Chapter

1
Chapter 3 Stoichiometry - Mole - Mass
Relationships in Chemical Systems
3.1 The Mole 3.2 Determining the Formula of an
Unknown Compound 3.3 Writing and
Balancing Chemical Equations 3.4 Calculating
the amounts of Reactant and Product 3.5
Fundamentals of Solution Stoichiometry
2
Mole

• The Mole is based upon the definition
• The amount of substance that contains as many
  elementary parts (atoms, molecules, or other?) as
  there are atoms in exactly
• 12 grams of carbon -12.
• 1 Mole 6.022045 x 1023 particles

3
Counting Objects of Fixed Relative Mass
12 red marbles _at_ 7g each 84g 12 yellow marbles
_at_4e each48g
55.85g Fe 6.022 x 1023 atoms Fe 32.07g S
6.022 x 1023 atoms S
Fig 3.1
4
Mole - Mass Relationships of Elements
Element Atom/Molecule Mass Mole Mass
Number of Atoms
1 atom of H 1.008 amu 1 mole of H 1.008 g
6.022 x 1023 atoms 1 atom of Fe 55.85 amu
1 mole of Fe 55.85 g 6.022 x 1023 atoms 1
atom of S 32.07 amu 1 mole of S 32.07 g
6.022 x 1023 atoms 1 atom of O 16.00 amu
1 mole of O 16.00 g 6.022 x 1023 atoms 1
molecule of O2 32.00 amu
1 mole of O2 32.00 g 6.022 x
1023 molecule 1 molecule of S8 256.52 amu
1 mole of S8
256.52 g 6.022 x 1023 molecules
5
Molecular Mass - Molar Mass ( M )
The Molecular mass of a compound expressed in amu
is numerically the same as the mass of one
mole of the compound expressed in grams.
For water H2O Molecular mass (2 x
atomic mass of H ) atomic mass of O
2 ( 1.008 amu) 16.00 amu
18.02 amu
Mass of one molecules of water 18.02 amu
Molar mass ( 2 x atomic mass of H ) atomic
mass of O 2 ( 1.008 g
) 16.00 g 18.02 g 18.02 g
H2O 6.022 x 1023 molecules of water 1 mole H2O
6
One Mole of Common Substances
CaCO3 100.09 g Oxygen 32.00 g Copper
63.55 g Water 18.02 g
Fig. 3.2
7
Information Contained in the Chemical Formula
of Glucose C6H12O6 ( M 180.16 g/mol)
Carbon (C) Hydrogen (H) Oxygen (O)
Atoms/molecule of compound Moles of atoms/ mole
of compound Atoms/mole of compound Mass/molecule
of compound Mass/mole of compound
6 atoms 12 atoms 6
atoms
6 moles of 12 moles of 6 moles
of atoms atoms
atoms
6(6.022 x 1023) 12(6.022 x 1023) 6(6.022
x 1023) atoms atoms
atoms
6(12.01 amu) 12(1.008 amu) 6(16.00
amu) 72.06 amu 12.10 amu
96.00 amu
72.06 g 12.10 g
96.00 g
Table 3.2
8
Mass - Mole Relationships of a Compound
For an Element
For a Compound
Mass (g) of Element
Mass (g) of compound
Moles of Element
Amount (mol) of compound
Amount (mol) of compound
Molecules (or formula units of compound)
Atoms of Element
9
Calculating the Number of Moles and Atoms in a
Given Mass of Element
Problem Tungsten (W) is the element used as the
filament in light bulbs, and
has the highest melting point of any element
3680oC. How many moles of
tungsten, and atoms of the
element are contained in a 35.0 mg sample of the
metal? Plan Convert mass into moles by dividing
the mass by the atomic weight of the
metal, then calculate the number of atoms by
multiplying by Avogadros
number! Solution Converting from mass of W to
moles Moles of W
10
Calculating the Number of Moles and Atoms in a
Given Mass of Element
Problem Tungsten (W) is the element used as the
filament in light bulbs, and
has the highest melting point of any element
3680oC. How many moles of
tungsten, and atoms of the
element are contained in a 35.0 mg sample of the
metal? Plan Convert mass into moles by dividing
the mass by the atomic weight of the
metal, then calculate the number of atoms by
multiplying by Avogadros
number! Solution Converting from mass of W to
moles Moles of W 35.0
mg W x


1 mol W 183.9 g W
11
Calculating the Number of Moles and Atoms in a
Given Mass of Element
Problem Tungsten (W) is the element used as the
filament in light bulbs, and
has the highest melting point of any element
3680oC. How many moles of
tungsten, and atoms of the
element are contained in a 35.0 mg sample of the
metal? Plan Convert mass into moles by dividing
the mass by the atomic weight of the
metal, then calculate the number of atoms by
multiplying by Avogadros
number! Solution Converting from mass of W to
moles Moles of W 35.0
mg W x 0.00019032
mol
1.90 x
10 - 4 mol NO. of W atoms


1 mol W 183.9 g W
12
Calculating the Number of Moles and Atoms in a
Given Mass of Element
Problem Tungsten (W) is the element used as the
filament in light bulbs, and
has the highest melting point of any element
3680oC. How many moles of
tungsten, and atoms of the
element are contained in a 35.0 mg sample of the
metal? Plan Convert mass into moles by dividing
the mass by the atomic weight of the
metal, then calculate the number of atoms by
multiplying by Avogadros
number! Solution Converting from mass of W to
moles Moles of W 35.0
mg W x 0.00019032
mol
1.90 x
10 - 4 mol NO. of W atoms 1.90 x 10 - 4 mol
W x



1 mol W 183.9 g W
6.022 x 1023 atoms 1 mole of W
13
Calculating the Number of Moles and Atoms in a
Given Mass of Element
Problem Tungsten (W) is the element used as the
filament in light bulbs, and
has the highest melting point of any element
3680oC. How many moles of
tungsten, and atoms of the
element are contained in a 35.0 mg sample of the
metal? Plan Convert mass into moles by dividing
the mass by the atomic weight of the
metal, then calculate the number of atoms by
multiplying by Avogadros
number! Solution Converting from mass of W to
moles Moles of W 35.0
mg W x 0.00019032
mol
1.90 x
10 - 4 mol NO. of W atoms 1.90 x 10 - 4 mol
W x


1.15 x 1020 atoms of Tungsten
1 mol W 183.9 g W
6.022 x 1023 atoms 1 mole of W
14
Calculating the Moles and Number of Formula
Units in a Given Mass of Cpd.
Problem Trisodium Phosphate is a component of
some detergents. How many moles
and formula units are in a 38.6 g sample? Plan
We need to determine the formula, and the
molecular mass from the atomic masses
of each element multiplied by the
coefficients. Solution The formula is

15
Calculating the Moles and Number of Formula
Units in a Given Mass of Cpd.
Problem Trisodium Phosphate is a component of
some detergents. How many moles
and formula units are in a 38.6 g sample? Plan
We need to determine the formula, and the
molecular mass from the atomic masses
of each element multiplied by the
coefficients. Solution The formula is Na3PO4.
Calculating the molar mass M
3x Sodium 1 x Phosphorous 4 x Oxygen
3 x 22.99 g/mol 1 x 30.97 g/mol
4 x 16.00 g/mol 68.97
g/mol 30.97 g/mol 64.00 g/mol 163.94 g/mol
Converting mass to moles
16
Calculating the Moles and Number of Formula
Units in a Given Mass of Cpd.
Problem Trisodium Phosphate is a component of
some detergents. How many moles
and formula units are in a 38.6 g sample? Plan
We need to determine the formula, and the
molecular mass from the atomic masses
of each element multiplied by the
coefficients. Solution The formula is Na3PO4.
Calculating the molar mass M
3x Sodium 1 x Phosphorous 4 x Oxygen
3 x 22.99 g/mol 1 x 30.97 g/mol
4 x 16.00 g/mol 68.97
g/mol 30.97 g/mol 64.00 g/mol 163.94 g/mol
Converting mass to moles
Moles Na3PO4 38.6 g Na3PO4 x (1 mol Na3PO4)

163.94 g Na3PO4
17
Calculating the Moles and Number of Formula
Units in a Given Mass of Cpd.
Problem Trisodium Phosphate is a component of
some detergents. How many moles
and formula units are in a 38.6 g sample? Plan
We need to determine the formula, and the
molecular mass from the atomic masses
of each element multiplied by the
coefficients. Solution The formula is Na3PO4.
Calculating the molar mass M
3x Sodium 1 x Phosphorous 4 x Oxygen
3 x 22.99 g/mol 1 x 30.97 g/mol
4 x 16.00 g/mol 68.97
g/mol 30.97 g/mol 64.00 g/mol 163.94 g/mol
Converting mass to moles
Moles Na3PO4 38.6 g Na3PO4 x (1 mol Na3PO4)

163.94 g Na3PO4 0.23545 mol
Na3PO4
Formula units
18
Calculating the Moles and Number of Formula
Units in a Given Mass of Cpd.
Problem Trisodium Phosphate is a component of
some detergents. How many moles
and formula units are in a 38.6 g sample? Plan
We need to determine the formula, and the
molecular mass from the atomic masses
of each element multiplied by the
coefficients. Solution The formula is Na3PO4.
Calculating the molar mass M
3x Sodium 1 x Phosphorous 4 x Oxygen
3 x 22.99 g/mol 1 x 30.97 g/mol
4 x 16.00 g/mol 68.97
g/mol 30.97 g/mol 64.00 g/mol 163.94 g/mol
Converting mass to moles
Moles Na3PO4 38.6 g Na3PO4 x (1 mol Na3PO4)

163.94 g Na3PO4 0.235 mol
Na3PO4
Formula units 0.235 mol Na3PO4 x 6.022 x 1023
formula units
1 mol Na3PO4
19
Calculating the Moles and Number of Formula
Units in a Given Mass of Cpd.
Problem Trisodium Phosphate is a component of
some detergents. How many moles
and formula units are in a 38.6 g sample? Plan
We need to determine the formula, and the
molecular mass from the atomic masses
of each element multiplied by the
coefficients. Solution The formula is Na3PO4.
Calculating the molar mass M
3x Sodium 1 x Phosphorous 4 x Oxygen
3 x 22.99 g/mol 1 x 30.97 g/mol
4 x 16.00 g/mol 68.97
g/mol 30.97 g/mol 64.00 g/mol 163.94 g/mol
Converting mass to moles
Moles Na3PO4 38.6 g Na3PO4 x (1 mol Na3PO4)

163.94 g Na3PO4 0.235 mol
Na3PO4
Formula units 0.23545 mol Na3PO4 x 6.022 x 1023
formula units
1 mol Na3PO4
1.42 x 1023 formula units
20
Flow Chart of Mass Percentage Calculation
Moles of X in one mole of Compound
M (g / mol) of X
Mass (g) of X in one mole of compound
Divide by mass (g) of one mole
of compound
Mass fraction of X
Multiply by 100
Mass of X
21
Mol wt and Composition of NH4NO3

• 2 mol N x
• 4 mol H x
• 3 mol O x
• 
  

N

H
O
22
Mol wt and Composition of NH4NO3

• 2 mol N x 14.01 g/mol 28.02 g N
• 4 mol H x 1.008 g/mol 4.032 g H
• 3 mol O x 15.999 g/mol 48.00 g O
• 
  80.05 g/mol
  

N

H
O
23
Mol wt and Composition of NH4NO3

• 2 mol N x 14.01 g/mol 28.02 g N
• 4 mol H x 1.008 g/mol 4.032 g H
• 3 mol O x 15.999 g/mol 48.00 g O
• 
  80.05 g/mol
  

28.02g N2 80.05g
N x 100 35.00
4.032g H2 80.05g
H x 100 5.037
48.00g O2 80.05g
O x 100 59.96
99.997
24
Calculating Mass Percentage and Masses of
Elements in a Sample of a Compound - I
Problem Sucrose (C12H22O11) is common table
sugar. ( a) What is the mass percent of each
element in sucrose? ( b) How many grams of
carbon are in 24.35 g of sucrose? (a)
Determining the mass percent of each element
mass of C 12 x 12.01 g C/mol
mass of H 22 x 1.008 g H/mol
mass of O 11 x 16.00 g O/mol



Mass Fraction of C

25
Calculating Mass Percentage and Masses of
Elements in a Sample of a Compound - I
Problem Sucrose (C12H22O11) is common table
sugar. ( a) What is the mass percent of each
element in sucrose? ( b) How many grams of
carbon are in 24.35 g of sucrose? (a)
Determining the mass percent of each element
mass of C 12 x 12.01 g C/mol
144.12 g C/mol mass of H
22 x 1.008 g H/mol 22.176 g H/mol
mass of O 11 x 16.00 g O/mol
176.00 g O/mol

342.296 g/mol Finding the mass fraction of
C in Sucrose C
Total mass of C
mass of 1 mole of
sucrose
Mass Fraction of C

26
Calculating Mass Percentage and Masses of
Elements in a Sample of a Compound - I
Problem Sucrose (C12H22O11) is common table
sugar. ( a) What is the mass percent of each
element in sucrose? ( b) How many grams of
carbon are in 24.35 g of sucrose? (a)
Determining the mass percent of each element
mass of C 12 x 12.01 g C/mol
144.12 g C/mol mass of H
22 x 1.008 g H/mol 22.176 g H/mol
mass of O 11 x 16.00 g O/mol
176.00 g O/mol

342.296 g/mol Finding the mass fraction of
C in Sucrose C
Total mass of C
144.12 g C
mass of 1 mole of sucrose 342.30 g Cpd
0.421046 To find mass of C
0.421046 x 100 42.11

Mass Fraction of C

27
Empirical and Molecular Formulas
Empirical Formula - The simplest formula for a
compound that agrees
with the elemental analysis! The
smallest set of whole numbers of
atoms. Molecular Formula - The formula of the
compound as it exists,
it may be a multiple of the Empirical
formula.
28
Steps to Determine Empirical Formulas
Mass (g) of Element
M (g/mol )
Moles of Element
use no. of moles as subscripts
Preliminary Formula
change to integer subscripts
Empirical Formula
29
Some Examples of Compounds with the Same
Elemental Ratios
Empirical Formula
Molecular Formula
CH2(unsaturated Hydrocarbons) C2H4 ,
C3H6 , C4H8 OH or HO
H2O2 S

S8 P
P4
Cl
Cl2 CH2O
(carbohydrates)
C6H12O6
30
Determining Empirical Formulas from
Masses of Elements - I
Problem The elemental analysis of a sample
compound gave the following results 5.677g Na,
6.420 g Cr, and 7.902 g O. What is the empirical
formula and name of the compound? Plan First we
have to convert mass of the elements to moles of
the elements using the molar masses. Then we
construct a preliminary formula and name of the
compound. Solution Finding the moles of the
elements Moles of Na 5.678 g Na x
0.2469 mol Na
Moles of Cr 6.420 g Cr x
0.12347 mol Cr Moles of O 7.902 g
O x 0.4939 mol O
1 mol Na 22.99 g Na
1 mol Cr 52.00 g Cr
1 mol O 16.00 g O
31
Determining Empirical Formulas from
Masses of Elements - I
Problem The elemental analysis of a sample
compound gave the following results 5.677g Na,
6.420 g Cr, and 7.902 g O. What is the empirical
formula and name of the compound? Plan First we
have to convert mass of the elements to moles of
the elements using the molar masses. Then we
construct a preliminary formula and name of the
compound. Solution Finding the moles of the
elements Moles of Na 5.678 g Na x
Moles of Cr
6.420 g Cr x
Moles of O 7.902 g O x
1 mol Na 22.99 g Na
1 mol Cr 52.00 g Cr
1 mol O 16.00 g O
32
Determining Empirical Formulas from
Masses of Elements - I
Problem The elemental analysis of a sample
compound gave the following results 5.677g Na,
6.420 g Cr, and 7.902 g O. What is the empirical
formula and name of the compound? Plan First we
have to convert mass of the elements to moles of
the elements using the molar masses. Then we
construct a preliminary formula and name of the
compound. Solution Finding the moles of the
elements Moles of Na 5.678 g Na x
0.2469 mol Na
Moles of Cr 6.420 g Cr x
0.12347 mol Cr Moles of O 7.902 g
O x 0.4939 mol O
1 mol Na 22.99 g Na
1 mol Cr 52.00 g Cr
1 mol O 16.00 g O
33
Determining Empirical Formulas from
Masses of Elements - II
Constructing the preliminary formula
Na0.2469 Cr0.1235 O0.4939
Converting to integer subscripts (dividing all by
smallest subscript)
Na1.99 Cr1.00 O4.02
Rounding off to whole numbers
Na2CrO4 Sodium Chromate
34
Determining the Molecular Formula from
Elemental Composition and Molar Mass - I
Problem The sugar burned for energy in cells of
the body is Glucose (M 180.16 g/mol), elemental
analysis shows that it contains 40.00 mass C,
6.719 mass H, and 53.27 mass O. (a)
Determine the empirical formula of glucose.
(b) Determine the molecular formula. Plan We are
only given mass , and no weight of the compound
so we will assume 100g of the compound,
and becomes grams, and we can do as
done previously with masses of the
elements. Solution Mass Carbon
40.00 x 100g/100 40.00 g C Mass
Hydrogen 6.719 x 100g/100 6.719g H
Mass Oxygen 53.27 x 100g/100 53.27 g
O
99.989 g Cpd
35
Determining the Molecular Formula from
Elemental Composition and Molar Mass - II
Converting from Grams of Elements to moles
Moles of C Mass of C x
3.3306 moles C Moles of H Mass of H x
6.6657 moles H Moles
of O Mass of O x 3.3294
moles O Constructing the preliminary formula
C 3.33 H 6.67 O 3.33 Converting to integer
subscripts, divide all subscripts by the
smallest
1 mole C 12.01 g C
1 mol H 1.008 g H
1 mol O 16.00 g O
36
Determining the Molecular Formula from
Elemental Composition and Molar Mass - II
Converting from Grams of Elements to moles
Moles of C Mass of C x
3.3306 moles C Moles of H Mass of H x
6.6657 moles H Moles
of O Mass of O x 3.3294
moles O Constructing the preliminary formula
C 3.33 H 6.67 O 3.33 Converting to integer
subscripts, divide all subscripts by the
smallest C 3.33/3.33 H 6.667 / 3.33 O3.33 /
3.33 CH2O
1 mole C 12.01 g C
1 mol H 1.008 g H
1 mol O 16.00 g O
37
Combustion Train for the Determination of the
Chemical Composition of Organic Compounds.
m 2
m 2
CnHm (n ) O2 n CO2(g) H2O(g)
Fig. 3.4
38
Ascorbic Acid ( Vitamin C ) - I Contains C , H ,
and O

• Upon combustion in excess oxygen, a 6.49 mg
  sample yielded 9.74 mg CO2 and 2.64 mg H2O
• Calculate its Empirical formula!
• C 9.74 x10-3g CO2 x(12.01 g C/44.01 g CO2)
• 2.65 x 10-3 g C
• H 2.64 x10-3g H2O x (2.016 g H2/18.02 gH2O)
• 2.92 x 10-4 g H
• Mass Oxygen 6.49 mg - 2.65 mg - 0.292 mg
• 3.54 mg O

39
Vitamin C Combustion - II

• C 2.65 x 10-3 g C / ( 12.01 g C / mol C )
• 2.21 x 10-4 mol C
• H 0.295 x 10-3 g H / ( 1.008 g H / mol H )
• 2.92 x 10-4 mol H
• O 3.54 x 10-3 g O / ( 16.00 g O / mol O )
• 2.21 x 10-4 mol O
• Divide each by 2.21 x 10-4
• C 1.00 Multiply each by 3 3.00 3.0
• H 1.32
  3.96 4.0
• O 1.00
  3.00 3.0

C3H4O3
40
Determining a Chemical Formula from
Combustion Analysis - I
Problem Erythrose (M 120 g/mol) is an
important chemical compound as
a starting material in chemical synthesis, and
contains Carbon Hydrogen, and
Oxygen. Combustion analysis of
a 700.0 mg sample yielded 1.027 g CO2 and
0.4194 g H2O. Plan We find the masses
of Hydrogen and Carbon using the mass
fractions of H in H2O, and C in CO2. The mass of
Carbon and Hydrogen are subtracted from
the sample mass to get the mass of
Oxygen. We then calculate moles, and construct
the empirical formula, and from the
given molar mass we can calculate the
molecular formula.
41
Determining a Chemical Formula from Combustion
Analysis - II
Calculating the mass fractions of the elements
Mass fraction of C in CO2

0.2729 g C
/ 1 g CO2 Mass fraction of H in H2O


0.1119 g H / 1 g H2O Calculating masses of C
and H Mass of Element mass of compound x
mass fraction of element
mol C x M of C mass of 1 mol CO2
1 mol C x 12.01 g C/ 1 mol C 44.01 g
CO2
mol H x M of H mass of 1 mol H2O
2 mol H x 1.008 g H / 1 mol H 18.02
g H2O
42
Determining a Chemical Formula from
Combustion Analysis - III
0.2729 g C 1 g CO2
Mass (g) of C 1.027 g CO2 x
0.2803 g C Mass (g) of H 0.4194 g H2O x
0.04693 g H Calculating
the mass of O Mass (g) of O Sample mass -(
mass of C mass of H )
0.700 g - 0.2803 g C - 0.04693 g H 0.37277 g
O Calculating moles of each element C
0.2803 g C / 12.01 g C/ mol C 0.02334 mol C
H 0.04693 g H / 1.008 g H / mol H 0.04656 mol
H O 0.37277 g O / 16.00 g O / mol O
0.02330 mol O C0.02334H0.04656O0.02330 CH2O
formula weight 30 g / formula 120 g /mol / 30 g
/ formula 4 formula units / cpd C4H8O4
0.1119 g H 1 g H2O
43
Some Compounds with Empirical Formula CH2O
(Composition by Mass 40.0 C, 6.71 H, 53.3O)
Molecular M Formula
(g/mol) Name Use or Function
CH2O 30.03 Formaldehyde
Disinfectant Biological

preservative C2H4O2 60.05
Acetic acid Acetate polymers vinegar

( 5 solution) C3H6O3
90.08 Lactic acid Causes milk
to sour forms
in muscle
during exercise C4H8O4 120.10
Erythrose Forms during sugar

metabolism C5H10O5
150.13 Ribose Component of
many nucleic
acids and
vitamin B2 C6H12O6 180.16
Glucose Major nutrient for energy

in cells
44
Two Compounds with Molecular Formula C2H6O
Property Ethanol
Dimethyl Ether
M (g/mol) 46.07
46.07 Color
Colorless
Colorless Melting point - 117oC
- 138.5oC Boiling point
78.5oC -
25oC Density (at 20oC) 0.789 g/mL
0.00195 g/mL Use
Intoxicant in In
refrigeration
alcoholic beverages
H H
H H H C C O
H H C O C H
H
H H
H
Table 3.4
45
Fig. 3.7
46
Molecular Formula
Molecules
Atoms
Avogadros Number
6.022 x 1023
Moles
Moles
47
Chemical Equations
Qualitative Information
Reactants
Products
States of Matter (s) solid (l)
liquid (g) gaseous (aq) aqueous
2 H2 (g) O2 (g) 2 H2O (g)
48
Balanced Equations

• mass balance (atom balance)- same number of each
  element (1) start with simplest element (2)
  progress to other elements (3) make all whole
  numbers (4) re-check atom balance
• charge balance (no spectator ions)

1 CH4 (g) O2 (g) 1 CO2 (g) H2O (g)
1 CH4 (g) O2 (g) 1 CO2 (g) 2 H2O (g)
1 CH4 (g) 2 O2 (g) 1 CO2 (g) 2 H2O (g)
Ca2 (aq) 2 OH- (aq) Ca(OH)2 (s)
Na
Na
49
Balancing Chemical Equations - I
Problem The hydrocarbon hexane is a component of
Gasoline that burns in an
automobile engine to produce carbon dioxide and
water as well as energy. Write the
balanced chemical equation for
the combustion of hexane (C6H14). Plan Write
the skeleton equation from the words into
chemical compounds with blanks
before each compound. begin the
balance with the most complex compound first, and
save oxygen until last! Solution
C6H14 (l) O2 (g)
CO2 (g) H2O(g) Energy
Begin with one Hexane molecule which says that we
will get 6 CO2s!
1
6
50
Balancing Chemical Equations - II
The H atoms in the hexane will end up as H2O, and
we have 14 H atoms, and since each water
molecule has two H atoms, we will get a total of
7 water molecules.
1
6
7
Since oxygen atoms only come as diatomic
molecules (two O atoms, O2),we must have even
numbers of oxygen atoms on the product side. We
do not since we have 7 water molecules!
Therefore multiply the hexane by 2, giving a
total of 12 CO2 molecules, and 14 H2O molecules.
This now gives 12 O2 from the carbon dioxide, and
14 O atoms from the water, which will be another
7 O2 molecules for a total of 19 O2 !
19
51
Information Contained in a Balanced Equation
Viewed in Reactants
Products terms of 2 C2H6 (g)
7 O2 (g) 4 CO2 (g) 6 H2O(g) Energy
Molecules 2 molecules of C2H6 7 molecules of
O2
4 molecules of CO2 6 molecules of
H2O Amount (mol) 2 mol C2H6 7 mol O2
4 mol CO2 6 mol H2O Mass (amu) 60.14 amu
C2H6 224.00 amu O2
176.04 amu CO2
108.10 amu H2O Mass (g) 60.14 g C2H6
224.00 g O2 176.04 g CO2 108.10 g H2O Total
Mass (g) 284.14g
284.14g
52
Fig. 3.8
53
Chemical Equation Calculation - I
Atoms (Molecules)
Avogadros Number
6.02 x 1023
Molecules
Reactants
Products
54
Chemical Equation Calculation - II
Mass
Atoms (Molecules)
Molecular Weight
Avogadros Number
g/mol
6.02 x 1023
Molecules
Reactants
Products
Moles
55
Sample Problem Calculating Reactants and
Products in a Chemical Reaction - I
Problem Given the following chemical reaction
between Aluminum Sulfide and water, if we are
given 65.80 g of Al2S3 a) How many moles of
water are required for the reaction? b) What mass
of H2S Al(OH)3 would be formed?
Al2S3 (s) 6 H2O(l) 2
Al(OH)3 (s) 3 H2S(g) Plan Calculate moles of
Aluminum Sulfide using its molar mass, then
from the equation, calculate the moles of Water,
and then the moles of Hydrogen Sulfide, and
finally the mass of Hydrogen Sulfide using its
molecular weight. Solution a) molar mass of
Aluminum Sulfide 150.17 g / mol moles
Al2S3
0.4382 moles Al2S3
65.80 g Al2S3 150.17 g Al2S3/ mol Al2S3
56
Calculating Reactants and Products in a
Chemical Reaction - II
a) cont. 0.4382 moles Al2S3 x
2.629 moles H2O b)
0.4382 moles Al2S3 x
1.314 moles H2S molar mass of H2S
34.09 g / mol mass H2S 1.314 moles H2S
x 44.81 g H2S
0.4382 moles Al2S3 x
0.4764 moles Al(OH)3 molar
mass of Al(OH)3 78.00 g / mol mass
Al(OH)3 0.4764 moles Al(OH)3 x

37.16 g Al(OH)3
6 moles H2O 1 mole Al2S3
3 moles H2S 1 mole Al2S3
34.09 g H2S 1 mole H2S
2 moles Al(OH)3 1 mole Al2S3
78.00 g Al(OH)3 1 mole Al(OH)3
57
Calculating the Amounts of Reactants and
Products in a Reaction Sequence - I
Problem Calcium Phosphate could be prepared in
the following reaction sequence 4 P4
(s) 10 KClO3 (s) 4
P4O10 (s) 10 KCl (s) P4O10
(s) 6 H2O (l) 4
H3PO4 (aq) 2 H3PO4 (aq) 3 Ca(OH)2 (aq)
6 H2O(aq) Ca3(PO4)2
(s) Given 15.5 g P4 and sufficient KClO3 , H2O
and Ca(OH)2. What mass of Calcium Phosphate
could be formed? Plan (1) Calculate moles of
P4. (2) Use molar ratios to get moles of
Ca3(PO4)2. (3) Convert the moles of product
back into mass by using the molar mass of
Calcium Phosphate.
58
Calculating the Amounts of Reactants and
Products in a Reaction Sequence - II
Solution moles of Phosphorous 15.50 g P4
x 0.1251 mol P4 For
Reaction 1 4 P4 (s) 10 KClO4 (s)
4 P4O10 (s) 10 KCl (s) For Reaction 2 1
P4O10 (s) 6 H2O (l) 4
H3PO4 (aq) For Reaction 3 2 H3PO4 3
Ca(OH)2 1 Ca3(PO4)2 6
H2O 0.1251 moles P4 x
x x 0.2502
moles Ca3(PO4)2
1 mole P4 123.88 g P4
4 moles H3PO4 1 mole P4O10
4 moles P4O10 4 moles P4
1 mole Ca3(PO4)2 2 moles H3PO4
59
Calculating the Amounts of Reactants and
Products in a Reaction Sequence - III
Molar mass of Ca3(PO4)2 310.18 g mole
mass of product 0.2502 moles Ca3(PO4)2 x

77.61 g Ca3(PO4)2
310.18 g Ca3(PO4)2 1 mole Ca3(PO4)2
60
An Ice Cream Sundae Analogy for Limiting
Reactions
Fig. 3.10
61
Limiting Reactant Problems
a A b B c C d D e E
f F
Steps to solve
1) Identify it as a limiting Reactant problem -
Information on the mass, number of moles,
number of molecules, volume and molarity of a
solution is given for more than one reactant! 2)
Calculate moles of each reactant! 3) Divide the
moles of each reactant by the coefficient (a,b,c
etc....)! 4) Which ever is smallest, that
reactant is the limiting reactant! 5) Use the
limiting reactant to calculate the moles of
product desired then convert to the units
needed (moles, mass, volume, number of atoms
etc....)!
62
Limiting Reactant Problem
Problem A fuel mixture used in the early days of
rocketry is composed of two liquids, hydrazine
(N2H4) and dinitrogen tetraoxide (N2O4). They
ignite on contact ( hypergolic) to form nitrogen
gas and water vapor. How many grams of nitrogen
gas form when exactly 1.00 x 102 g N2H4 and 2.00
x 102 g N2O4 are mixed? Plan First write the
balanced equation. Since amounts of both
reactants are given, it is a limiting reactant
problem. Calculate the moles of each reactant,
and then divide by the equation coefficient to
find which is limiting and use that one to
calculate the moles of nitrogen gas, then
calculate mass using the molecular weight of
nitrogen gas. Solution 2 N2H4 (l)
N2O4 (l) 3 N2 (g) 4
H2O (g) Energy
63
Limiting Reactant Problem - cont.
molar mass N2H4 ( 2 x 14.01 4 x 1.008 )
32.05 g/mol molar mass H2O4 ( 2 x 14.01 4 x
16.00 ) 92.02 g/mol
1.00 x 102 g 32.05 g/mol
Moles N2H4 3.12 moles
N2H4 Moles N2O4
2.17 moles N2O4 dividing by coefficients 3.12
mol / 2 1.56 mol N2H4
2.17 mol / 1 2.17 mol
N2O4 Nitrogen yielded 3.12 mol N2H4
4.68 moles N2 Mass of Nitrogen
4.68 moles N2 x 28.02 g N2 / mol 131 g N2
2.00 x 102 g 92.02 g/mol
Limiting !
3 mol N2 2 mol N2H4
64

Acid - Metal Limiting Reactant - I

• 2Al(s) 6HCl(g) 2AlCl3(s)
  3H2(g)
• Given 30.0g Al and 20.0g HCl, how many moles of
  Aluminum Chloride will be formed?
• 30.0g Al / 26.98g Al/mol Al 1.11 mol Al
• 1.11 mol Al / 2 0.555
• 20.0g HCl / 36.5gHCl/mol HCl 0.548 mol HCl
• O.548 mol HCl / 6 0.0913
• HCl is smaller therefore the Limiting reactant!

65

Acid - Metal Limiting Reactant - II

• since 6 moles of HCl yield 2 moles of AlCl3
• 0.548 moles of HCl will yield
• 0.548 mol HCl / 6 mol HCl x 2 moles of
• AlCl3 0.183 mol of AlCl3

66
Ostwald Process Limiting Reactant Problem

• What mass of NO could be formed by the reaction
  30.0g of Ammonia gas and 40.0g of Oxygen gas?
• 4NH3 (g) 5 O2 (g)
  4NO(g) 6 H2O(g)
• 30.0g NH3 / 17.0g NH3/mol NH3 1.76 mol NH3
• 1.76 mol NH3 / 4 0.44 mol NH3
• 40.0g O2 / 32.0g O2 /mol O2 1.25 mol O2
• 1.25 mol O2 / 5 0.25 mol O2
• Therefore Oxygen is the Limiting Reagent!
• 1.25 mol O2 x 1.00 mol NO
• mass NO 1.00 mol NO x
  30.0 g NO

4 mol NO 5 mol O2
30.0 g NO 1 mol NO
67
Percent Yield / Limiting Reactant Problem - I
Problem Ammonia is produced by the Haber Process
using Nitrogen and Hydrogen Gas.
If 85.90g of Nitrogen are reacted with
21.66 g Hydrogen and the reaction yielded
98.67 g of ammonia what was the
percent yield of the reaction.
N2 (g) 3 H2 (g)
2 NH3 (g)
Plan Since we are given the masses of both
reactants, this is a limiting reactant
problem. First determine which is the limiting
reagent then calculate the theoretical
yield, and then the percent yield. Solution
Moles of Nitrogen and Hydrogen
Divide by coefficient to get limiting 3.066 g
N2 1 10.74 g H2 3
85.90 g N2 28.02 g N2 1 mole N2
moles N2 3.066 mol N2
3.066
21.66 g H2 2.016 g H2 1 mole H2
moles H2 10.74 mol H2
3.582
68
Percent Yield/Limiting Reactant Problem - II
N2 (g) 3 H2 (g)
2 NH3 (g)
Solution Cont.
We have 3.066 moles of Nitrogen, and it is
limiting, therefore the theoretical yield of
ammonia is
2 mol NH3 1 mol N2
3.066 mol N2 x
6.132 mol NH3

(Theoretical Yield) 6.132 mol NH3 x
104.427 g NH3

(Theoretical Yield)
17.03 g NH3 1 mol NH3
Actual Yield Theoretical Yield
Percent Yield x
100
98.67 g NH3 104.427 g NH3
Percent Yield
x 100 94.49
69
Molarity (Concentration of Solutions) M
Moles of Solute Moles Liters of
Solution L
M
solute material dissolved into the solvent In
air , Nitrogen is the solvent and oxygen, carbon
dioxide, etc.

are the solutes. In sea water , Water is the
solvent, and salt, magnesium chloride, etc.

are the solutes. In
brass , Copper is the solvent (90), and Zinc is
the solute(10)
70
Fig. 3.11
71
Preparing a Solution - I

• Prepare a solution of Sodium Phosphate by
  dissolving 3.95g of Sodium Phosphate into water
  and diluting it to 300.0 ml or 0.300 l !
• What is the Molarity of the salt and each of the
  ions?
• Na3PO4 (s) H2O(solvent) 3 Na(aq)
  PO4-3(aq)

72
Preparing a Solution - II

• Mol wt of Na3PO4 163.94 g / mol
• 3.95 g / 163.94 g/mol 0.0241 mol Na3PO4
• dissolve and dilute to 300.0 ml
• M 0.0241 mol Na3PO4 / 0.300 l 0.0803 M
• 
  Na3PO4
• for PO4-3 ions 0.0803 M
• for Na ions 3 x 0.0803 M 0.241 M

73
Laboratory Preparation of Molar Solutions
Fig. 3.12
74
Make a Solution of Potassium Permanganate
Potassium Permanganate is KMnO4 and has a
molecular mass
of 158.04
g / mole
Problem Prepare a solution by dissolving 1.58
grams of KMnO4 into sufficient
water to make 250.00 ml of solution.
75
Make a Solution of Potassium Permanganate
Potassium Permanganate is KMnO4 and has a
molecular mass
of 158.04
g / mole
Problem Prepare a solution by dissolving 1.58
grams of KMnO4 into sufficient
water to make 250.00 ml of solution.
1 mole KMnO4 158.04 g KMnO4
1.58 g KMnO4 x
0.0100 moles KMnO4
0.0100 moles KMnO4 0.250 liters
Molarity
0.0400 M
Molarity of K ion K ion MnO4- ion
0.0400 M
76
Dilution of Solutions

• Take 25.00 ml of the 0.0400 M KMnO4
• Dilute the 25.00 ml to 1.000 l - What is the
  resulting Molarity of the diluted solution?
• moles Vol x M
• 0.0250 l x 0.0400 M 0.00100 Moles
• 0.00100 Mol / 1.00 l 0.00100 M

77
Converting a Concentrated Solution to a Dilute
Solution
Fig. 3.13
78
Chemical Equation Calculation - III
Mass
Atoms (Molecules)
Molecular Weight
Avogadros Number
g/mol
6.02 x 1023
Molecules
Reactants
Products
Moles
Molarity
moles / liter
Solutions
79
Calculating Mass of Solute from a Given Volume
of Solution
Volume (L) of Solution
Molarity M (mol solute / Liters of solution)
M/L
Moles of Solute
Molar Mass (M) ( mass / mole) g/mol
Mass (g) of Solute
80
Calculating Amounts of Reactants and Products
for a Reaction in Solution
Al(OH)3 (s) 3 HCl (aq)
3 H2O(l) AlCl3 (aq)

Given 10.0 g Al(OH)3, what volume of 1.50 M HCl
is required to neutralize the base?
Mass (g) of Al(OH)3
M (g/mol)
Moles of Al(OH)3
molar ratio
Moles of HCl
M ( mol/L)
Volume (L) of HCl
81
Calculating Amounts of Reactants and Products
for a Reaction in Solution
Al(OH)3 (s) 3 HCl (aq)
3 H2O(l) AlCl3 (aq)

Given 10.0 g Al(OH)3, what volume of 1.50 M HCl
is required to neutralize the base?
Mass (g) of Al(OH)3
M (g/mol)
10.0 g Al(OH)3 78.00 g/mol
0.128 mol Al(OH)3
Moles of Al(OH)3

molar ratio
Moles of HCl
M ( mol/L)
Volume (L) of HCl
82
Calculating Amounts of Reactants and Products
for a Reaction in Solution
Al(OH)3 (s) 3 HCl (aq)
3 H2O(l) AlCl3 (aq)

Given 10.0 g Al(OH)3, what volume of 1.50 M HCl
is required to neutralize the base?
Mass (g) of Al(OH)3
M (g/mol)
10.0 g Al(OH)3 78.00 g/mol
0.128 mol Al(OH)3
Moles of Al(OH)3
3 moles HCl moles Al(OH)3
0.128 mol Al(OH)3 x

molar ratio
0.385 Moles HCl
Moles of HCl
M ( mol/L)
Volume (L) of HCl
83
Calculating Amounts of Reactants and Products
for a Reaction in Solution
Al(OH)3 (s) 3 HCl (aq)
3 H2O(l) AlCl3 (aq)

Given 10.0 g Al(OH)3, what volume of 1.50 M HCl
is required to neutralize the base?
Mass (g) of Al(OH)3
M (g/mol)
10.0 g Al(OH)3 78.00 g/mol
0.128 mol Al(OH)3
Moles of Al(OH)3
3 moles HCl moles Al(OH)3
0.128 mol Al(OH)3 x

molar ratio
0.385 Moles HCl
Moles of HCl
1.00 L HCl 1.50 Moles HCl
Vol HCl x 0.385
Moles HCl Vol HCl 0.256 L
256 ml
M ( mol/L)
Volume (L) of HCl
84
Solving Limiting Reactant Problems in
Solution - Precipitation Problem - I
Problem Lead has been used as a glaze for
pottery for years, and can be a problem if not
fired properly in an oven, and is leachable from
the pottery. Vinegar is used in leaching tests,
followed by Lead precipitated as a sulfide. If
257.8 ml of a 0.0468 M solution of Lead nitrate
is added to 156.00 ml of a 0.095 M solution of
Sodium sulfide, what mass of solid Lead Sulfide
will be formed? Plan It is a limiting-reactant
problem because the amounts of two reactants are
given. After writing the balanced equation,
determine the limiting reactant, then calculate
the moles of product. Convert moles of product
to mass of the product using the molar
mass. Solution Writing the balanced equation
)
85
Solving Limiting Reactant Problems in
Solution - Precipitation Problem - I
Problem Lead has been used as a glaze for
pottery for years, and can be a problem if not
fired properly in an oven, and is leachable from
the pottery. Vinegar is used in leaching tests,
followed by Lead precipitated as a sulfide. If
257.8 ml of a 0.0468 M solution of Lead nitrate
is added to 156.00 ml of a 0.095 M solution of
Sodium sulfide, what mass of solid Lead Sulfide
will be formed? Plan It is a limiting-reactant
problem because the amounts of two reactants are
given. After writing the balanced equation,
determine the limiting reactant, then calculate
the moles of product. Convert moles of product
to mass of the product using the molar
mass. Solution Writing the balanced equation
Pb(NO3)2 (aq) Na2S (aq)
2 NaNO3 (aq) PbS (s)
86
Volume (L) of Pb(NO3)2 solution
Volume (L) of Na2S solution
Multiply by M (mol/L)
Multiply by M (mol/L)
Amount (mol) of Pb(NO3)2
Amount (mol) of Na2S
Molar Ratio
Molar Ratio
Amount (mol) of PbS
Amount (mol) of PbS
Choose the lower number of PbS and multiply by M
(g/mol)
Mass (g) of PbS
87
Volume (L) of Pb(NO3)2 solution
Volume (L) of Na2S solution
Multiply by M (mol/L)
Multiply by M (mol/L)
Amount (mol) of Pb(NO3)2
Amount (mol) of Na2S
Divide by equation coefficient
Divide by equation coefficient
Smallest
Molar Ratio
Amount (mol) of PbS
Mass (g) of PbS
88
Solving Limiting Reactant Problems in Solution -
Precipitation Problem - II
Moles Pb(NO3)2 V x M Moles Na2S


89
Solving Limiting Reactant Problems in Solution -
Precipitation Problem - II
Moles Pb(NO3)2 V x M 0.2578 L x (0.0468
Mol/L)

0.012065 Mol Pb2 Moles Na2S V x M
Calculation of product yield
2

90
Solving Limiting Reactant Problems in Solution -
Precipitation Problem - II
Moles Pb(NO3)2 V x M 0.2578 L x (0.0468
Mol/L)

0.012065 Mol Pb2 Moles Na2S V x M 0.156 L x
(0.095 Mol/L) 0.01482 mol S -2
Therefore Lead Nitrate is the Limiting Reactant!
Calculation of product yield
Moles PbS

91
Solving Limiting Reactant Problems in Solution -
Precipitation Problem - II
Moles Pb(NO3)2 V x M 0.2578 L x (0.0468
Mol/L)

0.012065 Mol Pb2 Moles Na2S V x M 0.156 L x
(0.095 Mol/L) 0.01482 mol S -2
Therefore Lead Nitrate is the Limiting Reactant!
Calculation of product yield
1 mol PbS 1 mol Pb(NO3)2
Moles PbS 0.012065 Mol Pb2x
0.012065 Mol Pb2
0.012065 Mol Pb2 0.012065 Mol PbS 0.012065
Mol PbS x 2.89 g PbS
239.3 g PbS 1 Mol PbS
92
Fig. 3.14