Chemistry, 08.10.2019 16:00 nicoledambrosia16

The volume of a sphere is (4/3)πr3 and the density of copper is 8.96g/cm3.

what is the radius (in cm) of a pure copper sphere that contains 1.41×1024 copper atoms?

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First, we need to get the mass of the copper, then we will use this mass along with the given density to find the volume and finally we will substitute in the rule of volume to get the radius.

First, calculating the mass:
number of atoms in one mole of an element = 6.022 x 10^23
So, we can use cross multiplication to find the number of moles containing 1.41×10^24 atoms as follows:
number of moles = (1.41×10^24 x 1) / (6.022 x 10^23) = 2.3414 moles
From the periodic table:
molar mass of copper = 63.5 grams
number of moles = mass / molar mass
2.3414 = mass / 63.5
mass = 2.3414 x 63.5 = 148.6789 grams

Then, we get the volume:
density = mass / volume
8.96 = 148.6789 / volume
volume = 16.59 cm^3

Finally, we get the radius:
volume = (4/3) x pi x (radius)^3
16.59 = (4/3) x (22/7) x (radius)^3
radius^3 = 3.9614
radius = 1.5822 cm

Answer from: VanessaMyers411

The radius (in cm) of a pure copper sphere that contains 1.41×10²⁴ copper atoms r = 1,583 cm

Further explanation

Density is a quantity derived from the mass and volume

density is the ratio of mass per unit volume

The unit of density can be expressed in g / cm3 or kg / m3

Density formula:

$\large {\boxed {\bold {\rho ~ = ~ \frac {m} {V}}}}$

ρ = density

m = mass

v = volume

Sphere is a 3-dimensional space constructed by many circles and the same center point

Ball volume is formulated

V = 4/3 . π r ³

Moles are units of particles where 1 mole is the number of particles contained in a substance which is equal to many atoms in 12 gr C-12

1 mol = 6.0210²³ particles

To find the radius of copper, we determine the mole and its mass first

relative atomic mass Cu = 63.5

1. mole Cu = particle number: 6.02.10²³

mole Cu = 1.41 × 1024: 6,02.10²³

mole Cu = 2,342

2. mass of Cu = mole x relative atomic mass

mass Cu = 2,342 x 63.5

mass Cu = 148,717 grams

3. Volume Cu = 4/3 πr³

densitiy Cu = mass: volume

volume = mass: density

4 / 3π r³ = 148.717: 8.96g / cm³

4 / 3π r³ = 16,597 cm³

4,186 r³ = 16,597 cm³

r³ = 3,965

r = 1,583 cm

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Keywords: density, Cu, sphere

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