Explaining the Concept of Density: Definition, Formula & Practice Problems

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What is Density?

Density is defined as mass per volume. You can think of it as how many particles of a substance are packed into a certain amount of space. If the particles are packed tightly together, the density would be greater than if they are loosely packed with a lot of empty space around them.

Here are some examples:

Two people get into an elevator on the 10th floor. As the elevator goes down, it stops at each floor and two more people get in. The density of people in the elevator increases as it descends, because there are more people crowded together in the same amount of space. On the 10th floor, there is a lot of space between the people and not very much mass in the elevator. As more and more people get in, the mass increases and the people are crowded closer and closer together, but the volume (amount of space inside the elevator) remains the same. Therefore, the density is much greater when the elevator reaches the ground floor than it was at the 10th floor.

If you put 10 Styrofoam peanuts into a shoe box, there is a lot of space between them, and the density is low. If you cram 1,000 Styrofoam peanuts into the shoe box, the mass will increase but the volume will remain the same, so the density will increase.

How to Calculate Density

Density is mass per volume. When you see the word “per” it always means “divide.” So to calculate the density, we divide the mass by the volume. Mass is measured in grams, and volume is measured in cubic centimeters, so density is usually expressed in grams per cubic centimeter, or g/cm3. Density can be calculated by dividing the mass in grams by the volume in cubic centimeters.

Density is an intrinsic physical property of a substance, and the density remains constant even if the total amount of the substance changes. The density of lead is 11.34 g/cm3. If you have a piece of lead with a volume of 1 cubic centimeter, the mass will be 11.34 grams and the density will be 11.34 divided by 1, or 11.34 g/cm3. If you have a larger piece of lead, say 5 cubic centimeters in volume, the mass will be 56.7 grams, but when we divide the mass by the volume, 56.7 divided by 5, the density will still be 11.34 g/cm3. The total mass and volume may change, but the density will always be the same for a particular substance.

Practice Problems

The formula for calculating density is D = M/V

1. A rock has a mass of 20 grams and a volume of 4 cubic centimeters. What is its density?

Solution: 20 g divided by 4 cm3 = 5 g/cm3

2. A piece of aluminum has a volume of 6 cm3 and a mass of 16.2 g. What is its density?

Solution: 16.2 g divided by 6 cm3 = 2.7 g/cm3

3. A gold nugget has a density of 19.3 g/cm3 and a mass of 135.1. What is its volume?

Solution: In this problem, you know the density and the mass, but not the volume. if you know two of the values, you can solve for the third by rearranging your formula, D= M/V, to solve for volume. The new formula is V = M/D. 135.1 g divided by 19.3 g/cm3 = 7 cm3

4. A brick has a density of 6 g/cm3 and a volume of 150 cm3. What is its mass?

Solution: Here again you have two of the values, and you can solve for the third by rearranging your formula to solve for mass. The new formula is M = D x V. 6 g/cm3 x 130 cm3 = 900 g.