A pure copper sphere ha a radius of 0.935in. How many moles of copper does it contain? The volume of a sphere is (4/3)3.14r^3, and the density of the copper is 8.96g/cm^3.
(1 in. = 2.54cm)
Convert 0.935 inches to cm.
Use (4/3)*pi*r^3 to find the volume of the sphere in cubic centimeters.
Use mass = volume x density to find the mass
Then mols = grams/atomic mass.
To find the number of moles of copper in the pure copper sphere, we need to follow these steps:
Step 1: Calculate the volume of the copper sphere:
The formula for the volume of a sphere is given as V = (4/3)πr^3, where V is the volume and r is the radius. Therefore, substituting the given values, we have:
V = (4/3)π(0.935in)^3
Step 2: Convert the radius from inches to centimeters:
As given, 1 in. = 2.54 cm. So, we need to convert the radius from inches to centimeters:
Radius(cm) = 0.935in × 2.54cm/in
Step 3: Substitute the radius in centimeters into the volume formula:
V = (4/3)π(0.935in × 2.54cm/in)^3
Step 4: Calculate the mass of copper using the volume and density:
The density of copper is given as 8.96 g/cm^3. So, the mass can be calculated using:
Mass = Density × Volume
Step 5: Convert the mass from grams to moles:
To convert the mass of copper to moles, we need to use the molar mass of copper, which is approximately 63.55 g/mol. The number of moles can be calculated using:
Moles = Mass(g) / Molar Mass(g/mol)
Let's calculate the number of moles of copper in the pure copper sphere:
Step 1: Calculate the volume of the copper sphere:
V = (4/3)π(0.935in)^3
Step 2: Convert the radius from inches to centimeters:
Radius(cm) = 0.935in × 2.54cm/in
Step 3: Substitute the radius in centimeters into the volume formula:
V = (4/3)π(0.935in × 2.54cm/in)^3
Step 4: Calculate the mass of copper using the volume and density:
Mass = Density × Volume
Step 5: Convert the mass from grams to moles:
Moles = Mass(g) / Molar Mass(g/mol)
By following these steps, we can accurately calculate the number of moles of copper in the given copper sphere.