Free energy and the direction of reactions

The second law means every energy conversion leaves some energy in an unusable, disordered form. So for any reaction, the useful question isn’t how much energy the molecules hold in total, but how much of it can actually do something.

Usable and unusable energy

A system’s total energy splits into two parts: energy that can cause change, and energy that can’t. Entropy is what makes the second part unusable. When a cell breaks down glucose to make ATP, for example, some of the usable energy is lost as heat.

Chemists give each part a symbol:

• Enthalpy (H) is the total energy of a system.
• Free energy (G) is the usable energy, the amount available to cause change or do work.
• Entropy (S), multiplied by the absolute temperature (T, measured in kelvins, a scale whose zero is the coldest possible temperature), gives the unusable energy.

The three fit together as H = G + TS. Rearranged to focus on free energy, that becomes G = H − TS: usable energy equals total energy minus the part tied up in disorder.

ΔG predicts which way a reaction goes

What matters for a reaction is how free energy changes between start and finish. The Greek letter Δ (delta) means “change in,” so ΔG is the change in free energy: the free energy of the products minus the free energy of the reactants. It’s calculated as ΔG = ΔH − TΔS: the change in total energy minus temperature times the change in entropy.

ΔG is usually given in kilocalories per mole (kcal/mol). A kilocalorie is the same unit as the Calorie on a food label, and a mole is a fixed, very large number of molecules (about 6 × 10²³).

The sign of ΔG sorts reactions into two kinds:

• Negative ΔG (ΔG < 0): the products end up with less free energy than the reactants started with, and the difference is released. This is an exergonic reaction. Exergonic reactions are spontaneous, meaning they can proceed on their own, with no overall input of free energy.
• Positive ΔG (ΔG > 0): the products have more free energy than the reactants, so free energy must be added to make them. This is an endergonic reaction, and it is not spontaneous.

The two kinds of reaction are mirror images, and each property of one is reversed in the other:

Spontaneous doesn’t mean fast

In chemistry, spontaneous means a reaction can proceed on its own, not that it happens quickly. Sugar breaking down into CO₂ and water is exergonic, yet the sugar in a sugar bowl sits unchanged for years. An exergonic reaction may be fast or extremely slow, and the same is true of an endergonic reaction once it’s supplied with energy. How fast a reaction goes is a separate question, answered by activation energy and enzymes.

Reactions can run either way

Many reactions are reversible. Written in general form:

aA + bB ⇌ cC + dD

Here A and B are the reactants, C and D are the products, and the lowercase letters give the number of moles of each. The reaction can run forward (A and B become C and D) or in reverse (C and D become A and B). Which way it goes depends on energy and on the concentrations of all four substances.

Running a reaction backward flips the sign of its ΔG, so if the forward reaction is endergonic, the reverse reaction is exergonic. That’s why a positive ΔG favors forming the reactants. If A, B, C, and D all start at 1 M (one mole per liter), a reaction with a negative ΔG runs forward, and one with a positive ΔG runs in reverse.

Check yourselfThe reaction X → Y has a ΔG of +4 kcal/mol. Is it exergonic or endergonic, and which way does it run if X and Y both start at 1 M?

It’s endergonic, because ΔG is positive. The reverse reaction, Y → X, has a ΔG of −4 kcal/mol and is exergonic, so the reaction runs toward X. The ΔG values don’t tell you how fast that will happen.