ATP-hydrolysis-coupled reactions have equilibrium constants that are – [Free] B74
ATP-hydrolysis-coupled reactions have equilibrium constants that are changed by a factor of
ATP Hydrolysis and Equilibrium Constants
Question
How would the equilibrium constant change if the reaction X with ΔG° = +12.2 kJ·mol−1 was coupled to the hydrolysis of ATP (ΔG° = −30.5 kJ·mol−1)? Consider that R×T = 2.47.
Options:
- Would increase by a factor of 105
- Would increase by a factor of 106
- Would decrease by 5.15
- Would increase by 5.15
- Would decrease by a factor of 106
Answer and Detailed Explanation
To determine how coupling affects the equilibrium constant, we first calculate the net standard Gibbs free energy change (ΔG°) of the combined reaction.
ΔG°(coupled) = ΔG°(original reaction) + ΔG°(ATP hydrolysis)
Substituting values:
ΔG°(coupled) = (+12.2 kJ/mol) + (−30.5 kJ/mol) = −18.3 kJ/mol
The relationship between Gibbs free energy and equilibrium constant (K) is given by:
ln(K) = −ΔG° / (R × T)
Step 1: Calculate K for the original reaction
ln(Koriginal) = −(+12.2) / (2.47) = −4.94
Exponentiating:
Koriginal = e^(−4.94) ≈ 7.1 × 10−3
Step 2: Calculate K for the coupled reaction
ln(Kcoupled) = −(−18.3) / (2.47) = +7.41
Exponentiating:
Kcoupled = e^(+7.41) ≈ 1.65 × 103
Step 3: Calculate the factor of change in equilibrium constant
The factor by which the equilibrium constant increases:
Factor = Kcoupled / Koriginal = (1.65 × 103) / (7.1 × 10−3) ≈ 2.3 × 105
Conclusion:
The equilibrium constant increases by approximately a factor of 105.
The equilibrium constant increases by approximately a factor of 105.
Key Takeaways
- ATP hydrolysis supplies a large negative ΔG°, driving unfavorable reactions forward.
- Coupling changes the equilibrium constant by several orders of magnitude.
- This principle underlies many biosynthetic processes in cells.