problem solving percentage composition back print

Copyright © by Holt, Rinehart and Winston. All rights reserved.

Holt Chemistry 40 The Mole and Chemical Composition

Percentage CompositionSuppose you are working in an industrial laboratory. Your supervisor gives you a

bottle containing a white crystalline compound and asks you to determine its

identity. Several unlabeled drums of this substance have been discovered in a

warehouse, and no one knows what it is. You take it into the laboratory and carry

out an analysis, which shows that the compound is composed of the elements

sodium, carbon, and oxygen. Immediately, you think of the compound sodium

carbonate, Na2CO3 , a very common substance found in most laboratories and

used in many industrial processes.

Before you report your conclusion to your boss, you decide to check a refer-

ence book to see if there are any other compounds that contain only the elements

sodium, carbon, and oxygen. You discover that there is another compound,

sodium oxalate, which has the formula Na2C2O4 . When you read about this com-

pound, you find that it is highly poisonous and can cause serious illness and even

death. Mistaking sodium carbonate for sodium oxalate could have very serious

consequences. What can you do to determine the identity of your sample? Is it

the common industrial substance or the dangerous poison?

Fortunately, you can determine not only which elements are in the compound,

but also how much of each element is present. As you have learned, every com-

pound has a definite composition. Every water molecule is made up of two

hydrogen atoms and one oxygen atom, no matter where the water came from. A

formula unit of sodium chloride is composed of one sodium atom and one chlo-

rine atom, no matter whether the salt came from a mine or was obtained by evap-

orating sea water.

Likewise, sodium carbonate always has two sodium atoms, one carbon atom,

and three oxygen atoms per formula unit, giving it the formula Na2CO3 ; and a for-

mula unit of sodium oxalate always contains two sodium atoms, two carbon

atoms, and four oxygen atoms, giving it the formula Na2C2O4 . Because each atom

has a definite mass, each compound will have a distinct composition by mass.

This composition is usually expressed as the percentage composition of the com-

pound—the percentage by mass of each element in a compound. To identify a

compound, you can compare the percentage composition obtained by laboratory

analysis with a calculated percentage composition of each possible compound.

Name Class Date

Problem SolvingSkills Worksheet



Name Class Date

Problem Solving continued

General Plan for Determining Percentage

Composition of a Compound

Convert using the

formula of the compound.

Convert by expressing

percentage as a fraction

and then multiplying by

the mass of the sample.

Molar mass

of

element

Convert by multiplying

by the inverse of the

molar mass of the

compound. Then convert

to a percentage by

multiplying by 100.

1

Percentage

element in the

compound

3Mass of

element in a

sample of

compound

5

Repeat 1, 2,

and 3 for each

remaining

element in the

compound.

Percentage

composition of

the compound

4

Mass of

element per

mole of

compound

2



Name Class Date


Sample Problem 1Determine the percentage composition of sodium carbonate, Na2CO3 .

SolutionANALYZE

What is given in the problem? the formula of sodium carbonate

What are you asked to find? the percentage of each element in sodium car-

bonate (the percentage composition)

PLANWhat step is needed to determine the mass of each element per mole of com-

pound?

Multiply the molar mass of each element by the ratio of the number of moles of

that element in a mole of the compound (the subscript of that element in the

compound’s formula).

What steps are needed to determine the portion of each element as a percentage

of the mass of the compound?

Multiply the mass of each element by the inverse of the molar mass of the

compound, and then multiply by 100 to convert to a percentage.

Step 1

multiply by the subscript of Na

in Na2CO3

Molar mass of Na1

Mass Na per mole

Na2CO3

2

ratio of mol Na per mol

Na2CO3 from formula

2 mol Na��

1 mol Na2CO3

molar mass Na

22.99 g Na

1 mol Na

g Na

1 mol Na2CO3

Items Data

Formula of sodium carbonate Na2CO3

Molar mass of each element* Na � 22.99 g/mol

C � 12.01 g/mol

O � 16.00 g/mol

Molar mass of sodium carbonate 105.99 g/mol

Percentage composition of sodium carbonate ?%

* determined from the periodic table



Name Class Date


Step 2

Now you can combine Step 1 and Step 2 into one calculation.

combining Steps 1 and 2

� � � 100 � percentage Na in Na2CO3

Finally, determine the percentage of carbon and oxygen in Na2CO3 by repeating

the calculation above with each of those elements.

COMPUTE

percentage sodium

percentage carbon

percentage oxygen

EVALUATEAre the units correct?

Yes; the composition is given in percentages.

3 mol O

1 mol Na2CO3

� 100 � 45.29% O�16.00 g O

1 mol O

1 mol Na2CO3

105.99 g Na2CO3

�

1 mol C

1 mol Na2CO3

� 100 � 11.33% C�12.01 g C

1 mol C

1 mol Na2CO3

105.99 g Na2CO3

�

2 mol Na

1 mol Na2CO3

� 100 � 43.38% Na�22.99 g Na

1 mol Na

1 mol Na2CO3

105.99 g Na2CO3

�

repeat Steps 1 and 2 for

each remaining element

Percentage of each

element in Na2CO3

3

Percentage composition4

1 mol Na2CO3��105.99 g Na2CO3

2 mol Na��1 mol Na2CO3

22.99 g Na��1 mol Na

�105.99 g Na2CO31 mol Na2CO3

from Step 1

g Na

1molar mass Na2CO3

1 mol Na2CO3� 100 � percentage Na in Na2CO3

multiply by the inverse of the

molar mass of Na2CO3 and

multiply by 100

Mass Na per

mole Na2CO3

2

Percentage Na in

Na2CO3

3

Element Percentage

sodium 43.38% Na

carbon 11.33% C

oxygen 45.29% O



Name Class Date


Is the number of significant figures correct?

Yes; four significant figures is correct because the molar masses have four

significant figures.

Is the answer reasonable?

Yes; the percentages add up to 100 percent.

Practice1. Determine the percentage composition of each of the following compounds:

a. sodium oxalate, Na2C2O4 ans: 34.31% Na, 17.93% C, 47.76% O

b. ethanol, C2H5OH ans: 52.13% C, 13.15% H, 34.72% O

c. aluminum oxide, Al2O3 ans: 52.92% Al, 47.08% O

d. potassium sulfate, K2SO4 ans: 44.87% K, 18.40% S, 36.72% O

2. Suppose that your laboratory analysis of the white powder discussed at the

beginning of this chapter showed 42.59% Na, 12.02% C, and 44.99% oxygen.

Would you report that the compound is sodium oxalate or sodium carbonate

(use the results of Practice Problem 1 and Sample Problem 1)? ans: sodium

carbonate



Name Class Date


Sample Problem 2Calculate the mass of zinc in a 30.00 g sample of zinc nitrate, Zn(NO3)2.

SolutionANALYZE

What is given in the problem? the mass in grams of zinc nitrate

What are you asked to find? the mass in grams of zinc in the sample

PLANWhat steps are needed to determine the mass of Zn in a given mass of Zn(NO3)2?

The percentage of Zn in Zn(NO3)2 can be calculated and used to find the mass of

Zn in the sample.

COMPUTE1 mol Zn

1 mol Zn(NO3)2

� 100 � 34.52% Zn�65.39 g Zn

1 mol Zn

1 mol Zn(NO3)2

189.41 g Zn(NO3)2

�

g Zn� g Zn(NO3)2 � g Zn in sample

100 g Zn(NO3)2

given

percentage Zn

expressed as a fraction

189.41 g Zn(NO3)2

� � � 100 � percentage Zn

1

molar mass Zn(NO3)2

1 mol

1 mol Zn

molar mass Zn

65.39 g Zn

1 mol Zn(NO3)2

ratio of mol Zn per mol

Zn(NO3)2 from formula

1 mol Zn

express percentage

as a fraction and

multiply by the

mass of the sample

multiply

by the mole

ratio of Zn to

Zn(NO3)2

Molar mass of Zn1

Mass Zn in g in sample5

Mass Zn per

mole Zn(NO3)2

2

Percentage Zn

in Zn(NO3)2

3

multiply by the inverse of

the molar mass of

Zn(NO3)2, then multiply

by 100

Items Data

Mass of zinc nitrate 30.00 g

Formula of zinc nitrate Zn(NO3)2

Molar mass of zinc nitrate 189.41 g/mol

Mass of zinc in the sample ? g



Name Class Date


Note that mass percentage is the same as grams per 100 g, so 34.52% Zn in

Zn(NO3)2 is the same as 34.52 g Zn in 100 g Zn(NO3)2 .


Yes; units cancel to give the correct units, grams of zinc.


Yes; four significant figures is correct because the data given have four signifi-

cant figures.


Yes; the molar mass of zinc is about one third of the molar mass of Zn(NO3)2,

and 10.36 g Zn is about one third of 30.00 g of Zn(NO3)2.

Practice1. Calculate the mass of the given element in each of the following compounds:

a. bromine in 50.0 g potassium bromide, KBr ans: 33.6 g Br

b. chromium in 1.00 kg sodium dichromate, Na2Cr2O7 ans: 397 g Cr

c. nitrogen in 85.0 mg of the amino acid lysine, C6H14N2O2 ans: 16.3 mg N

d. cobalt in 2.84 g cobalt(II) acetate, Co(C2H3O2)2 ans: 0.945 g Co

� 30.00 g Zn(NO3)2 � 10.36 g Zn34.52 g Zn

100 g Zn(NO3)2



Name Class Date


HYDRATESMany compounds, especially ionic compounds, are produced and purified by

crystallizing them from water solutions. When this happens, some compounds

incorporate water molecules into their crystal structure. These crystalline com-

pounds are called hydrates because they include water molecules. The number of

water molecules per formula unit is specific for each type of crystal. When you

have to measure a certain quantity of the compound, it is important to know how

much the water molecules contribute to the mass.

You may have seen blue crystals of copper(II) sulfate in the laboratory. When

this compound is crystallized from water solution, the crystals include five water

molecules for each formula unit of CuSO4 . The true name of the substance is

copper(II) sulfate pentahydrate, and its formula is written correctly as

CuSO4 �5H2O. Notice that the five water molecules are written separately. They

are preceded by a dot, which means they are attached to the copper sulfate mole-

cule. On a molar basis, a mole of CuSO4 �5H2O contains 5 mol of water per mole

of CuSO4 �5H2O. The water molecules contribute to the total mass of

CuSO4 �5H2O. When you determine the percentage water in a hydrate, the water

molecules are treated separately, as if they were another element.

Sample Problem 3Determine the percentage water in copper(II) sulfate penta hydrate,

CuSO4 �5H2O.

SolutionANALYZE

What is given in the problem? the formula of copper(II) sulfate pentahydrate

What are you asked to find? the percentage water in the hydrate

Items Data

Formula of copper(II) sulfate pentahydrate CuSO4 �5H2O

Molar mass of H2O 18.02 g/mol

Molar mass of copper(II) sulfate pentahydrate* 249.72 g/mol

Percentage H2O in CuSO4 �5H2O ?%

* molar mass of CuSO4 � mass of 5 mol H2O



Name Class Date


PLANWhat steps are needed to determine the percentage of water in CuSO4 �5H2O?

Find the mass of water per mole of hydrate, multiply by the inverse molar mass

of the hydrate, and multiply that by 100 to convert to a percentage.

COMPUTE


Yes; the percentage of water in copper(II) sulfate pentahydrate was needed.


Yes; four significant figures is correct because molar masses were given to at

least four significant figures.


Yes; five water molecules have a mass of about 90 g, and 90 g is a little more

than 1/3 of 250 g; the calculated percentage is a little more than 1/3.

5 mol H2O

1 mol CuSO4�5H2O� 100 � 36.08% H2O�

18.01 g H2O

1 mol H2O

1 mol CuSO4�5H2O

249.72 g CuSO4�5H2O�

249.72 g CuSO45H2O� �

� 100 � percentage H2O

1

molar mass CuSO45H2O

1 mol CuSO45H2O

1 mol H2O

molar mass H2O

18.01 g H2O

1 mol CuSO45H2O

ratio of moles H2O per mole

CuSO45H2O from formula

5 mol H2O

multiply by the inverse of

the molar mass of

CuSO45H2O; then

multiply by 100

multiply by the

mole ratio of

H2O to

CuSO45H2O

Molar mass of H2O1 3

Mass H2O per mole

CuSO45H2O

Percentage H2O in CuSO45H2O

2



Name Class Date


Practice1. Calculate the percentage of water in each of the following hydrates:

a. sodium carbonate decahydrate, Na2CO3 �10H2O ans: 62.97% H2O in

Na2CO3�10H2O

b. nickel(II) iodide hexahydrate, NiI2�6H2O ans: 25.71% H2O in NiI2�6H2O

c. ammonium hexacyanoferrate(III) trihydrate (commonly called ammonium

ferricyanide), (NH4)2Fe(CN)6 �3H2O ans: 17.89 % H2O in

(NH4)2Fe(CN)6�3H2O

d. aluminum bromide hexahydrate ans: 28.85% H2O in AlBr3�6H2O

problem solving percentage composition back print

Documents