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Ohio State Test - Physical Science: Practice & Study Guide17 chapters | 128 lessons | 9 flashcard sets

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Lesson Transcript

Instructor:
*Amanda Robb*

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.

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.

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.

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.

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.

Another way you can use mass versus volume graphs is to help identify unknown substances. Let's look at an example. Say Karen gets a ring from her boyfriend. He claims the ring is solid gold, but Karen is skeptical. From her physics class she knows that all elements have a characteristic density based on the size of their atoms. Using a mass versus volume graph for gold, Karen can easily find its density.

She'll use the formula for slope and two points on the graph. She picks 40g of mass with 2.0704 cubic centimeters of volume for her first point, and 60g of mass with 3.1056 cubic centimeters of volume for her second. Karen then uses the formula for slope: (60 - 40) / (3.1056 - 2.0704) = 20 / 1.0352, which equals 19.32 grams per cubic centimeter, the density of gold.

Now, Karen needs to take some measurements of her ring to figure out if its density matches that of gold. First, she uses the balance to measure the mass of the ring, which is 1.35g. She also needs the volume. To do this, Karen fills a graduated cylinder with 100 milliliters of water and then drops in the ring. The volume of the ring displaces the water. Karen measures the new volume of the water, 100.5 milliliters, and then subtracts 100 milliliters. She's left with 0.5mL, which is equal to 0.5 cubic centimeters, the volume of her ring.

Dividing the mass she measured by the volume gets her 2.7 grams per cubic centimeter, which is the density of aluminum. Looks like Karen's soon-to-be ex-boyfriend wasn't telling the truth after all.

Let's review. **Density** is the amount of matter contained in a specific volume. You can calculate density by dividing the mass of a substance by the volume. In a mass versus volume graph, mass is on the *y*-axis, and volume is on the *x*-axis. You can use this type of graph to calculate density by determining the **slope**, which is the change in *y* divided by the change in *x*. Mass versus volume graphs also can be used to help identify known substances and to compare the density of two objects based on the slope.

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Ohio State Test - Physical Science: Practice & Study Guide17 chapters | 128 lessons | 9 flashcard sets

- Matter: Physical and Chemical Properties 7:22
- Examples of Intensive & Extensive Properties of Matter 6:27
- The Rate of Dissolution: Factors and Definition 5:26
- Chromatography, Distillation and Filtration: Methods of Separating Mixtures 8:26
- States of Matter and Chemical Versus Physical Changes to Matter 6:42
- The Kinetic Molecular Theory: Properties of Solids and Liquids 8:07
- The Kinetic Molecular Theory: Properties of Gases 6:49
- Phase Diagrams: Critical Point, Triple Point and Phase Equilibrium Boundaries 3:29
- Phase Change: Evaporation, Condensation, Freezing, Melting, Sublimation & Deposition 5:03
- Heat of Fusion & Heat of Vaporization: Definitions & Equations 7:52
- Thermal Expansion: Importance & Examples 5:36
- Calculating Density with Mass vs. Volume Graphs 4:28
- Go to Ohio State Test - Physical Science: Matter

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