Density, Mass, & Volume
Concepts & Equations
Mass
• Measurement of the amount of matter, or
stuff, an object has
– Measured in grams (g)
Volume
• Measurement of the amount of space an
object takes up
– Measured in milliliters (mL) or cm3
Density
• Measurement of the amount of mass an
object has per its volume
– Derived unit:
g/mL
• Comes from units of mass per units of volume
Density as a ratio
• Density can be viewed as the ratio of an
object’s mass to its volume
Mass : Volume
Graphing Density
• On the vertical, or y-axis, mass is plotted
• On the horizontal, or x-axis, volume is
plotted
• The resulting line that comes from plotting
coordinates on the graph represents the
density
1cc = 1mL
Remember Slope?
• Rise over run
– It’s the amount that a y value changes
compared to how much an x value changes
• It’s a ratio of y values to x values
Slope of Mass v Volume
• If we figure out how much the mass
changes (∆) compared to how much the
volume changes, we get a slope that is a
ratio of mass to volume
– That slope will look like this:
∆Mass
∆Volume
THAT’S DENSITY!!!!!
The “bounceability” of a
ball depends on its
density, not on its mass or
on how big the ball is.
Drop height vs. Bounce height
Density
200
Large ball – 0.53 g/cm3
B ounc e he ight (c m )
Medium ball – 1.05 g/cm3
Small ball – 0.82 g/cm3
101 grams
100
62 grams
19 grams
0
190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30
Drop height (cm)
Density Equation
• Density = mass divided by volume
• g/mL = g divided by mL
Let’s use density!
D=m/v
m
d
v
How to use
the circle
m
d
v
• Using info from problem,
determine what you are
trying to find.
• Cover up the variable
you’re trying to find
• Do the calculation that’s
left.
EXAMPLE:
Covering up mass
leaves density x volume
Problem 1
The mass of a silver bracelet is 2.5
grams, it occupies a volume of 48cm3,
what is its density?
Problem 2
The density of silver (Ag) is 10.5 g/cm3.
Find the mass of Ag that occupies 965
cm3 of space.
Problem 3
A 2.75 kg sample of a substance occupies
a volume of 250.0 mL. What is its density?
Problem 4
A rectangular block of Lead (Pb)
measures 20.0 mm X 30.0 mm X 45.0
mm. If the mass of the Pb block is 10g,
find its density.
Problem 5
A cube of gold (Au), which has all equal
sides, has a side length of 1.55 cm. If the
sample is found to have a mass of 71.9 g,
find the density of Au.
Ways to Affect Density
• Change mass AND keep volume same
• Change volume AND keep mass same
Change Mass AND Keep Volume Same
• Increase the mass  increase density
• Decrease the mass  decrease in density
Which container has more density?
A
B
Change Volume AND Keep Mass Same
• Increase the volume  decrease density
• Decrease the volume  increase density
Which container has more density?
A
B
What 2 ways will INCREASE density?
What 2 ways will INCREASE density?
Keep the
same
mass AND
decrease
the volume
Keep the
same
volume
AND
increase
the mass
Comparing Densities
• Objects or substances with MORE density
will sink below objects or substances with
LESS density
– Which do you think is MORE dense,
Water or Oil???
Water, Oil…and a Superball
The oil is less dense than the water, so it’s on top. The superball
is less dense than water, but more dense than oil, so it sinks to
the bottom of the oil layer, yet floats on the top of the water layer.
Why does ice float in
water?
Have you wondered why hot air balloons rise?
When the air is heated, it becomes less dense until
the balloon's total density is less than that of the
atmosphere; A hot air balloon is literally floating on
the denser, colder air.
Why is cold air denser than hot air?
Do you know why volcanoes erupt?
The main reason that magma rises to the
surface to erupt at volcanoes is because it is
less dense than the rocks that surround it.
A ship floating on water is a great illustration of the difference
between mass and density. A ship must have a density of less
than 1.0 g/cm3 (the density of water), or it will sink. Ships have
a large mass, because they are made of steel, but because
they have a large volume, their density is less than 1.0 g/cm3. If
enough mass is added to them such that their density goes
above 1.0 g/cm3, they will sink.
In Conclusion
• If you have 2 substances,
– the MORE dense substance will be on bottom
– The LESS dense substance will be on top
Think About This
• The density of five liquids are measured
as follows:
– Liquid 1: 1.0 g/mL
– Liquid 2: 1.38 g/mL
– Liquid 3: 0.77 g/mL
– Liquid 4: 2.95 g/mL
– Liquid 5: 0.056 g/mL
• Draw a picture of all 5 liquids in a test tube
how they would layer according to density
Think About This
• The density of five liquids are measured
as follows:
– Liquid 1: 1.0 g/mL
– Liquid 2: 1.38 g/mL
– Liquid 3: 0.77 g/mL
– Liquid 4: 2.95 g/mL
– Liquid 5: 0.056 g/mL
Liquid 5
Liquid 3
Liquid 1
Liquid 2
Liquid 4
• Draw a picture of all 5 liquids in a test tube
how they would layer according to density