Rubidium chloride has the sodium chloride structure at normal pressures but assumes the cesium chloride structure at high pressures. (See Exercise 69.) What ratio of densities is expected for these two forms? Does this change in structure make sense on the basis of simple models? The ionic radius is 148 pm for Rb+ and 181 pm for CI−.
Interpretation:
Rubidium chloride has two structures at different pressures. The ratio of the density of these two forms has to be determined.
Concept introduction:
In packing of atoms or molecules of a solid, the atoms/molecules are imagined as spheres. The two major types of close packing of the spheres in the crystal are – hexagonal close packing and cubic close packing. Cubic close packing structure has face-centered cubic (FCC) unit cell. FCC unit cell has 4 units of atom/molecule per unit cell. In FCC unit cell the components touch along the edge of the cubic unit cell. A simple cubic unit cell has 1 unit of atom/molecule per unit cell. In this unit cell, the components touch along the body diagonal of the unit cell.
Answer to Problem 156CP
Answer
The ratio of the density of the two forms of Rubidium chloride is 1.30.
Explanation of Solution
Explanation
Calculate the volume of unit cell of
At normal pressure structure of Rubidium chloride is similar to that of Sodium chloride. The ionic radius of the
Calculate the mass and density of unit cell of
Each FCC unit cell contains 4
Calculate the volume of unit cell of
At high pressure structure of Rubidium chloride is similar to that of Cesium chloride. The ionic radius of the
Calculate the mass and density of unit cell of
Each simple cubic unit cell contains one
Compare the density of two forms of Rubidium chloride.
Let density of
Let density of
The ratio of densities of the two forms of
Conclusion
The structure of
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