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Case Study Questions

5 x 4 = 20

Read the passage given below and answer the following questions:
The idealized ionic solid consists of two interpenetrating lattices of oppositely-charged point charges that are held in place by a balance of coulombic force of long range. But real ions occupy space, no such "perfect" ionic solid exists in nature. Chemists usually apply the term "ionic solid" to binary compounds of the metallic elements of groups 1 - 2 with one of the halogen elements or oxygen. The most well known ionic solid is sodium chloride, also known by its geological names as rock-salt or halite. Structurally, each ion in sodium chloride is surrounded and held in tension by six neighbouring ions of opposite charge; this is known as (6, 6) coordination. The resulting crystal lattice is of a type known as simple cubic. There are many other fundamental ionic structures (not all cubic) and these are:
Zinc blende structure (ZnS) : having ccp arrangement of S^2- and Zn²⁺ in alternate tetrahedral voids; Wurtzite structure (ZnS) : having hcp arrangement of S^2- and Zn²⁺in alternate tetrahedral voids; Fluorite structure (CaF₂) : having ccp arrangement of Ca²⁺ and F^- in all tetrahedral voids; Antifluorite structure (Na₂O): having ccp arrangement of O^2- and Na⁺ in all tetrahedral voids. These solids tend to be quite hard and have high melting points.
The following questions are multiple choice questions. Choose the most appropriate answer:
(i) In NaCl crystal, each Cl^- ion is surrounded by

(a) 4 Na⁺ions

(b) 6 Na⁺ions

(c) 1Na⁺ion

(d) 2 Na⁺ions.

(ii) In an antifluorite structure, cations occupy

(a) tetrahedral voids

(b) centre of cube

(c) octahedral voids

(d) corners of cube

(iii) Antifluorite structure is derived from fluorite structure by

(a) heating fluorite crystal lattice

(b) subjecting fluorite structure to high pressure

(c) interchanging the positions of positive and negative ions in the lattice

(d) none of these.

(iv) Ionic solid BaF₂ has which kind of structure?

(a) Fluorite

(b) Antifluorite

(c) Wurtzite

(d) Rock-salt

Read the passage given below and answer the following questions:
In an ideal crystal, there must be regular repeating arrangement of the constituting particles and its entropy must be zero at absolute zero temperature. However, it is impossible to obtain an ideal crystal and it suffers from certain defects called imperfections. In pure crystal, these defects arises either due to disorder or dislocation of the constituting particles from their normal positions or due to the movement of the particles even at absolute zero temperature. Such defects increase with rise in temperature. In addition to this, certain defects arise due to the presence of some impurities. Such defects not only modify the existing properties of the crystalline solids but also impart certain new characteristics to them.
The following questions are multiple choice questions. Choose the most appropriate answer:
(i) AgCI is crystallized from molten AgCI containing a little CdCI₂. The solid obtained will have

(a) cationic vacancies equal to number of Cd²⁺ ions incorporated

(b) cationic vacancies equal to double the number of Cd²⁺ ions

(c) anionic vacancies

(d) neither cationic nor anionic vacancies.

(ii)The ionic substances in which the cation and anion are of almost similar size shows

(a) non-stoichiometric defect	(b) Schottky defect
(c) Frenkel defect	(d) all of these.

(iii) If A1³⁺ions replace Na⁺ ions at the edge centres of NaCl lattice, then the number of vacancies in 1mole of NaCI will be

(a) 3.01 x 10²³

(b) 6.02 x 10²³

(c) 9.03 x 10²³

(d) 12.04 x 10²³

(iv) Which of the following gives both Frenkel and Schottky defect?

(a) AgCl

(b) CsCI

(c) KCI

(d) AgBr

Read the passage given below and answer the following questions:
In ideally ionic structures, the coordination numbers of the ions are determined by electrostatic considerations. Cations surround themselves with as many anions as possible and vice versa. This maximizes the attractions between neighbouring ions of opposite charge and hence maximizes the lattice energy of the crystal. This requirement led to the formulation of the radius ratio rule for ionic structures in which the ions and the structure adopted for a particular compound depend on the relative sizes of the ions. Thus, for the stable ionic crystalline structures, there is definite radius ratio limit for a cation to fit perfectly in the lattice of anions, called radius ratio rule. This depends upon the ratio of radii of two types of ions, r₊/r_-.
This ratio for coordination numbers 3, 4, 6 and 8 are respectively 0.155 - 0.225, 0.225 - 0.414, 0.414 - 0.732 and 0.732 - 1.000. The coordination number of ionic solids also depends upon temperature and pressure. On applying high pressure, coordination number increases. On the other hand, on applying high temperature, it decreases.
The following questions are multiple choice questions. Choose the most appropriate answer:
(i) The ionic radii of K⁺, Rb⁺ and Br^-are 137, 148 and 195 pm. The coordination number of cation in RbBr and KBr structures are respectively

(a) 8,6

(b) 6,4

(c) 6,8

(d) 4,6

(ii) If the radius of Na⁺ion is 95 pm and that of Cl^-ion is 181 pm, the coordination number of Na⁺ion is

(a) 6

(b) 4

(c) 8

(d) 12

(iii) Which is not the correct statement for ionic solids in which positive and negative ions are held by strong electrostatic attractive forces?

(a) The radius ratio r₊/r_- increases as coordination number increases

(b) As the difference in size of ions increases, coordination number increases.

(c) When coordination number is eight, r₊/r_- ratio lies between 0.225 to 0.414

(d) In ionic solid of the type AX (ZnS, wurtzite), the coordination number of Zn²⁺ and S^2- respectively are 4 and 4

(iv) If the pressure of CsCl is increased, then its coordination number will

(a) increase

(b) remain the same

(c) decrease

(d) none of these

Read the passage given below and answer the following questions:
In contrast to the disorders of gases and liquids, there is translational order in crystals. However, disordered or amorphous solids also exist which lack such order, they are really highly viscous liquids. In translational order entire structure or lattice, can be generated by repeated replication of a small regular figure, termed as unit cell. The planes of any crystalline structure can be specified using Miller indices, which is also serve to identify single crystal faces.
The ordered structure or lattice, of a solid can be determined by X-ray or neutron diffraction studies, in which a beam of X-rays of neutrons is scattered from the sample to produce a diffraction pattern which can be analyzed to reveal the crystal structure of the sample. All crystal lattices can be classified into 14 Bravais lattices belonging to 7 systems. For example, the simple cubic, face-centred cubic and body-centred cubic lattices are the 3 lattices of the cubic system. Cubic and hexagonal close- packed structures have the structure of tightly packed spheres where each sphere touches 12 neighbours, 6 in the same plane and 3 above and 3 below. These two close-packed structures differ in the placement of successive planes or layers. For the hexagonal close packing, a third layer is laid down to reproduce the first layer, so that the structure could be represented by ABABAB .... For cubic close packing, third layer is again displaced, corn spending to ABCABC ...
The following questions are multiple choice questions. Choose the most a propriate answer:
(i) In hexagonal close packing, a sphere has coordination number of

(a) 4

(b) 6

(c) 8

(d) 12

(ii) Which of the following arrangements correctly represents hexagonal and cubic close packed structure respectively?

(a) ABCABC .. and ABAB ...	(b) ABAB ... and ABCABC ..
(c) Both have ABAB ... arrangement.	(d) Both have ABCABC .. arrangement

(iii) The arrangement of the first two layers, one above the other in hep and eep arrangements is

(a) exactly same in both cases	(b) partly same and partly different
(c) different from each other	(d) nothing definite

(iv) Which of the following statements about amorphous solids is incorrect?

(a) They melt over a range of temperature.

(b) There is no orderly arrangement of particles.

(c) They are anisotropic

(d) They are rigid and incompressible.

Read the passage given below and answer the following questions:
The adjective, 'crystalline' when applied to solids, implies an ideal crystal in which the structural units, termed as unit cells, are repeated regularly and indefinitely in three dimensions in space. The unit cell, containing at least one molecule, has a definite orientation and shape defined by the translational vectors, a, band c. The unit cell therefore has a definite volume, V that contains the atoms and molecules necessary for generating the crystal. Every crystal can be classified as a member of one of the seven possible crystal systems or crystal classes that are defined by the relationships between the individual dimensions, a, band c of the unit cell and between the individual angles, \(\alpha, \beta \ and \ \gamma\) of the unit cell. The structure of the given crystal may be assigned to one of the 7 crystal systems, to one of the 14 Bravais lattices, and to one of the 230 space groups. These uniquely define the possible ways of arranging atoms in a three-dimensional solid. Based on these observations, seven crystal systems were identified: triclinic, monoclinic, trigonal or rhombohedral, tetragonal, hexagonal, rhombic or orthorhombic and cubic.
The following questions are multiple choice questions. Choose the most appropriate answer :
(i) The crystal system of a compound with unit cell dimensions, a = 0.387 nm, b = 0.387 nm and c = 0.504 nm and \(\alpha, \beta \ =90^o\) and \(\gamma\) = 120° is

(a) cubic

(b) hexagonal

(c) orthorhombic

(d) rhombohedral.

(ii) The unit cell with the structure given below represents __________crystal system.

a) cubic

(b) orthorhombic

(c) tetragonal

(d) trigonal

(iii) In a triclinic crystal

\(\text { (a) } a=b=c, \quad \alpha=\beta=\gamma \neq 90^{\circ}\)	\(\text { (b) } a \neq b=c, \quad \alpha=\beta=\gamma=90^{\circ}\)
\(\text { (c) } a \neq b \neq c, \quad \alpha \neq \beta \neq \gamma \neq 90^{\circ}\)	\(\text { (d) } a \neq b \neq c, \quad \alpha=\gamma=90^{\circ}, \beta \neq 90^{\circ}\)

(iv) The unit cell with dimensions \(\alpha=\beta=\gamma=90^{\circ}, a=b \neq c \) is

(a) cubic

(b) triclinic

(c) hexagonal

(d) tetragonal

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Answers Key:

Case Study Questions

5 x 4 = 20

(i) (b): In NaCl crystal, each Cl^-ion is surrounded by 6 Na⁺ions.
(ii) (a): Anti-fluorite structure (NaCl) have eep arrangement of O^2- and Na⁺ in all tetrahedral voids.
(iii) (c) : Antifluorite structure is derived from fluorite structure by interchanging the positions of positive and negative ions.
(iv) (a) : BaF₂ has fluorite structure.

(i) (a): In the crystallisation, some Ag⁺ions will get replaced by Cd²⁺ ions and each Cd²⁺ ion replaces two Ag⁺ions so as to maintain electrical neutrality. Thus, the cation vacancies will be the same as the number of Cd²⁺ ions incorporated.
(ii) (b): Number of defects per mole of NaCl
\(=\frac{1 \times 6.02 \times 10^{23}}{10^{15}}=6.02 \times 10^{8}\)
(iii) (a) : There are 12 edge centres
Contribution of Na⁺ions at edge centres \(=12 \times \frac{1}{4}=3\)
Besides, there is one Na⁺ion at body centre
Thus, there are four Na⁺ions per unit cell.
\(\frac{3}{4}\) are replaced by Al³⁺ ions.
Total Na⁺ions in 1 mole of NaCl = 6.023 x 10²³
Na⁺ion replaced by Al³⁺= 3/4 x 6.023 x 10²³
1 Al³⁺ replaces 3 Na⁺ions thereby creating 2 vacancies.
\(\therefore\) No. of vacancies created \(=\frac{2}{3} \times\left(\frac{3}{4} \times 6.023 \times 10^{23}\right)\)
= 3.01 x 10²³
(iv) (d): In AgBr, Ag⁺ions are small in size and when removed from lattice point they can occupy interstitial site and therefore show both Frenkel and Schottky defects.

\(\text { (i) }(a): \frac{r\left(\mathrm{Rb}^{+}\right)}{r\left(\mathrm{Br}^{-}\right)}=\frac{148}{195}=0.76(\text { C.N. } 8 \text { above } 0.732)\)
\(\frac{r\left(\mathrm{~K}^{+}\right)}{r\left(\mathrm{Br}^{-}\right)}=\frac{137}{195}=0.702 \text { (C.N. } 6 \text { between } \left.0.414-0.732\right)\)
\({ (ii) }(a): \frac{r_{+}}{r_{-}}=\frac{r\left(\mathrm{Na}^{+}\right)}{r\left(\mathrm{Cl}^{-}\right)}=\frac{95}{181}=0.524\)
The radius ratio lies between 0.414 - 0.732.
Hence, Na ⁺ ions prefer to occupy octahedral holes having coordination number 6.
(iii) (c): When coordination number is 8, r₊/r_- ratio lies between 0.732 - 1.
(iv) (a): If the pressure of CsCl is increased, then its coordination number will increase.

(i) (d): For hep packing, the coordination number of each sphere is 12 (6 in its own layer, 3 in the upper layer and 3 in the lower layer).
(ii) (b): In hexagonal close packing, each sphere of third layer lies exactly above the sphere of first layer.
Thus, hep is abbreviated as ABAB ....
In cubic close packing, the spheres of third layer do not come over those of first layer and spheres of fourth layer correspond with those in first layer. Thus, it is represented as ABCABC ....
(iii) (a)
(iv) (c): They are isotropic as they show same properties in all directions.

(i) (b): For hexagonal crystal system, \(a=b \neq c\) and \(\alpha=\beta=90^{\circ}, \gamma=120^{\circ}\)
(ii) (a): Here, \(a=b=c ; \alpha=\beta=\gamma=90^{\circ}\) It belongs to cubic system.
(iii) (c)
(iv) (d): For tetragonal crystal system \(a=b \neq c \text { and }\)\(\alpha=\beta=\gamma=90^{\circ}\)