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Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

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BuyFindarrow_forward

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

CaTiO3, a perovskite, has the structure below.

  1. (a) If the density of the solid is 4.10 g/cm3, what is the length of a side of the unit cell?
  2. (b) Calculate the radius of the Ti4+ ion in the center of the unit cell. How well does your calculation agree with a literature value of 75 pm?

images

Unit cell of the perovskite CaTiO3

images

A sample of perovskite, СаТiO3

images

FIGURE 7.11 Relative sizes of some common ions. Rodii are given in picometers (1 pm 1 × 10‒12 m). (Data taken from J. Emsley, The Elements, Clarendon Press, Oxford, 1998, 3rd edition.)

(a)

Interpretation Introduction

Interpretation:

The length of the side of the unit cell, has to be calculated.

Concept introduction:

The volume of the atom is given below,

images

The density of the unit cell is calculated as follows,

images

images

Explanation

  

  

  Therefore,

  

(b)

Interpretation Introduction

Interpretation:

The radius of imagesin the center of the unit cell has to be calculated, and the radius of imageshas to be compared with literature value.

Concept introduction:

The volume of the atom is given below,

images

The density of the unit cell is calculated as follows,

images

images

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