10.3 percent composition and chemical formulas

10.3 Percent Composition

and Chemical Formulas

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Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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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



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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?



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Percent Composition of a Compound

How do you calculate the percent

composition of a compound?

Percent Composition of a

Compound



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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.


Compound



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The percent composition of potassium

chromate, K2CrO4, is:


Compound

K = 40.3%

Cr = 26.8%

O = 32.9%



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Compound

K = 40.3%

Cr = 26.8%

+ O = 32.9%

100%

These percents must total 100%.



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Compound

These percents must total 100%.

• The percent composition of a compound is

always the same.



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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.


Compound

Percent Composition from Mass Data



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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


Compound

% by mass of element =mass of element

mass of compound×100%



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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



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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



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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


= 60.3% Mg

= ×100%

8.20 g

13.60 g



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Determine the percent by mass of

O in the compound.

Sample Problem 10.9


% O =mass of O


5.40 g

= 39.7% O

= ×100%13.60 g



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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



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You can also calculate the percent

composition of a compound using its

chemical formula.

Percent Composition from the Chemical Formula


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.



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You can also calculate the percent

composition of a compound using its

chemical formula.

Percent Composition from the Chemical Formula


Compound

% by mass

of element

mass of element in 1 mol compound

molar mass of compound×100%

=



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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



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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


Analyze List the knowns and the unknowns.1



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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





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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





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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%).





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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


Compound



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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


Compound

81.8 g C

100 g C3H8

and18 g H

100 g C3H8



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What information can you get from the

percent composition of a compound?

CHEMISTRY & YOU



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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.



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Calculate the mass of carbon and

the mass of hydrogen in 82.0 g of

propane (C3H8).


Calculating the Mass of an

Element in a Compound Using

Percent Composition



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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


Analyze List the known and the unknowns.1

UNKNOWNS

mass of carbon = ? g C

mass of hydrogen = ? g H



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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%.



• Multiply the mass of C3H8 by the

conversion factor.81.8 g C

100 g C3H8

82.0 g C3H8 × = 67.1 g C



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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%.



• 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



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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).





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What data can you use to calculate

percent composition?



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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.



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Empirical Formulas

How can you calculate the empirical

formula of a compound?

Empirical 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.



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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.



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Empirical Formulas

For carbon dioxide, the empirical and

molecular

formulas

are the

same—

CO2.



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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



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The percent composition of a compound

can be used to calculate the empirical

formula of that compound.

Empirical Formulas



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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



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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?


Determining the Empirical

Formula of a Compound



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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?


Analyze List the knowns and the unknown.1



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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.


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.



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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





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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.





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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.





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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?



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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.



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Molecular Formulas

How does the molecular formula of a

compound compare with the

empirical formula?

Molecular 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



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formula

Molar mass

(g/mol)

CH Empirical 13



CH2O (methanal) Empirical and molecular 30



Methanal, ethanoic acid, and glucose have

the same empirical formula—CH2O.

Interpret Data



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formula

Molar mass

(g/mol)

CH Empirical 13



CH2O (methanal) Empirical and molecular 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



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Methanal

(formaldehyde),

ethanoic acid (acetic

acid), and glucose have

the same empirical

formula—CH2O.

Molecular 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



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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.



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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.



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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.



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Calculate the molecular formula of a

compound whose molar mass is 60.0 g/mol

and empirical formula is CH4N.


Finding the Molecular Formula of a

Compound



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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


UNKNOWN

molecular formula = C?H?N?



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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





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• Divide the molar mass by the

empirical formula mass.



molar mass

efm=

60.0 g/mol

30.0 g/mol

= 2

• Multiply the formula subscripts by this

value.

(CH4N) × 2 = C2H8N2



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The molecular formula has the molar

mass of the compound.





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What information, in addition to

empirical formula, is necessary to

determine the molecular formula of a

compound?



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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.



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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



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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%



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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



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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



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END OF 10.3

10.3 percent composition and chemical formulas

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