LecturePLUS Timberlake1 by Helen Hanson & John Macaluso An Introduction to Density.

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byHelen Hanson &John Macaluso

An Introduction to Density

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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/cm3

Note: 1 mL = 1 cm3

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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?

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Solution

Placing the mass and volume of the osmium metal into the density setup, we obtain

D = mass volume

= 50.00 g

2.22cm3

= 22.5225 g/cm3

= 22.52 g/cm3

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Volume Displacement

A solid displaces a matching volume of water when the solid is placed in water.

25 mL

25 mL33 mL

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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

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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 = 8 cm3

1 mLDensity of metal =

mass = 48 g = 6 g/cm3

volume 8 cm3

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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.

length

width

heightV=(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

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 = 250.0 g D = 0.318 g/cm3

r

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 3Which 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)

K

K

V

W K

W

V

V

W

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Solution (K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL)

1)

K

V

W

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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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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 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 gdensity metric

factor 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 = 375g = mass

1 can

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 Al2.70 g/mL

45 g of gold19.3 g/mL

75 g of Lead11.3 g/mL

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Solution

1) 25 g Al x 1 mL = 9.2 mL 2.70 g

25 g Al2.70 g/mL