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Ch.12 - Solids and Modern Materials
Chapter 12, Problem 62

At room temperature and pressure, RbI crystallizes with the NaCl-type structure. (a) Use ionic radii to predict the length of the cubic unit cell edge. (b) Use this value to estimate the density. (c) At high pressure, the structure transforms to one with a CsCl-type structure. Use ionic radii to predict the length of the cubic unit cell edge for the high-pressure form of RbI. (d) Use this value to estimate the density. How does this density compare with the density you calculated in part (b)?

Verified step by step guidance
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Step 1: Identify the ionic radii for Rb+ and I-. For Rb+, the ionic radius is approximately 166 pm, and for I-, it is approximately 220 pm.
Step 2: For the NaCl-type structure, the edge length of the cubic unit cell (a) can be estimated as 2 times the sum of the ionic radii of Rb+ and I-. Calculate a = 2 * (166 pm + 220 pm).
Step 3: To estimate the density of the NaCl-type structure, use the formula: density = (Z * M) / (N_A * a^3), where Z is the number of formula units per unit cell (Z = 4 for NaCl-type), M is the molar mass of RbI, N_A is Avogadro's number, and a is the edge length calculated in Step 2.
Step 4: For the CsCl-type structure, the edge length of the cubic unit cell (a) can be estimated as the sum of the ionic radii of Rb+ and I- multiplied by the square root of 3. Calculate a = sqrt(3) * (166 pm + 220 pm).
Step 5: Estimate the density of the CsCl-type structure using the same density formula as in Step 3, but with Z = 1 for the CsCl-type structure. Compare this density with the density calculated in Step 3 to see how they differ.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ionic Radii

Ionic radii refer to the effective size of an ion in a crystal lattice, which is crucial for predicting the arrangement of ions in a solid structure. The size of cations and anions affects how closely they can pack together, influencing the dimensions of the unit cell. For RbI, the ionic radii of Rb+ and I- can be used to calculate the edge length of the cubic unit cell based on their coordination in the NaCl-type structure.
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Cubic Unit Cell and Density Calculation

A cubic unit cell is the smallest repeating unit in a crystal lattice, characterized by its edge length. The density of a crystalline solid can be calculated using the formula: density = (mass of the formula unit / volume of the unit cell). Understanding how to derive the unit cell volume from the edge length and how to relate the mass of the ions to the unit cell is essential for estimating the density of RbI in both NaCl and CsCl structures.
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Crystal Structure Transformation

Crystal structure transformation refers to the change in the arrangement of atoms or ions in a solid under varying conditions, such as pressure. The transition from a NaCl-type structure to a CsCl-type structure in RbI at high pressure alters the coordination of ions and their packing efficiency. This change can significantly affect the calculated unit cell dimensions and, consequently, the density of the material, highlighting the relationship between structure and physical properties.
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