84
2/21/2015
85
86
87
88
89
90
91
92
93
94
95
96
97
Math-tastic!
Unit 9: Math of Chemistry
Part II - Stoichiometry
Lesson # 9.4: The Arithmetic of Equations
STOICHIOMETRY is
Let’s make some Cookies!
• When baking cookies, a recipe is usually used, telling the exact amount of each
ingredient.
– If you need more, you can double or triple the amount
• Thus, a recipe is much like a balanced equation.
• There are 4 ways to interpret a balanced chemical equation:
•
#1. In terms of Particles
• An Element is made of atoms
• A Molecular compound (made of only nonmetals) is made up of molecules (Don’t
forget the diatomic elements)
• Ionic Compounds (made of a metal and nonmetal parts) are made of formula units
Example: 2H2 + O2 → 2H2O
• Two molecules of hydrogen and one molecule of oxygen form two molecules of water.
• Another example: 2Al2O3 ® 4Al + 3O2
#2. In terms of Moles
• The coefficients tell us how many moles of each substance
2Al2O3 ® 4Al + 3O2
2Na + 2H2O ® 2NaOH + H2
• Remember: A balanced equation creates a Molar Ratio
#3. In terms of Mass
• The Law of Conservation of Mass applies
• We can check mass by using moles.
2H2 + O2 ® 2H2O
In terms of Mass (for products)
2H2 + O2 ® 2H2O
#4. In terms of Volume (@ STP)
• At STP, 1 mol of any gas = 22.4 L
2H2
+
O2
®
2H2O
(2 x 22.4 L H2) + (1 x 22.4 L O2) ® (2 x 22.4 L H2O)
•
NOTE: mass and atoms are ALWAYS conserved - however, molecules, formula units,
moles, and volumes will not necessarily be conserved!
•
Practice:
• Show that the following equation follows the Law of Conservation of Mass (show the
atoms balance, and the mass on both sides is equal)
2Al2O3 ® 4Al + 3O2
Mole-Mole Ratio
 A Conversion Factor that shows the mole-to-mole ratio between two of the substances
in a balanced equation
 Derived from the coefficients of any two substances in the equation

98
Writing Mole Ratios
Fe and O2
4 Fe + 3 O2
2 Fe2O3
1
2/21/2015
98
Fe and O2
4 mol Fe
3 mol O2
Fe and Fe2O3
4 mol Fe
2 mol Fe2O3
O2 and Fe2O3
3 mol O2
2 mol Fe2O3
99
and
4 mol Fe
3 mol O2
and
2 mol Fe2O3
4 mol Fe
and
2 mol Fe2O3
3 mol O2
Learning Check #1
3 H2(g) + N2(g)
2 NH3(g)
A. A mol ratio between H2 and N2 is
1) 3 mol N2
2) 1 mol N2
3) 1 mol N2
1 mol H2
3 mol H2
2 mol H2
B. A mol ratio between NH3 and H2 is
1) 1 mol H2
2) 3 mol H2
3) 3 mol H2
2 mol NH3
2 mol NH3
2 mol NH3
100
Chemical Calculations Mole to Mole Conversions
2Al2O3 ® 4Al + 3O2
– each time we use 2 moles of Al2O3 we will also make 3 moles of O2
101
Mole to Mole conversions
• How many moles of O2 are produced when 3.34 moles of Al2O3 decompose?
2Al2O3 ® 4Al + 3O2
102
Chemical Calculations
4 Fe + 3 O2
2 Fe2O3
How many moles of Fe2O3 are produced when 6.0 moles O2 react?
6.0 mol O2 x mol Fe2O3 = 4.0 mol Fe2O3
mol O2
103
Learning Check 2
4 Fe + 3 O2
2 Fe2O3
How many moles of Fe are needed to react with 12.0 mol of O 2?
1) 3.00 mol Fe
2) 9.00 mol Fe
3) 16.0 mol Fe
104
Solution #2
4 Fe
+
3 O2
12.0 mol O2 x
•
105
2 Fe2O3
mol Fe = 16.0 mol Fe
mol O2
Practice:
106
2
2/21/2015
105
Practice:
2C2H2 + 5 O2  4CO2 + 2 H2O
•If 3.84 moles of C2H2 are burned, how many moles of O2 are needed?
106
Steps to Calculate Stoichiometric Problems
1.
2.
3.
4.
5.
107
Correctly balance the equation.
Convert the given amount into moles.
Set up mole ratios.
Use mole ratios to calculate moles of desired chemical.
Convert moles back into final unit.
Example Calculation
The reaction between H2 and O2 produces 13.1 g of water. How many grams of O2
reacted?
Write the equation
H2 (g) + O2 (g)
H2O (g)
Balance the equation
2 H2 (g) + O2 (g)
2 H2O (g)
•
108
Organize data
mol bridge
2 H2 (g)
+ O2 (g)
?g
2 H2O (g)
13.1 g
Plan g of H2O
mol H2O
mol O2
g of O2
Setup
13.1 g H2O x 1 mol H2O x 1 mol O2 x 32.0 g O2
8.0 g H2O
2 mol H2O 1 mol O2
= 11.6 g O2
109
110
Mass-Mass Problem:
Another example:
• If 10.1 g of Fe are added to a solution of Copper (II) Sulfate, how many grams of solid
copper would form?
2Fe + 3CuSO4 ® Fe2(SO4)3 + 3Cu
111
Points to Remember
1.
2.
3.
4.
112
Read an equation in moles
Convert given amount to moles
Use mole factor to give desired moles
Convert moles to grams
grams (given
grams (desired)
moles (given)
moles (desired)
Learning Check # 3
How many O2 molecules will react with 505 grams of Na to form Na2O?
4 Na + O2
2 Na2O
3
2/21/2015
112
4 Na +
O2
2 Na2O
Complete the set up:
505 g Na x 1 mol Na x ________ x _______
23.0 g Na
113
Solution # 3
4 Na
+
O2
2 Na2O
505 g Na x 1 mol Na x 1 mol O2 x 6.02 x 1023
23.0 g Na
4 mol Na 1 mol O2
= 3.30 x 1024 molelcules
114
Acetylene gas C2H2 burns in the oxyactylene torch for welding. How many grams of
C2H2 are burned if the reaction produces 75.0 g of CO2?
2 C2H2 + 5 O2
4 CO2 + 2 H2O
75.0 g CO2 x _______ x _______ x _______
115
Solution # 4
2 C2H2 + 5 O2
4 CO + 2 H2O
75.0 g CO2 x 1 mol CO2 x 2 mol C2H2 x 26.0 g C2H2
44.0 g CO2 4 mol CO2
1 mol C2H2
= 22.2 g C2H2
116
Volume-Volume Calculations:
• How many liters of CH4 at STP are required to completely react with 17.5 L of O 2 ?
CH4 + 2O2  CO2 + 2H2O
117
Avogadro told us:
• Equal volumes of gas, at the same temperature and pressure contain the same
number of particles.
• Moles are numbers of particles
• You can treat reactions as if they happen liters at a time, as long as you keep the
temperature and pressure the same.
118
Shortcut for Volume-Volume?
• How many liters of CH4 at STP are required to completely react with 17.5 L of O 2?
CH4 + 2O2  CO2 + 2H2O
119
Pathways for Problems Using Equations
Given (A)
grams (A)
Needed (B)
grams (B)
moles (A)
moles (B)
particles (A)
particles (B)
120
121
4
2/21/2015
particles (A)
120
121
particles (B)
How do you get good at this?
Math-tastic!
122
123
124
125
126
127
128
5