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 appropriate answer with units.
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.
Get started:
**What fractions “equal to 1” help transition from days
to seconds?
Give it a try!
5.5 days 24 hours 60 minutes 60 seconds= ? seconds
1
1 day
1 hour
1 minute
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
M
O
Avogadro’s
L
Number
E
C
U
L
E
S
MOLE
Molar
Mass
G
R
A
M
S
Molar Mass
The mass in grams of 1
mole of the compound
C10 H6 O3
10 C = 10 X 12.01g = 120.11
6 H = 6 X 1.01g = 6.06
3 O = 3 X 16g = 48
TOTAL = *175.16 grams
*Remember sig figs
Molar Mass
The mass in grams of 1 mole
of the compound calcium
carbonate
CaCO3
Ca
C
O
1 X 40.08 grams = 40.08 grams
1 X 12.01 grams = 12.01 grams
3 X 16 grams = 48 grams
TOTAL = *100.09 grams
*Remember the sig figs
Give it a try!
• How many grams are in 4.92
moles of calcium carbonate?
Stoichiometric Calculations –
The Plan
1. Write the chemical equation.
2. Balance the chemical equation.
3. *Follow steps to dimensional
analysis:
1.
2.
3.
4.
5.
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.
Give it a try!
Stoichiometric Calculations
If you have 4.92 moles of
calcium carbonate how
many grams do you have?
4.92 mol CaCO3 X 100.09g CaCO3 =
1 mol CaCO3
Chemical Equations
• Recipe for a chemical reaction
• Relative number of reactants and
products
– Coefficients represent the relative
numbers.
CH4 + 2O2  CO2 + 2H2O
Coefficients
Law of Conservation of Matter:
Balancing
Chemical Equations
• Atoms are conserved in a chemical reaction.
• Coefficients are manipulated to balance
chemical reactions and create equivalent
measures.
• Identities cannot be changed.
_C2H5OH (l) + _O2 (g)  _CO2 (g) + _H2O (g)
Balancing
Chemical Equations
C2H5OH + O2  CO2 + H2O
Count Atoms:
Carbon 2
Carbon 1
Hydrogen 6
Hydrogen 2
Oxygen 3
Oxygen 3
Balancing
Chemical Equations
C2H5OH (l) + O2 (g)  CO2 (g) + H2O (g)
C2H5OH + 3O2  2CO2 + 3H2O
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 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 grams of lithium hydroxide
are used in a small scale experimental
device, how much carbon dioxide will
the device process?
Stoichiometric Calculations –
The Plan
1. Write the chemical equation.
2. Balance the chemical equation.
3. *Follow steps to dimensional
analysis:
1.
2.
3.
4.
5.
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
1. Write the chemical equation.
LiOH + CO2 (g)  Li2CO3 + H2O (g)
2. Balance the chemical
equation.
2 LiOH + CO2 (g)  Li2CO3 + H2O (g)
Stoichiometric Calculations –
The Plan
3. Follow steps to dimensional analysis:
48 g LiOH
1
X
1 mole LiOH
23.95 g LiOH
X
1 mole CO2
2 mole LiOH
X
44.01g CO2
1 mole CO2
2 LiOH + CO2 (g)  Li2CO3 (g) + H2O (g)
=
Stoichiometric Calculations –
The Answer
When 48 grams of lithium
hydroxide are available for use in
a reaction, 44.10 grams of carbon
dioxide can be processed by the
reaction.
*Remember the significant figures.
Set it up!
2.35 g of Barium chloride
react with sodium sulfate in
a precipitation reaction to
make how many grams of
barium sulfate?