Coupled Reactions — Overview & Importance

We defined Gibbs free energy as the energy available ("free") for work. But, what work are we doing? In chemistry, we care about chemical change. We want the energy to break bonds.

Some chemical reactions are always spontaneous. They have negative enthalpy and positive entropy. They're exothermic. So, they transfer energy via heat. The entropy change tells us the energy is more spread out. So, they always release and disperse energy. For spontaneous reactions, we only have to overcome their activation energy.

But, some chemical reactions are nonspontaneous. We have to add energy from the surroundings to the system. These reactions are endothermic with negative entropies. The products will have more potential energy than the reactants. Remember, molecules store potential energy in their bonds. So, changing the electrostatic interactions changes the potential energy. Endothermic reactions, increase bond strength by increasing the number of bonds or decreasing the bond length.

But, how can we use spontaneous reactions to do work? We use its energy to start nonspontaneous reactions. We call it coupling or coupled reactions.

What are Coupled Reactions?

Coupling uses a spontaneous reaction's free energy change to start a nonspontaneous reaction.

There are a couple of rules we need to follow.

1. The sum of all the reaction's free energy changes must be negative. So, the total process is still spontaneous. Since Gibbs free energy is a state function, we can sum the values of each reaction. The summation gives us the free energy of the process. The formula is $\Delta G_{process}=\Sigma\Delta G_{rxn's}$.

2. One product from the spontaneous reaction become a reactant in the nonspontaneous reaction.

Coupled Reactions Example with Calculations

The most common coupled reactions occur in biochemistry. Every second, your body's cells use thousands of coupled reactions. Cells generate chemical change by converting adenosine triphosphate (ATP) to adenosine diphosphate (ADP). Glucose is the source of carbohydrate fuel in cells. The mitochondria can convert one mole of glucose into 36 moles of ATP. But first, we need glucose to stay in the cell. So, we phosphorylate it to glucose-6-phosphate. Now it can't diffuse across the cell membrane. Let's look at the two reactions as a coupled pair.

$(1)\,ATP \rightarrow ADP + PO^{3-}_{4}\, \Delta G= -30.0\frac{KJ}{mol}$

$(2)\,C_{6}H_{12}O_{6} + PO^{3-}_{4} \rightarrow C_{6}H_{11}O_{9}P^{2-}\, \Delta G=9\frac{KJ}{mol}$

$\Delta G_{process}=-30\frac{KJ}{mol}+9\frac{KJ}{mol}=-21.0\frac{KJ}{mol}$

The phosphorylation (equation 2) is nonspontaneous. So, the cell uses an ATP molecule to create a spontaneous process. The overall process still has a negative free energy change. Also, notice the oxoanion phosphate is a product of the first equation and a reactant in the second equation. So, we obey both rules for coupled reactions.

As a side note, if you look up the $\Delta G$ values for equation 1, you'll find quite a range. The value I used ($\Delta G= -30.0\frac{KJ}{mol}$) is at standard concentrations. So, everything would be 1.0 molar. In the body, the concentrations are millimolar (mM). That $10^{-3}$! So, the concentrations are much lower. What's the result? The reaction isn't at equilibrium. The reaction quotient will be less than the equilibrium constant. So, our reaction will be in the forward direction. More energy is released than the standard conditions reaction. Also, magnesium ions ($Mg^{2+}) help to stabilize ATP. So, their concentration in cells also plays a role.

(Video) Let's Think about reaction coupling

by John Pollard

In this video, Dr. Pollard explains reaction coupling. He uses ATP as an example. You'll learn both a thermodynamic and mechanistic perspective. So, you'll understand how we can combine reactions to create spontaneity. This short video will help you understand coupled reactions!