Topic
16
Table of Contents
Topic
16
Topic 16: Stoichiometry
Basic Concepts
Additional Concepts
Stoichiometry: Basic Concepts
Topic
16
Stoichiometry
• Using the methods of stoichiometry, we can
measure the amounts of substances involved
in chemical reactions and relate them to one
another.
• For example, a sample’s mass or volume can
be converted to a count of the number of its
particles, such as atoms, ions, or molecules.
Stoichiometry: Basic Concepts
Topic
16
Stoichiometry
• Atoms are so tiny that an ordinary-sized
sample of a substance contains so many of
these submicroscopic particles that counting
them by grouping them in thousands would
be unmanageable.
• Even grouping them by millions would
not help.
Stoichiometry: Basic Concepts
Topic
16
Stoichiometry
• The group or unit of measure used to count
numbers of atoms, molecules, or formula units
of substances is the mole (abbreviated mol).
• The number of things in one mole is
6.02 x 1023. This big number has a
short name: the Avogadro constant.
• The most precise value of the Avogadro
constant is 6.0221367 x 1023. For most
purposes, rounding to 6.02 x 1023 is
sufficient.
Stoichiometry: Basic Concepts
Topic
16
Molar Mass
• Methanol is formed from CO2 gas and
hydrogen gas according to the balanced
chemical equation below.
Stoichiometry: Basic Concepts
Topic
16
Molar Mass
• Suppose you wanted to produce 500 g of
methanol.
• How many grams of CO2 gas and H2 gas
would you need? How many grams of
water would be produced as a by-product?
• Those are questions about the masses of
reactants and products.
Stoichiometry: Basic Concepts
Topic
16
Molar Mass
• But the balanced chemical equation shows
that three molecules of hydrogen gas react
with one molecule of carbon dioxide gas.
• The equation relates molecules, not masses,
of reactants and products.
Stoichiometry: Basic Concepts
Topic
16
Molar Mass
• Like Avogadro, you need to relate the
macroscopic measurements—the masses
of carbon dioxide and hydrogen—to the
number of molecules of methanol.
• To find the mass of carbon dioxide and the
mass of hydrogen needed to produce 500 g
of methanol, you first need to know how
many molecules of methanol are in 500 g
of methanol.
Stoichiometry: Basic Concepts
Topic
16
Molar Mass of an Element
• Average atomic masses of the elements are
given on the periodic table.
• For example, the average mass of one iron
atom is 55.8 u, where u means “atomic
mass units.”
Stoichiometry: Basic Concepts
Topic
16
Molar Mass of an Element
• The atomic mass unit is defined so that the
atomic mass of an atom of the most common
carbon isotope is exactly 12 u, and the mass
of 1 mol of the most common isotope of
carbon atoms is exactly 12 g.
Stoichiometry: Basic Concepts
Topic
16
Molar Mass of an Element
• The mass of 1 mol of a pure substance is
called its molar mass.
Stoichiometry: Basic Concepts
Topic
16
Molar Mass of an Element
• The molar mass is the mass in grams of the
average atomic mass.
• If an element exists as a molecule,
remember that the particles in 1 mol of that
element are themselves composed of atoms.
Stoichiometry: Basic Concepts
Topic
16
Molar Mass of an Element
• For example, the element oxygen exists as
molecules composed of two oxygen atoms,
so a mole of oxygen molecules contains 2
mol of oxygen atoms.
• Therefore, the molar mass of oxygen
molecules is twice the molar mass of oxygen
atoms: 2 x 16.00 g = 32.00 g.
Stoichiometry: Basic Concepts
Topic
16
•
•
•
•
Number of Atoms in a Sample of an
Element
The mass of an iron bar is 16.8 g. How many
Fe atoms are in the sample?
Use the periodic table to find the molar mass
of iron.
Use the periodic table to find the molar mass
of iron. The average mass of an iron atom is
55.8 u.
Then the mass of 1 mol of iron atoms is
55.8 g.
Stoichiometry: Basic Concepts
Topic
16
Number of Atoms in a Sample of an
Element
• To convert the mass of the iron bar to the
number of moles of iron, use the mass of 1
mol of iron atoms as a conversion factor.
• Now, use the number of atoms in a mole to
find the number of iron atoms in the bar.
Stoichiometry: Basic Concepts
Topic
16
Number of Atoms in a Sample of an
Element
• Simplify the expression above.
Stoichiometry: Basic Concepts
Topic
16
Molar Mass of a Compound
• Covalent compounds are composed of
molecules, and ionic compounds are
composed of formula units.
• The molecular mass of a covalent
compound is the mass in atomic mass units
of one molecule.
• Its molar mass is the mass in grams of 1 mol
of its molecules.
Stoichiometry: Basic Concepts
Topic
16
Molar Mass of a Compound
• The formula mass of an ionic compound is
the mass in atomic mass units of one
formula unit.
• Its molar mass is the mass in grams of 1 mol
of its formula units.
• How to calculate the molar mass for ethanol,
a covalent compound, and for calcium
chloride, an ionic compound, is shown.
Stoichiometry: Basic Concepts
Topic
16
Molar Mass of a Compound
• Ethanol, C2H6O, a covalent compound.
Stoichiometry: Basic Concepts
Topic
16
Molar Mass of a Compound
• Calcium chloride, CaCl2, an ionic compound.
Stoichiometry: Basic Concepts
Topic
16
Number of Formula Units in a Sample
of a Compound
• The mass of a quantity of iron(III) oxide is
16.8 g. How many formula units are in the
sample?
• Use the periodic table to calculate the mass
of one formula unit of Fe2O3.
Stoichiometry: Basic Concepts
Topic
16
Number of Formula Units in a Sample
of a Compound
• Therefore, the molar mass of Fe2O3 (rounded
off) is 160 g.
Stoichiometry: Basic Concepts
Topic
16
Number of Formula Units in a Sample
of a Compound
• Now, multiply the number of moles of iron
oxide by the number in a mole.
Stoichiometry: Basic Concepts
Topic
16
Mass of a Number of Moles of a
Compound
• What mass of water must be weighed to
obtain 7.50 mol of H2O?
• The molar mass of water is obtained from
its molecular mass.
• The molar mass of water is 18.0 g/mol.
Stoichiometry: Basic Concepts
Topic
16
Mass of a Number of Moles of a
Compound
• Use the molar mass to convert the number
of moles to a mass measurement.
Stoichiometry: Basic Concepts
Topic
16
Mass of a Number of Moles of a
Compound
• The concept of molar mass makes it easy to
determine the number of particles in a
sample of a substance by simply measuring
the mass of the sample.
• The concept is also useful in relating masses
of reactants and products in chemical
reactions.
Stoichiometry: Basic Concepts
Topic
16
Predicting Mass of a Reactant
• Ammonia gas is synthesized from nitrogen
gas and hydrogen gas according to the
balanced chemical equation below.
Stoichiometry: Basic Concepts
Topic
16
Predicting Mass of a Reactant
• How many grams of hydrogen gas are
required for 3.75 g of nitrogen gas to react
completely?
• Find the number of moles of N2 molecules
by using the molar mass of nitrogen.
Stoichiometry: Basic Concepts
Topic
16
Predicting Mass of a Reactant
• To find the mass of hydrogen needed, first
find the number of moles of H2 molecules
needed to react with all the moles of N2
molecules.
• The balanced chemical equation shows that
3 mol of H2 molecules react with 1 mol of
N2 molecules.
Stoichiometry: Basic Concepts
Topic
16
Predicting Mass of a Reactant
• Multiply the number of moles of N2
molecules by this ratio.
• The units in the expression above simplify
to moles of H2 molecules.
Stoichiometry: Basic Concepts
Topic
16
Predicting Mass of a Reactant
• To find the mass of hydrogen, multiply the
number of moles of hydrogen molecules by
the mass of 1 mol of H2 molecules, which
is 2.00 g.
Stoichiometry: Basic Concepts
Topic
16
Predicting Mass of a Product
• What mass of ammonia is formed when
3.75 g of nitrogen gas react with hydrogen
gas according to the balanced chemical
equation below?
• The amount of ammonia formed depends
upon the number of nitrogen molecules
present and the mole ratio of nitrogen and
ammonia in the balanced chemical equation.
Stoichiometry: Basic Concepts
Topic
16
Predicting Mass of a Product
• The number of moles of nitrogen molecules
is given by the expression below.
Stoichiometry: Basic Concepts
Topic
16
Predicting Mass of a Product
• To find the mass of ammonia produced, first
find the number of moles of ammonia
molecules that form from 3.75 g of nitrogen.
• Use the mole ratio of ammonia molecules to
nitrogen molecules to find the number of
moles of ammonia formed.
Stoichiometry: Basic Concepts
Topic
16
Predicting Mass of a Product
• Use the molar mass of ammonia, 17.0 g, to
find the mass of ammonia formed.
Stoichiometry: Basic Concepts
Topic
16
Using Molar Volumes in
Stoichiometric Problems
• In terms of moles, Avogadro’s principle
states that equal volumes of gases at the
same temperature and pressure contain
equal numbers of moles of gases.
• The molar volume of a gas is the volume
that a mole of a gas occupies at a pressure
of one atmosphere (equal to 101 kPa) and
a temperature of 0.00°C.
Stoichiometry: Basic Concepts
Topic
16
Using Molar Volumes in
Stoichiometric Problems
• Under these conditions of STP, the volume of
1 mol of any gas is 22.4 L.
• Like the
molar mass,
the molar
volume is
used in
stoichiometric
calculations.
Stoichiometry: Basic Concepts
Topic
16
Using Molar Volume
• In the space shuttle, exhaled carbon dioxide
gas is removed from the air by passing it
through canisters of lithium hydroxide. The
following reaction takes place.
• How many grams of lithium hydroxide are
required to remove 500.0 L of carbon dioxide
gas at 101 kPa pressure and 25.0°C?
Stoichiometry: Basic Concepts
Topic
16
Using Molar Volume
• The volume of gas at 25°C must be converted
to a volume at STP.
• Now, find the number of moles of CO2 gas
as below.
Stoichiometry: Basic Concepts
Topic
16
Using Molar Volume
• The chemical equation shows that the ratio
of moles of LiOH to CO2 is 2 to 1.
• Therefore, the number of moles of lithium
hydroxide is given by the expression below.
• To convert the number of moles of LiOH to
mass, use its molar mass, 23.9 g/mol.
Stoichiometry: Basic Concepts
Topic
16
Using Molar Volume
Stoichiometry: Basic Concepts
Topic
16
Ideal Gas Law
• Exactly how the pressure P, volume V,
temperature T, and number of particles n of
gas are related is given by the ideal gas law
shown here.
PV = nRT
Stoichiometry: Basic Concepts
Topic
16
Ideal Gas Law
• The value of the constant R can be
determined using the definition of molar
volume.
• At STP, 1 mol of gas occupies 22.4 L.
Therefore, when P = 101.3 kPa, V = 22.4 L,
n = 1 mol, and T = 273.15 K, the equation for
the ideal gas law can be shown as follows.
Stoichiometry: Basic Concepts
Topic
16
Ideal Gas Law
• Now, we can solve for R.
Stoichiometry: Basic Concepts
Topic
16
Using the Ideal Gas Law
• How many moles are contained in a 2.44-L
sample of gas at 25.0°C and 202 kPa?
• Solve the ideal gas law for n, the number
of moles.
Stoichiometry: Basic Concepts
Topic
16
Using the Ideal Gas Law
• First, find the volume that 2.44 L of a gas
would occupy at STP.
Stoichiometry: Basic Concepts
Topic
16
Using the Ideal Gas Law
• Then, find the number of moles in this
volume.
• 0.200 mol is close to the calculated value.
Stoichiometry: Basic Concepts
Topic
16
Determining Mass Percents
• The formula for geraniol
(the main compound that
gives a rose its scent) is
C10H18O.
Stoichiometry: Basic Concepts
Topic
16
Determining Mass Percents
• The formula shows that geraniol is
comprised of carbon, hydrogen, and oxygen.
• Because all these elements are nonmetals,
geraniol is probably covalent and comprised
of molecules.
Stoichiometry: Basic Concepts
Topic
16
Determining Mass Percents
• In addition, the formula C10H18O tells you
that each molecule of geraniol contains ten
carbon atoms, 18 hydrogen atoms, and one
oxygen atom.
• In terms of numbers of atoms, hydrogen is
the major element in geraniol.
Stoichiometry: Basic Concepts
Topic
16
Determining Mass Percents
• How can you tell whether it is the major
element by mass?
• You can answer this question by
determining the mass percents of each
element in geraniol.
Stoichiometry: Basic Concepts
Topic
16
Mass Percents of Elements in Geraniol
• This pie graph
shows the
composition
of geraniol in
terms of mass
percents of the
elements.
Stoichiometry: Basic Concepts
Topic
16
Mass Percents of Elements in Geraniol
• Suppose you have a mole of geraniol. Its
molar mass is 154 g/mol.
• Of this mass, how many grams do the
carbon atoms contribute?
• The formula shows that one molecule of
geraniol includes ten atoms of carbon.
• Therefore, 1 mol of geraniol contains 10 mol
of carbon.
Stoichiometry: Basic Concepts
Topic
16
Mass Percents of Elements in Geraniol
• Multiply the mass of 1 mol of carbon by
10 to get the mass of carbon in 1 mol of
geraniol.
• Now, use this mass of carbon to find the
mass percent of carbon in geraniol.
Stoichiometry: Basic Concepts
Topic
16
Mass Percents of Elements in Geraniol
• The mass percents of the other elements
are calculated below in a similar fashion.
• Mass of hydrogen in 1 mol geraniol:
Stoichiometry: Basic Concepts
Topic
16
Mass Percents of Elements in Geraniol
• Mass of oxygen in 1 mol geraniol:
Stoichiometry: Basic Concepts
Topic
16
Determining Chemical Formulas
• The formula of a compound having the
smallest whole-number ratio of atoms in the
compound is called the empirical formula.
• The empirical formula of this unknown
compound is NaClO4.
Basic Assessment Questions
Topic
16
Question 1
Determine the number of atoms in 45.6 g
gold, Au.
Basic Assessment Questions
Topic
16
Answer
1.39 x 1023 Au atoms
Basic Assessment Questions
Topic
16
Question 2
Determine the number of atoms in 17.5 g
copper(II) oxide, CuO.
Basic Assessment Questions
Topic
16
Answer
0.220 mol CuO
Basic Assessment Questions
Topic
16
Question 3
Determine the mass of 1.25 mol aspirin
C9H8O4.
Basic Assessment Questions
Topic
16
Answer
225g C9H8O4
Basic Assessment Questions
Topic
16
Question 4
What mass of sulfur must burn to produce
3.42 L of SO2 at 273°C and 101 kPa? The
reaction is
Basic Assessment Questions
Topic
16
Answer
2.45 g S
Stoichiometry: Additional Concepts
Topic
16
Additional Concepts
Stoichiometry: Additional Concepts
Topic
16
Stoichiometric Calculations
• There are three basic stoichiometric
calculations: mole-to-mole conversions,
mole-to-mass conversions, and mass-tomass conversions.
• All stoichiometric calculations begin with a
balanced equation and mole ratios.
Stoichiometric mole-to-mole conversion
• How can you determine the number of moles
of table salt (NaCl) produced from 0.02
moles of chlorine (Cl2)?
Stoichiometry: Additional Concepts
Topic
16
Stoichiometric mole-to-mole conversion
• First, write the balanced equation.
• Then, use the mole ratio to convert the
known number of moles of chlorine to the
number of moles of table salt. Use the
formula below.
Stoichiometry: Additional Concepts
Topic
16
Stoichiometric Moleto-Mass Conversion
• A mole-to-mass conversion allows you to
calculate the mass of a product or reactant
in a chemical reaction given the number of
moles of a reactant or product.
Stoichiometric Mole-to-Mass Conversion
• The following reaction occurs in plants
undergoing photosynthesis.
Stoichiometry: Additional Concepts
Topic
16
Stoichiometric Mole-to-Mass Conversion
• How many grams of glucose (C6H12O6)
are produced when 24.0 moles of carbon
dioxide reacts in excess water?
• Determine the number of moles of glucose
produced by the given amount of carbon
dioxide.
Stoichiometry: Additional Concepts
Topic
16
Stoichiometric Mole-to-Mass Conversion
• Multiply by the molar mass.
• 721 grams of glucose is produced from 24.0
moles of carbon dioxide.
Stoichiometry: Additional Concepts
Topic
16
Stoichiometric Mass-to-Mass
Conversion
• In this calculation, you can find the mass of
an unknown substance in a chemical equation
if you have the balanced chemical equation
and know the mass of one substance in the
equation.
Stoichiometry: Additional Concepts
Topic
16
Stoichiometric Mass-to-Mass Conversion
• How many grams of sodium hydroxide
(NaOH) are needed to completely react with
50.0 grams of sulfuric acid (H2SO4) to form
sodium sulfate (Na2SO4) and water?
• Write the balanced equation.
Stoichiometry: Additional Concepts
Topic
16
Stoichiometric Mass-to-Mass Conversion
• Convert grams of sulfuric acid to moles
NaOH.
Stoichiometry: Additional Concepts
Topic
16
Stoichiometric Mass-to-Mass Conversion
• Calculate the mass of NaOH needed.
• 50.0 grams of H2SO4 reacts completely
with 40.8 grams of NaOH.
Stoichiometry: Additional Concepts
Topic
16
Limiting Reactants
• Rarely are the reactants in a chemical
reaction present in the exact mole ratios
specified in the balanced equation.
• Usually, one or more of the reactants are
present in excess, and the reaction proceeds
until all of one reactant is used up.
• The reactant that is used up is called the
limiting reactant.
Stoichiometry: Additional Concepts
Topic
16
•
•
•
•
Limiting Reactants
The limiting reactant limits the reaction and,
thus, determines how much of the product
forms.
The left-over reactants are called excess
reactants.
How can you determine which reactant in a
chemical reaction is limited?
First, find the number of moles of each
reactant by multiplying the given mass of each
reactant by the inverse of the molar mass.
Stoichiometry: Additional Concepts
Topic
16
Determining the Limiting Reactant
• In the reaction below, 40.0 g of sodium
hydroxide (NaOH) reacts with 60.0 g of
sulfuric acid (H2SO4).
Stoichiometry: Additional Concepts
Topic
16
Determining the Limiting Reactant
• To determine the limiting reactant, calculate
the actual ratio of available moles of reactants.
Stoichiometry: Additional Concepts
Topic
16
Determining the Limiting Reactant
• So,
is available. Compare this
ratio with the mole ratio from the balanced
equation:
, or
• You can see that when 0.5 mol H2SO4 has
reacted, all of the 1.00 mol of NaOH would
be used up.
• Some H2SO4 would remain unreacted. Thus,
NaOH is the limiting reactant.
Stoichiometry: Additional Concepts
Topic
16
Determining the Limiting Reactant
• To calculate the mass of Na2SO4 that can
form from the given reactants, multiply the
number of moles of the limiting reactant
(NaOH) by the mole ratio of the product to
the limiting reactant and then multiply by the
molar mass of the product.
Stoichiometry: Additional Concepts
Topic
16
Determining the Limiting Reactant
• 71.0 g of Na2SO4 can form from the given
amounts of the reactants.
Additional Assessment Questions
Topic
16
Question 1
Balance the following equation. How many
moles of KClO3 are needed to produce 50
moles of O2?
Additional Assessment Questions
Topic
16
Answer
Additional Assessment Questions
Topic
16
Question 2
Calculate the mass of sodium chloride (NaCl)
produced when 5.50 moles of sodium reacts in
excess chlorine gas.
Additional Assessment Questions
Topic
16
Answer
321 g NaCl
Additional Assessment Questions
Topic
16
Question 3
Determine the mass of copper needed to react
completely with a solution containing 12.0 g
of silver nitrate (AgNO3).
Additional Assessment Questions
Topic
16
Answer
2.24 g Cu
Additional Assessment Questions
Topic
16
Question 4
Aluminum reacts with chlorine to produce
aluminum chloride.
Additional Assessment Questions
Topic
16
Question 4a
Balance the equation.
Answer 4a
Additional Assessment Questions
Topic
16
Question 4b
If you begin with 3.2 g of aluminum and 5.4 g
of chlorine, which is the limiting reactant?
Answer 4b
Cl2
Help
To advance to the next item or next page click on any
of the following keys: mouse, space bar, enter, down or
forward arrow.
Click on this icon to return to the table of contents
Click on this icon to return to the previous slide
Click on this icon to move to the next slide
Click on this icon to open the resources file.
Click on this icon to go to the end of the presentation.
End of Topic Summary File