Topic 9.7 Notes – Coupled Reactions

1. What Makes a Reaction Thermodynamically Favorable or Unfavorable

At constant temperature and pressure, Gibbs free energy change, ΔG°, determines spontaneity.

• ΔG° < 0 → thermodynamically favorable (spontaneous under standard conditions)
• ΔG° > 0 → thermodynamically unfavorable (nonspontaneous under standard conditions)
• ΔG° = 0 → system is at equilibrium

This connects directly to the equilibrium constant:

$$\Delta G^\circ = -RT \ln K$$

Where:

• $R$ = 8.314 J·mol$^{-1}$·K$^{-1}$
• $T$ = temperature in Kelvin
• $K$ = equilibrium constant

So:

• K > 1 → lnK > 0 → ΔG° < 0 → products favored
• K < 1 → lnK < 0 → ΔG° > 0 → reactants favored

If a reaction has ΔG° > 0, it will not occur on its own under standard conditions. That’s a thermodynamics statement. It says nothing about how fast it would go. Rate is a kinetics issue.

Now the question becomes: how can we make a reaction with ΔG° > 0 actually happen?

2. Two Ways to Drive a Thermodynamically Unfavorable Reaction

a. Using an External Energy Source

An outside energy input can make the overall process favorable.

Common AP examples:

• Electrical energy
  • Drives an electrolytic cell
  • Forces a nonspontaneous redox reaction to occur
  • Used to charge a battery by pushing electrons “uphill”

Electrolytic cell for silver plating

In the silver-plating setup shown, the power supply pulls electrons from the silver anode and pushes them onto the spoon cathode, forcing $\ce{Ag+}$ in solution to be reduced onto the spoon.

In an electrolytic cell:

• The redox reaction has ΔG° > 0
• The power supply provides electrical work
• The combined system (reaction + electricity) proceeds
• Light energy
  • Photosynthesis uses light to convert $\ce{CO2}$ and $\ce{H2O}$ into glucose.
  • Light energy is converted into chemical potential energy stored in bonds.

The reaction itself is not spontaneous. The energy input drives it.

On exams, if you see “electrolytic cell” or “light-driven reaction,” think external energy overcomes positive ΔG°.

b. Coupling to a Favorable Reaction

Instead of adding electricity or light, you can pair a nonspontaneous reaction with a spontaneous one.

Two reactions are coupled when:

• They share a common intermediate
• That intermediate cancels when the reactions are added
• The total free energy change is:

$$\Delta G^\circ_{\text{overall}} = \Delta G^\circ_{1} + \Delta G^\circ_{2}$$

Because ΔG° is a state function, it’s additive, just like ΔH in Hess’s Law.

If:

• Reaction 1: ΔG° > 0
• Reaction 2: ΔG° < 0
• The negative value is larger in magnitude

Then:

• ΔG°₍overall₎ < 0
• The combined process is thermodynamically favorable.

3. How Reaction Coupling Works

Let’s walk through the logic using a generic setup.

Step 1: Identify the reactions

Suppose:

$$\ce{A -> B} \qquad \Delta G^\circ = +40 \text{ kJ}$$

$$\ce{B -> C} \qquad \Delta G^\circ = -85 \text{ kJ}$$

Notice B is produced in one and consumed in the other. That makes it a candidate for an intermediate.

Step 2: Add the reactions

$$\ce{A -> B}$$ $$\ce{B -> C}$$

Cancel B:

$$\ce{A -> C}$$

Add ΔG° values:

$$\Delta G^\circ_{\text{overall}} = (+40) + (-85) = -45 \text{ kJ}$$

Now the overall reaction is spontaneous.

Key rules you must remember on tests:

• If you multiply a reaction by a factor, multiply ΔG° by the same factor.
• If intermediates do not cancel completely, the reactions are not properly coupled.
• This process is mathematically identical to Hess’s Law.

4. Common Intermediates and Why They Matter

An intermediate:

• Is formed in one reaction
• Is consumed in another
• Does not appear in the overall balanced equation

Without a shared intermediate, one reaction cannot directly “pull” the other forward.

On FRQs, they often give you two equations and ask whether coupling is possible. Scan for a species that appears as a product in one and a reactant in the other. Then check if scaling will allow full cancellation.

5. Biological and Real-World Examples of Coupling

a. ATP Hydrolysis

In cells:

$$\ce{ATP + H2O -> ADP + Pi} \qquad \Delta G^\circ < 0$$

Many cellular processes have ΔG° > 0. Cells chemically link them to ATP hydrolysis through shared intermediates. When added together, the overall ΔG° becomes negative.

ATP does not magically “release energy.” Its hydrolysis is chemically coupled through real reaction steps.

b. Industrial Chemistry

In metallurgy, a metal oxide that does not decompose spontaneously can be combined with a strongly spontaneous oxidation reaction. The favorable reaction drives the overall process so that ΔG°₍overall₎ < 0.

You may see this framed as adding equations and calculating total ΔG°.