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Multiple Choice
A cylindrical copper wire is used for the fences around a house. The copper wire has a diameter of 0.0750 in. How many copper atoms are found in 5.160 cm piece? The density of copper is 8.96 g/cm3. (V = π • r2 • h)
A
2.01 x 1022 Cu atoms
B
6.36 x 1021 Cu atoms
C
9.91 x 1021 Cu atoms
D
1.25 x 1022 Cu atoms
Verified step by step guidance
1
Convert the diameter of the copper wire from inches to centimeters. Use the conversion factor: 1 inch = 2.54 cm.
Calculate the radius of the wire in centimeters by dividing the diameter by 2.
Use the formula for the volume of a cylinder, V = π • r^2 • h, to calculate the volume of the copper wire. Here, r is the radius in cm and h is the length of the wire in cm.
Calculate the mass of the copper wire using the density formula: mass = density × volume. Use the given density of copper, 8.96 g/cm³.
Determine the number of copper atoms by dividing the mass of the copper wire by the molar mass of copper (approximately 63.55 g/mol) to find the number of moles, and then multiply by Avogadro's number (6.022 x 10^23 atoms/mol) to find the total number of atoms.