I need help with this delta G question!! (gen chem 2)

Question

A critical reaction in the production of energy to do work or drive chemical reactions in biological systems is the hydrolysis of ATP to ADP as described by the reaction

ATP(aq) + H₂O(l) --> ADP(aq) + HPO₄^2-(aq)

for which deltaG^o_rxn= -30.5 kJ/mol at 37.0 C and pH=7.0. Calculate the value of deltaG_rxn in a biological cell in which [ATP] = 5.0 mM, [ADP] = 0.40 mM, and [HPO₄^2- ] = 5.0 mM. Answer in kJ/mol and watch for units.

Answer 1

ATP(aq) + H₂O(l) --> ADP(aq) + HPO₄^2-(aq)

dG = dG^o + RT ln Q

Q = [ADP][HPO₄^2-] / [ATP] = (0.0004)(0.005)/(0.005) = 0.0004

dG = dG^o + RT ln Q

dG = -30.5 kJ/mol + (0.008314 kJ/Kmol)(310K) (-7.82)

dG = -30.5 kJ/mol + (-20.2 kJ/mol)

dG = -50.7 kJ/mole

Be sure to check all the math.

Note: the value is negative meaning the reaction is spontaneous under these conditions.