Chemistry of transition elements

A transition element 过渡元素 is a d-block element that forms one or more stable ions with incomplete d orbitals. (Scandium and zinc are in the d-block but are not transition elements, because their stable ions have empty or full d orbitals.)

The 3d orbitals 轨道 have set shapes: the $3\text{d}_{xy}$ orbital has four lobes pointing between the axes, and the $3\text{d}_{z^2}$ orbital has two lobes along the $z$-axis with a ring around the middle.

Four key properties (and why)

The four key properties of the transition elements

A ruby is red because of transition-metal (chromium) ions held in its crystal lattice

A transition metal ion can be surrounded by complex ions 配离子. The species attached are ligands.

A ligand 配体 is a species with a lone pair of electrons that forms a dative covalent bond 配位键 to the central metal ion. (The lone pair 孤对电子 is what it donates.) Ligands are grouped by how many such bonds they can form:

• monodentate 单齿: one bond ($\text{H}_2\text{O}$, $\text{NH}_3$, $\text{Cl}^-$, $\text{CN}^-$).
• bidentate 双齿: two bonds (1,2-diaminoethane "en", and the ethanedioate ion $\text{C}_2\text{O}_4^{2-}$).
• polydentate 多齿: many bonds ($\text{EDTA}^{4-}$, which uses six).

Ligands are grouped by how many dative bonds they form: monodentate (one), bidentate (two) or polydentate (many, like EDTA's six)

A complex 配合物 is a central metal atom or ion surrounded by one or more ligands. Its shape can be linear 直线形, square planar 平面正方形, tetrahedral 四面体形 or octahedral 八面体形.

The coordination number 配位数 is the number of dative bonds from the ligands to the central ion (6 → octahedral, 4 → tetrahedral or square planar, 2 → linear). To predict the charge of a complex, add the metal's charge and all the ligand charges.

Complex shapes follow the coordination number: 2 is linear, 4 is tetrahedral or square planar, 6 is octahedral

Ligand exchange

In ligand exchange 配体交换 one ligand replaces another, often with a colour change. For copper(II):

With concentrated $\text{HCl}$ it becomes yellow $[\text{CuCl}_4]^{2-}$; cobalt(II) behaves in a similar way.

Ligand exchange changes the colour of copper(II): pale blue with water, deep blue with ammonia, yellow with concentrated HCl

Redox reactions of transition ions

Use $E^{\ominus}$ values to predict whether a redox reaction is feasible. Common titrations you should be able to calculate include $\text{MnO}_4^-/\text{C}_2\text{O}_4^{2-}$ and $\text{MnO}_4^-/\text{Fe}^{2+}$ in acid (purple to colourless), and $\text{Cu}^{2+}/\text{I}^-$ (which makes iodine, then titrated with thiosulfate).

Worked example. In acid, $\text{MnO}_4^-$ reacts with $\text{Fe}^{2+}$ in the ratio $1:5$ (see the balanced equation above). A $25.0\ \text{cm}^3$ sample of $\text{Fe}^{2+}$ solution needs $22.0\ \text{cm}^3$ of $0.0200\ \text{mol dm}^{-3}$ $\text{KMnO}_4$ to reach the end point. Find the concentration of the $\text{Fe}^{2+}$.

Moles of $\text{MnO}_4^-$ used $= 0.0200 \times \dfrac{22.0}{1000} = 4.40 \times 10^{-4}\ \text{mol}$. Each mole of $\text{MnO}_4^-$ reacts with $5$ moles of $\text{Fe}^{2+}$, so moles of $\text{Fe}^{2+} = 5 \times 4.40 \times 10^{-4} = 2.20 \times 10^{-3}\ \text{mol}$. This was in $25.0\ \text{cm}^3$, so

In a free ion the five d orbitals are degenerate 简并 — they have the same energy. When ligands come close, they split the d orbitals into two non-degenerate 非简并 sets, separated by an energy gap $\Delta E$:

• octahedral: three lower and two higher orbitals.
• tetrahedral: two lower and three higher orbitals.

A complex absorbs light whose frequency matches $\Delta E$, promoting an electron from a lower to a higher d orbital. The colour you see is the complementary colour 互补色 of the light absorbed. Different ligands give a different $\Delta E$, so they change the frequency absorbed and hence the colour — which is why ligand exchange changes the colour.

Ligands split the five d orbitals into two sets separated by a gap $\Delta E$; the complex absorbs light of that energy, so we see the complementary colour

Different metals and oxidation states give different colours: cobalt(II) (red), dichromate (orange), chromate (yellow), nickel(II) (green), copper(II) (blue) and permanganate (violet)

• geometrical isomerism 几何异构 (cis 顺式 / trans 反式) appears in square planar complexes such as $[\text{Pt}(\text{NH}_3)_2\text{Cl}_2]$, and in octahedral complexes such as $[\text{Co}(\text{NH}_3)_4(\text{H}_2\text{O})_2]^{2+}$.

Geometrical isomerism in a square planar complex: the two identical ligands are adjacent (cis) or opposite (trans)

• optical isomerism 旋光异构 appears in octahedral complexes with bidentate ligands, such as $[\text{Ni}(\text{en})_3]^{2+}$, which has two non-superimposable mirror images.

You can also deduce the polarity of a complex: a cis form may be polar, while the matching trans form is often non-polar because its dipoles cancel.

The stability constant 稳定常数 ($K_{\text{stab}}$) is the equilibrium constant for forming a complex ion from the metal ion and its ligands in solution (water is left out of the expression).

A large $K_{\text{stab}}$ means a very stable complex. In a ligand exchange, the position moves towards the complex with the larger $K_{\text{stab}}$ — that is why a ligand that forms a more stable complex can push out a weaker one.

• Define a transition element: it forms at least one ion with a partially filled d sub-shell — so Sc and Zn are excluded.
• Colour comes from d-d transitions (ligands split the d orbitals); the colour seen is the complement of the light absorbed.
• State the ligand and coordination number and predict the shape (6 = octahedral, 4 = tetrahedral or square planar).
• Ligand exchange can change colour and coordination number; a larger stability constant = a more stable complex.