A critical reaction in the production of energy to do work or drive chemical reactions in biological systems is the hydrolysis of adenosine triphosphate, ATP, to adenosine diphosphate, ADP, as described by the reaction ATP(aq)+H2O(l)→ADP(aq)+HPO2−4(aq) f or which ΔGrxn=30.5 kJ/mol at 37.0∘C and pH 7.0.

Required:
Calculate the value of ΔGrxn in a biological cell in which [ATP]=5.0 mM, [ADP]=0.60 mM,  and [HPO2−4]=5.0 mM

ΔG  = -49.64 KJ/mol

Explanation:

The actual free energy change of the reaction under the given conditions,  ΔG is given by the formula below;

ΔG = ΔG'° + RT ln([ADP][HPO₂⁴⁻] / [ATP])

where ΔG'° = -30.5 KJ/mol; R = 8.315 J/mol.K; T = 37°C = 310 K; [ADP] = 5.0 mM = 0.005 M; [HPO₂⁴⁻] = 0.60 mM = 0.0006 M; [ATP] = 5.0 mM = 0.005 M

ΔG = -30.5 KJ/mol + (8.315 J/mol.K)(310 K) ln {(0.005)(0.0006)/(0.005)}

ΔG = -30.5 KJ/mol + (2.58 KJ/mol * -7.4186)

ΔG = -30.5 KJ/mol - 19.14 KJ/mol

ΔG  = -49.64 KJ/mol

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