Q.53 The concentrations of ATP, ADP and inorganic phosphate in a cell are 2.59, 0.73
and 2.72 mM, respectively. Under these conditions, free energy change for the
synthesis of ATP at 37 °C is. _ kJ/mol
(round off to 2 decimal places)
Given: free energy change for ATP hydrolysis under standard conditions is –30.5 kJ/mol and R = 8.315 kJ/mol.K
Free Energy Change for ATP Synthesis at 37°C: 2.59 mM ATP, 0.73 mM ADP, 2.72 mM Pi Calculation
The free energy change for ATP synthesis under the given cellular conditions is +35.81 kJ/mol. This value is calculated using the standard equation for non-standard Gibbs free energy, reflecting the endergonic nature of ATP formation.
🧮 Calculation Steps
The reaction for ATP synthesis is the reverse of hydrolysis: ADP + Pi → ATP + H2O
where ΔG°’ for synthesis = +30.5 kJ/mol (negative of hydrolysis)
R = 8.315 × 10-3 kJ/mol·K, T = 310 K (37°C)
Q = [ATP] / ([ADP][Pi])
Step 1: Convert concentrations to M
- [ATP] = 0.00259 M
- [ADP] = 0.00073 M
- [Pi] = 0.00272 M
Step 2: Calculate Reaction Quotient (Q)
Step 3: Calculate RT ln(Q)
ln(1302.14) ≈ 7.174
RT ln(Q) = 2.577 × 7.174 = 18.31 kJ/mol
Step 4: Final ΔG Calculation
📋 Detailed Breakdown
- ΔG°’: +30.5 kJ/mol for synthesis (hydrolysis releases -30.5 kJ/mol under standard conditions: 1 M, pH 7)
- Temperature: 37°C = 310 K (standard physiological temperature)
- Q Ratio: High [ATP]/[ADP][Pi] = 1302 makes synthesis unfavorable (ΔG > 0)
- Result: Rounded to two decimal places: 35.81 kJ/mol
🎯 Why ΔG is Positive Here
The mass-action ratio Q = 1302 far exceeds the equilibrium constant, making ΔG = +35.81 kJ/mol. This positive value indicates ATP synthesis requires energy input, unlike hydrolysis which is exergonic.
🏆 Step-by-Step for Exam Success (IIT JAM/GATE)
- Convert T to Kelvin: 37°C = 310 K
- Calculate Q = [ATP]/([ADP][Pi]) = 1302
- RT ln(Q) = 2.577 kJ/mol × ln(1302) ≈ +18.31 kJ/mol
- ΔG = +30.5 + 18.31 = +35.81 kJ/mol
💡 Exam Tip:
This matches GATE BT 2020 Q.53 pattern. Always check units (mM → M, kJ consistency) and remember ΔG°’ for synthesis is +30.5 kJ/mol.
