NOTES: 3.2 - Density

What is DENSITY and how is it determined? DENSITY = the ratio of the mass of an

object to its volume

Density = Mass

Volume

The density of a substance changes with temperature

Example:

38.6 g of gold was placed in a graduated cylinder and displaced 2.00 mL of water. What is the density of gold?

DENSITY = =

Example:

38.6 g of gold was placed in a graduated cylinder and displaced 2.00 mL of water. What is the density of gold?

DENSITY = 38.6 g = 19.3 g/mL

2.00 mL

Example: What is the mass of 10. mL of a liquid

that has a density of 3.76 g/mL?

D = m / V

m = D ● V

m =

m =

m = (correct # of sig. figs.)

Example: What is the mass of 10. mL of a liquid

that has a density of 3.76 g/mL?

D = m / V

m = D ● V

m = (3.76 g/mL)(10. mL)

m = 37.6 g

m = 38 g (correct # of sig. figs.)

EXAMPLE: The density of ethanol is 0.789 g/cm3. Calculate the volume, in liters, of a sample of ethanol that has a mass of 7.72 kg.

EXAMPLE: The density of ethanol is 0.789 g/cm3. Calculate the volume, in liters, of a sample of ethanol that has a mass of 7.72 kg.

**mass = 7.72 kg = 7720 g

D = m / V

EXAMPLE: The density of ethanol is 0.789 g/cm3. Calculate the volume, in liters, of a sample of ethanol that has a mass of 7.72 kg.

0.789 g/cm3 = 7720 g / V

V = 7720 g = 9,780 mL = 9.78 L

0.789 g/cm3

NOTES: 3.3 – Dimensional Analysis

Performing these conversions is a lot like going on a road

trip.

Let’s say you want to travel from Oracle Jct. to Casa Grande...

You must travel through Tucson… a two part trip.

Rule: You must stay on the roads

OK…Lets talk about making maps and solving conversion

problems. The method we use is called the “Factor-Label”

method, a.k.a. DIMENSIONAL ANALYSIS.

gallons kildurkins

For example: given 1 kildurkin = 18 gallons

This is our map.

gallons kildurkins

For example: given 1 kildurkin = 18 gallons

How many kildurkins is 14 gallons?

1 kildurkin

18 gallons

14 gallons= 0.78 kildurkins

General Format...

going to

coming from

given

gallons kildurkins

Also given: 2 farkins = 1 kildurkin

farkins

Let’s expand the map...

gallons kildurkins

Also given: 1 hogshead = 63 gallons

farkins

hogshead

1 barrel = 3.3 bushels

bushel barrel

1 bushel = 8 gallons

gallons kildurkins farkins

hogshead

bushel barrel

How many hogsheads are 14 barrels?

Given: Start Here

Finish Here

The trip will require 3 transitions

1

2

3

gallons

hogshead

bushel barrel

How many hogsheads are 14 barrels?

1

2

3

Given fromcoming

togoing

fromcoming

togoing

fromcoming

togoing

14 barrels 3.3 bushels

1 barrel

8 gallons

1 bushel

1 hogshead

63 gallons

= 5.9 hogsheads

gallons kildurkins farkins

hogshead

bushel barrel

Now you try one:

How many farkins is 3.00 bushels?

Start Here

End Here

This will require 3 conversions.

bushels gallons kildurkins farkins

3.00 bushels 8 gallons

1 bushel

1 kildurkin

18 gallons

2 farkins

1 kildurkin

= 2.67 farkins

Use dimensional analysis when converting between units.

Ex: How many inches are in 1500 meters?

in 59400ft 1

in 12

mile 1

ft 5280

m 1600

mile 1

1

m 1500

in 109.5 4

**Now let’s revisit the same density problem from earlier but solve it with DIMENSIONAL ANALYSIS.

EXAMPLE: The density of ethanol is 0.789 g/cm3. Calculate the volume, in liters, of a sample of ethanol that has a mass of 7.72 kg.

EXAMPLE: The density of ethanol is 0.789 g/cm3. Calculate the volume, in liters, of a sample of ethanol that has a mass of 7.72 kg.

L 78.9cm 1000

L 1

g 0.789

cm 1

kg 1

g 1000kg 7.723

3

Example:

If the density of Al is 2.71 g/cm3, what is the density of Al in kg/m3?

Example:

If the density of Al is 2.71 g/cm3, what is the density of Al in kg/m3?

33

3/710,2

m 1

cm 100

g 1000

kg 1

cm

g 2.71mkg