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.

Question

Quizplus · Accepted Answer

First, we need to calculate the volume of the wire:
radius = diameter/2 = 0.01598 in. = 0.04055 cm
V = πr^2h = π(0.04055 cm)^2 (75.0 cm) = 0.382 cm^3

Next, we can use the density of copper to calculate the mass of the wire:
m = DV = (8.92 g/cm^3) (0.382 cm^3) = 3.41 g

Finally, we can use the molar mass of copper to convert the mass to number of atoms:
1 mol Cu = 63.55 g Cu
1 atom Cu = 1 mol Cu/6.022 × 10^23 atoms Cu
n = m/M = (3.41 g)/(63.55 g/mol)/(6.022 × 10^23 atoms/mol) = 3.28 × 10^21 atoms

Therefore, there are 3.28 × 10^21 Cu atoms in the wire.

How Many Cu Atoms Are Present in a 75