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= 11.9 kJ/mol
B⇌C,ΔG= -26.7 kJ/mol
C⇌D,ΔG= 7.30 kJ/mol
What is the free energy, ΔG, for the overall reaction, A⇌D?

Answer 1

31.3 kJ/mol is the free energy, ΔG, for the overall reaction, A⇌D.

Step-by-step explanation:

A⇌B,
`\Delta G_1` = 11.9 kJ/mol ...[1]

B⇌C,
`\Delta G_2`= -26.7 kJ/mol ...[2]

C⇌D,
`\Delta G_3`= 7.30 kJ/mol ...[3]

A⇌D,
`\Delta G_4` = ?...[4]

[4] = [1] - [2] - [3] (Using Hess's law)

`\Delta G_4=\Delta G_1-(\Delta G_2+\Delta G_3)`

`=11.9 kJ/mol - (-26.7 kJ/mol+7.30 kJ/mol)`

`=\Delta G_4=31.3 kJ/mol`

31.3 kJ/mol is the free energy, ΔG, for the overall reaction, A⇌D.