![Q.43 Triose phosphate isomerase converts dihydroxyacetone phosphate (DHAP) to glyceraldehyde-3-phosphate (G-3-P) in a reversible reaction. At 298 K and pH 7.0, the equilibrium mixture contains 40 mM DHAP and 4 mM G-3-P. Assume that the reaction started with 44 mM DHAP and no G-3-P. The standard free-energy change in kJ/mol for the formation of G-3-P [R = 8.315 J/mol·K] is ______.](https://www.letstalkacademy.com/wp-content/uploads/2026/01/slide_43-1.jpg)
Q.43 Triose phosphate isomerase converts
dihydroxyacetone phosphate (DHAP) to glyceraldehyde-3-phosphate (G-3-P)
in a reversible reaction.
At 298 K and pH 7.0, the equilibrium mixture contains
40 mM DHAP and 4 mM G-3-P.
Assume that the reaction started with 44 mM DHAP and no G-3-P.
The standard free-energy change in kJ/mol for the formation of G-3-P
[R = 8.315 J/mol·K] is ______.
Standard Free Energy Change for Triose Phosphate Isomerase Reaction (DHAP ⇌ G-3-P)
Triose phosphate isomerase catalyzes the reversible interconversion of dihydroxyacetone phosphate (DHAP)
and glyceraldehyde-3-phosphate (G-3-P), an important step in glycolysis. The standard free energy change
(ΔG°′) of this reaction can be calculated using equilibrium concentrations and thermodynamic principles.
Given Data
- Temperature (T) = 298 K
- Gas constant (R) = 8.315 J mol-1 K-1
- Initial DHAP concentration = 44 mM
- Initial G-3-P concentration = 0 mM
- Equilibrium DHAP concentration = 40 mM
- Equilibrium G-3-P concentration = 4 mM
Reaction
DHAP ⇌ G-3-P
Step 1: Equilibrium Constant (K)
K = [G-3-P]⁄[DHAP]
K = 4⁄40
= 0.1
Step 2: Standard Free Energy Equation
ΔG°′ = −RT ln K
ΔG°′ = −(8.315 × 298) ln(0.1)
ln(0.1) = −2.303
ΔG°′ = 8.315 × 298 × 2.303
ΔG°′ ≈ 5699 J/mol
Final Answer
ΔG°′ ≈ +5.7 kJ/mol
Explanation
The positive value of ΔG°′ indicates that the formation of glyceraldehyde-3-phosphate from DHAP
is thermodynamically unfavorable under standard conditions. However, in living cells, this reaction
proceeds efficiently because G-3-P is continuously consumed in subsequent glycolytic steps, shifting
the equilibrium forward.
Key Takeaways
- Equilibrium concentrations determine the value of ΔG°′.
- A small positive ΔG°′ is common for reversible metabolic reactions.
- Enzyme activity and pathway coupling drive the reaction in vivo.
