Dimensional Analysis
Dimensional Analysis
Lesson 3
Lesson three
Terminal Objective
Students will demonstrate an
CA Science Content
Standards:
analysis to convert from one unit to
Chemistry: Conservation of
Matter and Stoichiometry
amount.
3.a D
escribe chemical
reactions by writing
balanced equations.
3.b K
now the quantity one
mole is set by defining one
mole of carbon 12 atoms
to have a mass of exactly
12 grams.
understanding of how to use dimensional
another, while keeping the same actual
Students will gain first hand knowledge
about the Port of Long Beach and its
imports and exports.
Students will be able to convert into
and out of standard and metric units
Materials
Dimensional Analysis
Powerpoint
molecules, atoms, and thermodynamic
Time Required
1 class
and chemical units including moles,
units.
Students will get practice working in
scientific notation and significant figures.
Dimensional Analysis
| 27
Introduction of Lesson
Anticipatory Set
Dimensional Analysis
Lesson 3
Ask the students about the huge cargo ships out on
the water just outside Long Beach.
What are they doing there?
Answer: They are importing and exporting goods.
What kinds of materials and items do you think
the cargo ships bring into the port?
Where do these items come from? Are they manmade or natural materials?
What types of chemicals do you think are imported
and exported?
How can they keep track of how much material is
being imported?
This lesson will show you math that is used to keep
track of materials in the Port, and is also used to
keep track of materials in a chemical reaction.
Lesson
Input
Using the PowerPoint presentation, provide
background on dimensional analysis.
Outline:
The math used in chemistry is not as hard as it
looks.................................... slides 1-3
Cross-canceling examples............ slides 4-5
Making conversion factors. ............. slide 6
Sample problem....................... slides 7-8
Transition to worksheet................. slide 9
Both in chemistry and in real life, you can use
dimensional analysis. The trick is to find two ways
to describe the same thing.
28 | Dimensional Analysis
Lesson cont’d
Like 1 mole of carbon = 12 g or $1.70 = 1 gallon of gas
Dimensional Analysis
Lesson 3
If you turn them into fractions, they become the
nearly magical conversion factors.
The trick is to have one unit on the top of the
fraction and another on the bottom. Then you can
use the fraction to convert from one of the units to
the other!
Solving problems involves just three steps.
1. List the given information. (done)
2. Decide what you want to end up with.
3. Arrange the conversion factors to cancel what
you don’t want and leave what you do want.
Dimensional Analysis
| 29
Lesson three
Dimensional Analysis
Dimensional Analysis
Directions
Have students complete the dimensional analysis worksheet.
This worksheet will provide you with dimensional analysis
practice. Dimensional Analysis conversion factors are below.
You will find molar masses (the conversion factors for going
between moles and grams) on a periodic table.
1000 Kg
1 metric ton
6.02 x 1023 units
1 mole
1000 g
1 Kg
Solve the following problems. Any conversion units not listed
above will be given in the problem.
1.
The Port of Long Beach imports more than 1.24 x 106 metric
tons of cement for construction in buildings every year.
Much of this cement is then shipped by train all over
America. How much mass is this in Kg?
2a. Thousands of construction items are shipped annually
through the Port. Gypsum is a compound that is used to
make “drywall” which is what makes up the inside walls of
your house. The formula for Gypsum is CaSO4 2H2O and is
Dimensional Analysis
Lesson 3
Worksheet
| 31
Questions
classified as a hydrate. Over 300,000 metric tons are shipped
Dimensional Analysis
Lesson 3
through the Port each year for many uses including the drywall,
and as an agent to help soften soil to help farming. How many
grams are shipped through the Port?
2b. The molar mass of gypsum, CaSO4 2H2O, is approximately
168.18 g/mol. How many moles of gypsum are shipped each
year through the Port?
3. The compound table salt, NaCl, is a common additive in many
chemical operations and is used in the food industry as a
preservative (and to make your food taste better). More than
8.5 x 105 metric tons are shipped into Long Beach each year.
If the molar mass of NaCl is 58.44 g/mol, how many moles are
shipped each year?
(Hint: Don’t forget to convert from metric tons to Kg, and from
Kg to g.)
4a. The Port of Long Beach exports 8.65 x 105 metric tons of
petroleum coke each year. Petroleum coke, which like coal is
made of carbon, is used in smelt factories to extract iron from
iron-ore. How many moles of carbon, molar mass of 12.01 g/
mol are imported every year into the US for industrial use?
4b. I f the heat produced by burning coal in oxygen is 635.5 Kilojoules for every mole (635.5KJ/mol), how much energy is
released by the burning of all of that coal (carbon) in the
United States?
32 | Dimensional Analysis
Questions cont’d
4c. 6.02 x 1023 atoms of carbon make up one mole of carbon. How
many atoms of carbon are imported into the United states
Lesson 3
annually?
Bonus Questions:
Dimensional Analysis
5a. A standard cargo container is 40 feet long by 8 feet wide by 9.5 feet
tall. How many cubic feet can a standard cargo container hold?
5b. A large container ship can carry 7,250 of these containers. What
total volume (in cubic feet) can a container ship hold?
Dimensional Analysis
| 33
Worksheet
Lesson three
Dimensional Analysis
Dimensional Analysis
Directions
Have students complete the dimensional analysis worksheet.
This worksheet will provide you with dimensional analysis
practice. Dimensional Analysis conversion factors are below.
You will find molar masses (the conversion factors for going
between moles and grams) on a periodic table.
1000 Kg
1 metric ton
6.02 x 1023 units
1 mole
1000 g
1 Kg
Solve the following problems. Any conversion units not listed
above will be given in the problem.
1.
The Port of Long Beach imports more than 1.24 x 106 metric
tons of cement for construction in buildings every year.
Much of this cement is then shipped by train all over
America. How much mass is this in Kg?
1.24 x 106 metric tons cement
1000 Kg
= 1.24 x 109 Kg cement
1 metric ton
Dimensional Analysis
Lesson 3
KEY
| 35
Questions
2a. Thousands of construction items are shipped annually
Dimensional Analysis
Lesson 3
through the Port. Gypsum is a compound that is used to
make “drywall” which is what makes up the inside walls of
your house. The formula for Gypsum is CaSO4 2H2O and is
classified as a hydrate. Over 300,000 metric tons are shipped
through the Port each year for many uses including the
drywall, and as an agent to help soften soil to help farming.
How many grams are shipped through the Port?
300,000 metric tons CaSO4 2H2O
1000 Kg
1000 g
1 metric ton
1 Kg
= 3 x 1011 g CaSO4 2H2O
2b. The molar mass of gypsum, CaSO4 2H2O, is approximately
168.18 g/mol. How many moles of gypsum are shipped each
year through the Port?
3 x 1011 g CaSO4 2H2O
1 mole
= 1.7938 x 109 mol ! 2 x 109 mol CaSO4 2H2O
168.18 g
3. The compound table salt, NaCl, is a common additive in many
chemical operations and is used in the food industry as a
preservative (and to make your food taste better). More than
8.5 x 105 metric tons are shipped into Long Beach each year.
If the molar mass of NaCl is 58.44 g/mol, how many moles are
shipped each year?
(Hint: Don’t forget to convert from metric tons to Kg, and from
Kg to g.)
8.5 x 105 metric tons NaCl
1000 Kg
1000 g
1 mol
1 metric ton
1 Kg
58.44
g
36 | Dimensional Analysis
= 1.5 x 1010 mol NaCl
Questions cont’d
4a. The Port of Long Beach exports 8.65 x 105 metric tons of petroleum
coke each year. Petroleum coke, which like coal is made of carbon,
Lesson 3
is used in smelt factories to extract iron from iron-ore. How many
moles of carbon, molar mass of 12.01 g/mol are imported every year
1000 Kg
5
8.65 x 10 metric tons C
1 metric ton
1000 g
1 Kg
1 mol
12.01 g
= 7.20 x 10
10
Dimensional Analysis
into the US for industrial use?
mol C
4b. I f the heat produced by burning coal in oxygen is 635.5 Kilo-joules
for every mole (635.5KJ/mol), how much energy is released by the
burning of all of that coal (carbon) in the Unites States?
7.20 x 1010 mol C
635.5 KJ
= 4.58 x 1013 KJ
1 mol C
… That’s almost 46 trillion kilojoules!
4c. 6.02 x 1023 atoms of carbon make up one mole of carbon. How
many atoms of carbon are imported into the United states
annually?
7.20 x 10
10
6.02 x 1023 atoms
mol C
= 4.33 x 1034 atoms C
1 mol
Bonus Questions:
5a. A standard cargo container is 40 feet long by 8 feet wide by 9.5 feet
tall. How many cubic feet can a standard cargo container hold?
1 container = 40 ft 8 ft 9.5 ft = 3040 ft3
5b. A large container ship can carry 7,250 of these containers. What
total volume (in cubic feet) can a container ship hold?
7,250 containers
3040 ft3
1 ship
1 container
= 22,040,000 ft3/ship = 2.204 x 107 ft3/ship
Dimensional Analysis
| 37