10.3 percent composition and chemical formulas
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10.3 Percent Composition
and Chemical Formulas
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Chapter 10Chemical Quantities
10.1 The Mole: A Measurement of
Matter
10.2 Mole-Mass and Mole-Volume
Relationships
10.3 Percent Composition and
Chemical Formulas
10.3 Percent Composition
and Chemical Formulas
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A tag sewn into the
seam of a shirt usually
tells you what fibers
were used to make
the cloth and the
percent of each.
CHEMISTRY & YOU
What does the percent composition of a
compound tell you?
10.3 Percent Composition
and Chemical Formulas
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Percent Composition of a Compound
How do you calculate the percent
composition of a compound?
Percent Composition of a
Compound
10.3 Percent Composition
and Chemical Formulas
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The relative amounts of the elements in a
compound are expressed as the percent
composition or the percent by mass of
each element in the compound.
Percent Composition of a
Compound
10.3 Percent Composition
and Chemical Formulas
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The percent composition of potassium
chromate, K2CrO4, is:
Percent Composition of a
Compound
K = 40.3%
Cr = 26.8%
O = 32.9%
10.3 Percent Composition
and Chemical Formulas
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Percent Composition of a
Compound
K = 40.3%
Cr = 26.8%
+ O = 32.9%
100%
These percents must total 100%.
10.3 Percent Composition
and Chemical Formulas
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Percent Composition of a
Compound
These percents must total 100%.
• The percent composition of a compound is
always the same.
10.3 Percent Composition
and Chemical Formulas
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If you know the relative masses of each
element in a compound, you can calculate
the percent composition of the compound.
Percent Composition of a
Compound
Percent Composition from Mass Data
10.3 Percent Composition
and Chemical Formulas
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The percent by mass of an element
in a compound is the number of
grams of the element divided by the
mass in grams of the compound,
multiplied by 100%.
Percent Composition from Mass Data
Percent Composition of a
Compound
% by mass of element =mass of element
mass of compound×100%
10.3 Percent Composition
and Chemical Formulas
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When a 13.60-g sample of a
compound containing only
magnesium and oxygen is
decomposed, 5.40 g of oxygen is
obtained. What is the percent
composition of this compound?
Sample Problem 10.9
Calculating Percent
Composition from Mass Data
10.3 Percent Composition
and Chemical Formulas
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The percent by mass of an element in a
compound is the mass of that element divided by
the mass of the compound multiplied by 100%.
KNOWNS
mass of compound = 13.60 g
mass of oxygen = 5.40 g O
mass of magnesium = 13.60 g – 5.40 g O = 8.20 g Mg
UNKNOWNS
percent by mass of Mg = ?% Mg
percent by mass of O = ?% O
Sample Problem 10.9
Analyze List the knowns and the unknowns.1
10.3 Percent Composition
and Chemical Formulas
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Determine the percent by mass of
Mg in the compound.
Sample Problem 10.9
Calculate Solve for the unknowns.2
% Mg =mass of Mg
mass of compound×100%
= 60.3% Mg
= ×100%
8.20 g
13.60 g
10.3 Percent Composition
and Chemical Formulas
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Determine the percent by mass of
O in the compound.
Sample Problem 10.9
Calculate Solve for the unknowns.2
% O =mass of O
mass of compound×100%
5.40 g
= 39.7% O
= ×100%13.60 g
10.3 Percent Composition
and Chemical Formulas
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The percents of the elements add up
to 100%.
60.3% + 39.7% = 100%
Sample Problem 10.9
Evaluate Does the result make sense?3
10.3 Percent Composition
and Chemical Formulas
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You can also calculate the percent
composition of a compound using its
chemical formula.
Percent Composition from the Chemical Formula
Percent Composition of a
Compound
• The subscripts in the formula are used to
calculate the mass of each element in a mole of
that compound.
• Using the individual masses of the elements and
the molar mass, you can calculate the percent
by mass of each element.
10.3 Percent Composition
and Chemical Formulas
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You can also calculate the percent
composition of a compound using its
chemical formula.
Percent Composition from the Chemical Formula
Percent Composition of a
Compound
% by mass
of element
mass of element in 1 mol compound
molar mass of compound×100%
=
10.3 Percent Composition
and Chemical Formulas
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Propane (C3H8), the fuel
commonly used in gas grills, is
one of the compounds obtained
from petroleum. Calculate the
percent composition of
propane.
Sample Problem 10.10
Calculating Percent Composition
from a Formula
10.3 Percent Composition
and Chemical Formulas
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Calculate the percent by mass of each element
by dividing the mass of that element in one mole
of the compound by the molar mass of the
compound and multiplying by 100%.
KNOWNS
mass of C in 1 mol C3H8 = 3 mol × 12.0 g/mol = 36.0 g
mass of H in 1 mol C3H8 = 8 mol × 1.0 g/mol = 8.0 g
molar mass of C3H8 = 36.0 g/mol + 8.0 g/mol = 44.0 g/mol
UNKNOWNS
percent by mass of C = ?% C
percent by mass of H = ?% H
Sample Problem 10.10
Analyze List the knowns and the unknowns.1
10.3 Percent Composition
and Chemical Formulas
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Determine the percent by mass of C
in C3H8.
% C =mass of C in 1 mol C3H8
molar mass of C3H8
×100%
= 81.8% C
= ×100%
36.0 g
44.0 g
Sample Problem 10.10
Calculate Solve for the unknowns.2
10.3 Percent Composition
and Chemical Formulas
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Determine the percent by mass of H
in C3H8.
% H =mass of H in 1 mol C3H8
molar mass of C3H8
×100%
= 18% H
= ×100%
8.0 g
44.0 g
Sample Problem 10.10
Calculate Solve for the unknowns.2
10.3 Percent Composition
and Chemical Formulas
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The percents of the elements add up to
100% when the answers are expressed to
two significant figures (82% + 18% =
100%).
Sample Problem 10.10
Evaluate Does the result make sense?3
10.3 Percent Composition
and Chemical Formulas
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You can use percent composition to
calculate the number of grams of any
element in a specific mass of a compound.
• To do this, multiply the mass of the
compound by a conversion factor based on
the percent composition of the element in
the compound.
Percent Composition as a Conversion Factor
Percent Composition of a
Compound
10.3 Percent Composition
and Chemical Formulas
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Propane is 81.8% carbon and 18%
hydrogen.
• You can use the following conversion factors
to solve for the mass of carbon or hydrogen
contained in a specific amount of propane.
Percent Composition as a Conversion Factor
Percent Composition of a
Compound
81.8 g C
100 g C3H8
and18 g H
100 g C3H8
10.3 Percent Composition
and Chemical Formulas
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What information can you get from the
percent composition of a compound?
CHEMISTRY & YOU
10.3 Percent Composition
and Chemical Formulas
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What information can you get from the
percent composition of a compound?
CHEMISTRY & YOU
You can use percent
composition to determine
the mass of an element in
a sample of a compound
of a given size. You can
also determine the
empirical formula of the
compound.
10.3 Percent Composition
and Chemical Formulas
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Calculate the mass of carbon and
the mass of hydrogen in 82.0 g of
propane (C3H8).
Sample Problem 10.11
Calculating the Mass of an
Element in a Compound Using
Percent Composition
10.3 Percent Composition
and Chemical Formulas
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Use the conversion factors based on the percent
composition of propane to make the following
conversions: grams C3H8 → grams C and grams
C3H8 → grams H.
KNOWN
mass of C3H8 = 82.0 g
Sample Problem 10.11
Analyze List the known and the unknowns.1
UNKNOWNS
mass of carbon = ? g C
mass of hydrogen = ? g H
10.3 Percent Composition
and Chemical Formulas
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• To calculate the mass of C, first write the
conversion factor to convert from mass of C3H8
to mass of C.
81.8 g C
100 g C3H8
From Sample
Problem 10.10, the
percent by mass of C
in C3H8 is 81.8%.
Sample Problem 10.11
Calculate Solve for the unknowns.2
• Multiply the mass of C3H8 by the
conversion factor.81.8 g C
100 g C3H8
82.0 g C3H8 × = 67.1 g C
10.3 Percent Composition
and Chemical Formulas
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• To calculate the mass of H, first write the
conversion factor to convert from mass of C3H8
to mass of H.From Sample
Problem 10.10, the
percent by mass of H
in C3H8 is 18%.
Sample Problem 10.11
Calculate Solve for the unknowns.2
• Multiply the mass of C3H8 by the
conversion factor.18 g H
100 g C3H8
82.0 g C3H8 × = 15 g H
18 g H
100 g C3H8
10.3 Percent Composition
and Chemical Formulas
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The sum of the two masses equals 82 g,
the sample size, to two significant figures
(67 g C + 15 g H = 82 g C3H8).
Sample Problem 10.11
Evaluate Does the result make sense?3
10.3 Percent Composition
and Chemical Formulas
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What data can you use to calculate
percent composition?
10.3 Percent Composition
and Chemical Formulas
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What data can you use to calculate
percent composition?
You can calculate percent composition if you
know the mass of a compound and the masses
of the elements contained in the compound, or if
you know the chemical formula, the molar mass
of the compound, and the atomic weights of the
elements contained in the compound.
10.3 Percent Composition
and Chemical Formulas
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Empirical Formulas
How can you calculate the empirical
formula of a compound?
Empirical Formulas
10.3 Percent Composition
and Chemical Formulas
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The empirical formula of a compound gives
the lowest whole-number ratio of the atoms
or moles of the elements in a compound.
Empirical Formulas
• An empirical formula may or may not be the
same as a molecular formula.
10.3 Percent Composition
and Chemical Formulas
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The empirical formula of a compound gives
the lowest whole-number ratio of the atoms
or moles of the elements in a compound.
Empirical Formulas
• An empirical formula may or may not be the
same as a molecular formula.
– For example, the lowest ratio of hydrogen to oxygen
in hydrogen peroxide is 1:1. Thus, the empirical
formula of hydrogen peroxide is HO.
– The molecular formula, H2O2, has twice the number of
atoms as the empirical formula.
– Notice that the ratio of hydrogen to oxygen is still the
same, 1:1.
10.3 Percent Composition
and Chemical Formulas
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Empirical Formulas
For carbon dioxide, the empirical and
molecular
formulas
are the
same—
CO2.
10.3 Percent Composition
and Chemical Formulas
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Ethyne (C2H2), also
called acetylene, is a gas
used in welders’ torches.
The figure below shows two compounds of
carbon and hydrogen having the same
empirical formula (CH) but different
molecular formulas.
Styrene (C8H8) is used
in making polystyrene.
Empirical Formulas
10.3 Percent Composition
and Chemical Formulas
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The percent composition of a compound
can be used to calculate the empirical
formula of that compound.
Empirical Formulas
10.3 Percent Composition
and Chemical Formulas
39
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The percent composition of a compound
can be used to calculate the empirical
formula of that compound.
• The percent composition tells the ratio of masses of
the elements in a compound.
• The ratio of masses can be changed to ratio of moles
by using conversion factors based on the molar mass
of each element.
• The mole ratio is then reduced to the lowest whole-
number ratio to obtain the empirical formula of the
compound.
Empirical Formulas
10.3 Percent Composition
and Chemical Formulas
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A compound is analyzed and
found to contain 25.9% nitrogen
and 74.1% oxygen. What is the
empirical formula of the
compound?
Sample Problem 10.12
Determining the Empirical
Formula of a Compound
10.3 Percent Composition
and Chemical Formulas
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The percent composition gives the ratio of the
mass of nitrogen atoms to the mass of oxygen
atoms in the compound. Change the ratio of
masses to a ratio of moles and reduce this ratio
to the lowest whole-number ratio.
KNOWNS
percent by mass of N = 25.9% N
percent by mass of O = 74.1% O
UNKNOWN
empirical formula = N?O?
Sample Problem 10.12
Analyze List the knowns and the unknown.1
10.3 Percent Composition
and Chemical Formulas
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Convert the percent by mass of
each element to moles.
25.9 g N ×1 mol N
14.0 g N= 1.85 mol N
74.1 g O ×1 mol O
16.0 g O= 4.63 mol O
The mole ratio of N to O is N1.85O4.63.
Sample Problem 10.12
Calculate Solve for the unknown.2
Percent means
“parts per 100,” so
100.0 g of the
compound
contains 25.9 g N
and 74.1 g O.
10.3 Percent Composition
and Chemical Formulas
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Divide each molar quantity by the smaller
number of moles to get 1 mol for the
element with the smaller number of moles.
The mole ratio of N to O is N1O2.5.
4.63 mol O
1.85= 2.50 mol O
1.85 mol N
1.85= 1 mol N
Sample Problem 10.12
Calculate Solve for the unknown.2
10.3 Percent Composition
and Chemical Formulas
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Multiply each part of the ratio by the
smallest whole number that will convert
both subscripts to whole numbers.
1 mol N × 2 = 2 mol N
2.5 mol O × 2 = 5 mol O
The empirical formula is N2O5.
Sample Problem 10.12
Calculate Solve for the unknown.2
10.3 Percent Composition
and Chemical Formulas
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The subscripts are whole numbers, and
the percent composition of this empirical
formula equals the percents given in the
original problem.
Sample Problem 10.12
Evaluate Does the result make sense?3
10.3 Percent Composition
and Chemical Formulas
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You are doing an experiment to try to find
the molecular formula of a compound. You
discover the percent composition. Can
you determine the molecular formula?
10.3 Percent Composition
and Chemical Formulas
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You are doing an experiment to try to find
the molecular formula of a compound. You
discover the percent composition. Can
you determine the molecular formula?
You can determine the empirical formula. This might be the same as the molecular formula, or it might not. You would need more data to be sure of the molecular formula.
10.3 Percent Composition
and Chemical Formulas
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Molecular Formulas
How does the molecular formula of a
compound compare with the
empirical formula?
Molecular Formulas
10.3 Percent Composition
and Chemical Formulas
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Comparison of Empirical and Molecular Formulas
Formula (name) Classification of
formula
Molar mass
(g/mol)
CH Empirical 13
C2H2 (ethyne) Molecular 26 (2 × 13)
C6H6 (benzene) Molecular 78 (6 × 13)
CH2O (methanol) Empirical and molecular 30
C2H4O2 (ethanoic acid) Molecular 60 (2 × 30)
C6H12O6 (glucose) Molecular 180 (6 × 30)
Ethyne and benzene have the same
empirical formula—CH.
Interpret Data
10.3 Percent Composition
and Chemical Formulas
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Comparison of Empirical and Molecular Formulas
Formula (name) Classification of
formula
Molar mass
(g/mol)
CH Empirical 13
C2H2 (ethyne) Molecular 26 (2 × 13)
C6H6 (benzene) Molecular 78 (6 × 13)
CH2O (methanal) Empirical and molecular 30
C2H4O2 (ethanoic acid) Molecular 60 (2 × 30)
C6H12O6 (glucose) Molecular 180 (6 × 30)
Methanal, ethanoic acid, and glucose have
the same empirical formula—CH2O.
Interpret Data
10.3 Percent Composition
and Chemical Formulas
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Comparison of Empirical and Molecular Formulas
Formula (name) Classification of
formula
Molar mass
(g/mol)
CH Empirical 13
C2H2 (ethyne) Molecular 26 (2 × 13)
C6H6 (benzene) Molecular 78 (6 × 13)
CH2O (methanal) Empirical and molecular 30
C2H4O2 (ethanoic acid) Molecular 60 (2 × 30)
C6H12O6 (glucose) Molecular 180 (6 × 30)
Notice that the molar masses of the compounds in these
two groups are simple whole-number multiples of the
molar masses of the empirical formulas, CH and CH2O.
Interpret Data
10.3 Percent Composition
and Chemical Formulas
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Methanal
(formaldehyde),
ethanoic acid (acetic
acid), and glucose have
the same empirical
formula—CH2O.
Molecular Formulas
10.3 Percent Composition
and Chemical Formulas
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The molecular formula of a compound is either the same as its experimentally determined empirical formula, or it is a simple whole-number multiple of its empirical formula.
Molecular Formulas
10.3 Percent Composition
and Chemical Formulas
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The molecular formula of a compound is either the same as its experimentally determined empirical formula, or it is a simple whole-number multiple of its empirical formula.
Molecular Formulas
• Once you have determined the empirical
formula of a compound, you can determine
its molecular formula, if you know the
compound’s molar mass.
10.3 Percent Composition
and Chemical Formulas
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You can calculate the empirical formula
mass (efm) of a compound from its empirical
formula.
Molecular Formulas
• This is simply the molar mass of the empirical
formula.
10.3 Percent Composition
and Chemical Formulas
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You can calculate the empirical formula
mass (efm) of a compound from its empirical
formula.
Molecular Formulas
• Then you can divide the experimentally
determined molar mass by the empirical formula
mass.
• This quotient gives the number of empirical
formula units in a molecule of the compound and
is the multiplier to convert the empirical formula
to the molecular formula.
10.3 Percent Composition
and Chemical Formulas
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Calculate the molecular formula of a
compound whose molar mass is 60.0 g/mol
and empirical formula is CH4N.
Sample Problem 10.13
Finding the Molecular Formula of a
Compound
10.3 Percent Composition
and Chemical Formulas
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• Divide the molar mass by the empirical
formula mass to obtain a whole number.
• Multiply the empirical formula subscripts by
this value to get the molecular formula.
KNOWNS
empirical formula = CH4N
molar mass = 60.0 g/mol
Analyze List the knowns and the unknown.1
Sample Problem 10.13
UNKNOWN
molecular formula = C?H?N?
10.3 Percent Composition
and Chemical Formulas
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First calculate the empirical formula
mass.
efm of CH4N = 12.0 g/mol + 4(1.0 g/mol) + 14.0 g/mol
= 30.0 g/mol
Calculate Solve for the unknown.2
Sample Problem 10.13
10.3 Percent Composition
and Chemical Formulas
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• Divide the molar mass by the
empirical formula mass.
Calculate Solve for the unknown.2
Sample Problem 10.13
molar mass
efm=
60.0 g/mol
30.0 g/mol
= 2
• Multiply the formula subscripts by this
value.
(CH4N) × 2 = C2H8N2
10.3 Percent Composition
and Chemical Formulas
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The molecular formula has the molar
mass of the compound.
Evaluate Does the result make sense?3
Sample Problem 10.13
10.3 Percent Composition
and Chemical Formulas
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.
What information, in addition to
empirical formula, is necessary to
determine the molecular formula of a
compound?
10.3 Percent Composition
and Chemical Formulas
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What information, in addition to
empirical formula, is necessary to
determine the molecular formula of a
compound?
Molecular formula can be determined if the empirical formula and the molecular mass of a compound are known.
10.3 Percent Composition
and Chemical Formulas
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The percent by mass of an element in a
compound is the number of grams of
the element divided by the mass in
grams of the compound, multiplied by
100%.
The percent composition of a
compound can be used to calculate the
empirical formula of that compound.
Key Concepts
10.3 Percent Composition
and Chemical Formulas
65
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The molecular formula of a compound is
either the same as its experimentally
determined formula, or it is a simple
whole-number multiple of its empirical
formula.
Key Concepts and
Key Equations
% by mass
of element
mass of element in 1 mol compound
molar mass of compound×100%
=
% by mass
of element
mass of element
mass of compound= × 100%
10.3 Percent Composition
and Chemical Formulas
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Glossary Terms
• percent composition: the percent by
mass of each element in a compound
• empirical formula: a formula with the
lowest whole-number ratio of
elements in a compound; the
empirical formula of hydrogen
peroxide (H2O2) is HO
10.3 Percent Composition
and Chemical Formulas
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• The molecular formula of a compound
can be determined by first finding the
percent composition of the compound
and determining the empirical formula.
• Using the empirical formula mass and
the molar mass of the compound, the
molecular formula can be determined.
BIG IDEA
The Mole and Quantifying Matter
10.3 Percent Composition
and Chemical Formulas
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END OF 10.3
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