Inorganic Solids Questions and Answers

Answer: B

The inverse spinel is Fe₃O₄.

In magnetite, Fe^IIFe^III₂O₄, the Fe³⁺ ions are split between tetrahedral and octahedral sites while all the Fe²⁺ ions are octahedral: Fe³⁺[Fe²⁺Fe³⁺]O₄. The reason is crystal field stabilisation. High-spin d⁵ Fe³⁺ gains no CFSE in either site, while high-spin d⁶ Fe²⁺ gains more in an octahedral site, so Fe²⁺ takes the octahedral holes.

Co₃O₄ is normal because low-spin d⁶ Co³⁺ has a very large octahedral preference. Mn₃O₄ is a (distorted) normal spinel with d⁵ Mn²⁺ tetrahedral, and the magnesium aluminium spinel is the prototype normal spinel.

Answer: D

The cations occupy ½ of the octahedral sites and ⅛ of the tetrahedral sites.

A cubic close-packed array of n anions has n octahedral holes and 2n tetrahedral holes. Per formula unit MgAl₂O₄ there are four oxide ions, so 4 octahedral and 8 tetrahedral holes.

MgAl₂O₄ is a normal spinel: the one Mg²⁺ sits in a tetrahedral hole and the two Al³⁺ in octahedral holes. So

\[ \begin{aligned} \text{octahedral} &= 2/4 = 1/2 \\ \text{tetrahedral} &= 1/8 \end{aligned} \]

The other options swap the two fractions or use the wrong number of sites: ¼ would mean one cation per four holes, which is neither the Mg nor the Al count.

Answer: A

The borides with isolated boron atoms are Tc₇B₃ and Re₇B₃.

In metal borides the arrangement of boron follows the metal-to-boron ratio. When metal is in large excess, as in M₃B and M₇B₃, the boron atoms are too far apart to bond to one another and sit isolated in holes of the metal lattice.

As the boron content rises, boron atoms link up: M₃B₂ borides such as V₃B₂ contain B₂ pairs, monoborides such as TiB and HfB contain zigzag chains of boron, and M₃B₄-type borides such as V₃B₄ contain double chains. So the options containing V₃B₂, V₃B₄, or TiB and HfB all include borides with boron-boron bonds.

Answer: B

The lattice energies increase as KF < NaF < CaO < MgO.

For compounds with the same (NaCl) structure, lattice energy varies roughly as \(z^{+}z^{-}/(r^{+} + r^{-})\). The oxides combine 2+ and 2− ions, so their charge product is four times that of the fluorides, and they lie far above them: MgO and CaO have lattice energies of several thousand kJ mol⁻¹, NaF and KF under one thousand.

Within each pair the smaller cation wins: Na⁺ is smaller than K⁺, and Mg²⁺ smaller than Ca²⁺. That gives KF < NaF and CaO < MgO. Options putting a fluoride above an oxide, or reversing the size order, fail.

Answer: B

The smallest detectable spacing is 0.77 Å.

Bragg's law for first-order diffraction is \(\lambda = 2d\sin\theta\). Since \(\sin\theta\) cannot exceed 1, a reflection exists only when \(d \ge \lambda/2\):

\[ \begin{aligned} d_{min} &= \frac{\lambda}{2} \\ &= \frac{1.54\ \text{Å}}{2} = 0.77\ \text{Å} \end{aligned} \]

A spacing of 0.38 Å is about \(\lambda/4\); it would need \(\sin\theta = 2\), so no first-order reflection is possible. Spacings of 1.02 and 2.05 Å do diffract, at smaller angles, but they are not the smallest value that can be detected.

Answer: B

The lowest melting point belongs to AlBr₃.

Aluminium bromide melts at about 98 ℃, while LiBr, NaBr and MgBr₂ all melt above 550 ℃. The reason is the nature of the bonding. Al³⁺ is very small and highly charged, so it strongly polarises the large, soft bromide ion (Fajans' rules). The bonding becomes largely covalent, and the solid is built from discrete Al₂Br₆ molecules held together only by weak intermolecular forces.

LiBr, NaBr and MgBr₂ are ionic lattices, in which melting means overcoming strong electrostatic attraction throughout the crystal. LiBr and MgBr₂ have some covalent character from their small cations, but far less than AlBr₃, so their melting points stay high.

Answer: A

The least efficiently packed solid is caesium chloride.

The comparison the question intends is between the frameworks of the four structures. In CsCl the chloride ions form a simple cubic arrangement, with Cs⁺ at the body centre and 8:8 coordination. A simple cubic array fills only about 52% of space, against 74% for a close-packed array.

The other three are all built on close-packed anions. In cadmium iodide the I⁻ ions are hexagonally close packed, with Cd²⁺ in half the octahedral holes, in alternate layers. Wurtzite has S²⁻ in hexagonal close packing and zinc blende has S²⁻ in cubic close packing, each with Zn²⁺ in half the tetrahedral holes. Since all three start from 74% packing, CsCl, with its non-close-packed cubic framework, is the least efficient.

Answer: B

Glass has Si-O bonds.

Ordinary glass is made mainly of silica (silicon dioxide) with sodium and calcium oxides. Its structure is a disordered network of \(\mathrm{SiO_{4}}\) tetrahedra joined through shared oxygen atoms, so the framework is held together by silicon-oxygen bonds.

Carbon-oxygen bonds belong to organic compounds and carbonates, and germanium or tin oxides are not the basis of common glass.

Answer: C

Concrete gains strength due to hydration of cement.

When water is added, the calcium silicates in cement react with it to form calcium silicate hydrate gel and calcium hydroxide. The gel binds the sand and aggregate together and hardens over time, which is why concrete must be cured (kept moist) to gain strength.

Sand and coarse aggregate are inert fillers and do not react with cement, and evaporation of water halts hydration and weakens concrete, so the other options are wrong.

Answer: D

Waterproof cement contains all of the above.

Waterproofing compounds are added to ordinary Portland cement to make the set concrete repel water. Metallic soaps such as calcium stearate and aluminium stearate line the pores with a water-repellent film, and tannic acid is another additive used to reduce permeability.

Since all three substances are used for this purpose, each single option is incomplete.