IChO 1999 · Theory problem 4

Iron and chromium complexes of ligand L

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Ligand L can form complexes with many transition metals. L is synthesized by heating a mixture of a bipyridine, glacial acetic acid and hydrogen peroxide to 70 – 80 °C for 3 hrs. The final product L crystallizes out as fine needles and its molecular mass is 188. An analogous reaction with pyridine is ;

Figure 1

Complexes of L with \(\ce{Fe}\) and \(\ce{Cr}\) have the formulae of \(\ce{FeL_m(ClO4)_n * 3H2O}\) (A) and \(\ce{CrL_xCl_y(ClO4)_z * H2O}\) (B), respectively. Their elemental analyses and physical properties are given in Tables 4a and 4b. The relationship of colour and wavelength is given in Table 4c.

Table 4a: Elemental analyses.

Complex Elemental analyses , (wt. %)
A Fe 5.740, C 37.030, H 3.090 , Cl 10.940, N 8.640
B Cr 8.440, C 38.930, H 2.920, Cl 17.250, N 9.080

Use the following data:

Atomic number: Cr = 24, Fe = 26

Relative atomic mass: H = 1, C = 12, N = 14, O = 16, Cl = 35.45, Cr = 52, Fe = 55.8

Table 4b: Physical properties

Complex Magnetic moment , \(\mu\) B.M. Colour
A 6.13 Yellow
B Not measured Purple

Table 4c Relationship of wavelength to colour.

Wavelength (nm) and colour absorbed Complementary colour
400 (violet) Yellow Green
450 (blue) Yellow
490 (blue green) Orange
500 (green) Red
570 (yellow green) Violet
580 (yellow) Blue
600 (orange) Blue green
650 (red) Green

4.1 Write down the molecular formula of L.

4.2 If L is a bidentate chelating ligand, draw the structure of the bipyridine used. Also draw the structure of L.

4.3 Does the ligand L have any charge, i. e. net charge?

4.4 Draw the structure when one molecule of L binds to metal ion (M).

4.5 From the data in Table 4a, determine the empirical formula of A. What are the values of m and n in \(\ce{FeL_m(ClO4)_n * 3H2O}\)? Write the complete formula of A in the usual IUPAC notation. What is the ratio of cation to anion when A dissolves in water?

4.6 What is the oxidation number of Fe in A? How many d-electrons are present in Fe ion in the complex? Write the high spin and the low spin configurations that may exist for this complex. Which configuration, high or low spin, is the correct one? What is the best evidence to support your answer?

4.7 From Table 4c, estimate \(\lambda_{\max}\) (nm) of A.

4.8 Detail analysis of B shows that it contains \(\ce{Cr^{3+}}\) ion. Calculate the ‘spin-only’ magnetic moment of this compound.

4.9 Compound B is a 1 : 1 type electrolyte. Determine the empirical formula of B and the values of x, y, z in \(\ce{CrL_xCl_y(ClO4)_z * H2O}\).

Official English text of the problem.

Answers

Names and SMILES for the structures are supplied in the corresponding solution parts.

  • 4.1 \(\boxed{\ce{L = C10H8N2O2}}\).
  • 4.2 The precursor is 2,2′-bipyridine; L is 2,2′-bipyridine N,N′-dioxide.
  • 4.3 L has zero net charge.
  • 4.4 Both N-oxide oxygen atoms coordinate to the same metal ion, giving an \(O,O'\)-chelating ligand and a seven-membered chelate ring.
  • 4.5 The empirical formula is \(\ce{C30H30Cl3FeN6O21}\).
    \[ \boxed{m=3,\qquad n=3,\qquad \ce{A = [Fe(C10H8N2O2)3](ClO4)3 * 3H2O}} \] The cation-to-anion ratio is \(\boxed{1:3}\).
  • 4.6 Iron has oxidation number \(\boxed{+3}\) and configuration \(d^5\). The possible octahedral configurations are high-spin \(t_{2g}^{3}e_g^{2}\) and low-spin \(t_{2g}^{5}e_g^{0}\). A is high-spin, supported by its measured magnetic moment of \(6.13\) B.M.
  • 4.7 \(\boxed{\lambda_{\max}\approx450\ \mathrm{nm}}\).
  • 4.8 \(\boxed{\mu_{\mathrm{so}}=\sqrt{15}\,\mu_{\mathrm B}=3.87\ \mathrm{B.M.}}\).
  • 4.9 The empirical formula is \(\ce{C20H18Cl3CrN4O9}\).
    \[ \boxed{x=2,\qquad y=2,\qquad z=1,\qquad \ce{B = [Cr(C10H8N2O2)2Cl2]ClO4 * H2O}} \]

Solution

In the coordination SMILES below, -> and <- denote dative bonds directed from the donor atom to the metal. Coordination geometry is described separately.

4.1 — Molecular formula of L

Pyridine, SMILES n1ccccc1, has molecular formula \(\ce{C5H5N}\). Joining two pyridine rings through a carbon–carbon bond replaces one hydrogen on each ring, giving a bipyridine formula of \(\ce{C10H8N2}\).

Its relative molecular mass is

\[ M_r(\text{bipyridine})=10(12)+8(1)+2(14)=156. \]

The illustrated reaction converts pyridine into pyridine N-oxide, SMILES [O-][n+]1ccccc1. The mass increase for the bipyridine is

\[ 188-156=32=2(16), \]

so both nitrogen atoms are oxidized, adding two oxygen atoms:

\[ \boxed{\ce{L = C10H8N2O2}}. \]

The ligand is 2,2′-bipyridine N,N′-dioxide, SMILES [O-][n+]1ccccc1-c1cccc[n+]1[O-].

The overall oxidation is balanced as

\[ \ce{C10H8N2 + 2H2O2 -> C10H8N2O2 + 2H2O}. \]

Here hydrogen peroxide, SMILES OO, is the oxidant; acetic acid, SMILES CC(=O)O, is the reaction medium; and water, SMILES O, is the coproduct.

4.2 — Structures of the precursor and L

The precursor is 2,2′-bipyridine, SMILES n1ccccc1-c1ccccn1.

To draw it:

  • Draw two aromatic six-membered pyridine rings.
  • Number the nitrogen in each ring as position 1.
  • Connect carbon 2 of one ring directly to carbon 2′ of the other.

To draw L, retain that framework and attach one oxygen atom to each ring nitrogen, showing each N-oxide group as \(\ce{N^{+}-O^{-}}\). Its SMILES is [O-][n+]1ccccc1-c1cccc[n+]1[O-].

The 2,2′ linkage allows rotation about the inter-ring bond to bring the two oxygen donors into a conformation suitable for binding the same metal ion.

4.3 — Charge of L

Each N-oxide group contains one formally positive nitrogen and one formally negative oxygen. Thus

\[ q(L)=2(+1)+2(-1)=\boxed{0}. \]

The ligand is electrically neutral overall.

4.4 — Coordination of one L molecule

Both oxygen atoms donate lone pairs to the same metal ion. Thus L is a \(\kappa^2O,O'\) ligand.

A generic metal–L chelate fragment has the dative-bond SMILES:

[*]1<-[O-][n+]2ccccc2-c2cccc[n+]2[O-]->1

The wildcard * represents M; its identity, charge and remaining ligands are unspecified in this generic fragment.

For the drawing, orient the N-oxide groups toward the metal and draw one coordination bond from each oxygen to M. Tracing the closed chelate ring gives:

M → first oxygen → first nitrogen → carbon 2 → carbon 2′ → second nitrogen → second oxygen → M.

There are therefore seven atoms in the chelate ring. The bonds to the metal are through oxygen.

4.5 — Composition and formula of A

Take a \(100.000\ \mathrm g\) sample. The amount of iron is

\[ n_{\ce{Fe}}= \frac{5.740\ \mathrm g}{55.8\ \mathrm{g\,mol^{-1}}} =0.10287\ \mathrm{mol}. \]

Each ligand contains ten carbon atoms, so

\[ n_L= \frac{37.030\ \mathrm g} {10(12)\ \mathrm{g\,mol^{-1}}} =0.30858\ \mathrm{mol}. \]

Consequently,

\[ m=\frac{n_L}{n_{\ce{Fe}}} =\frac{0.30858}{0.10287} \approx\boxed{3}. \]

All chlorine in the stated formula of A belongs to perchlorate:

\[ n= \frac{10.940/35.45}{5.740/55.8} =3.0000 \approx\boxed{3}. \]

For completeness, the oxygen percentage by difference is

\[ w_{\ce O} =100-(5.740+37.030+3.090+10.940+8.640) =34.560\%. \]

Dividing the elemental amounts by the amount of iron gives:

Element Atomic ratio relative to Fe
Fe 1.000
C 29.998
H 30.039
Cl 3.000
N 5.999
O 20.998

Thus the empirical formula is

\[ \boxed{\ce{C30H30Cl3FeN6O21}}. \]

Three bidentate ligands provide six oxygen donors, giving an approximately octahedral complex cation. The complete coordination formula is

\[ \boxed{\ce{[FeL3](ClO4)3 * 3H2O} =\ce{[Fe(C10H8N2O2)3](ClO4)3 * 3H2O}}. \]

Its name is tris(2,2′-bipyridine N,N′-dioxide)iron(III) perchlorate trihydrate, with SMILES:

[Fe+3]123(<-[O-][n+]4ccccc4-c4cccc[n+]4[O-]->1)(<-[O-][n+]4ccccc4-c4cccc[n+]4[O-]->2)<-[O-][n+]4ccccc4-c4cccc[n+]4[O-]->3.[O-]Cl(=O)(=O)=O.[O-]Cl(=O)(=O)=O.[O-]Cl(=O)(=O)=O.O.O.O

The tris(L)iron(III) cation is the first connected component:

[Fe+3]123(<-[O-][n+]4ccccc4-c4cccc[n+]4[O-]->1)(<-[O-][n+]4ccccc4-c4cccc[n+]4[O-]->2)<-[O-][n+]4ccccc4-c4cccc[n+]4[O-]->3

The counterion is perchlorate, \(\ce{ClO4^-}\), SMILES [O-]Cl(=O)(=O)=O.

Dissolution is represented by

\[ \ce{[FeL3](ClO4)3 * 3H2O(s) -> [FeL3]^3+(aq) + 3ClO4^-(aq) + 3H2O(l)}. \]

Therefore,

\[ \boxed{\text{cation : anion}=1:3}. \]

4.6 — Iron oxidation state, electron configuration and spin

The three perchlorate ions have total charge \(-3\). Because each L is neutral, iron must have oxidation number

\[ \boxed{+3}. \]

The metal is iron(III), \(\ce{Fe^{3+}}\), SMILES [Fe+3]. Its \(d\)-electron count is

\[ 26-3-18=5, \]

so it is a \(d^5\) ion.

For the approximately octahedral complex, the possibilities are:

State Configuration \(t_{2g}\) occupancy \(e_g\) occupancy Unpaired electrons
High spin \(t_{2g}^{3}e_g^{2}\) \((\uparrow)(\uparrow)(\uparrow)\) \((\uparrow)(\uparrow)\) 5
Low spin \(t_{2g}^{5}e_g^{0}\) \((\uparrow\downarrow)(\uparrow\downarrow)(\uparrow)\) \((\,)(\,)\) 1

For \(u\) unpaired electrons, the spin-only magnetic moment is

\[ \mu_{\mathrm{so}}=\sqrt{u(u+2)}\,\mu_{\mathrm B}. \]

Hence

\[ \mu_{\mathrm{HS}}=\sqrt{5(7)}\,\mu_{\mathrm B} =5.92\ \mathrm{B.M.}, \]

whereas

\[ \mu_{\mathrm{LS}}=\sqrt{1(3)}\,\mu_{\mathrm B} =1.73\ \mathrm{B.M.}. \]

The measured moment, \(6.13\ \mathrm{B.M.}\), is close to the five-unpaired-electron prediction. Therefore,

\[ \boxed{\text{A contains high-spin iron(III), }t_{2g}^{3}e_g^{2}}. \]

The measured magnetic moment is the best evidence.

4.7 — Absorption maximum of A

The observed colour is yellow. Table 4c identifies yellow as the complementary colour to absorbed blue light at \(450\ \mathrm{nm}\). Therefore,

\[ \boxed{\lambda_{\max}\approx450\ \mathrm{nm}}. \]

This is the estimate obtained from the supplied colour table.

4.8 — Spin-only magnetic moment of B

Chromium(III), \(\ce{Cr^{3+}}\), SMILES [Cr+3], has

\[ 24-3-18=3 \]

\(d\)-electrons.

In an octahedral field its configuration is \(t_{2g}^{3}e_g^{0}\), with one electron in each \(t_{2g}\) orbital. Thus there are three unpaired electrons:

\[ \mu_{\mathrm{so}} =\sqrt{3(3+2)}\,\mu_{\mathrm B} =\sqrt{15}\,\mu_{\mathrm B} =\boxed{3.87\ \mathrm{B.M.}}. \]

4.9 — Composition and formula of B

Again using a \(100.000\ \mathrm g\) sample,

\[ n_{\ce{Cr}}=\frac{8.440}{52} =0.16231\ \mathrm{mol}. \]

The ligand-to-chromium ratio from the carbon analysis is

\[ x= \frac{38.930/(10\times12)}{8.440/52} =1.9988 \approx\boxed{2}. \]

The total number of chlorine atoms per chromium atom is

\[ y+z= \frac{17.250/35.45}{8.440/52} =2.9980 \approx3. \]

The oxygen percentage by difference is

\[ w_{\ce O} =100-(8.440+38.930+2.920+17.250+9.080) =23.380\%. \]

The complete elemental ratios are:

Element Atomic ratio relative to Cr
Cr 1.000
C 19.988
H 17.991
Cl 2.998
N 3.996
O 9.003

Thus

\[ \boxed{\text{empirical formula of B}=\ce{C20H18Cl3CrN4O9}}. \]

Two ligands contribute four oxygen atoms and the water contributes one. The remaining four oxygen atoms belong to one perchlorate:

\[ 4+1+4z=9 \quad\Longrightarrow\quad \boxed{z=1}. \]

Since \(y+z=3\),

\[ \boxed{y=2}. \]

This agrees with the electrolyte information. Two neutral ligands and two coordinated chloride ions, SMILES [Cl-], give a complex cation of charge

\[ +3+2(0)+2(-1)=+1. \]

One perchlorate counterion then gives a 1 : 1 electrolyte:

\[ \boxed{\ce{B = [CrL2Cl2]ClO4 * H2O} =\ce{[Cr(C10H8N2O2)2Cl2]ClO4 * H2O}}. \]

The compound is bis(2,2′-bipyridine N,N′-dioxide)dichloridochromium(III) perchlorate monohydrate, with SMILES:

[Cr+3]12(<-[Cl-])(<-[Cl-])(<-[O-][n+]3ccccc3-c3cccc[n+]3[O-]->1)<-[O-][n+]3ccccc3-c3cccc[n+]3[O-]->2.[O-]Cl(=O)(=O)=O.O

Its bis(L)dichloridochromium(III) cation has SMILES:

[Cr+3]12(<-[Cl-])(<-[Cl-])(<-[O-][n+]3ccccc3-c3cccc[n+]3[O-]->1)<-[O-][n+]3ccccc3-c3cccc[n+]3[O-]->2

The four oxygen donors and two chlorido donors give approximately octahedral coordination. The information supplied does not select a cis or trans arrangement of the chlorido ligands.

The dissolution equation is

\[ \ce{[CrL2Cl2]ClO4 * H2O(s) -> [CrL2Cl2]^+(aq) + ClO4^-(aq) + H2O(l)}, \]

confirming the \(1:1\) cation-to-anion ratio.

The solution was checked against the official solution.