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) ATP(aq)+H2O(l)⟶ADP(aq)+HPO42−(aq) for which ΔG∘rxn=−30.5 kJ/molΔGrxn∘=−30.5 kJ/mol at 37.0 °C and pH 7.0. Calculate the value of ΔGrxnΔGrxn in a biological cell in which [ATP]=5.0 mM,[ATP]=5.0 mM, [ADP]=0.20 mM,[ADP]=0.20 mM, and [HPO2−4]=5.0 mM.

The value of delta G is -52.4 KJ/mol.

Explanation:

In the given question, the ATP's hydrolysis reaction is given as:  

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

The Q or the reaction quotient of the reaction will be as follows:  

Q = [ADP] [HPO4^2-] / [ATP]

The delta G or the Gibb's free energy is determined by using the formula, delta Grxn = ΔG°rxn + RTlnQ

Here R is the gas constant, T is the temperature and ΔG°rxn is the Gibb's free energy.  

Based on the given question, the values of [ATP] is 5.0 mM, [ADP] is 0.20 mM and [HPO4^2-] is 5.0 mM, now putting the values in the equation we get:  

Q = [0.20 mM] [5.0 mM] / [5.0 mM]

= 0.20 mM or 0.20 * 10^-3 M

The temperature or T given is 37 degree C, which in Kelvin will be 273 + 37 = 310 K, the value of R will be 8.314 JK^-1mol^-1 and value of ΔG°rxn will be -30.5 kJ/mol. Now substituting the values we get,  

ΔGrxn = ΔG°rxn + RTlnQ

= (-30.5kJ/mol) + (8.314 * 10^-3 kJ/K/mol) (310K) ln (0.20 * 10^-3)

= -52.4kJ/mol