1. lecturePLUS Timberlake
An Introduction to Density by
Helen Hanson &
John Macaluso
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2. lecturePLUS Timberlake
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
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3. lecturePLUS Timberlake
Learning Check 1
Osmium is a very dense metal. What is its
density in g/cm3 if g of the metal occupies
a volume of 2.22cm3?
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Solution
Placing the mass and volume of the osmium metal into the density setup, we obtain
D = mass
volume
= g
2.22cm3
= g/cm3
= g/cm3
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5. lecturePLUS Timberlake
Volume Displacement
A solid displaces a matching volume of water when the solid is placed in water.
25 mL
33 mL
25 mL
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6. lecturePLUS Timberlake
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) g/cm3
33 mL
25 mL
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Solution
2) 6 g/cm3
Volume (mL) of water displaced
= mL mL = mL
Volume of metal (cm3)
= 8 mL x 1 cm3 = cm3
1 mL
Density of metal =
mass = 48 g = 6 g/cm3
volume cm3
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8. 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
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9. lecturePLUS Timberlake
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
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10. lecturePLUS Timberlake
Density of a Cylinder
Vcylinder = лr2h = л x 5 x 5 x 10 (cm)(cm)(cm)
= 250л cm3
r = radius
h = height D = 250/(250л) g/cm3
D = m/V D =1/л g/cm3
m = g D = g/cm3 r h
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11. lecturePLUS Timberlake
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.
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12. lecturePLUS Timberlake
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) ) ) V W K W V K W K V
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13. lecturePLUS Timberlake
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
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14. Density as Conversion Factors
A substance has a density of 3.8 g/mL.
Density = g/mL
Equality g = 1 mL
Conversion factors:
3.8 g and mL
1 mL g
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15. lecturePLUS Timberlake
Density Connections
Mass Volume
kg L
g mL (cm3) mg
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Learning Check
The density of octane, a component of gasoline, is g/mL. What is the mass, in kg, of 875 mL of octane?
1) kg
2) 614 kg
3) 1.25 kg
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Solution
1) kg
Unit plan: mL  g  kg
Equalities: 1 mL = g and 1 kg = 1000 g
Setup:
875 mL x g x kg = kg
1 mL g
density metric
factor factor
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18. lecturePLUS Timberlake
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) L
2) L
3) L
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Solution
1) Unit Plan: g mL L
575 g x mL x 1 L = L
1.05 g mL
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20. lecturePLUS Timberlake
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) L 2) 207 L 3) L
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Solution
1) 1.0 L
125 cans x 3g = 375g = mass
1 can
So, V = mass = 375g = 139mL = 0.139L
density g/mL
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22. lecturePLUS Timberlake
Learning Check
You have 3 metal samples. Which one will displace the greatest volume of water?
25 g Al
2.70 g/mL
45 g of gold
19.3 g/mL
75 g of Lead
11.3 g/mL
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Solution
1) 25 g Al x mL = 9.2 mL g
25 g Al
2.70 g/mL
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