a. Outline the principles of Pauling’s 5 rules for predicting the crystal structures of ionic solids. b. Show how Pauling’s rules can be used, together with the data give in Tables 1 and 2, to explain the crystal structure of Na₂O, which is based on an fcc array of oxide ions. Draw a schematic diagram showing a unit cell of this structure. Explain which interstitial sites are occupied by the Na⁺ ions. c. Sketch a plan view of the Na₂O unit cell, marking on your diagram the height of all ions present. d. Calculate a theoretical value for the density of Na₂O, given that the relative atomic masses of sodium and oxygen are 22.99 and 16.00 respectively.

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a. The rules of Pauling’s relating crystal structures are: bonding strength, coordination of the polyhedral, linkage for polyhedral, cation evasion, environment homogeneity.

b. Na₂O

When two sodium atoms combine to form a molecule, they share two electrons. Each atom then has a complete shell of eight electrons. The electron structure of each atom is now like that of neon, the nearest noble gas. A shared pair of electrons, called a covalent bond, is represented by ‘-. ‘ A sodium molecule is written as;
Na – Na
This is the structural formula. It shows how the atoms in the molecule are bonded together. The molecular formula of sodium is Na₂. It shows how many of each type of atom there are in the molecule. After sharing electrons, both hydrogen atoms have complete outer electron shells. In an oxygen molecule, two pairs of electrons must be shared because each oxygen atom needs two extra electrons to have a complete shell.
A ‘double bond’ is formed when two pairs of electrons are shared. It is represented by ‘=.’ The structural formula of oxygen is;
O = O, and the molecular formula is 0₂. For a non-metal compound, a covalent bond holds different atoms together. A molecule of sodium oxide has two atoms of oxygen covalently bonded to an atom of sodium. Hence the structural formula Na₂O.

c. Each substance that crystallizes does so according to a particular geometric arrangement. It is possible to have more than one kind of unit cell with the same shape. For example, a unit cell in a tetragonal crystal may be simple tetragonal, or it may be body-centered. Considering the different kinds of three-dimensional unit cells, the three of the simplest unit cells are simple cubic, body-centered cubic, and face-centered cubic. In the simple cubic cell, each particle has six immediate neighbors. In the body-centered cell, each particle has eight immediate neighbors; and in the face-centered unit cell, each has twelve.
It should also be pointed out that space lattices and unit cells have no real physical existence. They are mental models that help demonstrate crystal structures.

Na⁺ ionic radius = 0.102 nm.
O^– ionic radius = 0.181 nm.
r_c/r_α=0.564
Implies octahedral [6] coordination for Na⁺ ions.
Second rule: bond strength for Na⁺ ion = +1/6
Thus, each O^– ion (charge -1) must also have 6 sodium ions around it to preserve charge neutrality.

d. Thus, lattice parameter (edge length of cube) is given by:

r_c=0.099 nm. and r_α=0.138 nm.
4 cations and 8 anions per unit cell
Density = mass / α³
Calculated density = 2.141 Mg m^-3
Actual density = 2.165 Mg m^-3

Ion	Ionic radius / nm
Na⁺	0.099
O^2-	0.138

Table 1. Ionic radii of Na⁺ and O^2- ions.

Coordination number	Range of cation : anion radius ration
8	r_c/r_α≥0.732
6	r_c/r_α≥0.414
4	r_c/r_α≥0.225

Table 2. Limiting ionic radius ratios for coordination polyhedral

Avogadro’s number N_A=6.022×10²³mol^-1

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Academic.Tips. (2021) 'a. Outline the principles of Pauling’s 5 rules for predicting the crystal structures of ionic solids. b. Show how Pauling’s rules can be used, together with the data give in Tables 1 and 2, to explain the crystal structure of Na₂O, which is based on an fcc array of oxide ions. Draw a schematic diagram showing a unit cell of this structure. Explain which interstitial sites are occupied by the Na⁺ ions. c. Sketch a plan view of the Na₂O unit cell, marking on your diagram the height of all ions present. d. Calculate a theoretical value for the density of Na₂O, given that the relative atomic masses of sodium and oxygen are 22.99 and 16.00 respectively'. 2 June.

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Academic.Tips. (2021, June 2). a. Outline the principles of Pauling’s 5 rules for predicting the crystal structures of ionic solids. b. Show how Pauling’s rules can be used, together with the data give in Tables 1 and 2, to explain the crystal structure of Na₂O, which is based on an fcc array of oxide ions. Draw a schematic diagram showing a unit cell of this structure. Explain which interstitial sites are occupied by the Na⁺ ions. c. Sketch a plan view of the Na₂O unit cell, marking on your diagram the height of all ions present. d. Calculate a theoretical value for the density of Na₂O, given that the relative atomic masses of sodium and oxygen are 22.99 and 16.00 respectively. https://academic.tips/question/a-outline-the-principles-of-paulings-5-rules-for-predicting-the-crystal-structures-of-ionic-solids-b-show-how-paulings-rules-can-be-used-together-with-the-data-give-in-tables-1-a/

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Academic.Tips. 2021. "a. Outline the principles of Pauling’s 5 rules for predicting the crystal structures of ionic solids. b. Show how Pauling’s rules can be used, together with the data give in Tables 1 and 2, to explain the crystal structure of Na₂O, which is based on an fcc array of oxide ions. Draw a schematic diagram showing a unit cell of this structure. Explain which interstitial sites are occupied by the Na⁺ ions. c. Sketch a plan view of the Na₂O unit cell, marking on your diagram the height of all ions present. d. Calculate a theoretical value for the density of Na₂O, given that the relative atomic masses of sodium and oxygen are 22.99 and 16.00 respectively." June 2, 2021. https://academic.tips/question/a-outline-the-principles-of-paulings-5-rules-for-predicting-the-crystal-structures-of-ionic-solids-b-show-how-paulings-rules-can-be-used-together-with-the-data-give-in-tables-1-a/.

1. Academic.Tips. "a. Outline the principles of Pauling’s 5 rules for predicting the crystal structures of ionic solids. b. Show how Pauling’s rules can be used, together with the data give in Tables 1 and 2, to explain the crystal structure of Na₂O, which is based on an fcc array of oxide ions. Draw a schematic diagram showing a unit cell of this structure. Explain which interstitial sites are occupied by the Na⁺ ions. c. Sketch a plan view of the Na₂O unit cell, marking on your diagram the height of all ions present. d. Calculate a theoretical value for the density of Na₂O, given that the relative atomic masses of sodium and oxygen are 22.99 and 16.00 respectively." June 2, 2021. https://academic.tips/question/a-outline-the-principles-of-paulings-5-rules-for-predicting-the-crystal-structures-of-ionic-solids-b-show-how-paulings-rules-can-be-used-together-with-the-data-give-in-tables-1-a/.

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Academic.Tips. "a. Outline the principles of Pauling’s 5 rules for predicting the crystal structures of ionic solids. b. Show how Pauling’s rules can be used, together with the data give in Tables 1 and 2, to explain the crystal structure of Na₂O, which is based on an fcc array of oxide ions. Draw a schematic diagram showing a unit cell of this structure. Explain which interstitial sites are occupied by the Na⁺ ions. c. Sketch a plan view of the Na₂O unit cell, marking on your diagram the height of all ions present. d. Calculate a theoretical value for the density of Na₂O, given that the relative atomic masses of sodium and oxygen are 22.99 and 16.00 respectively." June 2, 2021. https://academic.tips/question/a-outline-the-principles-of-paulings-5-rules-for-predicting-the-crystal-structures-of-ionic-solids-b-show-how-paulings-rules-can-be-used-together-with-the-data-give-in-tables-1-a/.

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"a. Outline the principles of Pauling’s 5 rules for predicting the crystal structures of ionic solids. b. Show how Pauling’s rules can be used, together with the data give in Tables 1 and 2, to explain the crystal structure of Na₂O, which is based on an fcc array of oxide ions. Draw a schematic diagram showing a unit cell of this structure. Explain which interstitial sites are occupied by the Na⁺ ions. c. Sketch a plan view of the Na₂O unit cell, marking on your diagram the height of all ions present. d. Calculate a theoretical value for the density of Na₂O, given that the relative atomic masses of sodium and oxygen are 22.99 and 16.00 respectively." Academic.Tips, 2 June 2021, academic.tips/question/a-outline-the-principles-of-paulings-5-rules-for-predicting-the-crystal-structures-of-ionic-solids-b-show-how-paulings-rules-can-be-used-together-with-the-data-give-in-tables-1-a/.

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