Stability Constants of Complexes
On this page
Direct answer
Thermodynamic stability of a complex MLn is quantified by stepwise constants Kn and their product, the overall formation constant βn = K1 K2 … Kn; larger β means more completely formed complex, and the dissociation constant is simply its reciprocal. Three levers move β: the metal (charge, size and crystal-field stabilisation — the Irving-Williams order for M2+ runs Mn < Fe < Co < Ni < Cu > Zn), the ligand's basicity, and chelation — the entropy-driven gap that makes NCERT's example pair [Ni(NH3)6]2+ (log β 8.6) and [Ni(en)3]2+ (log β 18.3) differ by nearly ten orders of magnitude.
What you must remember
- Definitions: K1 = [ML]/[M][L]; β2 = K1 × K2; βn is the product of all steps; Kd = 1/βn; values are quoted as log β.
- The NCERT chelate pair: log β 8.61 for [Ni(NH3)6]2+ against 18.3 for [Ni(en)3]2+ — six ammines traded for three diamine chelates, stability up roughly ten-billion-fold.
- Stepwise decline: K1 > K2 > K3 on statistical and steric grounds — later ligands find fewer open sites and crowd harder.
- Chelate effect is mainly entropy: [Ni(H2O)6]2+ + 3 en → [Ni(en)3]2+ + 6H2O raises the solute particle count from four to seven; ΔS does the heavy lifting with a modest enthalpy assist.
- Irving-Williams series (M2+): Mn2+ < Fe2+ < Co2+ < Ni2+ < Cu2+ > Zn2+ — field stabilisation builds to a copper maximum and zinc's d10 drops back.
- Charge-size rule: higher charge on smaller radius stabilises; Fe3+ complexes out-form their Fe2+ analogues.
- Denticity ladder: more teeth, tighter grip — EDTA is hexadentate, with log K about 10.7 for calcium and about 25 for iron(III), the numbers behind EDTA titrations and chelation therapy.
- Kinetic contrast: thermodynamic stability (large β) is not inertness — [Ni(CN)4]2− is thermodynamically robust yet exchanges ligands fast, while low-spin Co(III) ammines are the inert benchmarks.
The chelate arithmetic
Compare the two nickel complexes directly: β ratio = 10^(18.3 − 8.61), about 5 × 10^9. Swap six ammonias for three ethylenediamines and the equilibrium lies five billion times further right. The bookkeeping explains why: each en entering displaces two waters in a single binding event, so three chelates liberate six water molecules — a four-to-seven particle gain whose entropy term converts directly into free energy. Enthalpy helps only weakly, through slightly stronger Ni–N bonding in the chelate's fixed bite geometry. The same logic scales to EDTA: one ligand, six donor atoms, one metal seized — which is why calcium sits at log K near 10.7 and iron(III) at 25, and why the reagent serves both hardness titration and clinical lead poisoning treatment. Irving-Williams closes the circle as an energy story across the divalent first row: crystal-field stabilisation climbs with d electron count to a copper peak, and zinc, with a filled d10 shell and no LFSE, falls back below its neighbour.
Stability versus inertness
JEE Main keeps to identification: which complex is more stable and why — chelation, ligand basicity, metal oxidation state — with the NCERT log β numbers as quotable ammunition. Advanced probes the distinctions: why β is an equilibrium statement while inertness is a rate statement; why stepwise constants decline; and the thermodynamic cycle behind the chelate entropy. The exam trap is conflating the two — "high Kf means slow substitution" is false as a rule, and assertion-reason questions test exactly that seam. A complex can be thermodynamically stable yet labile (most zinc and nickel complexes exchange ligands in microseconds) or of modest formation constant yet kinetically inert (the low-spin cobalt(III) ammines Werner isolated a century ago, which survive in concentrated acid long enough to be recrystallised). Holding that pair of examples makes the distinction impossible to forget.
Frequently asked questions
Why is [Ni(en)3]2+ more stable than [Ni(NH3)6]2+?
Chelation: three bidentate ligands replace six monodentates, releasing more particles into solution — an entropy gain that lifts log β from 8.6 to 18.3.
State the Irving-Williams series.
For divalent first-row metals: Mn2+ < Fe2+ < Co2+ < Ni2+ < Cu2+ > Zn2+ — crystal-field stabilisation builds to copper, and zinc's d10 shell carries none.
How are β and Kd related?
The overall dissociation constant is the reciprocal of the overall formation constant, Kd = 1/βn; a large β means a small tendency to fall apart.
Why do stepwise stability constants decrease?
Each successive ligand finds fewer open sites, faces growing steric crowding and loses statistical advantage — hence K1 > K2 > K3 through the series.
Can a labile complex be thermodynamically stable?
Yes — stability is an equilibrium quantity (large β) while lability is kinetic (fast exchange); many high-β zinc and nickel complexes swap ligands almost instantly.