Alabandite is a mineral composed of manganese(II) sulfide (MnS). The mineral adopts the rock salt structure. The length of an edge of the MnS unit cell is 5.223 Å at 25 °C. Determine the density of MnS in g/cm³.

Name: Chemistry: The Central Science
Author: Brown
ISBN: 9780134414232

검증된 단계별 안내

Step 1: Identify the type of crystal structure. Alabandite adopts the rock salt structure, which is a face-centered cubic (FCC) lattice.

Step 2: Calculate the volume of the unit cell. The edge length of the unit cell is given as 5.223 Å. Convert this length to centimeters (1 Å = 1 x 10^-8 cm) and then calculate the volume using the formula for the volume of a cube: \( V = a^3 \), where \( a \) is the edge length.

Step 3: Determine the number of formula units per unit cell. In a rock salt structure, there are 4 formula units of MnS per unit cell.

Step 4: Calculate the molar mass of MnS. Use the periodic table to find the atomic masses of manganese (Mn) and sulfur (S), and sum them to find the molar mass of MnS.

Step 5: Calculate the density of MnS. Use the formula for density: \( \text{Density} = \frac{\text{mass of MnS in the unit cell}}{\text{volume of the unit cell}} \). The mass of MnS in the unit cell can be found by multiplying the number of formula units by the molar mass of MnS and converting to grams.

주요 개념

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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 a cubic structure. In the case of MnS, manganese ions (Mn²⁺) and sulfide ions (S²⁻) alternate in a three-dimensional grid, which is characteristic of ionic compounds. This arrangement is crucial for understanding the properties and density calculations of the mineral.

Unit Cell and Edge Length

A unit cell is the smallest repeating unit in a crystal lattice that reflects the overall symmetry and structure of the entire crystal. The edge length of the unit cell, given as 5.223 Å for MnS, is essential for calculating the volume of the unit cell, which is used in determining the density of the mineral. The volume can be calculated as the cube of the edge length.

Density Calculation

Density is defined as mass per unit volume and is typically expressed in g/cm³. To calculate the density of MnS, one must determine the mass of the formula unit and the volume of the unit cell. The mass can be derived from the molar mass of MnS, while the volume is calculated from the edge length of the unit cell. This relationship is fundamental in solid-state chemistry for characterizing materials.