Ligand substitution: labile and inert

Werner could separate the violet and green isomers of $\ce{[Co(NH3)4Cl2]+}$ because cobalt(III) complexes swap ligands extremely slowly — slowly enough to crystallise, weigh and study at leisure. Among aqua ions, a water molecule on $\ce{[Cu(H2O)6]^2+}$ stays less than a nanosecond on average, while half the water on $\ce{[Cr(H2O)6]^3+}$ takes more than three days to change. Stability (how large the equilibrium constant is) and lability (how fast equilibrium is reached) are different things. Taube (1952) drew a practical line: complexes that react within about a minute at 25 °C and about 0.1 M are labile; slower ones are inert.

Replace the coordinated water with ¹⁷O-labelled water, follow it by NMR, and out comes the first-order rate constant $k$ of water exchange. From $5.7\times10^9$ s⁻¹ for $\ce{Cu^2+}$ to $1.1\times10^{-10}$ s⁻¹ for $\ce{Ir^3+}$ spans almost 20 orders of magnitude: a water molecule on the first stays 0.2 ns on average; the second has a half-life of about 200 years.

Two factors set the pace. One is charge and radius: the higher the charge and the smaller the ion, the stronger the M–O bond, so $\ce{Mg^2+}$ ($5.3\times10^5$ s⁻¹) is about 400 000 times faster than $\ce{Al^3+}$. The other is the d-electron configuration, which for transition-metal ions can override everything else: $\ce{Fe^3+}$ and $\ce{Cr^3+}$, alike in size and charge, differ by a factor of 10⁸, and $\ce{Ni^2+}$ is 17 times slower than the almost equally sized $\ce{Mg^2+}$.

Substitution can break a bond before making one (dissociative, D, through an intermediate of lower coordination number) or make one first (associative, A, through an intermediate of higher coordination number) — like S_N1 and S_N2 in organic chemistry. Most octahedral complexes follow an interchange path in between: the entering ligand waits in the outer sphere and swaps places with the leaving one, labelled $I_\text{d}$ when bond breaking dominates and $I_\text{a}$ when bond making does. Water exchange on $\ce{[V(H2O)6]^2+}$ is $I_\text{a}$; on the slightly smaller $\ce{[Ni(H2O)6]^2+}$ it is $I_\text{d}$. Sixteen-electron square-planar complexes (Pt(II), Pd(II)) have room for an attacking ligand and react associatively.

On the dissociative path an octahedron loses a ligand and becomes, for a moment, a square pyramid. The d orbitals split anew and the ligand-field stabilisation changes with them. Work out the d-orbital energies of both shapes with the angular overlap model, fill them with the same spin state, and the difference is the ligand-field activation energy: 0.2 Δo for d³ and d⁸, 0.4 Δo for low-spin d⁶, zero for d⁰, high-spin d⁵ and d¹⁰, and even slightly negative for d⁴ and d⁹. That is exactly the pattern measured: $\ce{Cr^3+}$, $\ce{V^2+}$ (d³) and $\ce{Ni^2+}$ (d⁸) are the slowest of their series, low-spin d⁶ Co(III), Rh(III) and Ir(III) are famously inert, and $\ce{Cr^2+}$ and $\ce{Cu^2+}$ (d⁴ and d⁹, Jahn–Teller distorted) are astonishingly fast.

In square-planar complexes such as those of Pt(II), which ligand is replaced is not random: the one that leaves faces the ligand with the strongest trans effect. Chernyaev recognised and named the effect in 1926; the order since established runs roughly $\ce{H2O} < \ce{NH3} < \text{py} < \ce{Cl-} < \ce{Br-} < \ce{I-} \approx \ce{NO2-} < \ce{PR3} < \ce{CN-} \approx \ce{CO} \approx \ce{C2H4}$.

So the order of synthesis decides the geometry of the product. Add $\ce{NH3}$ twice to $\ce{[PtCl4]^2-}$: the second $\ce{NH3}$ replaces a $\ce{Cl-}$ that faces another $\ce{Cl-}$, giving cisplatin, cis-$\ce{[PtCl2(NH3)2]}$. Turn it round — add $\ce{Cl-}$ twice to $\ce{[Pt(NH3)4]^2+}$ — and the second $\ce{Cl-}$ replaces the $\ce{NH3}$ facing the first chloride, giving transplatin. The two isomers share one formula, and only cisplatin treats cancer.