A critical reaction In the production of energy to do work or drive chemical rea

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) + H_2 O (l) rightarrow ADP (aq) + HPO^2-_4 (aq) for which Delta G degree_rxn = -30.5 kJ/mol at 37.0 degree C and pH 7.0. Calculate the value of Delta G_rxn in a biological cell in which [ATP] = 5.0 mM, [ADP] = 0 90 mW, and [HPO_4^2-] = 5.0 mM. Is the hydrolysis of ATP spontaneous under these conditions? yes no

Explanation / Answer

       ATP(aq) + H2O (l) --> ADP (aq) + HPO42-(aq)

Grxn = G°rxn + RTlnQ

Grxn = free energy at any moment (we need to find)
G°rxn = standard-state free energy = -30.5 KJ/mol = -30500 J/mol
R is the ideal gas constant = 8.314 J/mol-K
T = the absolute temperature (Kelvin)= 37 +273 = 310 K
Q = the reaction quotient = [ADP]*[H2PO4^-]/[ATP]

Plug them in the gibbs free energy equation;

Grxn = 30500 J/mol+ (8.314 J/mol-K)*(310 K) ln[ADP]*[H2PO4^-]/[ATP]

[ATP] = 5.0 mM = 5 x 10-3 M
[ADP] = 0.9 mM = 0.9 x 10-3 M
[H2PO4^-] =5 mM = 5 x10-3 M

Grxn = -30500 J/mol+ (8.314 J/mol-K)*(310 K) ln(0.9 x 10-3 M) *(5 x10-3 M)/(5 x 10-3 M)

Grxn = -30500 J/mol - 18075 J/mol = 48575 J/mol = -48.6 KJ/mol

Since, Grxn is negative the hydrolysis of ATP is spontaneous (answer: yes)

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