Density Calculations

How do you calculate the density of a substance?

Covered in This Lesson

• This lesson will demonstrate how to calculate density to the correct number of significant figures(sig figs) using experimental measurements.–When calculating density we measure the

mass and the volume of the sample.– The volume can be measured using one of

several methods.

Density Formual

• When calculating density you measure the –mass of the sample using a balance – volume of the sample from one of the

methods– apply the formula: mass/volume = density or

m = dV

Methods: Volume

• There are three methods to measure the volume of a substance. The method used is determined by the type of substance.

• Methods for the;1. volume of liquid 2. volume of regular solid3. volume of irregular solid.

Volume of a Liquid

• If the substance is a liquid, measure it directly in a graduated cylinder.

Examples 1

• If a liquid sample has a mass of 4.83 g and a volume of 2.7 mL what is its density.

4.83 g = 1.788889 2.7 mL

Because 2.7 has 2 sig figs the final answer is 1.8 g/mL

Volume of a Regular Solid

• If you have a regular solid like a cylinder, cube, or rectangular solid measure the dimensions needed and apply the volume formula.

Examples 2• If cubic solid sample has a mass of 40.53 g and

the side is 2.55 cm, what is its density.

V = s3 = (2.55 cm) 3 = 16.581375 cm3

D = 40.53 g = 2.44430875 16.581375 cm3

Because 2.55 has 3 sig figs the final answer is 2.44 g/cm3

Volume of a Irregular Solid

• If you have an irregular solid use displacement, take initial volume of water in a graduated flask, submerging the sample in the flask, and take the final volume while the solid is submerged. Subtract final volume minus initial volume.

Examples 3• Find the density of a solid sample with a mass of

75.45 g and displacement is used to find the volume, the initial volume is 20.39 mL, the final volume is 73.57 mL. V = 73.57 mL – 20.39 mL = 53.18mL 75.45 g = 1.418766454 g/mL 53.18mL

Since both mass and volume have 4 sig figs the final answer is 1.419 g/mL

Practice Problems

1. Find the density of a liquid with a volume of 3.8 mL and a mass of 3.75 g.

2. Find the density of a rectangular solid with a length of 4.5 cm, a width of 2.5 cm, a height of 1.5 cm and a mass of 47.12 g.

3. Find the density of an irregular solid with a mass of 1.2 g, an initial volume of 25.7 mL and final volume of 18.4 mL when displacement is used.

Answers Practice Problems

1. Density = 0.99 g/mL2. Density = 2.79 g/cm3

3. Density = 8.8 g/mL