NAME _______________________________________
NOTES: UNIT 2: DIMENSIONAL ANALYSIS
I) Dimensional Analysis
A) Dimensional Analysis: (a.k.a. unit cancellation or factor label method) The goal is to arrange values and units so that
units of the numerator are cancelled by units in the denominator, until only a “desired” unit remains.
1) As long as you can keep canceling units, you are doing it correctly.
2) When the unit of the "desired" is in the numerator, you may stop and do the arithmetic.
3) For the purposes of sig figs, the answer must have the same number of sig figs as the * GIVEN #
4) Math Review: You have been prepared all year long for this topic…but to review:
a) Given the series of fraction:
2
4
2 x 4 x 9 x 5 x 7
4
7
3
2
9
4
7
9
3
5
2
You can re-write this series,
using what I call "goal-posts"
and then cancel.
7
9
a) Whatever you can do to a number, you can do to a unit:
What number of inches is equivalent to 5.00 km?
x inches = 5.00 km
1 mile 1760 yards 3.0 feet 12 inches = *196770 inches or
1.61 km
1 mile
1 yard
1 foot
*197,000 inches
5)
6) Conversion Factors: * a pair of values (measurements), equivalent to each other in meaning, but
measured in different units. They are considered to be exact numbers, and not used to determine
significant figures for the answer.
a) Examples
1 league = 20 teams
1 team consists = 14 players
1 player = 8 pairs of socks
1 pair of socks = $1.50 (dollars)
1 sock company =
1120 pairs of socks
or
or
or
or
or
20 teams = 1 league
The "Process" is one that will become very useful in this course. In the beginning it will take some time and effort to solve
problems that you can probably do in your head!!! I know that!! The objective here is to begin with very, very simple
problems so that you can learn the process. Later, when the problems become more difficult – when you can't do them in your
head – this process will become a very valuable and useful tool. YES, you must learn this process. …. Chemical education
research has found, “mole theory (stoichiometry) to be the one chemistry topic among a group of eight to be an important
predictor of college chemistry performance. . . The study of stoichiometry necessarily includes the application of mathematics,
which also appears as a highly significant predictor of college performance.” (Yager, R. E.; Snider, B.; Krajcik, J. J. Res. Sci. Teach. 1988, 25, 387–396.)
183
6) The process of dimensional analysis looks daunting, but with practice it becomes easy.




Set your desired unit = to the given value and unit
Draw a goal post
Drop the unit to the denominator of the goal post
Go to your conversion factors and begin plugging them into the goal posts.
7) In Honors, stoichiometry problems may be one, two, three or even more step-problems.
However, every problem begins in the same way… every time, with the equation:
DESIRED unit
= GIVEN#UNIT′|
|
UNIT′
One Step Problems: Ignore sig figs for these learning problems – We are working with counted numbers not
measurements. Counted numbers are exact values and thus not subject to sig fig rules.
Conversion Factors
1 league has 20 teams
1 team has 14 players
1 player needs 8 pr. of socks
1 pair of socks costs $1.50 (dollars)
1 sock company can produce 1120 pr. of socks.
remember: desired = given...goal posts, drop your units
....
desired = given...goal posts, drop your units ....
1) When 28 players are available, how many teams can you field?
2) When you have 8 teams, how many players will be able to play?
3) How many leagues can you have whe there are 80 teams?
(ans: 112 players)
(ans: 4 leagues)
4) When there are 6 leagues, how many teams will be playing?
5) How many dollars does it cost for 10 pairs of socks?
(ans: 2 teams)
(ans: 120 teams)
(ans: $15)
184
Two Step Problems:
desired = given...goal posts, drop your units
....
desired = given...goal posts, drop your units ....
Conversion Factors:
1 league has 20 teams
1 team has 14 players
1 player needs 8 pr. of socks
1 pair of socks costs $1.50 (dollars)
1 sock company can produce 1120 pr. of socks.
6) When a team has $120, how many players can be outfitted with socks?
7) When you have 8,400 players, how many leagues can you create?
8) How many pairs of socks are needed for 1 team?
Three (or more) Step Problems:
(ans: 10 players)
(ans: 30 leagues)
(ans: 112 pairs)
desired = given...goal posts, drop your units
....
desired = given...goal posts, drop your units ....
9) When there are 30 teams, how may sock companies are needed to outfit the teams?
10) How many teams can be provided with socks by 1 sock company each year?
11) How many dollars does 1 team need to provide socks for all of its players?
12) How many sock companies are needed to provide socks for 4 leagues?
(ans: 3 companies)
(ans: 10 teams)
(ans: $168)
(ans: 8 companies)
185
APPLYING DIMENSIONAL ANALYSIS TO METRICS
DIRECTIONS: Below is a list of conversion factors. Use these conversion factors and only these conversion
factors to complete each of the following problems. These conversion factors are NOT used to determine the
sig. figs. of an answer.
1,000 mm = 1meter
100 cm = 1meter
10 mm = 1cm
1,000 m = 1 km
2.54 cm = 1inch
12 inches = 1 foot
1.61 km = 1 mile
5,280 feet = 1 mile
454 grams = 1 pound (lb)
1,000 mL = 1 Liter
1,000 g = 1 kg
1 calorie = 4.18 Joules
1,000 calories = 1 kcal
1 kilocalorie = 4.18 kilojoule
1.06 quart = 1 L
4 cups = 1 quart
16 tablespoons = 1 cup
3 teaspoons = 1 tablespoon (tbsp)
desired = given...goal posts, drop your units ....
desired = given...goal posts, drop your units
....
1. How many centimeters are equal to 0.500 mile?
2. How many cups are equal to 3.00 Liters?
3. How many Liters are equal to 6.5 mL?
4. Calculate the number of Liters equivalent to 50.0 tablespoons.
5. How many pounds are equivalent to 5.00 kg?
6. Calculate the number of feet equivalent to 158 mm
186
7. How many mL are equivalent to 1.0 tsp?
8. How many kilojoules are equivalent to 75.2 calories?
9. Calculate the number joules equivalent to 54.8 kilocalories
Correct your work using the answers on the next page, and then complete the following comprehension piece.
Comprehension: Here “IT” is .. in a nutshell …A friend comes to you for help with unit cancellation. They
bring you a number of problems on which they have been
working. Identify and list 3 things you would scan their work
for, in order to see if they were doing a problem correctly (or
incorrectly.)
I would scan their work to see if they:
1) _______________________________________________________________
2) _______________________________________________________________
http://blog.sellsiusrealestate.com/wp-content/nutshell1.jpg
3) ______________________________________________________________
187
ANSWERS: Dimensional Analysis: There are alternative cancellations (as with # 1), for most problems.
A number of answers are given, using scientific notation, but it is not necessary to do so, unless requested ... I
have simply written in scientific notation, to reinforce the concept and to remind you that it is still valid.
1. How many cm are equal to 0.500 mile?
cm = 0.500 mile | 1.61 km | 1,000 meter | 100 cm | OR cm = 0.500 mile | 5,280ft | 12 in | 2.54 cm|
1 mile
1 km
1 meter
1 mile 1ft
1 inch
8.05 x 104cm
or 80,500 cm
2. How many cups are equal to 3.00 liters?
cups = 3.00 L | 1.06 qt | 4 cups |
1 Liter
1 qt
12.7 cups
3. How many liters are equal to 6.5 mL?
L = 6.5 mL | 1 liter
| 6.5 x 10-3 L or 0.0065 L The answer does NOT need to be in scientific
1,000 mL
notation – I am using it only to show what can be done.
4. Calculate the number of Liters equivalent to 50.0 tablespoons.
7.37 x 10-1L or 0.737 L
L = 50.0 tbsp | 1cup | 1 qt | 1L |
16 tbsp 4 cup
1.06 qt
5.
How many pounds are equivalent to 5.00 Kg?
lbs = 5.00 kg | 1,000 grams | 1 lbs
1 kg
454 g
|
11.0 lbs.
6. Calculate the number of feet equivalent to 158 mm?
ft = 158 mm | 1 meter
| 100 cm | 1 inch | 1 foot
|
1,000 mm
1meter 2.54 cm
12 inches
5.18 x 10-1 ft or 0.518 feet
7. How many mL are equivalent to 1.0 tsp?
mL = 1.0 tsp| 1tbsp
3 tsp
| 1cup
16 tbsp
8. kJ = 75.2 calories| 4.18 Joules
1 calorie
| 1 qt | 1L
4 cup
1.06 qt
| 1,000 mL |
1L
4.9 mL
| 1kJ
| = 0.314 kJ
1,000 Joules
9) joules = 54.8 kilocalories | 1,000 calories | 4.18 Joules
1kcal
1 cal
| = 2.29 x 105 J or 229,000 J
188
II) GETTING MORE ADVANCED:
The previous problems are pretty straight forward …. but the following problems do require an extension of
your understanding and some creativity on your part. Recall, that the overriding issue is to arrange conversion
factors so that they cancel out …. while, concomitantly working your way towards the desired unit in the
numerator.
A) What if I am given a derived unit such as: kg/L, or miles/hour?
Solution: deal with each unit separately … bringing the denominator up, and dropping the
numerator down. All the while be sure that the conversion factors are arranged so
as to cancel out undesirable units.
Example: Calculate the distance travelled, in kilometers, assuming one trip takes 138 minutes, in a car
travelling at 55.0 miles/hour
Notice how I wrote the
derived unit, miles/hour, as
fraction, clearly making a
numerator and
denominator.
Notice the only unit NOT
cancelled is kilometers
….which is your desired.
Notice that is still appears
in the numerator.
Notice the unit, minutes,
was raised to the numerator,
so that it could be cancelled.
km = 55.0 miles | 1 hour | 138 minutes
hour 60 min
1
Notice that the unit, “hr”
was brought from the
denominator UP to the
numerator, so that the unit
may be cancelled
Notice I have used a
denominator of 1, thus
avoiding the need to introduce
another unit to be cancelled
… I am simply stating that 138
minutes was an entire trip.
This is a nice little trick to keep
in mind.
| 1.61 kilometer | = 204 kilometer
1 mile
Notice that the unit of “mile” is
cancelled at some point, other than
the first conversion goalpost. This is
perfectly acceptable. You can cancel
a unit, just about anywhere you wish,
per its convenience and your design.
Of course, you would get the same answer had you chosen to deal with miles, before the “hour” unit.
km = 55.0 miles
hr
| 1.61 km | 138 minutes
1 mile
1
| 1 hr
60 min
| = 204 km
189
B) What if I am asked to convert from a derived unit to a second derived unit?
Example: Convert 17.09 m/s to km/hr
Notice that km is introduced in
the numerator, and that is
where it needs to be to get me
to my desired unit.
Notice how I wrote the
derived unit, m/s, as fraction,
clearly making a numerator
and denominator.
km = 17.09 m |
hr
s
60 s
1 min
|
Notice I raised “s” to the
numerator so it can be
cancelled out.
60 min
1 hr
|
1 km
1,000 m
Notice that in cancelling
minutes, I could introduce the
unit “hour” into my
expression.
This forced me to introduce
the unit “minutes” so I then
raised “minutes” to the
numerator so I could cancel it.
| = 61.52 km/hr
Notice that the answer has 4
sig figs, just as the given has
4 sig figs.
Notice that my desired has hr
in the denominator. And,
now, as long as I don’t cancel
it out, I too have “hr” in the
denominator. This is working
out…..
C) What if I am given a cubed unit (such as m3 and asked to convert to cm3) …That is, how can I
convert from one volume unit to another volume unit???
Solution: understand that combined units such as m3 are really just m  m  m and use this to
develop your conversion factors. e.g.) 15 m3 = 15 m  m  m (This is a key idea)
Example: Convert 28.7 m3 to km3
km3 = 28.7 m3 | 1 km
1,000 m
(we can use the conversion factor 1,000 m = 1 km)
| 1 km | 1 km |
1,000 m 1,000 m
Notice that these three values, when multiplied by each other give you m3 as a unit (and thus cancel the m3 of
the given’s numerator).
Notice that 1 km x 1 km x 1km = km3
D) What can I do when given a percent?
Solution: Imagine you are given: the mass of “x” is 8.5% larger. … Well you can write a
percentage value as a conversion factor: e.g) 8.5 % can be written as 8.5 grams
100 grams
190
TRY THES CHALLENGE PROBLEMS:
Challenge 1) The comic Phyllis Diller once asked her husband how to spell Mississippi...
He responded: "Do you mean the river or the state?”
Well this problem is all about the river... According to an article from Science News (12 June 2004 issue)
4.5000 x 106 gallons per second (or 4.5000 million gallons/s) of water are released into the Gulf of Mexico,
every day, from the mouth of the Mississippi River into the Gulf of Mexico.
Using unit cancellation, calculate the total number of gallons of water that flow into the Gulf, from the
Mississippi river, in 365.25 days. (Hint: I used 365.25 days as my "given" but you can use gallons/s as well)
gallons = * 365.25 days | 24 hrs | 60 min | 60 sec
1 day
1 hr
1 min
OR *with a lightly different unit:
gallons = 365.25 days | 24 hrs | 60 min | 60 sec
year
1 year
1 day
1 hr
1 min
| 4.5 x 106 gallons | = 1.4201 x 1014 gallons
1 sec
| 4.5 x 106 gallons | = 1.4201 x 1014 gallons
1 sec
year
Ans: 1.4201 x 1014 gallons
Challenge 2) It has been hypothesized that greenhouse gases are acting as a driving force for the changes in the
overall average temperature around the world.
In the atmosphere, a greenhouse gas helps to retain thermal energy, and thus warms the air, because the
greenhouse gas limits the loss of solar energy back to space. Greenhouse gases have helped life develop
here on Earth ...but perhaps the phenomenon is becoming too much of a good thing.
Carbon dioxide gas (CO2(g)) is a greenhouse gas, and possibly one of the more important. Carbon dioxide
gas concentrations have been increasing in the atmosphere possibly due to the combustion of fossil fuels,
such as coal, natural gas and gasoline.
Assuming:
9,000 grams of carbon dioxide per gallon of gasoline are produced, on average.
1 passenger vehicle (car, pickup truck, van etc) travels 12,000 miles
1gallon of gasoline moves an average vehicle about 20 miles
1 lbs = 454 grams
1 kg = 1,000 grams
1 million = 1 x 106
[That's about 19.8 lbs/gallon!!!]
Calculate the annual production of carbon dioxide, in kilograms, due to the 200 million passenger vehicles
on the US roads. One sig fig is fine, for your answer. Please note that 200 million is 200 x 106 or rather it is
equivalent to 2 x 108 cars.
*kg CO2 = 2 x108 cars | 12,000 miles | 1 gallon | 9,000 g of CO2 | 1 kg | = 1.08 x 1012 kg
1 car
20 miles
1 gallon
1,000g
or... 1 x 1012 kg
Ans: 1 x 1012 kg
191
Challenge 3) 1.0 gram of ordinary table salt (NaCl) contains about 8500 tiny cubic grains. How many ions
of sodium are contained in one grain? One formula unit of NaCl is equivalent to 58 µ [atomic
mass units].?
(Hints ... You really want to get to the number of formula units. Once you know the # of formula units, you also know the number of each ion
species since NaCl is in a 1:1 ratio . .... so consider that 1 gram has 8500 grains ...and that 1 formula unit of NaCl = 58 µ. You also know that
1 µ is equivalent to 1.66 x 10-24 grams, according to you independent packet on atomic structure …. oh my, lots of hints…..)
1µ
| 1 formula unit of NaCl | 1 ion of Cl
| = 1.2 x 1018 ions / grain
8500 grains 1.66 x10-24 grams
58 µ
1 formula unit NaCl
# ions / grain = * 1.0 gram
|
Ans: 1.2 x 1018 ions / grain
a) Knowing the formula of sodium chloride, how many chloride ions are contained in
one grain of NaCl? __________________________
Challenge 4) Convert the area of 41 square inches (41.0 in2 ) to cm2
cm2 = * 41.0 in2 | 2.54 cm
1 inch
| 2.54 cm
1 inch
| = 265 cm2
Ans: 265 cm2
Challenge 5) Which is faster, going 80.0 miles an hour or going 40.0 meters per second?
(Hint: to compare, you must have the same unites, so either convert 80 miles/hour to meters/second or vice versa
I’m going to convert miles/hour to meters/second)
meters = * 80.0 miles | 1 hour | 1 minute | 5,280 feet | 12 inches | 2.54 cm | 1meter | = 35.8 m/s
second
hour 60 min 60 seconds 1 mile
1 foot
1 inch
100 cm
Ans: 35.8 m/s
192
Challenge 6) The American Cancer Society many years ago ordered 40.0 billion units (4.00 x 1010) of a
bio-chemical called, interferon. It was believed that this chemical could help to prevent the
spread of cancer. The 40.0 billion units cost $2 million dollars, and were to be used in studies
on six types of cancer suffered by 150 patients. A unit of interferon masses at 1.00 picogram.
That year 100. mg of interferon were produced from 31,000 liters of blood. At that rate of production,
how many liters of blood did it take to supply the order for the A.C.S.?
Some conversion factors that may be
or may not be of help or necessary are:
1 lb = 454 grams
1 metric ton = 1,000,000 grams
1 kg = 1,000 grams
1 gram = 1,000 mg
1 picogram = 1 x 10-12gram
1 angstrom = 1 x 10-10 meters
* L of blood = 40.0 x 109 units | 1.00 x 10-12 gram | 1,000 mg | 31,000 Liters of Blood = 12,400 L
1 unit
1 gram
100. mg
Ans:12,400 L
Challenge 7) Suppose an object is moving at 66.0 feet/second. How fast would you have to drive a car, in
miles/hour to keep pace with this object?
miles = *66.0 feet
| 60 seconds| 60 minutes | 1 mile
|
hour
second
1 minute
1 hour
5,280 feet
Ans: 45.0 mile/hour
193
Answers To: Challenge Problems
Challenge 1)
gallons = * 365.25 days | 24 hrs | 60 min | 60 sec
1 day
1 hr
1 min
OR *with a lightly different unit:
gallons = 365.25 days | 24 hrs | 60 min | 60 sec
year
1 year
1 day
1 hr
1 min
| 4.5 x 106 gallons | = 1.4201 x 1014 gallons
1 sec
| 4.5 x 106 gallons | = 1.4201 x 1014 gallons
1 sec
year
Challenge 2)
*kg CO2 = 2 x108 cars | 12,000 miles | 1 gallon | 9,000 g of CO2 | 1 kg | = 1.08 x 1012 kg
1 car
20 miles
1 gallon
1,000g
or... 1 x 1012 kg
Challenge 3)
1µ
| 1 formula unit of NaCl | 1 ion of Cl
| = 1.2 x 1018 ions / grain
8500 grains 1.66 x10-24 grams
58 µ
1 formula unit NaCl
# ions / grain = * 1.0 gram
|
a) Since the ratio of Na: Cl in the compound is 1:1 there are the same number of ions of Na+
as there are Cl- thus: 1.2 x 1018 ions of Na+
Challenge 4)
cm2 = * 41.0 in2 | 2.54 cm
1 inch
| 2.54 cm
1 inch
| = 265 cm2
Challenge 5)
meters = * 80.0 miles | 1 hour | 1 minute | 5,280 feet | 12 inches | 2.54 cm | 1meter | = 35.8 m/s
second
hour 60 min 60 seconds 1 mile
1 foot
1 inch
100 cm
Challenge 6)
* L of blood = 40.0 x 109 units | 1.00 x 10-12 gram | 1,000 mg | 31,000 Liters of Blood = 12,400 L
1 unit
1 gram
100. mg
Challenge 7)
miles = *66.0 feet
| 60 seconds| 60 minutes | 1 mile
| =
hour
second
1 minute 1 hour
5,280 feet
194
NAME ____________________________________
SOME TOUGHER DIMENSIONAL ANALYSIS
DIRECTIONS: Use unit cancellation (dimensional analysis) to solve each of the following problems. A number of important
conversion factors are at the bottom of the last page. However, it is assumed that you know some necessary conversion factors, on
your own.
Some Conversion Factors That May Be Helpful
1 mile = 5,280 feet
1 inch = 2.54 cm
1 meter = 100 cm
1 lbs = 454 grams
1 kg = 1,000 grams
1 mL = 1 cm3
1,000 mL = 1 Liter
1 Liter = 1 dm3
1 Liter = 1.06 qt
1 m3 = 1,000 dm3
1 dm3 = 1,000 cm3
1 acre = 43,560 ft2
1 ft2 = 144 in2
1 in3 = 16.387064 cm3
1) The recommended adult dose of Elixophyllin, a drug used to treat asthma, is 6.00 mg per kg of body mass.
Calculate the dose for a 150. lbs. person (use this as the given).
* mg = 150. lbs | 454 grams | 1 kg
1 lbs
1,000 grams
| 6.00 mg |
1 kg body mass
Ans: 409 mg
2) The speed of sound in air at room temperature is about 343 m/s. Calculate this speed in miles per hour.
Learn This: Given two units with which to work, will require you at some point to bring the denominator (in this case,
the “s” of m/s into the numerator, in order to cancel it….Think hard about that)
*miles = 343 meters | 60 sec | 60 min | 100 cm | 1 inch | 1 ft
| 1 mile |
hour
second
1 min
1 hour 1 meter 2.54 cm 12 inches 5,280 ft
Ans: 767 mile/hour
3) Aluminum is a relatively low-density metal (density = 2.70 g/cm3) used in aircraft construction, high voltage
transmission lines, beverage cans and of course, aluminum foil. What is its density in units of kg/m3?
Learn This: When given two units with which to work (called a derived unit), you will at some point need to bring the
denominator (in this case, the “cm3”, of your given 2.70 g/cm3 into the numerator, in order to cancel it)
kg =
m3
2.70 grams
cm3
| 1 kg
| 1,000 cm3 | 1,000 dm3 |
1,000 grams
1 dm3
1 m3
Ans: 2.70 x 103 kg/m3
4) What is the density of mercury (13.6 g/cm3) in units of kg/m3?
kg = 13.6 g | 1 kg
m3
cm3 1,000 grams
| 1,000 cm3 | 1,000 dm3 | = 13,600 kg/m3
1 dm3
1m
Ans: 13,600 kg/m3
195
5) How many atoms of hydrogen are equal to 45 g of ammonia, NH3? (omit for 15/16) …we’ll do this later
atoms H * = 45 grams | 1 mole |
17 grams
3 atoms
| 6.02 x 1023 molecules |
1 molecule
1 mol
Ans: 4.8 x 1024 atoms of
6) An unknown mass of calcium nitrate, Ca(NO3)2, has 5.00 x 1027 atoms of oxygen. How many kilograms of
Ca(NO3)2 are in the sample? (omit 15/16) ..we’ll do it later
kg = 5.00 x 1027 atoms O | 1 f.u.
6 atoms O
| 1mole
6.02 x 1023 f.u.
| 164 grams | 1 kg
| = 227 kg
1 mole
1,000 grams
Ans: 227 kg Ca(NO3)2
7) The roof of a building measures 2.44 acres. During a rainstorm one evening, 1.25 inches of rain fell.
Assuming the density of the rain that fell was 1.00 gram per cm3, what is the weight, in pounds, of the rain
on top of the building? (very tough…)
lbs = 2.44 acres | 43,560 ft2 | 144 in2
1 acre
1 ft2
| 1.25 inch | 16.387064 cm3 | 1 gram | 1 lbs |
1
1 in3
1 cm3
454 g
Ans: 691,171.17 lbs
or with sig figs: 691,000 lbs
8) When you are going 50.0 miles per hour, how many feet per second are you traveling?
ft = 50.0 miles | 1 hr
s
hr
60 minutes
| 1 minutes
60 s
| 5,280 feet | = 73.3 ft/s
1 mile
Ans: 73.3 ft/s
9) Calculate the number of mL of a concentrated bleach solution required to make 1.0 quart of 5.0 % bleach
solution?
mL = 1.0 quart | 1 Liter
1.06 qt
| 1,000 mL | 5 mL |
1L
100 mL
= 47 mL
Ans: 47 mL
10) You weigh 175 lbs and you feel a bit under the weather. Your mom has sent you an old family remedy with
the instructions: Take 1 drop per 10 kg. of body weight per day, four times per day.
How many drops must you use for 1 day's medication?
drops = 175 lbs | 454 grams | 1 kg
| 1 drop | 4
day
1 lbs
1,000 grams 10 kg
day
| = 31.8 drops/day
Ans: 31.8 drops/day
196
Answers:
1)
2)
mg = 150. lbs | 454 grams | 1 kg
| 6.00 mg | = 409 mg
1 lbs
1,000 grams
1 kg body mass
miles = 343 meters
hour
second
3) kg =
m3
2.70 grams
cm3
| 60 sec | 60 min | 100 cm
1 min
1 hour 1 meter
| 1 inch | 1 ft
| 1 mile | = 767 mi/hr
2.54 cm 12 inches 5,280 ft
| 1 kg
| 1,000 cm3 | 1,000 dm3 | = 2.70 x 103 kg/m3
1,000 grams
1 dm3
1 m3
4) kg = 13.6 g | 1 kg
| 1,000 cm3 | 1,000 dm3 | = 13,600 kg/m3
m3
cm3 1,000 grams
1 dm3
1 m3
5) atoms H = 45 grams | 1 mole
17 grams
|
3 atoms
1 molecule
| 6.02 x 1023 molecules | = 4.8 x 1024 atoms of H
1 mol
6) kg = 5.00 x 1027 atoms O | 1 f.u. | 1mole
| 164 grams | 1 kg
| = 227 kg Ca(NO3)2
6 atoms O
6.02 x 1023 f.u.
1 mole
1,000 grams
7) lbs = 2.44 acres| 43,560 ft2| 144 in2| 1.25 inch| 16.387064 cm3| 1 gram | 1 lbs | = 691,171.17 lbs or, with
1 acre
1 ft2
1
1 in3
1 cm3 454 g
sig figs: 691,000 lbs
8) ft =
s
9)
50.0 miles | 1 hr
hr
60 minutes
| 1 minutes
60 s
| 5,280 feet | = 73.3 ft/s
1 mile
mL = 1.0 quart | 1 Liter
|1,000 mL| 5 mL
|
1.06 quart 1 Liter 100 mL
= 47 mL
This set of conversion factors deals with the 5%. You’ll note that 5% means that 5 mL
of every 100 mL of the solution is the chemical bleach …the other 95 mL are water.
10) drops = 175 lbs | 454 grams | 1 kg
| 1 drop | 4
| = 31.8 drops/day
day
1 lbs
1,000 grams 10 kg
1 day
197