Chapter 3 - Stoichiometry
Average Atomic Mass
• Many elements have a # of naturally
occurring isotopes.
• Their atom percents in nature are known
as their isotopic abundances.
• Isotopic abundances and isotopic masses
can be measured using mass
spectroscopy.
• When calculating average atomic mass:
atomic mass Y = (atomic mass Y1) x %Y1 +
100%
(atomic mass Y2) x %Y2 + ….
100%
Determining Average Atomic Mass
• Silver (Ag; Z = 47) has 46 known isotopes, but
only two occur naturally, 107Ag and 109Ag. Given
the following mass spectrometric data, calculate
the atomic mass of Ag:
• Atomic mass of Ag = 55.42 amu + 52.45 amu = 107.87 amu
Avg. Atomic Mass Example Problem
• Bromine consists of two isotopes: Bromine-79
(78.92 amu) and Bromine-81 (80.92 amu). What
is the abundance of the heavier isotope?
• 79.90 = 78.92 (100-x) + 80.92 (x)
100
100
or
• 79.90 = .7892 (100-x) + .8092 (x)
x = 49% of Br-81
The Mole
• The mole represents 6.022 x 1023 items
– Atoms, formula units, molecules
• The MM, in grams/mole, is equal to the
sum of the masses of the atoms in the
formula.
– i.e. MM of H2O = ?
• Mole-gram conversions: m = MM x n
• Mole-liters conversions: 22.4 L = 1 mole
– This may only be used at STP
Information Contained in
the Chemical Formula of
Glucose, C6H12O6 (MM =
180.16 g/mol)
Mole Conversions - Example
•
Acetylsalicylic acid, C9H8O4, is the active
ingredient in aspirin.
a) What is the mass (g) of 0.509 mol of acetylsalicylic
acid?
b) What is the mass of H in this sample?
c) How many moles of acetylsalicylic acid are in a onegram sample of aspirin that contains 91.6% by
mass of acetylsalicylic acid?
•
a) 91.7 g C9H8O4 b) 4.10g H c) 5.08 x 10-3 mol
Percent Composition
• This allows us to determine the mass
percents of the elements present in a
compound.
• Calculate the % composition of all
elements in water:
– Hydrogen - 11.19%
– Oxygen - 88.81%
% Composition Example
•
Metallic iron is most often extracted from
hematite ore, which consists of iron (III) oxide
mixed with impurities such as silicon dioxide.
a) What are the mass percents of iron and oxygen in
iron (III) oxide?
b) How many grams of iron can be extracted from one
kilogram of iron (III) oxide?
c) How many metric tons of hematite ore, 66.4% iron
(III) oxide, must be processed to produce one
kilogram of iron?
•
(a)69.94% Fe, 30.06% O (b) 699.4g Fe (c)2.14 x 10-3 metric tons
% Composition Example 2
• Hexachlorophene, a compound made up
of atoms of carbon, hydrogen, chlorine,
and oxygen. Combustion of a 1.000gsample yields 1.407g of carbon dioxide,
0.134 g of water, & 0.523 g of chlorine
gas. What are the mass percents of all the
elements that make up hexachlorophene?
– 38.40% C, 1.50% H, 52.3% Cl, 7.80% O
Empirical Formula
• The empirical formula of a compound is
the simplest ratio possible for 2 or more
elements.
– CH4
C2H6
– CH5N
C2H10N2
– To solve for the empirical formula you are
generally given the %composition or masses
of the elements in the compound from
combustion analysis.
Combustion Analysis
Empirical Formula - Example
• Determine the empirical formula for a
compound that gives the following
percentages on analysis:
• 71.65% Cl, 24.27% C, 4.07% H
• ClCH2
Steps to an Empirical Formula
Molecular Formula
• This is basically multiples of the empirical.
• You need to know the molar mass of the
sample and its empirical formula to find.
• In the last example we determined the
empirical formula to be ClCH2, what if you
were told this sample had a molar mass of
98.96 g/mol, how would you find the
molecular formula?
• Cl2C2H4
Empirical & Molecular Formula Example 1
• A white powder is analyzed and found to
contain 43.64% phosphorous and 56.36%
oxygen by mass. The compound has a
molar mass of 283.88 g/mol. What are the
compounds empirical and molecular
formulas?
• Empirical = P2O5 Molecular = P4O10
Empirical & Molecular Formula Example 2
• The compound that gives vinegar a sour
taste is acetic acid, which contains the
elements carbon, hydrogen, and oxygen.
– A)Using combustion analysis, if a 5.000 g
sample of acetic acid yields 7.33 g of carbon
dioxide and 3.00 g of water, determine the
empirical formula.
– B) The MM of acetic acid, as determined with
a mass spectrometer, is 60 g/mol. Determine
the molecular formula for acetic acid.
Chemical Equations
• Reactants & products in a chemical
equations represent what is happening in
a chemical reaction.
• Coefficients are used to balance these
equations.
• States of matter are not required on the
AP Chemistry exam however any aqueous
solution must be written as ions in
aqueous solution.
Balancing Chemical Equations
» (a) A characteristic reaction of Group 1A(1) elements: chunks of
sodium react violently with water to form hydrogen gas and sodium
hydroxide solution.
» (b) The destruction of marble statuary by acid rain: aqueous nitric
acid reacts with calcium carbonate to form carbon dioxide, water, and
aqueous calcium nitrate.
» (c) Halogen compounds exchanging bonding partners: phosphorus
trifluoride is prepared by the reaction of phosphorus trichloride and
hydrogen fluoride; hydrogen chloride is the other product. The reaction
involves gases only.
» (d) Explosive decomposition of dynamite: liquid nitroglycerine
(C3H5N3O9) explodes to produce a mixture of gases—carbon dioxide,
water vapor, nitrogen, and oxygen
Stoichiometric Calculations
• The coefficients in a balanced equation give you
a molar ratio of the reactants and products.
This ratio is used to convert from one substance
to another in a balanced chemical equation.
• Solid lithium hydroxide is use in space vehicles
to remove exhaled carbon dioxide from the living
environment by forming solid lithium carbonate
and liquid water. What mass of gaseous carbon
dioxide can be absorbed by 1.00 kg of lithium
hydroxide?
– 9.20 x 102 g of CO2
Stoichiometric Calculation - Example
• Baking soda is often used as an antacid. It
neutralizes excess HCl acid secreted by the
stomach:
NaHCO3(s) + HCl(aq)  NaCl(aq) + H2O(l) + CO2(aq)
Milk of Magnesia, which is an aqueous
suspension of magnesium hydroxide, is also
used as an antacid:
Mg(OH)2(s) + 2HCl(aq)  2H2O(l) + MgCl2(aq)
Which is the more effective antacid per gram,
the baking soda or milk of magnesia?
-Baking soda neutralizes 1.19 x10-2 mol HCl
while milk of magnesia neutralizes 3.42 x10-2
mol HCl. So milk of magnesia is more
effective.
The Limiting Reactant
The Limiting Reactant
• This reactant limits the amount of product
produced because it runs out first:
– Nitrogen gas can be prepared by passing
gaseous ammonia over solid copper (II) oxide
at high temperatures. The other products of
the reaction are solid copper and water vapor.
If a sample containing 18.1 g of ammonia is
reacted with 90.4 g of copper (II) oxide, how
many grams of nitrogen will be formed?
• 10.6 g of N2
Percent Yield
• The actual yield of product is generally
given as a percentage calculated from the
following formula:
% Yield =
actual yield
x 100
theoretical yield
% Yield Example
• Silicon carbide (SiC) is an important ceramic
material that is made by allowing sand (silicon
dioxide, SiO2) to react with powdered carbon at
high temperature. Carbon monoxide is also
formed. When 100.0 kg of sand is processed,
51.4 kg of SiC is recovered. What is the percent
yield?
Sources
• (Silberberg, Martin S.. Chemistry: The
Molecular Nature of Matter and Change,
5th Edition. McGraw-Hill, 012009. 3.7.5).
MC #1
How many grams of calcium nitrate,
Ca(NO3)2, contains 24 grams of oxygen
atoms?
(A) 164 grams
(B) 96 grams
(C) 62 grams
(D) 50. grams
(E) 41 grams
MC #2
The simplest formula for an oxide of
nitrogen that is 36.8 percent nitrogen by
weight is
(A) N2O
(B) NO
(C) NO2
(D) N2O3
(E) N2O5
MC #3
When a hydrate of Na2CO3 is heated until
all the water is removed, it loses 54.3
percent of its mass. The formula of the
hydrate is
(A) Na2CO3 . 10 H2O
(B) Na2CO3 . 7 H2O
(C) Na2CO3 . 5 H2O
(D) Na2CO3 . 3 H2O
(E) Na2CO3 . H2O
MC #4
In which of the following compounds is the
mass ratio of chromium to oxygen closest
to 1.6 to 1.0?
(A) CrO3
(B) CrO2
(C) CrO
(D) Cr20
(E) Cr2O3
MC #5
When hafnium metal is heated in an atmosphere
of chlorine gas, the product of the reaction is
found to contain 62.2 percent Hf by mass and
37.4 percent Cl by mass. What is the empirical
formula for this compound?
(A) HfCl
(B) HfCl2
(C) HfCl3
(D) HfCl4
(E) Hf2Cl3
FRQ #1
The molecular formula of a hydrocarbon is to be
determined by analyzing its combustion
products.
• (a) The hydrocarbon burns completely,
producing 7.2 grams of water and 7.2 liters of
CO2 at standard conditions. What is the
empirical formula of the hydrocarbon?
• (b) Calculate the mass in grams of O2 required
for the complete combustion of the sample of the
hydrocarbon described in (a).
• (c) With a molar mass of 56.2 g/mol, what is the
molecular formula of the hydrocarbon?
FRQ #2
CH4(g) + 2 Cl2(g)  CH2Cl2 (g) + 2 HCl(g)
• Methane gas reacts with chlorine gas to form
dichloromethane and hydrogen chloride, as represented
by the equation above.
(a) A 25.0 g sample of methane is placed in a reaction
vessel containing 2.58 mol of Cl2(g).
(i) Identify the limiting reactant when the methane
and chlorine gases are combined. Justify your answer
with a calculation.
(ii) Calculate the total number of moles of CH2Cl2(g)
in the container after the limiting reactant has been
totally consumed.
FRQ #3
Answer the following questions about acetylsalicylic acid,
the active ingredient in aspirin.
• (a) The amount of acetylsalicylic acid in a single aspirin
tablet is 325 mg, yet the tablet has a mass of 2.00 g.
Calculate the mass percent of acetylsalicylic acid in the
tablet.
• (b) The elements contained in acetylsalicylic acid are
hydrogen, carbon, and oxygen. The combustion of 3.000
g of the pure compound yields 1.200 g of water and
6.602 g of carbon dioxide. Calculate the mass, in g, of
each element in the 3.000 g sample.