Potassium chloride crystallizes in the rock salt structure. Estimate the density of potassium chloride using the ionic radii provided in Chapter 8.

Verified step by step guidance

Identify the type of crystal structure: Potassium chloride (KCl) crystallizes in the rock salt structure, which is a face-centered cubic (FCC) lattice.

Determine the formula unit mass of KCl: Use the atomic masses of potassium (K) and chlorine (Cl) from the periodic table to calculate the molar mass of KCl.

Calculate the volume of the unit cell: Use the ionic radii provided to estimate the edge length of the cubic unit cell. In the rock salt structure, the edge length (a) can be approximated as twice the sum of the radii of the cation and anion.

Determine the number of formula units per unit cell: In the rock salt structure, there are 4 formula units of KCl per unit cell.

Estimate the density: Use the formula for density, \( \text{density} = \frac{\text{mass of formula units in unit cell}}{\text{volume of unit cell}} \), to calculate the density of KCl.

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. They are crucial for understanding the arrangement of ions in ionic compounds like potassium chloride (KCl). The size of the potassium ion (K+) and the chloride ion (Cl-) influences the lattice structure and the overall density of the compound.

Rock Salt Structure

The rock salt structure is a type of crystal lattice arrangement where each ion is surrounded by six ions of the opposite charge, forming an octahedral geometry. In KCl, K+ and Cl- ions alternate in a three-dimensional grid, which is essential for calculating the density based on the arrangement and the volume occupied by the ions.

Density Calculation

Density is defined as mass per unit volume and can be calculated for ionic compounds by using the formula: density = (mass of formula unit) / (volume of unit cell). For KCl, the mass can be derived from the molar masses of K+ and Cl-, while the volume is determined from the dimensions of the unit cell based on the ionic radii and the structure type.

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Textbook Question

The density of an unknown metal is 12.3 g/cm³, and its atomic radius is 0.134 nm. It has a face-centered cubic lattice. Find the atomic mass of this metal

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An unknown metal is found to have a density of 7.8748 g/cm³ and to crystallize in a body-centered cubic lattice. The edge of the unit cell is 0.28664 nm. Calculate the atomic mass of the metal.

When spheres of radius r are packed in a body-centered cubic arrangement, they occupy 68.0% of the available volume. Use the fraction of occupied volume to calculate the value of a, the length of the edge of the cube, in terms of r.

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Calculate the fraction of empty space in cubic closest packing to five significant figures.

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Open Question

What is a tetrahedral site in a closest-packed lattice formed by?

Textbook Question

X-ray diffractometers often use metals that have had their core electrons excited as a source of X-rays. Consider the 2p → 1s transition for copper, which is called the K⍺ transition. Calculate the wavelength of X-rays (in Å) given off by the K⍺ transition if the energy given off by a mole of copper atoms is 7.77⨉10⁵ kJ.(1Å = 10^-10 m)

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