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.
