Mixed Reasoning, Numericals & Long-Answer Questions

CHEExam Practice & Reasoning

This subtopic pulls together the whole chapter: Werner's theory, VBT-vs-CFT comparisons, magnetic-moment numericals, ligand-field reasoning, and applied chemistry (tests, extraction, double salts). It rewards being able to justify a property with the right theory rather than just stating a result.

Spin-only magnetic moment

\mu = \sqrt{n(n+2)}\ \text{BM}

n

= number of unpaired electrons;

\mu

in Bohr magnetons (BM)

Unpaired-electron readout

n=1\Rightarrow 1.73\quad n=2\Rightarrow 2.83\quad n=3\Rightarrow 3.87\quad n=4\Rightarrow 4.90\quad n=5\Rightarrow 5.92

\mu

values in BM, used to back-calculate

n

Oxidation number from charge

x = (\text{net charge}) - \sum(\text{ligand charges})

x

= oxidation number of the central metal

Gold cyanide leaching

4Au + 8CN^- + O_2 + 2H_2O \rightarrow 4[Au(CN)_2]^- + 4OH^-

MacArthur-Forrest process;

Au

recovered by adding

Zn

Werner's theory: a metal has two valencies — primary (ionisable, satisfied by anions, equal to the oxidation number) and secondary (non-ionisable, directional, equal to the coordination number). Confirmed by counting ions via molar conductance and by $AgNO_3$ precipitating only the ionisable $Cl^-$ .
Spin-only moment $\mu = \sqrt{n(n+2)}$ BM gives the unpaired-electron count: $\mu = 4.90$ BM $\Rightarrow n = 4$ (e.g. a high-spin, weak-field, outer-orbital $sp^3d^2$ octahedral ion); $\mu = 0 \Rightarrow$ all electrons paired, i.e. a low-spin, strong-field, inner-orbital $d^2sp^3$ complex.
Strong-field ligands ( $CN^-$ , CO) pair electrons giving low spin/diamagnetic; weak-field ligands ( $H_2O$ , $F^-$ ) leave electrons unpaired giving high spin/paramagnetic. This explains $[Fe(CN)_6]^{4-}$ diamagnetic vs $[Fe(H_2O)_6]^{2+}$ paramagnetic (both $Fe^{2+}$ , $d^6$ ).
CO is a stronger-field ligand than $NH_3$ because of synergic bonding: $\sigma$ -donation plus $\pi$ -back-bonding from filled metal $d$ -orbitals into empty CO $\pi^*$ orbitals, which $NH_3$ cannot do.
VBT vs CFT: VBT explains geometry, hybridisation and magnetism but cannot explain colour or the spectrochemical order; CFT explains colour, $d$ -orbital splitting and stability but ignores the covalent (orbital-overlap) character of M–L bonds.
Identification tests: $Fe^{3+}$ gives blood-red $[Fe(SCN)]^{2+}$ with $KSCN$ ; $Cu^{2+}$ gives deep-blue tetraamminecopper(II), $[Cu(NH_3)_4]^{2+}$ , with excess $NH_3$ .
Cyanide (leaching) process: gold dissolves as $[Au(CN)_2]^-$ — $4Au + 8CN^- + O_2 + 2H_2O \rightarrow 4[Au(CN)_2]^- + 4OH^-$ — then displaced by $Zn$ .
Double salt vs coordination compound: a double salt (e.g. $K_2SO_4\cdot Al_2(SO_4)_3\cdot 24H_2O$ ) dissociates fully into all its ions in water, whereas a complex (e.g. $K_4[Fe(CN)_6]$ ) keeps the complex ion intact and does not give tests for the coordinated ions.
Geometry-from-CN-and-ligand reasoning: for CN 4, a strong field with $d^8$ ( $Ni^{2+}$ , $Pd^{2+}$ , $Pt^{2+}$ ) forces $dsp^2$ square planar and diamagnetism; a weak field gives $sp^3$ tetrahedral and paramagnetism. Hence $[Ni(CN)_4]^{2-}$ is square planar/diamagnetic while $[NiCl_4]^{2-}$ is tetrahedral/paramagnetic.
Molar conductance counts ions: $[Co(NH_3)_6]Cl_3$ gives 4 ions (highest conductance), $[Co(NH_3)_5Cl]Cl_2$ gives 3, $[Co(NH_3)_4Cl_2]Cl$ gives 2, and $[Co(NH_3)_3Cl_3]$ is a non-electrolyte (no ions) — this is how Werner assigned coordination spheres.
Colour reasoning: a complex is coloured if it can undergo a d–d transition ( $d^1$ to $d^9$ ); $d^0$ ( $Sc^{3+}$ , $Ti^{4+}$ ) and $d^{10}$ ( $Zn^{2+}$ , $Cu^+$ ) are colourless. A larger $\Delta_o$ (stronger ligand) means absorption of shorter wavelengths, shifting the observed colour.
Stability/EAN reasoning: chelation raises stability via the entropy-driven chelate effect; metal carbonyls owe their stability to obeying the EAN/18-electron rule, with strong M–C bonding reinforced by $\pi$ -back-bonding.

Where the marks go

Using $\mu = \sqrt{n(n+2)}$ with the number of $d$ -electrons instead of the number of UNPAIRED electrons — only unpaired electrons contribute.
Assuming $NH_3$ is a weak-field ligand because it is neutral — it sits above $H_2O$ in the spectrochemical series and gives low-spin $d^6$ ( $[Co(NH_3)_6]^{3+}$ is diamagnetic).
Counting counter-ions inside the coordination sphere when finding the oxidation number, e.g. treating the outer $Cl$ in $[Co(NH_3)_4Cl_2]Cl$ as bonded to the metal.
Calling every two-component salt a double salt — a species that retains a discrete complex ion in solution is a coordination compound and fails the free-ion tests.
Saying VBT explains colour: it does not; only CFT (via $\Delta_o$ and d–d transitions) accounts for colour and the spectrochemical series.

How the board asks it

Give reasonsstrong-field vs weak-field ligands and spin state
Account for the following: $[Fe(CN)_6]^{4-}$ is diamagnetic whereas $[Fe(H_2O)_6]^{2+}$ is paramagnetic, although the metal is $Fe^{2+}$ ( $d^6$ ) in both. Explain in terms of the nature of the ligand.
Numericalspin-only magnetic moment $\mu = \sqrt{n(n+2)}$ BM
An octahedral complex of $Mn^{2+}$ has a measured magnetic moment of $5.92$ BM. Calculate the number of unpaired electrons and state, with reason, whether the complex is high-spin or low-spin.
Numericalwerner's theory and ion counting
For $[Co(NH_3)_5Cl]Cl_2$ , determine the oxidation number and coordination number of cobalt, the number of ions furnished in aqueous solution, and the moles of $AgCl$ precipitated per mole of complex by excess $AgNO_3$ .
Predict the productgeometry-from-CN-and-ligand reasoning ( $dsp^2$ vs $sp^3$ )
Predict the geometry, hybridisation and magnetic behaviour of $[Ni(CN)_4]^{2-}$ and $[NiCl_4]^{2-}$ , giving reasons for the difference between the two.
Distinguishdouble salt vs coordination compound
How will you distinguish between a double salt such as $K_2SO_4 \cdot Al_2(SO_4)_3 \cdot 24H_2O$ and a coordination compound such as $K_4[Fe(CN)_6]$ on the basis of their behaviour in aqueous solution?
DistinguishVBT vs CFT scope
Compare Valence Bond Theory and Crystal Field Theory, stating one limitation of each. Why is VBT unable to explain the colour of $[Ti(H_2O)_6]^{3+}$ ?

PreviousColour & Why Some Complexes Are Colourless

Written for Sublevo. Question text quoted anywhere in these notes is the Council’s and carries its year and paper; the board’s own diagrams are not reproduced.