Two urges argue in every reaction. Energy wants to go downhill — that is enthalpy. Matter wants to spread out — that is entropy. Josiah Willard Gibbs settled the argument with one subtraction: $\Delta G = \Delta H - T\,\Delta S$, read aloud delta-G equals delta-H minus T delta-S. $\Delta G$ is the free energy change in kJ/mol and its SIGN is the verdict; $\Delta H$ is the enthalpy change in kJ/mol, negative when heat comes out; $T$ is the absolute temperature in kelvin, always; and $\Delta S$ is the entropy change, which tables print in J/(mol·K). Negative $\Delta G$ means spontaneous — allowed, not necessarily quick. Diamond turning to graphite is spontaneous and in no hurry whatsoever.

The marquee trap sits right there in that sentence: $\Delta H$ arrives in kilojoules and $\Delta S$ in joules. Reconcile them BEFORE the subtraction or your answer is out by a factor of a thousand and wearing a straight face. And notice what $T$ does: it is the exchange rate between the two urges. Turn the temperature up and entropy's vote gets louder, which is why some reactions only switch on in a furnace. Where the two terms match exactly, $\Delta G = 0$ and $T = \dfrac{\Delta H}{\Delta S}$ — the crossover temperature at which a reaction changes its mind.

Then the bridge that ties this chapter together: $\Delta G^{\circ} = -RT\ln K$, delta-G-standard equals minus R T natural-log K, with $R = 8.314\ \mathrm{J/(mol \cdot K)}$ — the energy R now, in joules. Thermodynamics and equilibrium turn out to be one fact read two ways. Carry the exchange rate in your head: at 298 K, about $-5.7\ \mathrm{kJ/mol}$ buys one decade of $K$. Negative $\Delta G^{\circ}$ means $K > 1$ means products favoured; the three statements are the same sentence in three costumes.