A reaction has a free-energy landscape
Picture a reaction not as a one-way leap from reactants to products, but as a journey across a landscape whose height is the total Gibbs energy of the mixture. On the far left sits 'all reactants'; on the far right, 'all products'. As reactants slowly convert to products, the mixture's total G traces a smooth curve between those ends. Because spontaneity means rolling downhill in G, the mixture will always drift toward whatever point is *lowest* on that curve.
Here is the surprise: that lowest point almost never sits at the pure-reactants end *or* the pure-products end. It usually sits somewhere in between — a mixture. That bottom-of-the-valley point is chemical equilibrium: the composition at which G can fall no further, so the reaction appears to stop even though molecules keep reacting both ways underneath. Mixing the species, it turns out, is itself worth a chunk of entropy, which is why the valley floor lands in the middle.
The slope of the landscape
What we usually want is not the height of the curve but its slope at the mixture we actually have — does converting a little more reactant *lower* G or *raise* it? That slope is the Gibbs energy of reaction, written ΔG (or ΔᵣG). A negative slope means 'more product lowers G': the reaction runs forward. A positive slope means it runs backward. A zero slope means you are standing on the valley floor — equilibrium.
Notice this is subtler than the ΔG of the last guide. Earlier we treated ΔG as the gap between pure reactants and pure products. Now we see it really depends on *how much* of each you have right now. A pile of nearly-pure products has a different slope than a pile of nearly-pure reactants. To pin the language down, chemists agree on a reference composition to measure against.
The standard state: a fair baseline
To compare reactions fairly, everyone needs to quote free energies against the same agreed conditions. That agreed reference is the standard state: a pure substance at a chosen reference pressure (1 bar), or a solute at a reference concentration (typically 1 mol/L), at a stated temperature (usually 25 °C). The free-energy change measured under these tidy conditions is the standard Gibbs energy of reaction, written ΔG°. It is a single fixed number for each reaction — a label on the bottle, not a property of your particular beaker.
Where the slope vanishes: the equilibrium constant
The live slope and the fixed baseline are joined by one of chemistry's most useful equations: ΔG = ΔG° + R·T·ln Q. Here R is the gas constant, T the temperature, and Q is the reaction quotient — a number that simply reports how much product versus reactant you have *right now*. Far from equilibrium, Q tells you which way and how steeply you are tilted. As the reaction proceeds, Q changes, and the slope ΔG glides toward zero.
At the valley floor the slope is zero, so set ΔG = 0. The equation collapses to a gem: ΔG° = −R·T·ln K, where K is the equilibrium constant — the special value Q takes *at* equilibrium. Read it slowly: the fixed standard free energy alone fixes where equilibrium lands. A strongly negative ΔG° forces K large, so equilibrium hugs the products. A positive ΔG° makes K small, so equilibrium favours reactants. The whole position of free energy and equilibrium is set by one number you can look up in a table.
- Look up ΔG° for the reaction (the fixed baseline at standard conditions).
- Use ΔG° = −R·T·ln K to find where equilibrium sits — products-favoured or reactants-favoured.
- For a real mixture, plug your current Q into ΔG = ΔG° + R·T·ln Q to read off the live slope and which way it will move.
A caution about strong words
Two honest cautions. First, a positive ΔG° does not mean 'no reaction' — it means equilibrium merely *favours* reactants, and a small but real amount of product still forms. Almost nothing goes 100% one way. Second, the slope ΔG is the genuine thermodynamic driving force for your real mixture; ΔG° is just its value at the reference composition. Confusing the two is the single most common slip in this whole subject, so keep the catalogue price and the checkout price clearly apart.