NOTES: 3'4 Density

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NOTES 3.4 - Density
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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

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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

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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

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• 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.)

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• 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.)

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• 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.

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• 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

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• 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

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NOTES 4.3 Dimensional Analysis
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Dimensional Analysis
Performing these conversions is a lot like going
on a road trip.
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Lets say you want to travel from Oracle Jct. to
Casa Grande...
You must travel through Tucson a two part trip.
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Rule You must stay on the roads
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OKLets talk about making maps and solving
conversion problems. The method we use is called
the Factor-Label method, a.k.a. DIMENSIONAL
ANALYSIS.
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For example given 1 kildurkin 18 gallons
kildurkins
gallons
This is our map.
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For example given 1 kildurkin 18 gallons
kildurkins
gallons
How many kildurkins is 14 gallons?
1 kildurkin
14 gallons
0.78 kildurkins
18 gallons
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General Format...
going to
given
coming from
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Lets expand the map...
Also given 2 farkins 1 kildurkin
kildurkins
farkins
gallons
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Also given 1 hogshead 63 gallons
1 barrel 3.3 bushels
hogshead
1 bushel 8 gallons
kildurkins
farkins
gallons
barrel
bushel
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How many hogsheads are 14 barrels?
Finish Here
hogshead
kildurkins
farkins
3
gallons
2
barrel
bushel
Given Start Here
1
The trip will require 3 transitions
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How many hogsheads are 14 barrels?
hogshead
Given
3
gallons
14 barrels
3.3 bushels
8 gallons
1 hogshead
63 gallons
1 barrel
1 bushel
2
5.9 hogsheads
barrel
bushel
1
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Now you try one How many farkins is 3.00
bushels?
End Here
hogshead
kildurkins
farkins
gallons
Start Here
barrel
bushel
This will require 3 conversions.
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farkins
bushels
gallons
kildurkins
3.00 bushels
8 gallons
1 kildurkin
2 farkins
1 kildurkin
1 bushel
18 gallons
2.67 farkins
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Use dimensional analysis when converting between
units.

• Ex How many inches are in 1500 meters?

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• Now lets revisit the same density problem from
  earlier but solve it with DIMENSIONAL ANALYSIS.

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• 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.

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• 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.

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Example

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

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Example

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