Estimate the density of cesium iodide from its crystal structure.The ionic radii of Cs⁺ and Cl ^- are 170 and 220 pm,respectively.

Question

Quizplus · Accepted Answer

To estimate the density of cesium iodide, we need to consider its crystal structure. Cesium iodide has a simple cubic crystal structure, where each cesium ion is surrounded by 8 iodide ions and each iodide ion is surrounded by 8 cesium ions. The ionic radii of Cs and I are 170 and 220 pm, respectively.

The edge length of the unit cell can be calculated as 2*(ionic radius of Cs + ionic radius of I) = 2*(170 + 220) pm = 780 pm = 7.80 Å.

The volume of the unit cell can be calculated as (edge length)^3 = (7.80 Å)^3 = 474.56 Å^3.

The formula unit of cesium iodide is CsI, which means there is 1 Cs ion and 1 I ion per unit cell. The molar mass of CsI is 259.81 g/mol.

The number of formula units in one unit cell can be calculated as the ratio of the volume of the unit cell to the volume of one CsI molecule:

Number of formula units = (Volume of unit cell) / (Volume of 1 CsI molecule)
= 474.56 Å^3 / (1.71 Å^3/molecule)
= 277.54 molecules

The mass of one unit cell can be calculated as the product of the number of molecules and the molar mass:

Mass of one unit cell = (Number of formula units) * (Molar mass of CsI)
= 277.54 molecules * 259.81 g/mol
= 72.03 g

Finally, the density of cesium iodide can be calculated as the mass of one unit cell divided by the volume of one unit cell:

Density = (Mass of one unit cell) / (Volume of unit cell)
= 72.03 g / 474.56 Å^3
= 4.72 g/cm^3

Therefore, the best choice is D) 4.72 g/cm^3.

Estimate the Density of Cesium Iodide from Its Crystal Structure