Free energy and spontaneity

Whether a process runs on its own is decided by the entropy of the universe, not of the system — but tracking the surroundings for every reaction would be impractical. Gibbs free energy, G = H − TS, is the accounting trick that avoids it. At constant temperature and pressure, a negative change in the system's G is exactly equivalent to an increase in the total entropy, so you can predict spontaneity from the system alone.

The formula makes the competition explicit. ΔH favours processes that release energy, ΔS favours those that increase the system's own disorder, and T decides how much the second term counts. This is why an endothermic process can still be spontaneous: melting ice absorbs heat, so ΔH is positive, but the entropy gain from a rigid lattice becoming a liquid is large enough that above 0 °C the TΔS term wins. Below 0 °C it does not, and water freezes instead. Spontaneity is not a fixed property of a substance — temperature can and does flip its sign.

One thing free energy deliberately does not tell you is how long anything takes. A diamond at room temperature has a negative ΔG for turning into graphite, and shows no inclination to do so on any human timescale, because the atomic rearrangement has an enormous activation barrier. Thermodynamics says which way the system would go if it could get there; kinetics decides whether it ever gets there. "Spontaneous" is a statement about direction, not speed.