What is the density of the iron nugget?

Question

An iron nugget weighing 8.14 g was placed in a graduated cylinder and 25.1 cm3 of water was added to the cylinder. The total volume after adding the water was 26.2 cm3.

What is the density of the iron nugget?

Express your answer in units of g/cm3. Report your answer to the correct number of significant figures.

Answer 1

Hello, Yasmine,

Density is defined as mass per unit volume. Typically, grams are used as the mass, but many other units can be found. The volume is usually expressed in cm³ . 1 cm³ is equivalent to 1 ml. Again, other units may be found. For this problem we will use g/cm³ to represent the density. So all we need to do is divide the nugget's mass (in grams) by it's volume( in cm³).

In this problem, we know the mass of the iron nugget is 8.14 g. We need it's volume. This was achieved by determining how much water (in ml) is displaced by the nugget. A measured volume of water (25.1cm³) was added to a graduated cylinder, but the final volume was measured to be 26.2 cm³. The difference between these two values represents the volume of the nugget. (1.1 cm³).

Density, then, is simply 8.14 g/(1.1 cm³) = 7.40 g/cm³. Three significant digits, since both inputs also have three sig figs.

I looked up the accepted value for iron's density: 7.874 g/cm³. Close, but there may impurities in the tested nugget, or the experiment had some error (e.g., inaccurate measurements or sloppy lab partner).

Bob