notes: 3.2 - density what is density and how is it determined? density = the ratio of the mass of an...
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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