The ionic compound CaO crystallizes with the same structure...

The ionic compound CaO crystallizes with the same structure as sodium chloride (Figure 8.3). (a) In this structure, how many $\mathrm{O}^{2-}$ are in contact with each $\mathrm{Ca}^{2+}$ ion $($ Hint $: \mathrm{Re}-$ member the pattern of ions shown in Figure 8.3 repeats over and over again in all three directions.) (b) Would energy be consumed or released if a crystal of $\mathrm{CaO}$ was converted to a collection of widely separated Ca-O ion pairs? (c) From the ionic radii given in Figure 7.8 , calculate the potential energy of a single $\mathrm{Ca}-\mathrm{O}$ ion pair that is just touching (the magnitude of electronic charge is given on the inside back cover). (d) Calculate the energy of a mole of such pairs. How does this compare to the lattice energy of CaO? (e) What factor do you think accounts for most of the discrepancy between the energies in part (d)- the bonding in CaO is more covalent than ionic, or the electrostatic interactions in a crystal lattice are more complicated than those in a single ion pair?

Key Concepts

Electrostatic (Coulombic) Potential Energy

Electrostatic potential energy is the energy between two charged ions due to Coulomb’s law. This concept is used to calculate the potential energy of ion pairs when they are just touching, providing insight into the strength and nature of the ionic bond at the molecular level.

Ionic Crystal Structures

Ionic crystal structures describe the orderly, repeating arrangement of positively and negatively charged ions in a solid. Understanding these structures, such as the sodium chloride (NaCl) type, is key to determining how ions are packed, how they interact, and how the physical properties of the material arise from those interactions.

Coordination Number

The coordination number refers to the number of oppositely charged ions that are in direct contact with a given ion in the crystal. This concept is essential for understanding the geometrical arrangement and immediate local environment around an ion, which influences both structural stability and ionic interactions.

Lattice Energy

Lattice energy is the energy released when oppositely charged gaseous ions come together to form an ionic solid. It is a critical concept, as it indicates the strength of the forces holding the ions in place and is directly related to the stability of the ionic compound.

Ionic Radii

Ionic radii determine the effective size of an ion within a crystal lattice and are used in calculations to establish distances between ion centers. They are crucial for estimating both the potential energy between ion pairs and the overall lattice energy of the crystal.

Madelung Constant

The Madelung constant is a dimensionless value that accounts for the geometric arrangement of ions in an ionic crystal, affecting the calculation of the net electrostatic interactions within the lattice. It highlights how the specific arrangement of ions influences the total lattice energy compared to that of a single ion pair.

Ionic versus Covalent Character

This concept discusses the extent to which bonding in a compound is purely ionic or has some covalent character. It is important for understanding discrepancies between simple pairwise calculations of potential energy and the actual lattice energy of a crystal, as real materials often exhibit a slight degree of covalent bonding.

Transcript

00:01 In this problem, we're asked to do a kulom's law calculation.

00:05 We're given the following information.

00:07 The ionic compound, ionic compound, calcium oxide, crystallizes with the same structure as sodium chloride.

00:34 There is a diagram in your text.

00:36 If you're watching this, you have a text reference, and what i'm looking at says it is figure 8 .3.

00:43 And in this structure, it's going to ask us how many 02s, excuse me, o2 minuses, are in contact with each calcium ion.

01:13 And if you can examine this, i decided not to pull this up here.

01:16 But you'll see that each one of these, i'm going to draw what would be the o2 here.

01:24 This will be my o2.

01:26 That's red.

01:28 And it is going to be, what have i got here, calcium? let's just make calcium a very different color.

01:34 How about gold, top, bottom, left, right, front.

01:47 Back.

01:49 I am a terrible artist.

02:00 So that would be the structure that we're going to have.

02:03 Six is the coordination number for sodium chloride.

02:21 And since we're specifically told that the c .a .o.

02:24 As this crystallizes with the same structure, the answer would be six.

02:32 Part b says would the energy be consumed or released? if a crystal of calcium oxide was converted to a widely separated c -a -o -ion pair.

02:55 So would energy be consumed or released? would it be an endo or exothermic reaction if a crystal, and that would be a crystal and a crystal lattice, was converted to widely separated, and this is sort of the interesting part on this one, and it didn't ask for specific ions, but it said a c -a -o -ion pair.

03:50 And of course, energy is required, so energy would be consumed in this process.

04:03 Energy is required to break bonds.

04:17 For part c, we're going to use the ionic radii given in figure 7 .8, and i think that's it.

04:43 We're going to calculate the potential energy, calculating potential energy, of a single c -a -o -ion pair.

05:09 Use the magnitude of the electronic charge that's given in the text.

05:12 So equation for this is going to be as follows.

05:24 And the values we have given inside the front cover, we have 8 .99, i believe it was times 10 to the 9th joule meter per coulum.

05:41 And we're going to use 3 .2 times 10 to the minus 19th coolums for our calcium charge.

05:53 We're going to use 3 .2 times 10 to the minus 19th coulums for the 02 minus charge...

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