KEY
Activity 151-2
Dimensional Analysis
Directions: This Guided Learning Activity (GLA) focuses on using dimensional analysis to solve chemical
problems. Part A describes the dimensional analysis approach, Part B gives examples of using
dimensional analysis to solve chemical problems, and Part C discusses how to identify conversion factors
for dimensional analysis. The worksheet is accompanied by instructional videos.
http://www.canyons.edu/Departments/CHEM/GLA for additional materials.
Part A – Dimensional Analysis Strategy
Writing conversion factors for dimensional analysis is discussed in the “Unit Conversion”
guidedlearning activity. Please refer to that GLA for more guidance in this area.
In chemistry, many calculations rely in the units used to express the quantities. Many of the problems you
see will utilize a process termed dimensional analysis, or the factor-based method. Dimensional
analysis involves adding, subtracting, dividing, and multiplying units just as you would real numbers. In
chemistry, dimensional analysis relies on ‘cancelling’ units to guide the problem solving strategy.
Dimensional Analysis Strategy
1. Write known measurements with their units as fractions. If the measurement has multiple units,
write the units separately.
9.35 mL becomes (
9.35 𝑚𝑚𝑚𝑚
1
)
7.87 g/cm3 becomes (7
.87 𝑔𝑔3)
1 𝑐𝑐𝑐𝑐
2. Identify equalities that relate the given units to the desired units, and write these equalities as
conversion factors by dividing one side by the other. 3 becomes (1 𝑐𝑐𝑐𝑐3) or ( 1 𝑚𝑚𝑚𝑚3)
1
lb. = 453.6 g becomes (4531 𝑙𝑙𝑙𝑙.6. 𝑔𝑔) or (4531 𝑙𝑙𝑙𝑙.6. 𝑔𝑔)
1 mL = 1 cm
1 𝑚𝑚𝑚𝑚
1 𝑐𝑐𝑐𝑐
3. Multiply given quantities by conversion factors that allow you to ‘cancel’ unwanted units (divide
like units), and acquire desired units.
9.35 𝑚𝑚𝑚𝑚 1 𝑐𝑐𝑐𝑐3
3
(
) ( ) = 9.35 𝑐𝑐𝑐𝑐 1 1 𝑚𝑚𝑚𝑚
7.87 𝑔𝑔
1 𝑙𝑙𝑙𝑙.
𝑙𝑙𝑙𝑙.
(
𝑚𝑚3
3) (453.6 𝑔𝑔) = 0.174 𝑐𝑐
1 𝑐𝑐𝑐𝑐
Chemistry Guided Learning Activities
Activity 151 – 2
College of the Canyons
Page 1 of 4
Example #1. How many jelly beans will fit in a 32.0 oz. mason jar?
To solve this problem, we must know how much space is occupied by a single jelly bean. If we know that
one jelly bean occupies 3.5 cm3, then we can write:
We must also know the unit conversion between ounces and cubic centimeters:
The goal of dimensional analysis is to arrange the conversion factors in a way that will allow unwanted
units to divide out, or
‘cancel.’
Part B – Identifying Conversion Factors for Dimensional Analysis
One of the challenging parts of dimensional analysis is learning how to identify and write conversion
factors. Here are a few common types of dimensional analysis conversion factors:
1. Unit Conversion Factors
Example: An inch is equivalent to 2.54 cm, 0.254 m, and 1/12 ft.
Conversion Factors: (
𝟏𝟏 𝒊𝒊𝒊𝒊.
)
(
𝟐𝟐.𝟓𝟓𝟓𝟓 𝒄𝒄𝒄𝒄
𝟏𝟏 𝒎𝒎
)
𝟏𝟏𝟏𝟏𝟏𝟏 𝒄𝒄𝒄𝒄
𝟏𝟏𝟏𝟏 𝒊𝒊𝒊𝒊.
(
𝟏𝟏 𝒇𝒇𝒇𝒇
)
2. Physical Properties or Quantities like density, percent composition, concentration, or speed
Example: A 68% nitric acid solution has a concentration of 15.8 M and a density of 1.42 g/cm3
Conversion Factors: (𝟔𝟔𝟔𝟔
𝟏𝟏𝟏𝟏𝟏𝟏 𝒈𝒈 𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂)
(𝟏𝟏𝟏𝟏
.𝟏𝟏𝟏𝟏𝟏𝟏 𝒄𝒄𝒄𝒄 𝒈𝒈𝟑𝟑 𝒏𝒏𝒏𝒏𝒏𝒏𝒏𝒏𝒏𝒏𝒏𝒏 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂)
𝑳𝑳 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝒏𝒏𝒏𝒏𝒏𝒏𝒏𝒏𝒏𝒏𝒏𝒏 𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂) (𝟏𝟏
3. Stoichiometric Coefficients
Example: 𝐶𝐶3𝐻𝐻8(𝑔𝑔) + 5𝑂𝑂2(𝑔𝑔) → 3𝐶𝐶𝐶𝐶2(𝑔𝑔) + 4𝐻𝐻2𝑂𝑂(𝑔𝑔)
Conversion Factors: (
𝒌𝒌𝒌𝒌 )
𝟏𝟏 𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎 𝑪𝑪𝟑𝟑𝑯𝑯𝟖𝟖
Chemistry Guided Learning Activities
Activity 151 – 2
𝟓𝟓 𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎 𝑶𝑶𝟐𝟐
.𝟖𝟖 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏
∆𝐻𝐻𝑟𝑟𝑟𝑟𝑟𝑟 = −2220 𝑘𝑘𝑘𝑘
𝟓𝟓 𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎 𝑶𝑶𝟐𝟐 ) (𝟑𝟑 𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎 𝑪𝑪𝑪𝑪𝟐𝟐)
𝟏𝟏 𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎 𝑪𝑪𝟑𝟑𝑯𝑯𝟖𝟖
( −𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐
College of the Canyons
Page 2 of 4
Keep in mind that the conversion factor that is used is chosen based on the given units and the desired
units, so these must be identified at the beginning of each problem.
Example #2. Perform the following calculations by identifying and employing appropriate conversion
factors.
a.
A pharmaceutical company produced 7885 g of a drug in one reactor. If one tablet of the
drug will contain 425 mg, how many tablets can be prepared from that reactor?
Given unit: grams
𝟕𝟕𝟕𝟕𝟕𝟕𝟕𝟕 𝒈𝒈
() (
𝟏𝟏
Desired unit: tablets
𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 𝒎𝒎𝒎𝒎
𝟏𝟏 𝒈𝒈
)(
𝟏𝟏 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕
𝟒𝟒𝟒𝟒𝟒𝟒 𝒎𝒎𝒎𝒎
) = 𝟏𝟏𝟏𝟏, 𝟔𝟔𝟔𝟔𝟔𝟔 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕
b.
Mia’s car has an average mileage of 26 mpg, and has a 16.0 gal gas tank. How many
times can Mia go to work (8.4 mile round trip) before needing to refill the tank?
Part B – Performing Multiple Unit Conversions
Often, conversion factors need to be combined to find the final solution to a problem. Using dimensional
analysis, you can use the units to guide the problem solving strategy.
Example #3. Perform the following calculations.
a.
The speed of light is 2.998 x 108 m/s. How far does light travel in 60.0 seconds? Report
the answer in miles. (1 mi = 1.61 km).
Given unit: seconds
Desired unit: miles
(𝟔𝟔𝟔𝟔. 𝟎𝟎 𝒔𝒔) (𝟐𝟐. 𝟗𝟗𝟗𝟗𝟗𝟗 𝒙𝒙 𝟏𝟏𝟏𝟏𝟖𝟖 𝒎𝒎) ( 𝟏𝟏 𝒌𝒌𝒌𝒌 ) (
𝟏𝟏
𝟏𝟏 𝒔𝒔
𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 𝒎𝒎
𝟏𝟏 𝒎𝒎𝒎𝒎
𝟏𝟏.𝟔𝟔𝟔𝟔 𝒌𝒌𝒌𝒌
) = 𝟏𝟏. 𝟏𝟏𝟏𝟏 𝒙𝒙 𝟏𝟏𝟏𝟏
𝟕𝟕 𝒎𝒎𝒎𝒎
b.
A sample of ore contains 34.0% malachite, a copper mineral. Malachite is 57.5% copper.
What is the maximum amount of pure copper that could be extracted from 250 kg of the ore?
Chemistry Guided Learning Activities
Activity 151 – 2
College of the Canyons
Page 3 of 4
Part D – Extra Practice
1. A light-year is the distance that light will travel in a year. Express this distance in kilometers.
2. 18.0 mL of water contains 6.022 x 1023 water molecules. How many hydrogen atoms are in 1.00 L of
water? (Each water molecule, H2O, contains two hydrogen atoms.)
3. What is the volume occupied by one water molecule? (See #2).
4. A certain ore contains 34% hematite, Fe2O3. Hematite is 69.9% iron. How much iron can be isolated
from 250 tons of this ore? (1 ton = 2000 lb.)
5. An ounce of coffee contains 12 mg of caffeine, while a dark chocolate Hershey’s kiss contains 2.2 mg
of caffeine. How many Hershey’s kisses contain as much caffeine as a cup (8 oz) of coffee?
6. The lava from a volcano can travel up to 100 km/hr. If a village is located 3.6 mi from the volcano,
how many minutes will it take the lava to reach the village?
Chemistry Guided Learning Activities
Activity 151 – 2
College of the Canyons
Page 4 of 4