Question

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

ATP_(aq) + H2O_(l) --> ADP_(aq) + HPO_4(aq)

or which ΔG°rxn = –30.5 kJ/mol at 37.0 °C and pH 7.0. Calculate the value of ΔGrxn in a biological cell in which [ATP] = 5.0 mM, [ADP] = 0.50 mM, and [HPO42–] = 5.0 mM.

Delta G_rxn =

Answer 1

Given:-

standard free energy change ($\Delta$G⁰_rxn) = - 30.5 KJ/mol = - 30500 J /mol

free energy change ($\Delta$G_rxn) = ?

As we know that

biological temperature (T) = 37 ⁰C = 273 + 37 = 310 K

Gas constant (R) = 8.314 JK^-1mol^-1

molar concentration ATP i.e [ATP] = 5.0 mM = 5.0 $\times$ 10^-3 M

molar concentration ADP i.e [ADP] = 5.0 mM = 5.0 $\times$ 10^-3 M

molar concentration HPO₄^2- i.e [ HPO₄^2-] = 5.0 mM = 5.0 $\times$ 10^-3 M

Since we know that

ATP_(aq) + H₂O_(l)  $\rightleftharpoons$ ADP_(aq) + HPO₄^2-_(aq)

therefore

Equilibrium constant (K_eq) = [ADP][ HPO₄^2-] / [ATP][ H₂O]

Equilibrium constant (K_eq) = 5.0 $\times$​​​​​​​ 10^-3$\times$ 5.0 $\times$​​​​​​​ 10^-3  / 5.0 $\times$​​​​​​​ 10^-3$\times$ 1 (since [ H₂O] = 1)

Equilibrium constant (K_eq) = 25.0 $\times$​​​​​​​ 10^-6   / 5.0 $\times$​​​​​​​ 10^-3

Equilibrium constant (K_eq) = 5.0 $\times$​​​​​​​ 10^-3

As we know that according to the formula

free energy change ($\Delta$G_rxn) =  ($\Delta$G⁰_rxn) + 2.303RT $\times$ (K_eq)

free energy change ($\Delta$G_rxn) =   - 30500 J /mol   + ( 2.303 $\times$ 8.314 JK^-1mol^-1$\times$ 310 K $\times$ 5.0 $\times$​​​​​​​ 10^-3 )

free energy change ($\Delta$G_rxn) =   - 30500 J /mol   + ( 29678.07 $\times$​​​​​​​ 10^-3 J / mol )

free energy change ($\Delta$G_rxn) =   - 30500 J /mol   + ( 29.67807 J / mol )

free energy change ($\Delta$G_rxn) =   - 30500 J /mol   + 29.67807 J / mol

free energy change ($\Delta$G_rxn) =   - 30470.32 J /mol  

free energy change ($\Delta$G_rxn) =   - 30.47032 KJ /mol (i.e the answer)