Calculate the density of Na metal. The length of the body-centered cubic unit cell is 4.24 Å.

Name: Problem 90, Chapter 13: Chemistry
Uploaded: 2021-07-13T17:28:44-08:00
Duration: 2 min 49 s
Channel: Lottie Adams
Description: Calculate the density of Na metal. The length of the body-centered cubic unit cell is 4.24 Å.

step 1 The body -centered cubic is a sort of unit cell. And so if the cube is drawn with the sides of t

Calculate the density of Na metal. The length of the...

Key Concepts

Calculation Methodology

The density of a crystalline material is calculated by determining the total mass of the atoms in the unit cell (using the number of atoms per cell, atomic mass, and Avogadro's number) and dividing this mass by the physical volume of the unit cell. This structured approach combines crystallography, atomic theory, and unit conversions.

Unit Conversion

Converting units appropriately is critical in density calculations. For example, converting the unit cell dimensions given in angstroms to a volume in cubic centimeters ensures that the mass (often in grams) and the volume are in compatible units when using Avogadro's number in the calculation.

Body-Centered Cubic (BCC) Structure

In a body-centered cubic structure, atoms are positioned at the eight corners of a cube with an additional atom at the cube's center. This structure results in a specific count of atoms per unit cell, which is essential for accurately computing the density.

Crystallography and Unit Cells

A unit cell is the smallest repeating unit that fully describes the crystal structure of a material. Characteristics such as edge length and the arrangement of atoms within the cell directly influence properties, including density.

Density

Density is defined as the mass per unit volume of a substance. In materials science, calculating the density of a crystalline solid involves determining the mass of the atoms contained within a repeating unit (unit cell) and dividing this mass by the cell’s volume.

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