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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 1. luciferin + O2 ⇌ oxyluciferin + light 2. ATP ⇌ AMP + PPi ΔG∘=-45.28 kJ/mol If the overall ΔG∘ of the coupled reaction is -8.03 kJ/mol , what is the standard free energy of the first reaction at 27∘C?

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ajeigbeibraheem

Answer:

[tex]3.28*10^{-7}[/tex]

Explanation:

ΔG° = - 8.03 kJ/mol & ΔG = -45.28 kJ/mol

Thus:

Overall ΔG = (- 8.03 + 45.28) kJ/mol

ΔG = 37.25 kJ/mol

ΔG = 37250 J/mol

Temperature = 27 °C

= (27 + 273)K

= 300 K

Therefore :

ΔG = -RTInK

In K = [tex]\frac{\delta G}{RT}[/tex]

In K =  [tex]\frac{37250}{300*8.314}[/tex]

In K = [tex]\frac{37250}{2494.2}[/tex]

In K = 14. 93

    K = [tex]e^{-14.93}[/tex]

    K = [tex]3.28*10^{-7}[/tex]

the standard free energy of the first reaction at 27 °C = [tex]3.28*10^{-7}[/tex]

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