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

19018017016015014013012011010090 80 70 60 50 40 300

100

200

Drop height (cm)

Bo

un

ce

he

igh

t (c

m)

101 grams

62 grams

19 grams

Density

Large ball – 0.53 g/cm3

Medium ball – 1.05 g/cm3

Small ball – 0.82 g/cm3

Density Equation

• Density = mass divided by volume

• g/mL = g divided by mL

Let’s use density!

d v

m

D = m / v

How to use the circle

• 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

d v

m

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 SuperballThe 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

• Draw a picture of all 5 liquids in a test tube how they would layer according to density

Liquid 5

Liquid 3

Liquid 1

Liquid 2

Liquid 4