The Mathematics of
Chemistry
Stoichiometry
Dimensional Analysis
Stoichiometry
• Stoichiometry is a branch of chemistry
that deals with the relative quantities of
reactants and products in chemical
reactions.
• Greek root words:
– Stoicheion meaning " element“
– Metron meaning "measure"
What is Dimensional
Analysis?
• Using the units, or dimensions, of
measurements to express and
calculate chemical quantities
What is the relationship?
• Dimensional analysis is a strategy
used for doing stoichiometric
calculations.
What are some common
equivalent measurements?
• 1 inch =______centimeter(s)
• 1 week = ______ day(s)
• 60 seconds = ______minute(s)
• 1 lb =______ ounce(s)
• 1 cup = _____ fluid ounces
• 1 tablespoon = _____ teaspoon(s)
• 4 quarts = _____ gallon(s)
Common Equivalent
Measurements
• 1 mile = _____ feet
• 1 kg = _____ 2.2 lb
• 1 ft = ____ inches
• 365 days = _____ year(s)
• 1 ton = _____ pounds
Dimensional Analysis –
The Plan 1. What is given? Start your calculation with this
quantity with units.
2. What is your goal? What you are solving for is
your goal and should be on top of the last step of
the problem.
3. Set up a series of equivalent measures that
cancels out all units except the goal units.
4. Solve the problem, and remember to mark through
the cancelled units.
5. Record the answer with appropriate units and sig
figs.
Give it a try! How many seconds are there
in 5.5 days?
Follow the steps:
1.What is given? 5.5 days
2.What is your goal, and what are the units?
Determine # of seconds in 5.5 days
3.Set up a series of equivalent measure that
cancels out all units except the goal units.
Give it a try!
5.5 days X 24 hours X 60 minutes X 60 seconds= ? seconds
1 1 day 1 hour 1 minute 1
4.Record the appropriate answer with units.
What are some common
equivalent measurements in
chemistry?
• 1,000 g = _____kg
• 100 cm = ______ m
• 1 m = _____dm
• 1 L = _____ml
• 1 mole = _______ particles/atoms
• molar mass = _____ mole(s)
• Avogadro’s number = _____ mole(s)
Mole equivalents
MOLE
P
A
R
T
I
C
L
E
S
G
R
A
M
S
Avogadro’s
Number Molar
Mass
Give it a try!
• How many grams are in 4.92
moles of calcium carbonate?
Molar Mass
The mass in grams of 1 mole of
the compound calcium carbonate
CaCO3 Ca 1 X 40.078 grams = 40.078 grams
C 1 X 12.011 grams = 12.011 grams
O 3 X 15.999 grams = 47.997 grams
TOTAL = 100.086 grams
Give it a try!
Stoichiometric Calculations
4.92 mol CaCO3 X 100.086g CaCO3 =
1 mol CaCO3
Stoichiometric Calculations – The Plan
1. Write the chemical equation.
2. Balance the chemical equation.
3. *Follow steps to dimensional analysis: Start with what is given.
Set up a series of equivalent measures.
End with your goal.
Solve the problem by cancelling units.
Record the appropriate answer with units.
Stoichiometric Calculations – The Plan
There are three types of equivalent measures for
stoichiometry:
1. moles to grams 1 mole = molar mass
2. moles to moles using the mole ratio from
the balance chemical reaction
3. moles to avogadro’s number 6.02 x 1023
particles = 1 mole
Balancing
Chemical Equations
C2H5OH (l) + O2 (g) CO2 (g) + H2O (g)
C2H5OH (l) + 3O2 (g) 2CO2 (g) + 3H2O (g)
Chemical Equations as
Equivalents
• Coefficients from a balanced equation
represent the number of theoretical
mole equivalents and can be used in
stoichiometric calculations.
Stoichiometric Calculations – The Plan
1. Write the Chemical Equation.
2. Balance the Chemical Equation.
3. Follow steps to Dimensional Analysis: Start with what is given.
Set up a series of equivalent measures.
End with your goal.
Solve the problem by cancelling units.
Record the appropriate answer with units.
Stoichiometric Calculations – The Problem
Lithium hydroxide is used in an outer space environment to
remove excess exhaled carbon dioxide from the living
environment. The products of the reaction are lithium
carbonate and water. If 48.0 grams of lithium hydroxide are
used in a small scale experimental device, how much carbon
dioxide will the device process? The Plan:
1. Write the chemical equation.
2. Balance the chemical equation.
3. Follow steps to dimensional analysis: Start with what is given.
Set up a series of equivalent measures.
End with your goal.
Solve the problem by cancelling units.
Record the appropriate answer with units.
* Remember Significant Figures.
Stoichiometric Calculations – The Plan
LiOH + CO2 (g) Li2CO3 + H2O (g)
2. Balance the chemical equation.
1. Write the chemical equation.
2 LiOH + CO2 (g) Li2CO3 + H2O (g)
Stoichiometric Calculations – The Plan
2 LiOH + CO2 (g) Li2CO3 (g) + H2O (g)
48.0 g LiOH X 1 mole LiOH X 1 mole CO2 X 44.009g CO2 =
1 23.948 g LiOH 2 mole LiOH 1 mole CO2
3. Follow steps to dimensional analysis:
Stoichiometric Calculations – The Answer
When 48.0 grams of lithium hydroxide are available for
use in a reaction, 44.1 grams of carbon dioxide can be
processed by the reaction.
*Remember the significant figures.
Partner Share
Write your own stoichiometry question
for this reaction, and switch with your
table partner:
Barium chloride reacts with sodium
sulfate in a precipitation reaction to
make barium sulfate.