A pure copper sphere has a radius 0.929 in. How many copper atoms does it contain? (density of copper 8.96 #"g/cm"^3#)

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Jan 17, 2015

The answer is #4.67 * 10^(24)# #"atoms"#.

So, start by converting inches to cm

#"0.929 cm" * ("2.54 cm")/("1 inch") = "2.360 cm"#

Use this value to determine the volume of the sphere

#V_("sphere") = 4/3 * pi * r^3 = 4/3 * 3.14 * 2.360^3 = 55.03# #"cm"^3#

Use density to determine the mass of copper

#rho = m/V => m = rho * V = 8.96# #"g"/"cm"^3 * 55.03# #"cm"^3 = 493# #"g"#

From here, you can determine the number of atoms you have by

#"493 g" * (6.022 * 10^23 "atoms")/("63.55 g") = 4.67 * 10^24# #"atoms"#

I've used the fact that 1 mole of copper has #6.022 * 10^23# atoms and weighs #"63.55 g"#.

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