# 10.6 Lattice structures in crystalline solids  (Page 6/29)

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## Occupancy of tetrahedral holes

Zinc sulfide is an important industrial source of zinc and is also used as a white pigment in paint. Zinc sulfide crystallizes with zinc ions occupying one-half of the tetrahedral holes in a closest-packed array of sulfide ions. What is the formula of zinc sulfide?

## Solution

Because there are two tetrahedral holes per anion (sulfide ion) and one-half of these holes are occupied by zinc ions, there must be $\frac{1}{2}\phantom{\rule{0.4em}{0ex}}×\phantom{\rule{0.2em}{0ex}}2,$ or 1, zinc ion per sulfide ion. Thus, the formula is ZnS.

## Check your learning

Lithium selenide can be described as a closest-packed array of selenide ions with lithium ions in all of the tetrahedral holes. What it the formula of lithium selenide?

Li 2 Se

The ratio of octahedral holes to anions in either an HCP or CCP structure is 1:1. Thus, compounds with cations in octahedral holes in a closest-packed array of anions can have a maximum cation:anion ratio of 1:1. In NiO, MnS, NaCl, and KH, for example, all of the octahedral holes are filled. Ratios of less than 1:1 are observed when some of the octahedral holes remain empty.

## Stoichiometry of ionic compounds

Sapphire is aluminum oxide. Aluminum oxide crystallizes with aluminum ions in two-thirds of the octahedral holes in a closest-packed array of oxide ions. What is the formula of aluminum oxide?

## Solution

Because there is one octahedral hole per anion (oxide ion) and only two-thirds of these holes are occupied, the ratio of aluminum to oxygen must be $\frac{2}{3}$ :1, which would give ${\text{Al}}_{2\text{/}3}\text{O}.$ The simplest whole number ratio is 2:3, so the formula is Al 2 O 3 .

## Check your learning

The white pigment titanium oxide crystallizes with titanium ions in one-half of the octahedral holes in a closest-packed array of oxide ions. What is the formula of titanium oxide?

TiO 2

In a simple cubic array of anions, there is one cubic hole that can be occupied by a cation for each anion in the array. In CsCl, and in other compounds with the same structure, all of the cubic holes are occupied. Half of the cubic holes are occupied in SrH 2 , UO 2 , SrCl 2 , and CaF 2 .

Different types of ionic compounds often crystallize in the same structure when the relative sizes of their ions and their stoichiometries (the two principal features that determine structure) are similar.

## Unit cells of ionic compounds

Many ionic compounds crystallize with cubic unit cells, and we will use these compounds to describe the general features of ionic structures.

When an ionic compound is composed of cations and anions of similar size in a 1:1 ratio, it typically forms a simple cubic structure. Cesium chloride, CsCl, (illustrated in [link] ) is an example of this, with Cs + and Cl having radii of 174 pm and 181 pm, respectively. We can think of this as chloride ions forming a simple cubic unit cell, with a cesium ion in the center; or as cesium ions forming a unit cell with a chloride ion in the center; or as simple cubic unit cells formed by Cs + ions overlapping unit cells formed by Cl ions. Cesium ions and chloride ions touch along the body diagonals of the unit cells. One cesium ion and one chloride ion are present per unit cell, giving the l:l stoichiometry required by the formula for cesium chloride. Note that there is no lattice point in the center of the cell, and CsCl is not a BCC structure because a cesium ion is not identical to a chloride ion.

#### Questions & Answers

mention some examples of ester
do you mean ether?
Megan
what do converging lines on a mass Spectra represent
would I do to help me know this topic ?
Bulus
oi
Amargo
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who is albert heistein?
Bassidi
similarities between elements in the same group and period
what is the ratio of hydrogen to oxulygen in carbohydrates
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what is poh and ph
please what is the chemical configuration of sodium
Sharon
2.8.1
david
1s²2s²2p⁶3s¹
Haile
2, 6, 2, 1
Salman
1s2, 2s2, 2px2, 2py2, 2pz2, 3s1
Justice
1s2,2s2,2py2,2
Maryify
1s2,2s2,2p6,
Francis
1s2,2s2,2px2,2py2,2pz2,3s1
Nnyila
what is criteria purity
cathode is a negative ion why is it that u said is negative
cathode is a negative electrode while cation is a positive ion. cation move towards cathode plate.
king
CH3COOH +NaOH ,complete the equation
compare and contrast the electrical conductivity of HCl and CH3cooH
The must be in dissolved in water (aqueous). Electrical conductivity is measured in Siemens (s). HCl (aq) has higher conductivity, as it fully ionises (small portion of CH3COOH (aq) ionises) when dissolved in water. Thus, more free ions to carry charge.
Abdelkarim
HCl being an strong acid will fully ionize in water thus producing more mobile ions for electrical conduction than the carboxylic acid
Valentine
differiante between a weak and a strong acid
david
how can I tell when an acid is weak or Strong
Amarachi
an aqueous solution of copper sulphate was electrolysed between graphite electrodes. state what was observed at the cathode
write the equation for the reaction that took place at the anode
Bakanya
what is enthalpy of combustion
Bakanya
Enthalpy change of combustion: It is the enthalpy change when 1 mole of substance is combusted with excess oxygen under standard conditions. Elements are in their standard states. Conditions: pressure = 1 atm Temperature =25°C
Abdelkarim
Observation at Cathode: Cu metal deposit (pink/red solid).
Abdelkarim
Equation at Anode: (SO4)^2- + 4H^+ + 2e^- __> SO2 + 2H2O
Abdelkarim
Equation : CuSO4 -> Cu^2+ + SO4^2- equation at katode: 2Cu^2+ + 4e -> 2Cu equation at anode: 2H2O -> 4H+ + O2 +4e at the anode which reacts is water because SO4 ^ 2- cannot be electrolyzed in the anode
Niken
what is the electrolysis of sulphuric acid
why is electrolysis difficult using solid lead chloride
Bakanya
what is heat formation
what are atoms
this are small substances that form together and complained one
Belvine
okay gud
Bol
what's covalent bonding
Covalent bonds are characterized by the sharing of electrons between two or more atoms. These bonds mostly occur between nonmetals or between two of the same (or similar) elements.
Haile
covalent bonding is the mutual sharing of electrons between two element in a molecule, usually it involves non metals as they are less ionic and more electronegative than metals( ionic). and these bonds have high enthalpy of formation. and are strong bonds than most of the bond.
Chiranjeev
covalent bonding involves both nonmetals where there is complete sharing of electrons on the outermost energy level
david
I don't understand
Belvine