Chapter 12, Problem 12.86QP

(a)

Interpretation Introduction

Interpretation: The given question stated that ${\text{C}}_{60}$ reacts with alkali metals to form ${\text{M}}_3{\text{C}}_{60}$ (where $\text{M}$ is $\text{Na}$ or $\text{K}$). The crystal structure of ${\text{M}}_3{\text{C}}_{60}$ contains cubic closest-packed spheres of ${\text{C}}_{60}$ with metal ions in holes. When radius of an ${\text{K}}^{+}$ ion is $138\text{pm}$ then the type of holes ${\text{K}}^{+}$ ion likely to occupy and the density of a crystal of ${\text{K}}_6{\text{C}}_{60}$ is to be explained.

Concept introduction: The cubic closest-packed has eight atoms at the corners of the cube and six atoms at the centers of each face of the cube. The big atoms create the void space in the ccp arrangement and this space is occupied by the small atoms.

To determine: The type of holes ${\text{K}}^{+}$ ion is likely to occupy and the fraction of the holes that will be occupied.

(b)

Interpretation Introduction

To determine: The density of a crystal of ${\text{K}}_6{\text{C}}_{60}$