Lesson Video: Matter and Density | Nagwa Lesson Video: Matter and Density | Nagwa

Lesson Video: Matter and Density Science

In this video, we will learn how to define density, calculate the density of a substance, and predict whether it will float or sink in water.

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Video Transcript

In this video, we will learn how to define density and examine how the densities of different objects cause them to sink or float. We will also learn how to calculate density and how to use density to identify unknown materials.

So, what is density? We use observations to gather information about objects around us. By observing the physical properties of objects, we can identify them. One physical property of matter is density. Density can be defined as the amount of mass per unit volume. We know that mass is the amount of matter in an object. We often measure mass using a balance or scale. Mass can be measured in grams. The volume of an object measures how much space an object takes up.

There are many ways to measure volume. One unit that can be used to measure volume is cubic centimeters. So, the density of an object measures how much mass occupies a certain amount of space. This is why density can be referred to as the compactness of a substance. For example, two objects could occupy the same amount of space. But one object may have more matter, in other words, mass, in that space. The substance with more mass in the same amount of space is more dense. Since density is mass per volume, where a unit for mass is grams and a unit for volume is cubic centimeters, density can be measured in grams per cubic centimeter. Let’s take a look at how density can be used.

Comparing densities of objects can allow us to identify and learn more about a material. The behavior of a material in a liquid or gas can tell us about its density. One liquid we can use is water. Water usually has a density of one gram per cubic centimeter. If we add wood to water, it will most likely float. The density of many types of wood is 0.6 grams per cubic centimeter. When the density of an object is less than the density of the liquid or gas into which it is placed, in this case water, it will float. Since the density of wood is less than the density of water, wood floats in water.

Aluminum has a density of 2.7 grams per cubic centimeter. When added to water, it sinks. This is because when the density of an object is greater than the density of water, it sinks. Water is one type of substance that can be used to compare the densities of objects, but let’s look at another example.

Balloons are often filled with a gas, such as helium. Helium gas has a very low density of 0.000178 grams per cubic centimeter. The air surrounding us generally has a density of 0.001225 grams per cubic centimeter. So, air has quite a low density as well. We can compare the density of helium to the density of the surrounding air to explain how helium balloons behave. While the densities of both gases are very small, the density of helium is much lower than the density of air. Therefore, helium balloons float up in the air. They will float away unless we hold them down.

Let’s have a look at some other ways we can use the densities of materials.

We can calculate the density of an object. The equation for the density of an object in grams per cubic centimeter is density equals the mass of the object in grams divided by the volume of that object in cubic centimeters. The densities of many materials are well known, and we can use the known densities to identify objects. For example, we might have a block of unidentified metal. We measure that the mass of the block is 965.0 grams and the volume is 50.0 cubic centimeters. To find the density of the block, we can divide the mass of 965.0 grams by the volume of 50.0 cubic centimeters. This gives us a density of 19.3 grams per cubic centimeter.

If we compare this to a list of known densities, we can see that the block is likely gold. More tests would be needed to confirm this, but density is an excellent way to begin identifying unknown materials. We can also use the density equation to find the mass or volume of an object. The equation can be rearranged to solve for mass in grams. The mass of an object is equal to the density of the object multiplied by the volume. The equation can also be rearranged to solve for volume in cubic centimeters. The volume of an object is equal to the mass of the object divided by its density.

Let’s take, for example, a sample of cork. Since we know the object is cork, we can state its known density, which is 0.2 grams per cubic centimeter. We are given that the volume of the cork is 10 cubic centimeters. We can solve for the mass of the cork using the equation mass equals density times volume. So the mass of the cork will be equal to the density of 0.2 grams per cubic centimeter times the volume of 10 cubic centimeters. Therefore, the mass of the cork is two grams.

Now, let’s look at some practice problems.

A substance has a mass of 13.5 grams and occupies a volume of five cubic centimeters. What is its density?

In this question, we are calculating density. We must find the density of an unidentified substance. Density is defined as the mass per unit volume. Density can be measured in grams per cubic centimeter. The density of an object is equal to the mass of the object in grams divided by the volume of the object in cubic centimeters. We are given the mass of the object, which is 13.5 grams. We are also given the volume, which is five cubic centimeters. We can use the equation and the values we are given to find the density of the substance. So the density will be equal to 13.5 grams divided by five cubic centimeters. This is equal to 2.7 grams per cubic centimeter. Therefore, the density of this substance is 2.7 grams per cubic centimeter.

The image below shows a tank of water into which various objects have been placed. Which of the following statements might explain what is observed? (A) The ice cube and cork have densities greater than the density of water. (B) The cork and stone have densities less than the density of water. (C) The stone and iron nail have densities greater than the density of water. (D) The piece of wood and iron nail have densities less than the density of water. Or (E) the objects all have the same density as water.

The relationship between the density of an object and the density of water tells us whether an object will sink or float. If an object has a density that is less than the density of water, it will float when placed in water. The ice cube, piece of wood, and cork are all floating in the tank of water. We know that these objects must have densities less than the density of water. When an object has a density greater than the density of water, it will sink. The stone and iron nail have densities greater than the density of water since they sink in the tank of water. Looking at the answer choices, we can see that statement (C) is correct. Therefore, the statement that explains what is observed in the tank of water is the stone and iron nail have densities greater than the density of water.

A student wants to determine the density of a liquid. They first weigh a glass beaker and then add exactly 50 cubic centimeters of the liquid into the beaker. Finally, the glass beaker is weighed again. The student records their measurements in the table shown below. Using this information, what is the density of the liquid to one decimal place?

We are asked to calculate the density of an unknown liquid. The density of a material is equal to its mass divided by its volume. We are told that the volume of the liquid is 50 cubic centimeters. We know that the student finds the mass of the empty glass beaker, which is 67 grams. The student adds the liquid into the same beaker and finds the mass of both the beaker and liquid to be 112 grams. To find the density of the liquid, we first need to calculate the mass of the liquid only. The mass of the liquid only will be the mass of the glass beaker and liquid minus the mass of just the glass beaker. So, we need to take the mass of the beaker and liquid, which is 112 grams, and subtract the mass of the beaker only, which is 67 grams. Therefore, the mass of the liquid only is 45 grams.

Now that we know the mass of the liquid, we can use the equation for density to find the density of the liquid. The density will be equal to the mass of 45 grams divided by the volume of 50 cubic centimeters. Performing the calculation, we find the density to be 0.9 grams per cubic centimeter. Our answer is already to one decimal place. Therefore, the density of the liquid is 0.9 grams per cubic centimeter.

Let’s review what we have learned. Density is the amount of mass per unit volume. The density in grams per cubic centimeter is equal to the mass in grams divided by the volume in cubic centimeters. The equation for density can be rearranged to solve for the mass or volume of an object whose density we know. The differences in densities of an object and its surroundings determine if the object will sink or float in the surrounding liquid or gas. If an object has a density less than the density of water, it will float in water. If an object has a density that is greater than the density of water, it will sink. The density of unknown materials can be used to identify them.