Question

A pure copper sphere has a radius of 0.935 in. How many copper atoms does it contain? [The volume of a sphere is (4>3)pr3 and the density of copper is 8.96 g>cm3.]

Answer 1

Answer:

=4.8*10^-24atoms

Explanation:

To find volume of a sphere

= 5.61*10^-5m³ x 8.96gx 100³m³

=502.7g

So we use density of copper to convert volume to mass so

1atm of cux( 1mol of cu/6.02Eatm of cu)*(63.54g of cu/1 mole of cu)

So = 1.055*10-22g cu

So

= 502.7/1.055*10-22g cu

=4.8*10^-24atoms

Answer 2

Answer:

47.68 x 10²³ or 4.768 x 10²⁴ copper atoms

Explanation:

Given:

Radius of the copper sphere (r) = 0.935 in

First convert the radius from inches to centimeters

1 in = 2.54cm

0.935in =  0.935 x 2.54cm = 2.3749cm

∴ r = 2.3749cm

Calculate the volume of the copper sphere as follows

Volume = $\frac{4}{3}\pi r^{3}$          [substitute r = 2.3749cm and π = 22 / 7]

Volume = $\frac{4}{3}(\frac{22}{7} ) (2.3749)^{3}$

Volume = 56.108cm³

From the volume and given density, calculate the mass of the copper sphere

mass = density x volume           [density = 8.96g/cm³]

mass = 8.96 x 56.108 = 502.73g

From known facts

1 mole of copper = 63.5g of copper = 6.022 x 10²³ copper atoms.

Then,

502.73 g of copper = $\frac{502.73 * 6.022*10^{23}}{63.5}$  = 47.68 x 10²³ copper atoms

Therefore, the sphere contains 47.68 x 10²³ copper atoms