10.3 percent composition and chemical formulas 1 > copyright © pearson education, inc., or its...

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10.3 Percent Composition 10.3 Percent Composition and Chemical Formulasand 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



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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 & YOUCHEMISTRY & 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 Percent Composition of a CompoundCompound



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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.




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The percent composition of potassium chromate, K2CrO4, is:


K = 40.3%Cr = 26.8%O = 32.9%



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>>Percent Composition of a Percent Composition of a CompoundCompound

K = 40.3%Cr = 26.8%

+ O = 32.9% 100%

These percents must total 100%.



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>>Percent Composition of a Percent Composition of a CompoundCompound

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.


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


% 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 10.9Sample 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%.

KNOWNSmass of compound = 13.60 gmass of oxygen = 5.40 g Omass of magnesium = 13.60 g – 5.40 g O = 8.20 g Mg

UNKNOWNSpercent by mass of Mg = ?% Mgpercent by mass of O = ?% O


Analyze List the knowns and the unknowns.1



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Determine the percent by mass of Mg in the compound.


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.



% 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%


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


• 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


% by massof 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.


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%.KNOWNSmass of C in 1 mol C3H8 = 3 mol × 12.0 g/mol = 36.0 gmass of H in 1 mol C3H8 = 8 mol × 1.0 g/mol = 8.0 gmolar mass of C3H8 = 36.0 g/mol + 8.0 g/mol = 44.0 g/mol

UNKNOWNSpercent by mass of C = ?% Cpercent 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




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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


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?




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What information can you get from the percent composition of a compound?


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.

KNOWNmass of C3H8 = 82.0 g


Analyze List the known and the unknowns.1

UNKNOWNSmass of carbon = ? g Cmass 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 FormulasEmpirical 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.


• 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.


• 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 FormulasEmpirical 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.




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The percent composition of a compound can be used to calculate the empirical formula of that compound.




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• 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.




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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.

KNOWNSpercent by mass of N = 25.9% Npercent by mass of O = 74.1% O

UNKNOWNempirical 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

O16.0 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 FormulasMolecular 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 DataInterpret Data



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Molar mass (g/mol)

CH Empirical 13



CH2O (methanal) Empirical and molecular 30



Methanal, ethanoic acid, and glucose have the same empirical formula—CH2O.




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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.




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Methanal (formaldehyde), ethanoic acid (acetic acid), and glucose have the same empirical formula—CH2O.




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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.




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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.


• 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.


• 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.


• 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.

KNOWNSempirical formula = CH4Nmolar mass = 60.0 g/mol

Analyze List the knowns and the unknown.1


UNKNOWNmolecular 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%.


Key ConceptsKey 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 Concepts and Key EquationsKey Equations

% by massof 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 TermsGlossary 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 IDEABIG IDEA

The Mole and Quantifying Matter



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END OF 10.3END OF 10.3

10.3 percent composition and chemical formulas 1 > copyright © pearson education, inc., or its...

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