Question

1)

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+O2ATP⇌⇌oxyluciferin+lightAMP+PPi

If the overall ΔG of the coupled reaction is -4.30 kJ/mol , what is the equilibrium constant, K, of the first reactions at 29 ∘C ? The ΔG for the hydrolysis of ATP to AMP is −31.6 kJ/mol.

Express your answer numerically.

Answer 1

This equation should be used to find K.

K = e^(-standard ΔG/(RT))

R is 8.314J/(molK) and T is 302K. The standard ΔG is found by subtracting the standard ΔG for the hydrolysis of ATP to AMP from the standard ΔG of the coupled reaction.

standard ΔG of first reaction = ΔG of the coupled reaction - ΔG for the hydrolysis of ATP to AMP
standard ΔG of first reaction = -4.30kJ/mol - (−31.6 kJ/mol)
standard ΔG of first reaction = -4.30kJ/mol + 31.6 kJ/mol
standard ΔG of first reaction = 27.3kJ/mol
standard ΔG of first reaction = 27300J/mol

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

K = e^(-(27300J/mol)/(8.314J/(molK)*302K))
K = e^(-(27300J/mol)/(2510.828J/mol))
K = e^(-10.8729072641)
K = 0.00001896515