Bohemian garnet (pyrope) is a famous Czech blood coloured semi-precious stone. The chemical composit — Physical Chemistry Chemistry Question
Bohemian garnet
Bohemian garnet (pyrope) is a famous Czech blood coloured semi-precious stone. The chemical composition of natural garnets is expressed by the general stoichiometric formula of A3B2(SiO4)3, where AII is a divalent cation and BIII is a trivalent cation. Garnets have a cubic unit cell that contains 8 formula units. The structure comprises 3 types of polyhedra: the AII cation occupies a dodecahedral position (it is surrounded with eight O atoms), the BIII cation occupies an octahedral position (it is surrounded with six O atoms) and the SiIV cation occupies a tetrahedral position (it is surrounded with four O atoms).
Calculate the theoretical density of almandine.
Model Answer
M(almandine) = 497.75 g mol−1
ρ = m / V = (8 × M) / (NA × a3) = (8 × 497.75) / [6.022×10^23 × (11.50×10−8)3] = 4.35 g cm−3
Draw the splitting diagram for the [CrIIIO6]oct d-orbitals and fill it with electrons.
Identify the 1st transition row element(s) whose trivalent cation(s) MIII placed in an octahedral position is/are diamagnetic in the low-spin arrangement and paramagnetic in the high-spin arrangement.
The figure below shows d-orbitals splitting in the dodecahedral crystal field. Fill in the electrons for the [FeIIO8]dod chromophore for both existing arrangements.
Derive the inequalities (e.g. P < E1 + E2 + E3) for the pairing energy (P) magnitude Cr, Ni in relation to energies E1, E2 and E3 for both arrangements.
Assuming that P > E3, identify the 1st transition row element(s) whose divalent cation MII placed in dodecahedral position is diamagnetic in the low-spin arrangement and paramagnetic in the high-spin arrangement.
Match the spectra with the minerals.
Model Answer
Bohemian garnet: B
Sapphire: D
Uvarovite: C
Citrine: A
If illuminated with monochromatic blue-green light, how will the Bohemian garnet look?
Options: Red / Blue / Yellow-orange / Black / Yellow / Blue-green / Violet / White
Model Answer
Black
Calculate the percentage of SiIV ions in a sample of schorlomite that must be substituted with FeIII, if we know that 5% of FeIII ions in octahedral position are substituted with TiIV.
Model Answer
Both substitutions change the charge by 1 unit per ion. Taking total number of ions in formula into consideration we get:
5% × 2 = p × 3
p = 3.33%
The figures below show simplified absorption spectra of four coloured minerals –
5.10 Draw the d-orbitals splitting diagrams for both chromophores and fill in the ...
Model Answer
[FeIIIO6]oct: [FeIIIO4]tet:
Calculate the size of pairing energy (P) and the sizes of Δoct and Δtet splitting. Assume that the pairing energy is equal in both chromophores.
Model Answer
Because Δoct < P (high-spin configuration in tetrahedral as well as in octahedral field), the wavenumber corresponds to electron transition from the upper to the lower level in both cases and thus:
11 000 cm−1 = P − Δoct
22 000 cm−1 = P − Δtet = P − (4/9)Δoct
By solving the system of these equations we get:
P = 30 800 cm−1
Δoct = 19 800 cm−1
Δtet = 8 800 cm−1
Alternative solution (low-spin octahedral, high-spin tetrahedral):
11 000 cm–1 = Δoct – P
22 000 cm−1 = P − Δtet = P − (4/9)Δoct
P = 48 400 cm−1, Δoct = 59 400 cm−1, Δtet = 26 400 cm−1
Based on your knowledge of the relative ion radii, determine which cation occupies which position.
Model Answer
A: YIII B: AllII Si: AlIII
For the use in LED technology, YAG is doped with CeIII. Determine the values of x and y in the formula of YAG in which 5% of yttrium atoms are substituted with cerium. (If you don’t get result, use x = 2.25 and y = 0.75.)
Model Answer
YxCeyAl5O12 x = 2.85 y = 0.15
The CeIII-doped YAG is prepared by annealing the mixture of Y2O3, Al2O3 and CeO2 in H2 atmosphere. Use the formula from 5.13, write down a balanced equation for this reaction with the smallest whole-number stoichiometric coefficients.
Model Answer
57 Y2O3 + 6 CeO2 + 100 Al2O3 + 3 H2 40 Y2.85Ce0.15Al5O12 + 3 H2O
(or 2 Y57Ce3Al100O240 + 3 H2O)
for x = 2.25 and y = 0.75:
9 Y2O3 + 6 CeO2 + 20 Al2O3 + 3 H2 8 Y2.25Ce0.75Al5O12 + 3 H2O
(or 2 Y9Ce3Al20O48 + 3 H2O)
Doping the YAG structure with rare-earths ions enables the production of lasers with emission wavelengths ranging from the UV to the mid-IR region. In the scheme below, simplified f–f energy transitions of selected rare-earths ions are shown.
5.15 Which cation has a transition which corresponds to blue light emission.
Er3+ Sm3+
Tm3+ Pr3+
Yb3+ Nd3+ Tb3+
Model Answer
Er3+
Calculate the emission wavelength of this light.
Model Answer
λ = 1 / 2127700 m = 4.70 × 10−7 m = 470 nm
According to a legend, Noah used a stick with a garnet stone for illumination during his voyage. Assuming only the photoluminescence effect, determine the colour of the laser light emitted from his stick if the stone were the blood-coloured Bohemian garnet.
Red Blue Yellow-orange Black
Yellow Blue-green Violet White
Model Answer
Blue-green