Chemistry Objective Questions and Answers: The Solid State
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Multiple Choice Questions
(a) 1
(b) 2
(c) 3
(d) 4
Show Answer & Explanation
Answer: (d) 4
Explanation:
1. Let Fe²⁺ = x and Fe³⁺ = y: x + y = 0.93 and 2x + 3y = 2 (charge balance), giving x = 0.79 and y = 0.14 (B true).
2. Only Fe²⁺ is oxidised to Fe³⁺, so 0.79 mol of electrons are lost per mole: equivalent weight = M/0.79 (A true).
3. The oxide ions form a ccp lattice with some Fe sites vacant (C true). % Fe²⁺ = 0.79/0.93 = 85 %, Fe³⁺ = 15 % (D true). All four are correct.
Teacher's Note:
1. Use charge neutrality to find the Fe²⁺ : Fe³⁺ ratio in non-stoichiometric oxides.
2. Metal deficiency defect: some cations are missing and some others are in a higher oxidation state.
(a) X₂Y1.5
(b) X2.5Y
(c) XY2.5
(d) X1.5Y₂
Show Answer & Explanation
Answer: (d) X1.5Y₂
Explanation:
1. X: 4 alternate corners × 1/8 = 0.5, plus 1 at the centre = 1.5.
2. Y: two-thirds of 6 faces = 4 faces, each shared by 2 cells: 4 × 1/2 = 2.
3. Formula = X1.5Y₂.
Teacher's Note:
1. A corner atom contributes 1/8, a face-centre atom 1/2 and a body-centre atom 1 to the unit cell.
2. Count the atoms of each element, then write the simplest ratio.
(a) 1.20 × 10²²
(b) 2.41 × 10²²
(c) 3.61 × 10²²
(d) 7.22 × 10²²
Show Answer & Explanation
Answer: (c) 3.61 × 10²²
Explanation:
1. In a close-packed structure each atom has 1 octahedral void and 2 tetrahedral voids, i.e. 3 voids per atom.
2. Number of atoms = 0.02 × 6.02 × 10²³ = 1.204 × 10²².
3. Total voids = 3 × 1.204 × 10²² = 3.61 × 10²² (that is 36 × 10²¹).
Teacher's Note:
1. Voids per atom: octahedral 1 and tetrahedral 2 in both ccp and hcp.
2. Convert moles to atoms with Avogadro's number first.
(a) 2
(b) 4
(c) 6
(d) 8
Show Answer & Explanation
Answer: (b) 4
Explanation:
1. Z = ρ a³ NA/M with a = 5.0 × 10⁻⁸ cm, so a³ = 1.25 × 10⁻²² cm³.
2. Z = 4.0 × 1.25 × 10⁻²² × 6.0 × 10²³/72 = 300/72 = 4.17.
3. Nearest integer: Z = 4.
Teacher's Note:
1. Convert the edge to cm before cubing it.
2. Z must be a whole number; round off to the nearest integer.
(a) 59 %
(b) 41 %
(c) 83 %
(d) 17 %
Show Answer & Explanation
Answer: (a) 59 %
Explanation:
1. Let M²⁺ = x and M³⁺ = y per formula unit: x + y = 0.83 and 2x + 3y = 2.
2. Solving: y = 2 − 1.66 = 0.34 and x = 0.49.
3. % M²⁺ = 0.49/0.83 × 100 ≈ 59 %.
Teacher's Note:
1. Use charge balance with the oxide ion charge of −2.
2. The cation deficiency is compensated by some ions being in the higher oxidation state.
(a) 2
(b) 1
(c) 8
(d) 4
Show Answer & Explanation
Answer: (d) 4
Explanation:
1. Density ρ = ZM/(NAa³), so the ratio ρfcc/ρbcc = (Zfcc/afcc³)/(Zbcc/abcc³).
2. Zfcc = 4 and Zbcc = 2: ratio = (4/8)/(2/15.625) = 0.5/0.128 = 3.9.
3. Nearest integer: 4.
Teacher's Note:
1. For the same metal M and NA cancel.
2. Z = 4 for fcc and Z = 2 for bcc.
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FAQs
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