KEY
Activity 151-1
Unit Conversions
Directions: This Guided Learning Activity (GLA) focuses on performing unit conversions. Part A
discusses how to write conversion factors and use them to perform single-step conversions, Part B
introduces using multiple conversion factors in one problem, and Part C discusses unit conversions for
temperature and units with powers. The worksheet is accompanied by instructional videos. See
http://www.canyons.edu/Departments/CHEM/GLA. for additional materials.
Part A – Writing Conversion Factors
Converting between units is an important part of any science. Below is a table with measurements that are
common in chemistry:
Measure
Base unit
Abbreviation
Length
meter
m
Conversion to
Know
1 in. = 2.54 cm
Mass
gram
g
1 lb = 453.6 g
Volume
liter
L
Temperature
⁰Celsius
⁰C
Energy
joule
1 L = 1.057 qt
1 mL = 1 cm3
⁰C = (⁰F - 32)/1.8 K
= ⁰C + 273.15
J
1 cal = 4.184 J
To convert between different systems of measure, conversion factors can be applied. A conversion factor
is written based on the equality between the two units. For example, a conversion factor for inches and
centimeters can be written two ways:
𝟐𝟐.𝟓𝟓𝟓𝟓 𝒄𝒄𝒎𝒎
Or
𝟏𝟏 𝒊𝒊𝒊𝒊.
𝟏𝟏 𝒊𝒊𝒊𝒊.
𝟐𝟐.𝟓𝟓𝟓𝟓 𝒄𝒄𝒄𝒄
Which of these two conversion factors is used depends on the desired conversion.
Example 1. Write two conversion factors for the following unit equalities:
a.12 inches = 1 feet
b.1 mile = 1.61 kilometer
𝟏𝟏 𝒇𝒇𝒇𝒇
𝟏𝟏 𝒇𝒇𝒇𝒇
𝟏𝟏𝟏𝟏 𝒊𝒊𝒊𝒊.
c.4 cups = 1 quart
𝟏𝟏𝟏𝟏 𝒊𝒊𝒊𝒊.
Another set of conversion factors that you’ll need to know are the metric prefixes. The metric system
includes a set of prefixes that are based on factors of 10. These prefixes are extremely useful because they
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Activity 151 – 1
College of the Canyons
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are applied to many different types of measurements (e.g. length measurements, mass measurements, etc.)
The following table includes a shortened list of unit prefixes and equalities that Chemistry 151 students
should know.
Prefix
Equality (using meter as an example)
Name
Abbreviation
General Notation
Scientific Notation
nano-
n
1 m = 1,000,000,000 nm
1 m = 109 nm
micro-
μ
1 m = 1,000,000 μm
1 m = 106 μm
milli-
m
1 m = 1,000 mm
1 m = 103 mm
centi-
c
1 m = 100 cm
1 m = 102 cm
(base units: g, m, L, J, M)
kilo-
k
1,000 m = 1 km
103 m = 1 km
mega-
M
1,000,000 m = 1 Mm
106 m = 1 Mm
giga-
G
1,000,000,000 m = 1 Gm
109 m = 1 Gm
Example 2. Write two conversion factors that can be used to convert between:
𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 𝒎𝒎
𝟏𝟏 𝒌𝒌𝒌𝒌
a.meters and kilometers
𝟏𝟏 𝒌𝒌𝒌𝒌
𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 𝒎𝒎
b.microliters and liters
c.milligrams and kilograms
Often, conversion factors are not unit conversion factors per say, but are equivalencies that can be derived
from physical or chemical properties of substances or systems. For example, the density of a substance is
often used to relate its volume to its mass. Other common examples are given below.
Property
Common Units
density
g/mL, g/cm3, lb/ft3
velocity
m/s, mi/hr
concentration
mol/L (e.g. M)
percent composition
Example 3. Write a conversion factor for each of the following relationships.
a. Gold has a density of 19.32
g/cm
𝟏𝟏 𝒄𝒄𝒄𝒄
3
.
𝟏𝟏𝟏𝟏.𝟑𝟑𝟑𝟑 𝒈𝒈
𝟑𝟑
𝟏𝟏 𝒄𝒄𝒎𝒎𝟑𝟑
𝟏𝟏𝟏𝟏.𝟑𝟑𝟑𝟑 𝒈𝒈
b. 1 tablet contains 250
milligrams of acetaminophen.
c. A water molecule has two
hydrogen atoms.
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d. Sodium chloride is 39.2% sodium.
Part B – Performing Simple Conversions
To perform single step conversions, a conversion factor that relates the given value to the desired value is
identified. The given value is multiplied by the conversion factor so that the given units are divided from
the quantity.
𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑠𝑠
𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 𝑥𝑥 (
) = 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣
𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢
When using this approach, it is important to include all units in calculations, treating them as algebraic
quantities.
Example 4. Perform the following conversions.
a. 𝟑𝟑𝟑𝟑. 𝟎𝟎 𝒊𝒊𝒊𝒊. ( 𝟐𝟐.𝟓𝟓𝟓𝟓 𝒄𝒄𝒄𝒄) = 𝟗𝟗𝟗𝟗. 𝟒𝟒 𝒄𝒄𝒎𝒎∗
b. 𝟓𝟓𝟓𝟓. 𝟎𝟎 𝒄𝒄𝒄𝒄
𝟏𝟏 𝒊𝒊𝒊𝒊.
c. 𝟒𝟒. 𝟓𝟓𝟓𝟓 𝒙𝒙 𝟏𝟏𝟏𝟏𝟒𝟒 𝒏𝒏𝒏𝒏
=
=
𝒊𝒊𝒊𝒊.
𝒎𝒎
As mentioned above, sometimes the conversion factors are based on chemical or physical properties.
Example 5. Perform the following calculations.
a. The density of iron is 7.87 g/cm3. How much volume does 24.5 g of iron occupy?
𝟐𝟐𝟐𝟐. 𝟓𝟓
𝟕𝟕.𝟖𝟖𝟖𝟖 𝒈𝒈
𝒈𝒈 ( 𝟏𝟏 𝒄𝒄𝒄𝒄𝟑𝟑 𝟑𝟑
) = 𝟑𝟑. 𝟏𝟏𝟏𝟏 𝒄𝒄𝒄𝒄
b. How far does light travel in 60.0 seconds? (c = 2.998 x 108 m/s)
=
𝟔𝟔𝟔𝟔. 𝟎𝟎 𝒔𝒔
𝒎𝒎
c. Magnesium chloride is 25.5% magnesium. How many grams of magnesium are present in
5.24x104 g of magnesium chloride (MgCl2)?
𝟓𝟓.𝟐𝟐𝟐𝟐 𝒙𝒙 𝟏𝟏𝟏𝟏𝟒𝟒 𝒈𝒈 𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝟐𝟐
=
𝒈𝒈 𝑴𝑴𝑴𝑴
Part C – Special Cases in Unit Conversions – Temperature and Units with Powers
Temperature conversions between the Celsius scale and the Kelvin scale require only subtraction, since
the size of a degree in the Celsius and Kelvin scales is identical. When converting to and from the
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Fahrenheit scale, both the size of the degree and the occurrence of 0° must be accounted for. The
conversion equations are given in the first table.
Example 6. Perform
the following
conversions:
a. 37.0 ℃
=
℉
𝐾𝐾
b. 350 ℉ =
c. What is absolute zero in the Fahrenheit scale?
Finally, to convert between units with powers, we must account for the power in the unit conversion. To
do so, the entire conversion equality is raised to the desired power. For example, the conversion factor
between cubic inches (in.3) and cubic centimeters (cm3) can be determined from the inches to centimeters
conversion factor.
We know: 𝟏𝟏 𝒊𝒊𝒊𝒊. = 𝟐𝟐.𝟓𝟓𝟓𝟓 𝒄𝒄𝒄𝒄
Cubing the equality:
Example 7.
(𝟏𝟏 𝒊𝒊𝒊𝒊.= 𝟐𝟐. 𝟓𝟓𝟓𝟓 𝒄𝒄𝒄𝒄)𝟑𝟑
𝟏𝟏𝟑𝟑 𝒊𝒊𝒊𝒊.𝟑𝟑 = 𝟐𝟐. 𝟓𝟓𝟓𝟓𝟑𝟑 𝒄𝒄𝒄𝒄𝟑𝟑
𝟏𝟏 𝒊𝒊𝒊𝒊.𝟑𝟑 = 𝟏𝟏𝟏𝟏. 𝟒𝟒 𝒄𝒄𝒄𝒄𝟑𝟑
a. How many cubic centimeters (cm3) are equivalent to 2.00 in.3?
Using the calculated conversion factor from above: 𝟐𝟐.
𝟎𝟎𝟎𝟎 𝒊𝒊𝒊𝒊. (𝟏𝟏𝟏𝟏.𝟒𝟒 𝒄𝒄𝒄𝒄𝟑𝟑
𝟑𝟑
b.
𝟏𝟏 𝒊𝒊𝒊𝒊.𝟑𝟑
) = 𝟑𝟑𝟑𝟑. 𝟖𝟖 𝒄𝒄𝒎𝒎𝟑𝟑
How many square meters does
an 80. ft2 rug occupy? (1 ft = 12 in.)
The unit conversion discussion is continued in the Dimensional Analysis guided-learning activity.
Please refer to that GLA for more guidance.
Part D – Extra Practice
1. Perform the following unit conversions.
a. 12 mg = ______________ lb.
b. 67.3 km = ______________ mm
c. 39.3 in. = ______________ cm
d. 60.0 cal = ______________ J
e. 1.2 x 10-9 mg = ______________ μg
Chemistry Guided Learning Activities
Activity 151 – 1
h. 12 L = ______________ cm3
i. 0.00245 m = ______________ in.
j. 1.00 g = ______________ oz. (1 lb. = 16 oz.)
k. 170 g/cm2 = ______________ lb/in2
l. 2.5 x 107 km = ______________ in.
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f. 5.2 m3 = ______________ ft3
m. 45 °F = ______________ °C
g. 62 °C = ______________ K
n. -264 °F = ______________ K
2. How many liters of air are in a room that is 1200 m3?
3. What is the volume of a 59.5 g silver spoon? (dAg = 10.5 g/cm3).
4. The combustion of one gallon of gasoline will produce approximately 8.39 kg of carbon dioxide (CO2).
What volume will the CO2 occupy? (dCO2 = 1.96 g/L).
5. The density of silver is 10.5 g/cm3. Express this density in terms of lb/ft3.
6. The USDA recommends that a person’s sodium intake be limited to 2,400 mg. Table salt is 39.33%
sodium. How many grams of table salt can Jenny consume without surpassing this limit? (Assume
there are no other sources of sodium in her diet.)
7. If one cup of coffee contains 95 milligrams of caffeine, how many cups of coffee will contain 5.00
grams of caffeine?
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