Transcript Density
An Introduction to Density
by Helen Hanson & John Macaluso
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Density
Density is the ratio of the mass of an object to its volume D = mass = m volume V Units are g/cm 3 Note: 1 mL = 1 cm 3
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Learning Check 1
Osmium is a very dense metal. What is its density in g/cm 3 if 50.00 g of the metal occupies a volume of 2.22cm
3 ?
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Solution
Placing the mass and volume of the osmium metal into the density setup, we obtain D = mass = 50.00 g volume 2.22cm
3 = 22.5225 g/cm 3 = 22.52 g/cm 3
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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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Learning Check 2
What is the density (g/cm 3 ) 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/ cm 3 2) 6 g/m 3 3) 252 g/cm 3 25 mL 33 mL
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Solution
2) 6 g/cm 3 Volume (mL) of water displaced = 33 mL - 25 mL = 8 mL Volume of metal (cm 3 ) = 8 mL x 1 cm 3 = 8 cm 3 1 mL Density of metal = mass = 48 g = 6 g/cm 3 volume 8 cm 3
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Methods for Finding Volume
The density can also be found by calculating the volume of an object and measuring its mass.
V=(length)(width)(height)
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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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Density of a Cylinder
V cylinder = лr 2 h = л x 5 x 5 x 10 (cm)(cm)(cm) = 250л cm 3
r
r = radius h = height D = 250/(250л) g/cm 3 D = m/V D =1/л g/cm 3 m = 250.0 g D = 0.318 g/cm 3
h
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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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Learning Check 3
Which diagram represents the liquid layers in the cylinder?
1) (K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL) 2) 3) V W K W K V
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K V W
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1)
Solution
(K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL) V W K
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Density as Conversion Factors
A substance has a density of 3.8 g/mL. Density = 3.8 g/mL Equality 3.8 g = 1 mL Conversion factors: 3.8 g and 1 mL 1 mL 3.8 g
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Mass
Density Connections
Volume
kg g L mL (cm 3 ) 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
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Solution
1) 0.614 kg Unit plan : mL
g
kg Equalities : 1 mL = 0.702 g and 1 kg = 1000 g Setup: 875 mL x 0.702 g x 1 kg = 0.614 kg 1 mL 1000 g
density factor metric factor
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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
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Solution
1) Unit Plan: g mL L 575 g x 1 mL x 1 L = 0.548 L 1.05 g 1000 mL
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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
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Solution
1) 1.0 L 125 cans x 3g 1 can = 375g = mass So, V = mass = 375g = 139mL = 0.139L
density 2.7 g/mL
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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 75 g of Lead 11.3 g/mL
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Solution
1)
25 g Al x 1 mL = 9.2 mL 2.70 g
25 g Al 2.70 g/mL
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