2.7: Practice with Density

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Exercise \(\PageIndex{1}\)

What is the density of a material if a sample with a mass of 45.82 g takes up a volume of 8.75 mL?

Answer: 5.24 g/mL

What mass would a sample of 32.6 cm³ of copper be? The density of copper is 8.96 g/cm³.

Answer: 292 g

What volume of acetone would have a mass of 142.5 g? The density of acetone is 0.784 g/mL.

Answer: 182 mL

Exercise \(\PageIndex{1}\)

An empty beaker has a mass of 65.873 g. You add 23.8 mL of solution, and the beaker now has a mass of 85.347 g. What is the density of your solution?

Answer: 0.818 g/mL

You have a rectangular block of metal that measures 4.82 cm long, 3.44 cm wide, and 2.65 cm high. The mass is 197.7 g. What is the density of the metal?

Answer: 4.50 g/cm³

To a graduated cylinder with 22.5 mL of water you add 38.95 g of metal pieces. The water level rises to 28.0 mL. What is the density of the metal?

Answer: 7.1 g/mL

Exercise \(\PageIndex{1}\)

You have a copper metal cylinder that is 5.80 cm high. The diameter of the cylinder is 1.44 cm. What would the mass of this cylinder be? The density of copper is 8.96 g/cm³. The formula to calculate the volume of a cylinder is \(V = (\pi)r^2h\), where \(r\) is the radius (half the diameter) and \(h\) is the height. If your calculator doesn't have a button for pi, use the value \(\pi = 3.14159\).

Hint: The volume of the cylinder is 9.45 cm³. (9.44589... cm³ with 3 significant figures)

Answer: 84.6 g (If you round the volume to 9.45 cm³, you get 84.7 g. If you keep the digits in your calculator and round at the very end, it is 84.6 g.)

You have a graduated cylinder with the water level at 30.8 mL. You add 72.88 g of copper to the water. The density of copper is 8.96 g/cm³. What is the final water level?

Hint: The volume of copper added is 8.13 cm³, which equals 8.13 mL.

Answer: 38.9 mL is the water level after the copper is added.

Before you add acetone to a beaker, the mass is 59.43 g. After you add the acetone, the mass is 81.09 g. The density of acetone is 0.784 g/mL. What volume of acetone is in the beaker?

Hint: The mass of acetone added is 21.66 g.

Answer: 27.6 mL