Solubility is controlled by a balance of energetic and entropic changes that often oppose each other. Because these competing contributions can be similar in magnitude, small differences in structure, temperature, or solvent can flip the predicted outcome.

Why “predicting solubility” is thermodynamically subtle

Solubility under a given set of conditions reflects whether dissolving is thermodynamically favourable overall. The difficulty is that dissolution is rarely driven by a single effect; instead, multiple free-energy contributions add together, and their sum may be small.

A small net $\Delta G^\circ$ means the system is “on the fence,” so predictions based on one dominant factor (e.g., “ionic = soluble”) can fail.

Competing terms that can offset during dissolution

Enthalpy–entropy competition

Dissolution commonly features opposing signs in $\Delta H^\circ$ and $\Delta S^\circ$, so the net free energy depends on which term wins at the temperature of interest.

Even when you can qualitatively guess the signs, the magnitudes of $\Delta H^\circ$ and $T\Delta S^\circ$ may be close enough to partially cancel.

Enthalpic “give-and-take” can nearly balance

In many dissolutions, enthalpy includes both energy costs and energy releases, such as:

Born–Haber-type thermochemical cycle diagram showing enthalpy changes as a sequence of steps with arrows (energy increasing upward). This kind of stepwise energy accounting is the same logic used in dissolution: large positive steps (separating species) can be offset by large negative steps (forming stabilizing interactions), so the net $\Delta H^\circ$ can end up small. Source

• Costs from separating solute particles (breaking an extended solid structure)

• Releases from forming new solute–solvent attractions

If these are similar in magnitude, $\Delta H^\circ$ ends up near zero, and the outcome becomes dominated by entropy (or vice versa). Because these interactions depend on ion size, charge density, and molecular polarity, small chemical changes can shift the balance.

Entropy is not “always increasing” in a simple way

A frequent pitfall is assuming “mixing increases disorder, so $\Delta S^\circ > 0$.” In reality, $\Delta S^\circ$ for dissolution is a sum of multiple, sometimes opposing, contributions:

• Dispersal of solute particles into solution (often increases entropy)

• Solvent organisation around solute particles (can decrease entropy)

• Changes in the number and freedom of independently moving species (context-dependent)

Because these can offset, $\Delta S^\circ$ can be small or even negative, especially when dissolving species that strongly constrain nearby solvent motion.

Why cancellations make predictions fragile

Small net $\Delta G^\circ$ amplifies “minor” effects

When cancellations occur, the net free energy can be comparable to typical uncertainties in estimation.

Ellingham diagram: a set of straight-line plots of $\Delta G$ versus temperature, where the slope relates to $-\Delta S$ and the intercept relates to $\Delta H$. The key study takeaway is that modest temperature changes can move a borderline process across $\Delta G=0$, illustrating why ‘free-energy cancellation’ makes predictions fragile. Source

Then, seemingly minor factors become decisive:

• Temperature: changing $T$ rescales the entropy term $T\Delta S^\circ$, so a borderline process can switch from unfavourable to favourable (or the reverse).

• Different solid forms: changes in crystal packing (polymorphs) alter the balance of terms.

• Solvent identity: a solvent that stabilises solute particles slightly better can change the net sign of $\Delta G^\circ$.

Qualitative rules can contradict each other

Heuristics like “higher charge = stronger solute–solvent attractions” compete with “higher charge = harder to separate the solid.” Both can be true simultaneously, so the net effect is not obvious without knowing which term dominates for that specific solute–solvent pair.

The net result can be close to zero

If $\Delta G^\circ$ is small because of cancellation, the system may show:

• Only modest solubility (neither “insoluble” nor “highly soluble”)

• Strong sensitivity to conditions (temperature changes or slight formulation changes)

In this regime, predicting solubility is hard precisely because the process is governed by a difference of large numbers, not a single large driving force.