An Introduction to Density
by
Helen Hanson &
John Macaluso
lecturePLUS Timberlake
1
Density
Density is the ratio of the mass of an object to
its volume
D =
mass
= m
volume
V
Units are g/cm3
Note: 1 mL = 1 cm3
lecturePLUS Timberlake
2
Learning Check 1
Osmium is a very dense metal. What is its
density in g/cm3 if 50.00 g of the metal occupies
a volume of 2.22cm3?
lecturePLUS Timberlake
3
Solution
Placing the mass and volume of the osmium metal
into the density setup, we obtain
D = mass = 50.00 g
volume 2.22cm3
= 22.5225 g/cm3
= 22.52 g/cm3
lecturePLUS Timberlake
4
Volume Displacement
A solid displaces a matching volume of water
when the solid is placed in water.
25 mL
33 mL
25 mL
lecturePLUS Timberlake
5
Learning Check 2
What is the density (g/cm3) of 48 g of a metal if
the metal raises the level of water in a graduated
cylinder from 25 mL to 33 mL?
1) 0.2 g/ cm3 2) 6 g/m3 3) 252 g/cm3
33 mL
25 mL
lecturePLUS Timberlake
6
Solution
2) 6 g/cm3
Volume (mL) of water displaced
= 33 mL - 25 mL = 8 mL
Volume of metal (cm3)
= 8 mL x 1 cm3 =
1 mL
Density of metal =
mass
= 48 g
volume
8 cm3
= 6 g/cm3
8 cm3
lecturePLUS Timberlake
7
Methods for Finding Volume
The density can also be found by
calculating the volume of an object and
measuring its mass.
height
V=(length)(width)(height)
width
length
lecturePLUS Timberlake
8
Density of a Cylinder

What is the density of a cylinder with a
mass of 250.0g, a radius of 2.0 cm, and a
height of 10.0 cm?
r
h
lecturePLUS Timberlake
9
Density of a Cylinder
Vcylinder = лr2h = л x 5 x 5 x 10 (cm)(cm)(cm)
= 250л cm3
r
r = radius
h = height
D = 250/(250л) g/cm3
D = m/V
D =1/л g/cm3
m = 250.0 g
D = 0.318 g/cm3
lecturePLUS Timberlake
h
10
Why Do Things Float?
Things (whether solid, liquid or gas) with
LESS density will float in a liquid with
GREATER density.
For example, this is why a stone (with HIGH
density) will sink in water (LOW density), but
a cork (LOW density) will float in water.
lecturePLUS Timberlake
11
Learning Check 3
Which diagram represents the liquid layers in
the cylinder?
(K) Karo syrup (1.4 g/mL), (V) vegetable oil
(0.91 g/mL,) (W) water (1.0 g/mL)
1)
2)
3)
V
W
K
W
K
V
K
V
W
lecturePLUS Timberlake
12
Solution
(K) Karo syrup (1.4 g/mL), (V) vegetable oil
(0.91 g/mL,) (W) water (1.0 g/mL)
1)
V
W
K
lecturePLUS Timberlake
13
Density as Conversion Factors
A substance has a density of 3.8 g/mL.
Density
= 3.8
Equality
g/mL
3.8 g = 1 mL
Conversion factors:
3.8 g
1 mL
and
1 mL
3.8 g
lecturePLUS Timberlake
14
Density Connections
Mass
Volume
kg
L
g
mL (cm3)
mg
lecturePLUS Timberlake
15
Learning Check
The density of octane, a component of
gasoline, is 0.702 g/mL. What is the
mass, in kg, of 875 mL of octane?
1) 0.614 kg
2) 614 kg
3) 1.25 kg
lecturePLUS Timberlake
16
Solution
1) 0.614 kg
Unit plan: mL  g  kg
Equalities: 1 mL = 0.702 g
Setup:
875 mL x 0.702 g
1 mL
density
factor
x
and 1 kg = 1000 g
1 kg
1000 g
= 0.614 kg
metric
factor
lecturePLUS Timberlake
17
Learning Check
If blood has a density of 1.05 g/mL, how
many liters of blood are donated if 575 g of
blood are given?
1) 0.548 L
2) 1.25 L
3) 1.83 L
lecturePLUS Timberlake
18
Solution
1) Unit Plan: g
575 g x
mL
L
1 mL x 1 L
= 0.548 L
1.05 g
1000 mL
lecturePLUS Timberlake
19
Learning Check
A group of students collected 125 empty
aluminum cans to take to the recycling
center. If each can has a mass of 3g what
volume of aluminum can be made if the
cans were melted (Hint: d = 2.7 g/mL)?
1) 0.139L 2) 207 L 3) 4.85 L
lecturePLUS Timberlake
20
Solution
1) 1.0 L
125 cans x
3g
= 375g = mass
1 can
So, V = mass = 375g = 139mL = 0.139L
density 2.7 g/mL
lecturePLUS Timberlake
21
Learning Check
You have 3 metal samples. Which one will displace
the greatest volume of water?
1
2
3
25 g Al
2.70 g/mL
45 g of gold
19.3 g/mL
lecturePLUS Timberlake
75 g of Lead
11.3 g/mL
22
Solution
1)
25 g Al x 1 mL = 9.2 mL
2.70 g
25 g Al
2.70 g/mL
lecturePLUS Timberlake
23