Calculating Density with Mass vs. Volume Graphs

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  • 0:00 What Is Density?
  • 0:56 Mass vs. Volume Graphs
  • 1:45 Comparing Density
  • 2:09 Identifying Substances
  • 3:51 Lesson Summary
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Lesson Transcript
Instructor: Amanda Robb

Amanda holds a Masters in Science from Tufts Medical School in Cellular and Molecular Physiology. She has taught high school Biology and Physics for 8 years.

In this lesson, we'll learn what density is and how to calculate it. We'll also learn how to graph mass versus volume to find density for different objects.

What Is Density?

Picture dropping a penny and a bottle cork into a pond. You'd probably expect the penny to sink, even though it's smaller in size than the cork, but why? It has to do with density, or the amount of mass contained in a certain volume. If something has a greater density, like the penny, it means there is more matter in the same amount of volume. The penny is more dense than the cork and water, so it sinks. Although larger than the penny, the cork is less dense than the penny. It's also less dense than the water, so it floats. But without this experiment, how can we figure out which object is denser?

Density is equal to mass divided by volume (D = m / v), so if you know the mass and volume of an object, you can calculate density. Sometimes, you'll be given this information outright, but other times you might be given a graph of mass versus volume. Let's learn how you can use the information in this type of graph to calculate density.

Mass vs. Volume Graphs

A mass versus volume graph has mass, usually in grams or kilograms, on the y-axis, which is the vertical axis, and volume on the x-axis, which is the horizontal access.

You can use this graph to figure out how much mass is in any given volume of a substance. Using the x-axis, locate the volume you're wondering about, then find the y-intercept and use the y-axis to find how much mass there is in that much volume. For example, if we had a sample of copper with a volume of six cubic centimeters, based on the mass versus volume graph, the mass would be 50 grams.

Mass versus volume graph for copper
density graph for copper

The formula for the slope of a straight line is the change in y divided by the change in x. Since the y axis is equal to mass, and the x axis is equal to volume, slope is equal to mass divided by volume. Therefore, the slope of a mass versus volume graph is equal to density.

Calculation of slope using the change in mass divided by the change in volume gives you density for any substance
density graph calculations

Comparing Density

Since slope is equal to density, simply glancing at a mass versus volume graph can sometimes help you identify which of the two substances has a greater density. A steeper line indicates a greater slope and thus a greater density. So, whichever substance has a steeper line has a greater density. You can also use the calculations we just discussed to find the density of a substance. We'll do this in an example in the next section of the lesson.

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