Firefly luciferase is the enzyme that allows fireflies to illuminate their abdom

Question

Firefly luciferase is the enzyme that allows fireflies to illuminate their abdomens. Because this light generation is an ATP-requiring reaction, firefly luciferase can be used to test for the presence of ATP. In this way, luciferase can test for the presence of life. The coupled reactions are

luciferin+O2ATPoxyluciferin+lightAMP+PPi

If the overall G of the coupled reaction is -5.40 kJ/mol , what is the equilibrium constant, K, of the first reactions at 13 C ? The G for the hydrolysis of ATP to AMP is 31.6 kJ/mol.

Explanation / Answer

K = e^(-standard G/(RT))

R is 8.314J/(molK) and T is 286K. The standard G is found by subtracting the standard G for the hydrolysis of ATP to AMP from the standard G of the coupled reaction.

standard G of first reaction = G of the coupled reaction - G for the hydrolysis of ATP to AMP
standard G of first reaction = -5.4 kJ/mol - (31.6 kJ/mol)
standard G of first reaction = -5.4 kJ/mol + 31.6 kJ/mol
standard G of first reaction = 26.2 kJ/mol
standard G of first reaction = 26200J/mol

Plug in the known values into the first equation to find K.

K = e^(-(26200J/mol)/(8.314J/(molK)*286K))
K = e^(-(26200J/mol)/(2377.804J/mol))
K = e(-11.01857)
K = 11.01857 x 10-5

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