Transition Metals

(c) +7

In the 3d series the highest oxidation state is shown by manganese ($\mathrm{3d^5 4s^2}$), which can use all seven of its 4s and 3d electrons, as in $\mathrm{KMnO_4}$ and $\mathrm{Mn_2O_7}$. Elements after Mn have more d electrons, but their higher nuclear charge holds the electrons more tightly, so their maximum oxidation states fall (e.g. Fe shows at most +6). +8 occurs only in the heavier 4d/5d elements (Ru, Os, as in $\mathrm{OsO_4}$).

Four general characteristics of transition metals:

1. Variable oxidation states. The (n−1)d and ns electrons are close in energy, so different numbers of them can be lost. For example, Fe shows +2 and +3, and Mn shows +2 to +7.
2. Formation of coloured ions/compounds. Partially filled d orbitals allow d–d transitions that absorb visible light. For example, $\mathrm{Cu^{2+}}$ is blue and $\mathrm{Fe^{3+}}$ is yellow.
3. Paramagnetism. Most transition metal ions have unpaired d electrons, so they are attracted by a magnetic field. For example, $\mathrm{Fe^{3+}}$ has 5 unpaired electrons.
4. Formation of complex compounds. Their small, highly charged ions with vacant d orbitals accept lone pairs from ligands. For example, $\mathrm{[Cu(NH_3)_4]^{2+}}$ and $\mathrm{[Fe(CN)_6]^{4-}}$.

(Other characteristics: catalytic activity (Fe, Ni, $\mathrm{V_2O_5}$), formation of alloys and interstitial compounds, high melting points and hardness.)

(b) $\mathrm{[NiCl_4]^{2-}}$

$\mathrm{Ni^{2+}}$ is $3d^8$. $\mathrm{Cl^-}$ is a weak-field ligand and cannot pair up the d electrons, so the empty 4s and 4p orbitals are used. This gives $sp^3$ hybridisation and a tetrahedral, paramagnetic complex with 2 unpaired electrons. $\mathrm{CN^-}$ is a strong-field ligand: it pairs the electrons, giving $dsp^2$ (square planar) $\mathrm{[Ni(CN)_4]^{2-}}$. $\mathrm{[PtCl_4]^{2-}}$ is also square planar ($5d^8$), and $\mathrm{[CoF_6]^{3-}}$ is octahedral.

(a) $\mathrm{CO_2}$

A ligand must donate a lone pair of electrons to the metal ion. $\mathrm{NH_3}$ (lone pair on N), $\mathrm{H_2O}$ (lone pairs on O) and CO (lone pair on C) do this readily. In $\mathrm{CO_2}$ (O=C=O) the lone pairs on the oxygen atoms are held tightly by the highly electronegative oxygen, and the molecule is linear and non-polar. So it has practically no tendency to donate electrons and does not act as a ligand.

(a) $(n-1)s^2p^6d^{1-10}\,ns^{0-2}$

Transition metals are d-block elements whose differentiating electron enters the penultimate $(n-1)d$ subshell. Their general outer configuration is therefore $(n-1)d^{1-10}\,ns^{0-2}$. The $ns^{0}$ case is Pd ($\mathrm{4d^{10}5s^0}$), and the $ns^{1}$ cases include Cr and Cu. Options (b) and (d) describe p-block and s-block elements, and option (c) is the special configuration of Cr/Mo only.

a. Why the splitting occurs (CFT)

• In a free metal ion, or in a spherically symmetrical field, all five d orbitals have the same energy (they are degenerate).
• Crystal field theory treats the ligands as point negative charges (or dipoles). In an octahedral complex six ligands approach the metal ion along the $\pm x$, $\pm y$ and $\pm z$ axes.
• The $d_{x^2-y^2}$ and $d_{z^2}$ orbitals point directly along these axes, towards the ligands. Their electrons feel strong repulsion from the ligands' lone pairs, so these two orbitals are raised in energy. They form the $e_g$ set (+0.6 Δo).
• The $d_{xy}$, $d_{yz}$ and $d_{xz}$ orbitals point between the axes and feel less repulsion, so they are lowered in energy. They form the $t_{2g}$ set (−0.4 Δo).
• The energy gap between $e_g$ and $t_{2g}$ is the crystal field splitting energy, Δo. The average energy (barycentre) stays the same: $2(+0.6\Delta_o) + 3(-0.4\Delta_o) = 0$.

b. Why $\mathrm{[Cu(H_2O)_6]^{2+}}$ is blue

$\mathrm{Cu^{2+}}$ is $3d^9$, which in the octahedral field is $t_{2g}^6 e_g^3$. The $e_g$ set has a vacancy, so an electron from $t_{2g}$ can absorb visible light of energy equal to Δo (in the red-orange region, about 600–800 nm) and jump to $e_g$. This is a d–d transition. The light that is not absorbed reaches the eye as the complementary colour, blue.

c. $\mathrm{Fe^{2+}}$ or $\mathrm{Fe^{3+}}$: which is more stable?

• $\mathrm{Fe^{2+}}$: $3d^6$, which is $t_{2g}^4 e_g^2$ in a weak (high-spin) field. One $t_{2g}$ orbital holds a pair of electrons, so the arrangement is unsymmetrical.
• $\mathrm{Fe^{3+}}$: $3d^5$, which is $t_{2g}^3 e_g^2$. Every orbital of both the $t_{2g}$ and $e_g$ sets holds exactly one electron, a half-filled, symmetrical arrangement with maximum exchange energy.

So $\mathrm{Fe^{3+}}$ is more stable. This is why $\mathrm{Fe^{2+}}$ salts are easily oxidised to $\mathrm{Fe^{3+}}$ in air.

d. Why such elements are good catalysts

Elements with partially filled d orbitals (which show this splitting):

• show variable oxidation states, so they can easily gain and lose electrons and form unstable intermediates with the reactants. This gives a new path of lower activation energy.
• have vacant d orbitals that can bond with (adsorb) reactant molecules on their surface. This increases the concentration of reactants at the surface and weakens their bonds.

Examples: Fe in the Haber process, $\mathrm{V_2O_5}$ in the contact process, Ni in the hydrogenation of oils.

d–d electron transition (1 mark)

In a transition metal ion with partially filled d orbitals, the surrounding ligands split the five degenerate d orbitals into two sets of different energy: $t_{2g}$ (lower) and $e_g$ (higher) in an octahedral field. When visible light falls on the ion, an electron in the lower d level absorbs energy equal to the splitting energy (Δo) and jumps to the higher d level ($t_{2g} \to e_g$). This movement of an electron from one d orbital to another is called a d–d transition. The transmitted, complementary light gives the compound its colour. For example, $\mathrm{[Ti(H_2O)_6]^{3+}}$ ($3d^1$) absorbs light of about 500 nm (blue-green to yellow-green region) and appears purple (violet).

        ___ ___         eg
          ^
          |  hv (visible light absorbed)
        _|_ ___ ___     t2g
     d-d transition: t2g --> eg

Characteristics of transition metals (4 marks)

1. Electronic configuration. Their outer configuration is $(n-1)d^{1-10}\,ns^{0-2}$, with partially filled d orbitals in the atom or in a common ion.

2. Metallic nature. They are hard (except Zn, Cd and Hg, which is a liquid), lustrous, malleable and ductile metals, and good conductors of heat and electricity. They have high melting and boiling points (except Zn, Cd, Hg) because of strong metallic bonding involving both ns and unpaired (n−1)d electrons.

3. Variable oxidation states. The (n−1)d and ns electrons have nearly the same energy, so different numbers can take part in bonding. For example, Fe is +2 and +3, Cu is +1 and +2, and Mn ranges from +2 to +7.

4. Formation of coloured ions. Partially filled d orbitals allow d–d transitions in the visible region. For example, $\mathrm{Cu^{2+}}$ is blue, $\mathrm{Fe^{2+}}$ is pale green and $\mathrm{Ni^{2+}}$ is green. Ions with $d^0$ or $d^{10}$ configurations ($\mathrm{Sc^{3+}}$, $\mathrm{Zn^{2+}}$) have no d–d transitions and are colourless. (The purple colour of $\mathrm{MnO_4^-}$, a $d^0$ ion, comes from charge transfer, not a d–d transition.)

5. Magnetic properties. Ions with unpaired d electrons are paramagnetic. The magnetic moment is $\mu = \sqrt{n(n+2)}$ BM, where n is the number of unpaired electrons. Fe, Co and Ni are ferromagnetic.

6. Formation of complexes. Their small size, high charge and vacant d orbitals let them accept lone pairs from ligands. For example, $\mathrm{[Cu(NH_3)_4]^{2+}}$, $\mathrm{[Fe(CN)_6]^{4-}}$ and $\mathrm{[Ag(NH_3)_2]^+}$.

7. Catalytic properties. Variable oxidation states and the ability to adsorb reactants on their surface make them good catalysts. For example, Fe in the Haber process, Ni in hydrogenation and $\mathrm{V_2O_5}$ in the contact process.

8. Formation of interstitial compounds and alloys. Small atoms (H, C, N, B) fit into the gaps in their crystal lattices, giving hard, high-melting interstitial compounds such as steel and $\mathrm{Fe_3C}$. Their similar atomic sizes let them form alloys, such as brass and bronze.

9. Atomic radii and ionisation energy. Their atomic radii are small and change only slightly across a series, because each added electron enters the inner (n−1)d subshell, where it screens the outer ns electrons and largely offsets the increase in nuclear charge. Their ionisation energies lie between those of s-block and p-block elements.

(b) 3

Cr has the configuration $[Ar]\,3d^5\,4s^1$. In $[Cr(H_2O)_6]^{3+}$ the oxidation state of Cr is $+3$, so it loses the $4s^1$ electron and two $3d$ electrons, giving $Cr^{3+}: [Ar]\,3d^3$. It therefore has 3 d-electrons, all unpaired ($t_{2g}^3$).

Assumptions of crystal field theory

1. The bond between the central metal ion and the ligands is purely electrostatic, with no covalent character. The metal ion is a positive point charge, and the ligands are negative point charges (anions) or dipoles (neutral molecules like $H_2O$, $NH_3$).
2. In the free metal ion the five d orbitals are degenerate (equal energy).
3. When ligands approach, the d electrons are repelled by the ligand electrons. The orbitals that point towards the ligands are raised in energy more than those that point between them, so the degeneracy is lifted (the d orbitals split).
4. The magnitude of the splitting depends on the metal ion (charge, size), the geometry of the complex and the nature of the ligand (spectrochemical series).
5. The ligands do not have orbitals that overlap with the metal orbitals, so there is no orbital overlap in this model.

Splitting in an octahedral complex

In an octahedral field the six ligands approach along the $x$, $y$, $z$ axes. The $d_{x^2-y^2}$ and $d_{z^2}$ orbitals point directly at the ligands and are raised ($e_g$ set). The $d_{xy}$, $d_{yz}$ and $d_{xz}$ orbitals point between the ligands and are lowered ($t_{2g}$ set).

Energy
  ^
  |                        ___ ___   e_g  (d_x2-y2, d_z2)
  |                          ^       (+0.6 Δo)
  |   ___ ___ ___ ___ ___    |
  |   free ion (degenerate)  | Δo
  |   d orbitals             |
  |                          v
  |                    ___ ___ ___   t2g (d_xy, d_yz, d_xz)
  |                                  (-0.4 Δo)
  +-------------------------------------------
     Free ion   Spherical    Octahedral field
                field        (splitting)

The energy gap between the two sets is the crystal field splitting energy $\Delta_o$. The $e_g$ set lies $0.6\Delta_o$ above and the $t_{2g}$ set lies $0.4\Delta_o$ below the barycentre (average energy).