a significant driving force for the phosphorylation of fructose, making it a vital step in metabolic pathways such as glycolysis. In cellular metabolism, this reaction contributes to the overall energy transfer processes that sustain life.