Coupled Reactions Firefly luciferase is the enzyme that allowsfireflies to illum

Question

Coupled Reactions Firefly luciferase is the enzyme that allowsfireflies to illuminate their abdomens. Because this lightgeneration is an ATP-requiring reaction, firefly luciferase can beused to test for the presence of ATP. In this way, luciferase cantest for the presence of life. The coupled reactions are luciferin O2 oxyluciferinlight ATP AMPPPi If the overall delta G of the coupled reaction is -8.70 kJ/mol , what is the equilibrium constant, K , of the first reactions at 7 Degree C ? The Delta G for the hydrolysis of ATP to AMP is 31.6 kJ/mol . Express your answernumerically.

Explanation / Answer

Your gonna get your answer with the equation: G=-RTlnK You are given: Gtotal=-8.70 kJ/mol 7 C Gsecond=-31.6 kJ/mol The value for R=8.314 1) Find G for the first reaction Gtotal=Gfirst+Gsecond -8.70 kJ/mol =Gfirst+-31.6 kJ/mol Gfirst= 22.9 kJ/mol 2) Convert kJ to J 22.9 kj x 1000= 22900 J/mol 3)Convert C to K C+273.=K 7+273= 280 K 4)Put into first equation G=-RTlnK 22900=-8.314(280)lnK lnK=22900/(-8.314x280)=-9.8371 (anti ln)= e^(-9.8371)= 5.34 x 10^-5 Answer) K=5.34 x 10^-5

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