Download 12.2 Chemical Calculations

12.2 Chemical Calculations >
Chapter 12
Stoichiometry
12.1 The Arithmetic of Equations
12.2 Chemical Calculations
12.3 Limiting Reagent and
Percent Yield
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12.2 Chemical Calculations >
CHEMISTRY
& YOU
How do manufacturers know how to make
enough of their desired product?
If chemical plants
produce too much
ammonia, then it
might be wasted. But
if too little is produced,
then there might not
be enough for all their
customers.
2
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12.2 Chemical Calculations >
Writing and Using Mole Ratios
Writing and Using Mole Ratios
How are mole ratios used in chemical
calculations?
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12.2 Chemical Calculations >
Writing and Using Mole Ratios
A mole ratio is a conversion factor
derived from the coefficients of a
balanced chemical equation
interpreted in terms of moles.
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12.2 Chemical Calculations >
Types of Stoichiometry Problems to
solve using the mole ratios of
balanced chemical equations.
1. Mole-Mole Problems
2. Mole-Mass Problems
3. Mass-mass
4. Mass-volume
5. Volume-volume
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12.2 Chemical Calculations >
Mole-Mole Problems
Example:
NH4NO3 ------> N2O + 2 H2O
Find the number of moles of N2O
and H2O produced from the
decomposition of 2.25 mole of
NH4NO3?
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12.2 Chemical Calculations >
Mole-Mole Problems
The balanced chemical equation
states that for every 1 mole of
NH4NO3 that decomposes, 1 mole
of N2O and 2 moles of water are
produced.
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12.2 Chemical Calculations >
Mole-Mole Problems
Use this mole ratio from the chemical equation to
calculated the number of moles of N20 & H2O
produced:
2.25 mol NH4NO3 1 mole N20
1mol NH4NO3 = 2.25 mole N20
2.25 mol NH4NO3 2 mole H20
1mol NH4NO3 = 4.5 mole H20
NH4NO3 ------> N2O + 2 H2O
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12.2 Chemical Calculations >
Mole-Mole Problems
Magnesium burns in oxygen to produce magnesium
oxide. How many moles of oxygen are needed to
burn 0.52 moles of magnesium?
Write a balanced equation for this reaction:
2 Mg + O2  2 MgO
Solve:
0.52 mol Mg 1 mol 02
2 mol Mg = .26 mol O2
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12.2 Chemical Calculations >
Mole-Mole Problems
The equation for the composition of water is:
2 H2 + O2 ---> 2 H2O
How many moles of H2O are produced when
5.00 moles of oxygen are used?
5 moles O2 2 mole H2O
1 moles O2
= 10 moles H20
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12.2 Chemical Calculations >
Writing and Using Mole Ratios
In chemical calculations, -mole ratios are used to convert between a given number
of moles of a reactant or product to moles of
a different reactant or product.
These mole ratios are represented by
the coefficients of a balanced chemical
equation
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12.2 Chemical Calculations >
Writing and Using Mole Ratios
Mass-Mass Calculations
In the laboratory, the amount of a substance is
usually determined by measuring its mass in grams.
• If a given sample is measured in grams, then the mass
can be converted to moles by using the molar mass.
• Then the mole ratio from the balanced equation can be
used to calculate the number of moles of the unknown.
• If it is the mass of the unknown that needs to be
determined, the number of moles of the unknown can
be multiplied by the molar mass.
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12.2 Chemical Calculations > I. Mass-Mass Problems
Mass-Mass Calculations
In a mass-mass problem you are
given the mass of one
substance and ask to find the
mass of another substance
involved in the same reaction.
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12.2 Chemical Calculations > I. Mass-Mass Problems
Mass-Mass Calculations
All mass-mass problems can be solved by
following these steps:
1. Write a balanced equation for the chemical reaction
2.
3.
4.
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involved.
Convert the given mass of the substance given (A) to moles
of substance (A) using the molar mass of the substance(A) .
Convert the moles of the substance given (A) to the moles
of the substance (B) by using the mole ratio from the
balanced chemical equation.
Change moles of substance (B) to the mass of substance (B)
using the molar mass of the substance.
12.2 Chemical Calculations >
Summary of Mass-Mass Problem
1.
2.
3.
4.
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Write a balanced equation for
the chemical reaction involved.
Convert the given mass of the
substance given (A) to moles
of substance (A) using the
molar mass of the substance(A)
.
Convert the moles of the
substance given (A) to the
moles of the substance (B) by
using the mole ratio from the
balanced chemical equation.
Change moles of substance (B)
to the mass of substance (B)
using the molar mass of the
substance.
12.2 Chemical Calculations >
Sample Problem 12.4
Calculating the Mass of a Product
Calculate the number of
grams of NH3 produced by
the reaction of 5.40 g of
hydrogen with an excess of
nitrogen. The balanced
equation is:
N2(g) + 3H2(g)  2NH3(g)
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12.2 Chemical Calculations >
Sample Problem 12.4
Calculate Solve for the unknown.
Start with the given quantity, and convert
from mass to moles.
1 mol H2
5.40 g H2 
2.0 g H2
Given
quantity
17
Change
given unit to
moles
Don’t forget to cancel
the units at each step.
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12.2 Chemical Calculations >
Sample Problem 12.4
Calculate Solve for the unknown.
Then convert from moles of reactant to
moles of product by using the correct
mole ratio.
1 mol H2
2 mol NH3
5.40 g H2  2.0 g H  3 mol H
2
2
Given
quantity
18
Change
given unit to
moles
Mole ratio
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12.2 Chemical Calculations >
Sample Problem 12.4
Calculate Solve for the unknown.
Finish by converting from moles to grams.
Use the molar mass of NH3.
1 mol H2
2 mol NH3
17.0 g NH3
5.40 g H2  2.0 g H  3 mol H  1 mol NH
2
2
3
Given
quantity
Change
given unit to
moles
Mole ratio
Change
moles to
grams
= 31 g NH3
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12.2 Chemical Calculations >
Phosphorus burns in air to produce a
phosphorus oxide in the following reaction:
4P(s) + 5O2(g)  P4O10(s)
What mass of phosphorus will be needed to
produce 3.25 mol of P4O10?
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12.2 Chemical Calculations >
Phosphorus burns in air to produce a
phosphorus oxide in the following reaction:
4P(s) + 5O2(g)  P4O10(s)
What mass of phosphorus will be needed to
produce 3.25 mol of P4O10?
4 mol P
31.0 g P
3.25 mol P4O10  1 mol P O
 1 mol P = 403 g P
4 10
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12.2 Chemical Calculations >
Mass-Mass Calculations
Example: 50 g of Ammonium
dichromate, (NH4)2Cr2O7,
decomposes when heated strongly
to generate nitrogen gas, N2,
gaseous water, H2O, and the green
crystalline compound
chromium(III) oxide, Cr2O3.
How many grams of water are produced?
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12.2 Chemical Calculations >
Mass-Mass Calculations
Write a balanced chemical
equation for the reaction.
(NH4)2Cr2O7 N2 + 4 H2O + Cr2O3
50 g (NH4)2Cr2O7 1 mol (NH4)2Cr2O7 4 mol H2O
18 g H20
252 g (NH4)2Cr2O7 1 mol (NH4)2Cr2O7 1 mol H20
= 14.28 g H20
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II. Mass-Volume
12.2 Chemical Calculations > Problems
Mass-Volume Calculations
In Mass-volume problems you
are given the mass of one
substance in a chemical
reaction asked to find the
volume of another
substance- in this case a gas.
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II. Mass-Volume
12.2 Chemical Calculations > Problems
Mass-Volume Calculations
1. Write the balanced equation.
2. Convert the given mass (A) into moles (A)
using the molar mass of the substance
3. Convert the moles of the substance given
(A) to the moles of the substance (B) by
using the mole ratio from the balanced
chemical equation.
4. Convert the number of moles (B) of the
unknown quantity to volume (B) using the
molar volume of a gas
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12.2 Chemical Calculations >
Summary of Mass-Volume Calculations
1. Write the balanced equation.
2. Convert the given mass (A)
into moles (A) using the
molar mass of the substance
3. Convert the moles of the
substance given (A) to the
moles of the substance (B)
by using the mole ratio from
the balanced chemical
equation.
4. Convert the number of moles
(B) of the unknown quantity
to volume (B) using the
molar volume of a gas
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II. Mass-Volume
12.2 Chemical Calculations > Problems
Mass-Volume Calculations
Example: 10.0 g of Zn react with HCl
acid to produce zinc chloride and
hydrogen gas. How many liters of
hydrogen gas will be produced?
1. Write the balanced equation:
Zn + 2 HCl  ZnCl2 + H2
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II. Mass-Volume
12.2 Chemical Calculations > Problems
Mass-Volume Calculations
1. Convert the given mass (A) into moles
(A) using the molar mass of the
substance
Zn + 2 HCl  ZnCl2 + H2
10 g Zn 1 mol Zn
65.4 g Zn
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II. Mass-Volume
12.2 Chemical Calculations > Problems
Mass-Volume Calculations
Convert the moles of the substance given (A)
to the moles of the substance (B) by
using the mole ratio from the balanced
chemical equation:
Zn + 2 HCl  ZnCl2 + H2
10 g Zn 1 mol Zn
65.4 g Zn
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1 mol H2
1 mol Zn
II. Mass-Volume
12.2 Chemical Calculations > Problems
Mass-Volume Calculations
Convert the number of moles (B) of the
unknown quantity to volume (B) using the
molar volume of a gas at STP (22.4 L)
Zn + 2 HCl  ZnCl2 + H2
10 g Zn 1 mol Zn
65.4 g Zn
= 3.4 L H2
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1 mol H2 22.4 L H2
1 mol Zn 1 mol H2
12.2 Chemical Calculations >
Sample Problem 12.5
Calculating the Molecules of a Product
How many molecules of
oxygen are produced when
29.2 g of water is decomposed
by electrolysis according to
this balanced equation?
2H2O(l)
31
electricity
2H2(g) + O2(g)
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12.2 Chemical Calculations >
Sample Problem 12.5
1 Analyze List the knowns and the unknown.
The following calculations need to be
performed:
g H2O  mol H2O  mol O2  molecules O2
The appropriate mole ratio relating mol O2 to
mol H2O from the balanced equation is:
1 mol O2
2 mol H2O
32
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12.2 Chemical Calculations >
Sample Problem 12.5
Calculate Solve for the unknown.
Start with the given quantity, and convert
from mass to moles.
29.2 g H2O 
Given
quantity
1 mol H2O
18.0 g H2O
Change
to moles
Remember to also start your calculations
with the given quantity, even if the given
quantity is a product in the reaction.
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12.2 Chemical Calculations >
Sample Problem 12.5
2 Calculate Solve for the unknown.
Then, convert from moles of reactant to
moles of product.
29.2 g H2O 
Given
quantity
34
1 mol H2O
1 mol O2

18.0 g H2O
2 mol H2O
Change
to moles
Mole ratio
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12.2 Chemical Calculations >
Sample Problem 12.5
2 Calculate Solve for the unknown.
Finish by converting from moles to
molecules.
1 mol H2O
1 mol O2
6.02  1023 molecules O2
29.2 g H2O 


18.0 g H2O
2 mol H2O
1 mol O2
Given
quantity
35
Change
to moles
Mole ratio
Change to molecules
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12.2 Chemical Calculations >
Sample Problem 12.5
2 Calculate Solve for the unknown.
Finish by converting from moles to
molecules.
1 mol H2O
1 mol O2
6.02  1023 molecules O2
29.2 g H2O 


18.0 g H2O
2 mol H2O
1 mol O2
Given
quantity
Change
to moles
Mole ratio
Change to molecules
= 4.88  1023 molecules O2
36
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12.2 Chemical Calculations >
Sample Problem 12.5
3 Evaluate Does the result make sense?
• The given mass of water should produce
a little less than 1 mol of oxygen, or a little
less than Avogadro’s number of
molecules.
• The answer should have three significant
figures.
37
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12.2 Chemical Calculations >
Sample Problem 12.6
Volume-Volume Stoichiometric Calculations
Nitrogen monoxide and oxygen
gas combine to form the brown
gas nitrogen dioxide, which
contributes to photochemical
smog. How many liters of nitrogen
dioxide are produced when 34 L of
oxygen react with an excess of
nitrogen monoxide? Assume
conditions are at STP.
2NO(g) + O2(g)  2NO2(g)
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12.2 Chemical Calculations >
Sample Problem 12.6
1 Analyze List the knowns and the unknown.
For gaseous reactants and products at STP,
1 mol of a gas is equal to 22.4 L.
KNOWNS
volume of oxygen = 34 L O2
2 mol NO2/1 mol O2 (mole ratio from balanced equation)
1 mol O2 = 22.4 L O2 (at STP)
1 mol NO2 = 22.4 L NO2 (at STP)
UNKNOWN
volume of nitrogen dioxide = ? L NO2
39
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12.2 Chemical Calculations >
Sample Problem 12.6
2 Calculate Solve for the unknown.
Start with the given quantity, and convert
from volume to moles by using the
volume ratio.
34 L O2 
Given
quantity
1 mol O2
22.4 L O2
Change
to moles
Did you notice that the 22.4 L/mol factors
canceled out? This will always be true in
a volume-volume problem.
40
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12.2 Chemical Calculations >
Sample Problem 12.6
2 Calculate Solve for the unknown.
Then, convert from moles of reactant to
moles of product by using the correct
mole ratio.
34 L O2 
Given
quantity
41
1 mol O2
2 mol NO2
22.4 L O2  1 mol O2
Change
to moles
Mole ratio
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12.2 Chemical Calculations >
Sample Problem 12.6
2 Calculate Solve for the unknown.
Finish by converting from moles to liters.
Use the volume ratio.
34 L O2 
Given
quantity
1 mol O2
2 mol NO2
22.4 L NO2
22.4 L O2  1 mol O2  1 mol NO2
Change
to moles
Mole ratio
Change to
liters
= 68 L NO2
42
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12.2 Chemical Calculations >
Sample Problem 12.6
3 Evaluate Does the result make sense?
• Because 2 mol NO2 are produced for each
1 mol O2 that reacts, the volume of NO2
should be twice the given volume of O2.
• The answer should have two significant
figures.
43
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12.2 Chemical Calculations >
Sample Problem 12.7
Finding the Volume of a Gas Needed
for a Reaction
Assuming STP, how many milliliters of
oxygen are needed to produce 20.4 mL SO3
according to this balanced equation?
2SO2(g) + O2(g)  2SO3(g)
44
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12.2 Chemical Calculations >
Sample Problem 12.7
1 Analyze List the knowns and the unknown.
• For a reaction involving gaseous reactants or
products, the coefficients also indicate relative
amounts of each gas.
• You can use the volume ratios in the same way
you have used mole ratios.
KNOWNS
volume of sulfur trioxide = 20.4 mL
2 mL SO3/1 mL O2 (volume ratio from balanced equation)
UNKNOWN
volume of oxygen = ? mL O2
45
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12.2 Chemical Calculations >
Sample Problem 12.7
2 Calculate Solve for the unknown.
Multiply the given volume by the
appropriate volume ratio.
20.4 mL SO3 
1 mL O2
2 mL SO3
= 10.2 mL O2
The volume ratio can be
written using milliliters as
the units instead of liters.
46
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12.2 Chemical Calculations >
Sample Problem 12.7
3 Evaluate Does the result make sense?
• Because the volume ratio is 2 volumes
SO3 to 1 volume O2, the volume of O2
should be half the volume of SO3.
• The answer should have three significant
figures.
47
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12.2 Chemical Calculations >
Methane burns in air by the following
reaction:
CH4(g) + 2O2(g)  CO2(g) + 2H2O(g)
What volume of water vapor is produced
at STP by burning 501 g of methane?
48
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12.2 Chemical Calculations >
Methane burns in air by the following
reaction:
CH4(g) + 2O2(g)  CO2(g) + 2H2O(g)
What volume of water vapor is produced
at STP by burning 501 g of methane?
501 g CH4
49

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12.2 Chemical Calculations >
Methane burns in air by the following
reaction:
CH4(g) + 2O2(g)  CO2(g) + 2H2O(g)
What volume of water vapor is produced
at STP by burning 501 g of methane?
501 g CH4
50
1 mol CH4
16.05 g CH4 

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12.2 Chemical Calculations >
Methane burns in air by the following
reaction:
CH4(g) + 2O2(g)  CO2(g) + 2H2O(g)
What volume of water vapor is produced
at STP by burning 501 g of methane?
501 g CH4
51
1 mol CH4
2 mol H2O
16.05 g CH4  1 mol CH4 
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12.2 Chemical Calculations >
Methane burns in air by the following
reaction:
CH4(g) + 2O2(g)  CO2(g) + 2H2O(g)
What volume of water vapor is produced
at STP by burning 501 g of methane?
501 g CH4
1 mol CH4
16.05 g CH4
2 mol H2O
1 mol CH4
22.4 L H2O
1 mol H2O
= 1398.4 L
52
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12.2 Chemical Calculations > Key Concepts
In chemical calculations, mole ratios are used
to convert between moles of reactant and
moles of product, between moles of
reactants, or between moles of products.
In a typical stoichiometric problem, the given
quantity is first converted to moles. Then, the
mole ratio from the balanced equation is
used to calculate the moles of the wanted
substance. Finally, the moles are converted
to any other unit of measurement related to
the unit mole.
53
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12.2 Chemical Calculations > Glossary Terms
mole ratio: a conversion factor derived
from the coefficients of a balanced
chemical equation interpreted in terms
of moles
54
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12.2 Chemical Calculations >
BIG IDEA
The Mole and Quantifying Matter
Mole ratios from the balanced equation are used
to calculate the amount of a reactant or product
in a chemical reaction from a given amount of
one of the reactants or products.
55
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12.2 Chemical Calculations >
END OF 12.2
56
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