Chemistry: An Atoms-Focused Approach (Second Edition)
Chemistry: An Atoms-Focused Approach (Second Edition)
2nd Edition
ISBN: 9780393614053
Author: Thomas R. Gilbert, Rein V. Kirss, Stacey Lowery Bretz, Natalie Foster
Publisher: W. W. Norton & Company
Question
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Chapter 4, Problem 4.19QA
Interpretation Introduction

To find:

The most negative lattice energy substance out of (a) KCl, (b) TiO2, (c) BaCl2, (d) KI

Expert Solution & Answer
Check Mark

Answer to Problem 4.19QA

Solution:

TiO2 has the most negative lattice energy.

Explanation of Solution

1) Concept: Using the formula below, we can calculate the lattice energy. Here, Q1 and Q2 are charges of cation and anion respectively and d is the distance between nuclei of cation and anion.

Ionization reactions for all four compounds:

aKClK++Cl-

bTiO2Ti+2+2Cl-

cBaCl2Ba+2+2Cl-

dKIK++I-

2) Formula:

 Eel=2.31×10-19 J.nm [Q1×Q2d]

3) Given information: Ionic radii of ions are:

Ions Ionic radius
K+ 138 pm
Cl- 181 pm
Ti+2 100 pm
O-2 140 pm
Ba+2 149 pm
I- 206 pm

4) Calculations: The distance between nuclei of cation and anion is calculated as

ad=(K+  ionic radius+Cl- ionic radius)

d=(138 pm+181 pm)

d=319 pm

319 pm ×1nm1000pm=0.319 nm

And so, for the rest of compounds:b 0.240 nm, c 0.330 nm, and (d) 0.344 nm

Now product of charges for all compounds

a1×+1×1×-1=-1

b1×+2×2-1=-4

c1×+2×2-1= -4

a1×+1×1×-1=-1

Q1×Q2dfor all compouds:

a-10.19=-5.26

b-40.24=-16.67

c-40.33=-12.12

d-10.344=-2.91

When the factor Q1×Q2d is large, it will lead to the most negative lattice energy. It is large for TiO2. Therefore, TiO2 has the most negative lattice energy.

Conclusion:

TiO2 has the most negative lattice energy because the product of the charges is the highest.

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Chapter 4 Solutions

Chemistry: An Atoms-Focused Approach (Second Edition)

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