Honors Chemistry
Dimensional Analysis (Factor – label method)
Directions: Complete all
and
Name_____________________ period____
(Part I,II, VI, VII, VIII). Complete
(Part III, IV,V ) as directed.
A conversion factor is a fraction that has equivalent values in the numerator and denominator. For example,
60 seconds = 1 minute. Therefore, we can write 2 different conversation factors: 60 sec or 1 min
1 min
60 sec
Both measurements represent the same length of time, even if they do not look the same.
Abbreviated dimensional analysis rules:
1. Start with the original number and unit that was given. Do not start with a conversion factor.
2. Multiply by a conversion factor being sure that the unit to be discarded is on the bottom and the desired unit is
on the top.
3. Cancel the units
4. Perform numerical calculations. Please note, the sig figs will be limited by the original number that was given.
It will not be limited by numbers included in conversion factors.
Ex. 1. How many milligrams are in 20 kilograms?
Solve with dimensional analysis.
Conversion factors: 1000mg = 1 g and 1000g = 1 kg
20.0 kg x 1000 g x 1000 mg = 2.00 x 107 mg
1 kg
1g
Ex. 2. Convert 250 cm to __________m
250 cm x
The following lists some common conversion factors that you need to know:
1 km = 1000 m
1 m = 100cm
1 g = 1000 mg
1 m = 1000 mm
1L = 1000 mL
1 in = 2.54 cm
1 cm = 10 mm
1kg = 1000 g
Here are some conversions factors that you are not expected to know:
1 mi = 1.61 km
1 qt = 0.946 L
1 lb = 454 g
1 mi = 1.61 km
1 L = 1.06 qt
1kg = 2.2 lbs
1 m = 2.5 m
100 cm
1cm3 = 1 mL
1 mL = 20 drops
1 oz = 28.3 g
1 ton = 2000lb
1 mi = 5280 feet
Part I Easy Dimensional Analysis:
Directions: Solve the following with dimensional analysis. Set up with the factor label method. Show all of your work.
Be sure to cancel out the units. If you get these correct skip part III.
Grade for part I _________/4
1.
502 mL = ________ L
2. 25.0 g =___________ kg
each.
3. 401 mg = ________ g
If
you
score
d
4. 25 cm = _________ mm100%
you
may
skip
part
VI
Part II Harder Dimensional Analysis
Directions: Solve the following with dimensional analysis. Set up with the factor label method. Show all of your work.
Be sure to cancel out the units. If you get these 100 % correct skip part IV, V. Grade for part II _________/6
each.
5. If my car gets 26 miles to the gallon and the tank can hold 13.2 gallons of
gas, how many miles can I travel?
If
you
score
d
6. How many minutes are there in 1.6 years?
100%
you
may
skip
part
Part III Easy Dimensional Analysis Review: Directions: Solve the following with dimensional analysis. Set
VI up with the
factor label method. Show all of your work. Be sure to cancel out the units.
1. 55 mm = _____________m
4. 0.156 g = ______________ mg
2. 155 mg = _____________ g
5. 1.25 L = _______________ mL
3. 159 g = ______________ kg
6. 3.3 L = ______________ mL
Part IV Medium Dimensional Analysis Review: Directions: Solve the following with dimensional analysis. Set up with
the factor label method. Show all of your work. Be sure to cancel out the units
7. 0.35 km = ___________ cm
9. 578 mL = _______ quarts
8. 231 grams = __________ounces.
10. 0.0032 gallons = __________ L
Part V Hard Dimensional Analysis Review: Directions: Solve the following with dimensional analysis. Set up with the
factor label method. Show all of your work. Be sure to cancel out the units
11. An atom of gold has a mass of 3.271 x 10-22g. How many atoms of gold are in 5.00 grams of gold?
12. Earth is approximately 1.5 x 108 km from the sun. How many minutes does it take light to travel from the sun to
Earth? (The speed of light is 3.00 x 108 m/sec)
Part VI Challenge Dimensional Analysis. Directions: Solve the following with dimensional analysis. Set up with the
factor label method. Show all of your work. Be sure to cancel out the units.
1. An experiment requires each student to use 8.5 cm of Mg ribbon. How many students can do the experiment if
there are 572 cm of Mg ribbon available?
2. If a lab requires each lab group to have 25ml of a solution and it takes 15 grams of CuNO3, cuprous nitrate, to
make 1 liter of solution, how many grams are needed to make enough solution for 22 lab groups?
3. If you are going 55 mph, what is your speed in m per second?
4. The density of an unknown rock is 19.3 g/ml. What would its density be if were expressed in kg/L?
5. Suppose that gold is selling for $375 / ounce. How many milligrams of gold could you buy for one cent? (16 oz =
1 lb; 1 lb= 454g)
6. The density of a solid is 4.7 g/cm3. What is it in ounce per qt?
Part VII Density problems: Show your work and report your answer with proper sig figs and units.
1. Calculate the density of an object with a mass of 28.461 g and a volume of 5.26 cm 3 .
2. The volume of a certain wooden block is 63 cm3. The mass is 11.392 g. Find the density.
3. The density of copper is 4.44 g/mL. If the mass of a piece of copper is 26.326 g, find the volume.
4.
Sodium has a density of 1.95 g/mL.. If the volume of some sodium is 9.0 L, what is the mass?
5. A piece of wood that measures 3.0 cm by 6.0 cm by 4.0 cm has a mass of 80.0 grams. What is the density of the
wood? Would the piece of wood float in water? (volume = L xW x H)
6. A cup of gold colored metal beads was measured to have a mass 425 grams. By water displacement, the volume
of the beads was calculated to be 48.0 cm3. Given the following densities, identify the metal. Gold: 19.3 g/mL;
Copper: 8.86 g/mL; Bronze: 9.87 g/mL
Part VIII Temp Conversions: Show your work and report your answer with proper sig figs and units.
1. Our room is 69 °F. What is the temperature in Celsius?
TK  T C + 273
T C  TK  273
TC 
T F
2. Aluminum metal melts at 660.37 °C. What is the temperature in Kelvin?
3. Express normal body temperature, 98.6°F, in °C and K.
 32 
1.80
T F  1.80 T C  + 32