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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