chelate effect
Here is a puzzle. Take a nickel ion bound to six ammonia molecules, and a nickel ion bound to three ethylenediamine molecules. The metal-nitrogen bonds are almost identical in kind and number — six Ni-N bonds either way. Yet the ethylenediamine complex is hundreds to thousands of times more stable. Why should joining the nitrogen donors in pairs make such a difference? That extra stability is the chelate effect.
The answer is mostly entropy, the measure of disorder, rather than stronger bonds. Consider the swap: [Ni(H2O)6]2+ plus three ethylenediamine molecules gives [Ni(en)3]2+ plus six water molecules. On the left, four particles go in (the complex plus three en); on the right, seven particles come out (the complex plus six freed waters). The reaction increases the number of free molecules, raising the disorder of the solution, which is thermodynamically favorable. With six separate ammonias instead, six particles would go in and six come out — no net gain in particle count, so no entropy bonus. A helpful smaller picture: once one end of a chelating ligand is attached, the second donor is dangling right next to the metal, so it clips on almost for free instead of a whole new molecule having to find its way in from solution.
The chelate effect is why chelating and multidentate ligands dominate practical chemistry whenever a metal must be held firmly: EDTA in water treatment and analysis, chelation therapy to strip toxic metals from the body, and the multidentate frameworks nature uses in metalloproteins. It is honestly a thermodynamic trend, strongest for five- and six-membered rings, and it can be diminished by ring strain or unfavorable enthalpy; the related macrocyclic effect adds even more stability when the donor set is pre-organized in a ring.
For nickel(II), the formation constant of [Ni(en)3]2+ is roughly ten orders of magnitude larger than that of [Ni(NH3)6]2+, even though both bind through six nitrogens. The huge difference comes almost entirely from the favorable entropy of releasing more free molecules when the chelate forms.
Three chelating en ligands vastly out-stabilize six separate ammonias, mostly through entropy.
The chelate effect is largely entropic, not a sign of intrinsically stronger metal-ligand bonds. Per-bond enthalpies are often similar to monodentate analogues; the win comes from freeing more particles into solution and from the second donor already being held nearby.