chemistry : class12 Unit Cells of Ionic Solids : Ionic solids : Solid State MCQ Questions and Answers
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Unit Cells of Ionic Solids
MCQ questions and answers.
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MCQ Questions
1. In the conventional unit cell of sodium chloride, chloride ions occupy the corners and face centres, while sodium ions occupy the edge centres and body centre. How many NaCl formula units are contained in one unit cell?
A.
1
B.
2
C.
4
D.
8
Correct Answer:
4
Explanation:
The chloride ions contribute 8 × 1/8 + 6 × 1/2 = 4 ions, and the sodium ions contribute 12 × 1/4 + 1 = 4 ions. Therefore, the unit cell contains four NaCl formula units, so Z = 4.
2. For an ideal caesium chloride unit cell, the Cs+ ion is at the body centre and Cl− ions are at the eight corners. If the ionic radii are rCs and rCl and the edge length is a, which relation represents the limiting contact condition?
A.
a = rCs + rCl
B.
√2a = 2(rCs + rCl)
C.
√3a = 2(rCs + rCl)
D.
3a = 2(rCs + rCl)
Correct Answer:
√3a = 2(rCs + rCl)
Explanation:
In the CsCl structure, a central Cs+ ion touches the corner Cl− ions along the body diagonal. The body diagonal is √3a, and it equals twice the sum of the ionic radii: √3a = 2(rCs + rCl).
3. An ionic solid has an anion face-centred cubic lattice, with cations occupying all tetrahedral voids. Which combination correctly describes its unit cell?
A.
4 anions, 4 cations, and coordination number 6 for both ions
B.
4 anions, 8 cations, with cation and anion coordination numbers 4 and 8 respectively
C.
4 anions, 8 cations, with cation and anion coordination numbers 8 and 4 respectively
D.
8 anions, 4 cations, with coordination number 4 for both ions
Correct Answer:
4 anions, 8 cations, with cation and anion coordination numbers 4 and 8 respectively
Explanation:
An FCC lattice contains four anions per unit cell, and an FCC unit cell has eight tetrahedral voids. Filling all of them gives the AB2 stoichiometry, as in an antifluorite arrangement. Each cation is surrounded by four anions, while each anion is surrounded by eight cations.
4. The edge length of a NaCl unit cell is 564 pm. Taking Z = 4 and the molar mass of NaCl as 58.5 g mol−1, what is the approximate theoretical density of NaCl?
A.
1.09 g cm−3
B.
2.17 g cm−3
C.
3.42 g cm−3
D.
4.34 g cm−3
Correct Answer:
2.17 g cm−3
Explanation:
Using ρ = ZM/(N_Aa^3), with a = 564 pm = 5.64 × 10−8 cm, gives ρ = [4 × 58.5]/[6.022 × 10^23 × (5.64 × 10−8)^3] ≈ 2.17 g cm−3.
5. An ionic crystal has one type of ion at the eight corners and the other type at the body centre of a cubic unit cell. If the ions touch along the body diagonal, which statement is correct?
A.
The unit cell contains two formula units and each ion has coordination number 6
B.
The unit cell contains one formula unit and each ion has coordination number 8
C.
The unit cell contains four formula units and each ion has coordination number 4
D.
The unit cell contains one formula unit and each ion has coordination number 12
Correct Answer:
The unit cell contains one formula unit and each ion has coordination number 8
Explanation:
The eight corner ions together contribute one ion, and the body-centred ion contributes one ion, giving one AB formula unit per unit cell. The body-centred ion is surrounded by eight corner ions, and each corner ion is similarly surrounded by eight body-centred ions.
6. For a cubic ionic crystal of the CsCl type, the minimum radius ratio required for the central cation to maintain eightfold coordination is approximately:
A.
0.225
B.
0.414
C.
0.732
D.
1.000
Correct Answer:
0.732
Explanation:
For eightfold cubic coordination, the limiting radius-ratio value is obtained from contact along the body diagonal and is (r+/r−)min = √3 − 1 ≈ 0.732. Below this value, the cation cannot touch all eight surrounding anions without destabilizing the cubic arrangement.
7. In the NaCl structure, anions form an FCC lattice and cations occupy all octahedral voids. How many octahedral voids are present per FCC unit cell, and what fraction of them is occupied?
A.
4 voids; all are occupied
B.
4 voids; half are occupied
C.
8 voids; half are occupied
D.
8 voids; all are occupied
Correct Answer:
4 voids; all are occupied
Explanation:
An FCC unit cell contains one octahedral void at its body centre and twelve edge-centred voids contributing 12 × 1/4 = 3, giving four octahedral voids. In NaCl, all four are occupied, producing four cations and four anions per unit cell.
8. In a NaCl-type unit cell with edge length 560 pm, the nearest Na+–Cl− distance and the number of nearest oppositely charged neighbours for each ion are, respectively:
A.
280 pm and 4
B.
280 pm and 6
C.
560 pm and 6
D.
396 pm and 8
Correct Answer:
280 pm and 6
Explanation:
In the NaCl structure, nearest Na+ and Cl− ions lie along an edge direction with separation a/2. Thus the separation is 560/2 = 280 pm. Each ion has six nearest neighbours of opposite charge, giving octahedral coordination.
9. A cubic ionic solid has density 4.00 g cm−3, molar mass 80.0 g mol−1, and four formula units per unit cell. What is its approximate unit-cell edge length?
A.
316 pm
B.
438 pm
C.
550 pm
D.
780 pm
Correct Answer:
550 pm
Explanation:
From ρ = ZM/(N_Aa^3), a^3 = (4 × 80.0)/(4.00 × 6.022 × 10^23) cm3. Taking the cube root gives a ≈ 5.50 × 10−8 cm = 550 pm.
10. Zinc blende (sphalerite) consists of an FCC arrangement of S2− ions with Zn2+ ions occupying half of the tetrahedral voids. How many ZnS formula units are present in its conventional cubic unit cell, and what is the coordination number of each ion?
A.
2 formula units; coordination number 4
B.
4 formula units; coordination number 4
C.
4 formula units; coordination number 6
D.
8 formula units; coordination number 8
Correct Answer:
4 formula units; coordination number 4
Explanation:
The FCC sulfur lattice contributes four S2− ions per unit cell. Half of the eight tetrahedral voids are occupied, giving four Zn2+ ions. Hence there are four ZnS formula units, and each ion has tetrahedral coordination number 4.
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