Stuck on a density = mass / volume equation

Question

A chemist encounters an unknown metal. They drop the metal into a graduated cylinder containing water, and find the volume change is 3.2 mL. If the metal weighs 2.3 g, what is the density in g/mL of the metal?

Answer 1

Hello, Patricia,

This technique is a fun way to identify unknown (but pure) metals. The volume of the metal is 3.2ml. The mass of that metal sample is 3.2 grams. Density is defined as mass/unit volume.

So the density of our metal sample is 3.2 g/3.2 ml, or 1 gm/ml. This could be expressed in other units, such as kg/ml, in which case it would be 0.001 kg/ml.

But 1gm/ml is an exceptionally low density for a metal. Even aluminum has a density of 2.7 g/ml. So this might be an alloy or have air pockets inside. More than likely, however, it is a made-up problem with an easy-to-calculate answer of 1 g/ml.

Bob