Forgetful Freddie placed 25.0 mL of a liquid in a graduated cylinder with a mass of 89.450 g when empty. When Freddie placed a metal slug with a mass of 15.454 g into the cylinder, the volume rose to 30.7 mL. Freddie was asked to calculate the density of the liquid and of the metal slug from his data, but he forgot to obtain the mass of the liquid. He was told that if he found the mass of the cylinder containing the liquid and the slug, he would have enough data for the calculations. He did so and found its mass to be 125.934 g. Calculate the density of the liquid and of the metal slug.

Density Liquid = 0.841 g/mL Density Metal = 2.711 g/cm³

Explanation:

The density of the liquid is:

Mass Liquid / Volume Liquid

From the problem we know that Volume Liquid = 25.0 mL, the mass of the liquid can be calculated by substracting masses:

Mass Liquid + Mass Slug + Mass Empty Cylinder = 125.934 g Mass Liquid + 15.454 g + 89.450 g = 125.934 g Mass Liquid = 125.934 g - 15.454 g - 89.450 g Mass Liquid = 21.030 g

Thus the density of the liquid is:

Density Liquid = 21.030 g / 25.0 mL = 0.841 g/mL

2. The density of the metal slug is:

Mass Metal / Volume Metal

We already know that the mass of the slug is 15.454 g. Its volume can be calculated using Archimede's principle, which states that the volume of an object is equal to the volume of liquid it displaces, in other words:

Volume Metal = 30.7 mL - 25.0 mL = 5.7 mL

Thus the density of the metal slug is

Density Metal = 15.454 g / 5.7 mL = 2.711 g/mL = 2.711 g/cm³