Question

In nature, one common strategy to make thermodynamically unfavorable reactions proceed is to couple them chemically to reactions that are thermodynamically favorable. As long as the overall reaction is thermodynamically favorable, even the unfavorable reaction will proceed.

Part A Consider these hypothetical chemical reactions: A⇌B,ΔG= 12.8 kJ/mol B⇌C,ΔG= -26.6 kJ/mol C⇌D,ΔG= 6.70 kJ/mol

What is the free energy, ΔG, for the overall reaction, A⇌D?

Express your answer with the appropriate units.

Part C 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 -5.90 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

1) A ---> B

2) B --> C

3) C ----> D

4) A ---> D

we can see that

4 = 1 + 2 + 3

so

dG4 = dG1 + dG2 + dG3

dG4 = 12.8 - 26.6 + 6.7

dG4 = -7.1

so

dG for the overall reaction A --> D is -7.1 kJ/mol

2)

write the individual reactions

a) luciferin + 02 ---> oxyluciferin + light

b) ATP --> AMP + PPi

c) luciferin + O2 + ATP ⇌⇌ oxyluciferin + light + AMP + PPi

c = a + b

so

dGo c = dGo a + dGo b

-5.9 = dGo a -31.6

dGo a = 25.7 kJ/mol

now

we know that

dGo = -RT lnK

so

25.7 x 1000 = -8.314 x 302 x ln K

K =3.5868 x 10-5

so

equilibrium constant K for the first reaction is 3.5868 x 10-5