Multiple Choice
A block of metal has a width of 3.2 cm, a length of 17.1 cm, and a height of 4.3 cm. Its mass is 1.1 kg. Calculate the density of the metal in g/cm³.
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1. Intro to General Chemistry
Density of Geometric Objects
Multiple Choice
Palladium crystallizes with a face-centered cubic unit cell. The edge length of palladium is 390 pm, and the molar mass of palladium is 106.42 g/mol. What is the density of palladium in g/cm³?
A
11.8 g/cm³
B
13.2 g/cm³
C
12.0 g/cm³
D
10.5 g/cm³
Verified step by step guidance1
Understand that palladium crystallizes in a face-centered cubic (FCC) unit cell. In an FCC unit cell, there are atoms at each corner and one atom at the center of each face of the cube.
Calculate the number of atoms per unit cell in an FCC structure. Each corner atom is shared by eight unit cells, and each face atom is shared by two unit cells. Therefore, the total number of atoms per unit cell is: \( \text{Number of atoms} = 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 4 \).
Convert the edge length from picometers to centimeters. Since 1 pm = \( 10^{-12} \) m, and 1 m = 100 cm, the edge length in cm is: \( 390 \text{ pm} \times 10^{-12} \text{ m/pm} \times 100 \text{ cm/m} = 3.90 \times 10^{-8} \text{ cm} \).
Calculate the volume of the unit cell using the edge length: \( \text{Volume} = (3.90 \times 10^{-8} \text{ cm})^3 \).
Determine the density using the formula \( \text{Density} = \frac{\text{Mass of atoms in unit cell}}{\text{Volume of unit cell}} \). First, calculate the mass of the atoms in the unit cell using the molar mass and Avogadro's number: \( \text{Mass} = \frac{4 \text{ atoms} \times 106.42 \text{ g/mol}}{6.022 \times 10^{23} \text{ atoms/mol}} \). Then, divide this mass by the volume calculated in the previous step to find the density in g/cm³.
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