Ch.12 - Solids and Solid-State Materials

McMurry8th EditionChemistryISBN: 9781292336145Non è quello che usi tu?Cambia libro di testo

McMurry 8th Edition

Ch.12 - Solids and Solid-State Materials

Problema 137c

Capitolo 12, Problema 137c

A cube-shaped crystal of an alkali metal, 1.62 mm on an edge, was vaporized in a 500.0 mL evacuated flask. The resulting vapor pressure was 12.5 mm Hg at 802 °C. The structure of the solid metal is known to be body-centered cubic. (c) What are the densities of the solid and the vapor in g>cm3?

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Calculate the volume of the cube-shaped crystal using the formula for the volume of a cube, V = s^3, where s is the length of an edge of the cube.

Determine the number of unit cells in the crystal by considering the body-centered cubic (bcc) structure. In a bcc lattice, there are 2 atoms per unit cell. Calculate the number of unit cells by dividing the total volume of the cube by the volume of a single unit cell.

Calculate the molar mass of the alkali metal using the Avogadro's number and the number of atoms obtained from the number of unit cells.

Use the ideal gas law, PV = nRT, to find the number of moles of the alkali metal in the vapor phase. Use the temperature in Kelvin and the vapor pressure in atmospheres.

Calculate the density of the solid and the vapor. For the solid, use the mass (from molar mass and number of moles) and the volume of the cube. For the vapor, use the mass and the volume of the flask.

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Density

Density is defined as mass per unit volume, typically expressed in grams per cubic centimeter (g/cm³). It is a crucial property that helps in identifying substances and understanding their behavior in different states. For solids, density can be calculated using the formula density = mass/volume, while for gases, it can be derived from the ideal gas law under specific conditions.

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01:56

Density Concepts

Body-Centered Cubic (BCC) Structure

The body-centered cubic (BCC) structure is a type of crystal lattice where atoms are located at each corner of a cube and a single atom is positioned at the center of the cube. This arrangement affects the packing efficiency and density of the solid. Understanding the BCC structure is essential for calculating the mass and volume of the alkali metal crystal, which are needed to determine its density.

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00:40

Body Centered Cubic Example

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. It is an important concept in thermodynamics and helps in understanding the behavior of substances in the gaseous state. In this question, the vapor pressure of the alkali metal at 802 °C is used to calculate the density of the vapor, which is essential for comparing it to the density of the solid.

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Raoult's Law and Vapor Pressure

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A cube-shaped crystal of an alkali metal, 1.62 mm on an edge, was vaporized in a 500.0 mL evacuated flask. The resulting vapor pressure was 12.5 mm Hg at 802 °C. The structure of the solid metal is known to be body-centered cubic. (b) Use the data in Figure 5.19 to identify the alkali metal.

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