How many Cu atoms are present in a 75.0 cm length of 20-gauge copper wire? A 20-gauge wire has a diameter of 0.03196 in.Copper's density is 8.92 g/cm³. A)1.31 × 10²¹ B)3.28 × 10²² C)8.08 × 10²¹ D)1.04 × 10²² E)2.08 × 10²²

Question

Quizplus · Accepted Answer

First, we need to calculate the volume of the wire:
radius = diameter/2 = 0.01598 in = 0.0004051 cm
length = 75.0 cm
V = πr²l = π(0.0004051 cm)²(75.0 cm) = 0.001533 cm³

Next, we can calculate the mass of the wire using its density and volume:
m = density x V = (8.92 g/cm³)(0.001533 cm³) = 0.01366 g

Finally, we can calculate the number of copper atoms using Avogadro's number and the atomic mass of copper (63.55 g/mol):
moles of Cu = mass/molar mass = 0.01366 g/63.55 g/mol = 0.000215 mol
number of Cu atoms = moles of Cu x Avogadro's number = 0.000215 mol x (6.022 x 10²³ atoms/mol) = 1.30 x 10²² atoms

Therefore, the answer is B) 3.28 x 10²² atoms.

How Many Cu Atoms Are Present in a 75