Cellular ATP, ADP and inorganic phosphate concentrations are 2.59, 0.73 and 2.72 mM. Find free-energy change for ATP synthesis at 37°C in kJ/mol, rounded to 2 decimals. Standard free-energy change for ATP hydrolysis is −30.5 kJ/mol. The source gives R = 8.315 kJ/(mol K).
Correct answer: 48.50 to 49.50 OR 18521.20 to 18521.30
Explanation
For synthesis, $\Delta G=30.5+RT\ln([ATP]/([ADP][P_i]))$, using concentrations relative to the 1 M standard state. Convert mM to M: $Q=0.00259/(0.00073\times0.00272)=1304.39$. At approximately 310 K, using physically consistent $R=0.008315$ kJ/(mol K) gives about 48.99 kJ/mol. Taking the printed R = 8.315 kJ/(mol K) literally gives about 18521.25 kJ/mol. The official key accepts the separate intervals 48.50–49.50 OR 18521.20–18521.30, reflecting this unit discrepancy; their intervening gap is not accepted.
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