Calculations from Chemical Equations
Accurate measurement and dosage calculations are critical
in dispensing medicine to patients all over the world.
Foundations of College Chemistry, 14th Ed.
Morris Hein and Susan Arena
Copyright © 2014 John Wiley & Sons, Inc. All rights reserved.
Chapter Outline
9.1 Introduction to Stoichiometry
9.2 Mole-Mole Calculations
9.3 Mole-Mass Calculations
9.4 Mass-Mass Calculations
9.5 Limiting Reactant and Yield Calculations
© 2014 John Wiley & Sons, Inc. All rights reserved.
Mole/Molar Mass Review
Molar Mass (MM): sum of the atomic mass of the atoms
in an element, compound, or formula unit.
Mole: Avogadro’s number (6.022 x 1023) of units
(atoms, molecules, ions etc.)
Useful Conversion Factors
grams of a substance
Molar mass =
moles of the substance
MM allows conversion between g and mol of a substance.
number of units of substance
Moles of a substance =
6.022 x 1023 units of substance
© 2014 John Wiley & Sons, Inc. All rights reserved.
Introduction to Stoichiometry
Equations must always be balanced before calculation of
any mass, moles, or volume of a reactant or product!
Stoichiometry: area of chemistry that deals with
quantitative relationships between products and
reactants in chemical equations.
Example
aA+bB
cC+dD
Using X.X g of A, how much C will be formed?
Solving stoichiometry problems always requires the use of:
1. A balanced chemical equation (coefficients must be known!)
2. Conversion factors in units of moles (i.e. mole ratios)
© 2014 John Wiley & Sons, Inc. All rights reserved.
Mole Ratios
Mole ratio: ratio (conversion factor) between any two
species in a chemical reaction.
Example
2 H2 (g) + O2 (g)
2 H2O (l)
The coefficients of a balanced chemical equation are
used to generate mole ratios.
6 possible mole ratios exist:
2 mol H2
1 mol O2
2 mol H2
2 mol H2O
1 mol O2
2 mol H2O
1 mol O2
2 mol H2
2 mol H2O
2 mol H2
2 mol H2O
1 mol O2
© 2014 John Wiley & Sons, Inc. All rights reserved.
Mole Ratios
The mole ratio can be used as a conversion factor to
convert between moles of one substance and another.
Example
2 H2 (g) + O2 (g)
2 H2O (l)
If 4.0 mol of oxygen are present,
how many moles of H2O could be formed?
4.0 mol O2
2 mol H2O
×
1 mol O2
= 8.0 mol H2O
© 2014 John Wiley & Sons, Inc. All rights reserved.
Mole Ratios Practice
Given the following balanced chemical equation, write
the mole ratio need to calculate:
a. The moles of H2O produced from 3 moles of CO2
b. The moles of H2 needed to produce 3 moles of H2O.
CO2 (g) + 4 H2 (g)
a.
3.0 mol CO2 ×
CH4 (g) + 2 H2O (l)
2 mol H2O
1 mol CO2
= 6.0 mol H2O
Mole ratio
Desired quantity in the numerator of the mole ratio:
known quantity in the denominator
© 2014 John Wiley & Sons, Inc. All rights reserved.
Mole Ratios Practice
Given the following balanced chemical equation, write
the mole ratio need to calculate:
a. The moles of H2O produced from 3 moles of CO2
b. The moles of H2 needed to produce 3 moles of H2O.
CO2 (g) + 4 H2 (g)
b.
3.0 mol H2O ×
CH4 (g) + 2 H2O (l)
4 mol H2
2 mol H2O
= 6.0 mol H2
Mole ratio
Desired quantity in the numerator of the mole ratio:
known quantity in the denominator
© 2014 John Wiley & Sons, Inc. All rights reserved.
Mole Ratios Practice
Given the following balanced chemical equation,
what is the mole ratio needed to calculate the following:
the moles of KCl produced when 4.5 moles of
O2 are formed?
2 KClO3 (s)
2 mol KCl
3 mol O2
2 KCl (s) + 3 O2 (g)
3 mol O2
2 mol KCl
3 mol KCl
2 mol O2
2 mol O2
3 mol KCl
Calculate
4.5 mol O2 ×
2 mol KCl
3 mol O2
= 3.0 mol KCl
Mole ratio
© 2014 John Wiley & Sons, Inc. All rights reserved.
Problem Solving for
Stoichiometry Problems
1. Make sure the equation is balanced!
2. If needed, convert the quantity of known substance to
moles.
1 mol substance
Moles = (grams) x
molar mass substance
3. Convert the moles of known substance to desired
substance using a mole ratio.
Mole ratio =
moles of desired substance
moles of known substance
Moles desired substance = Moles of known substance x Mole ratio
From Step 2
© 2014 John Wiley & Sons, Inc. All rights reserved.
Problem Solving for
Stoichiometry Problems
4. Convert moles of desired substance to the desired units
from the problem.
If answer is in moles, you are finished.
If answer is in grams, multiply by the compound’s molar mass.
grams = (moles) x
Molar mass (in g)
1 mole
If answer is in atoms/molecules, multiply by Avogadro’s number.
6.022 x 1023 molecules
Atoms/molecules = (moles) x
1 mole
© 2014 John Wiley & Sons, Inc. All rights reserved.
Problem Solving for
Stoichiometry Problems
Flow Chart for Stoichiometry Problems
Grams of Known
Grams of Desired
Step 2
Step 4
Step 3
Moles of Desired
Moles of Known
Step 2
Using the
Mole Ratio
Step 4
Atoms/Molecules
of Desired
Atoms/Molecules
of Known
© 2014 John Wiley & Sons, Inc. All rights reserved.
Mole-Mole Calculations
Known substance is given in moles;
desired substance is requested in moles.
How many moles of CO2 will be produced by reaction of
2.0 mol of glucose, given the following balanced equation?
C6H12O6 + 6 O2
Solution Map
6 CO2 + 6 H2O
mol C6H12O6
mol CO2
The mole ratio needed relates mol C6H12O6 to mol CO2.
6 mol CO2
1 mol C6H12O6
Calculate
2.0 mol C6H12O6 ×
6 mol CO2
1 mol C6H12O6
= 12 mol CO2
© 2014 John Wiley & Sons, Inc. All rights reserved.
Mole-Mole Calculations Practice
How many H2O molecules are produced when
0.010 mol O2 react, given the following balanced equation?
2 H2 + O2
2 H2 O
a. 8.3 x 10-27 molecules
b. 3.3 x 10-26 molecules mol O2
c. 3.0 x 1021 molecules
d. 1.2 x 1022 molecules
Calculate
Solution Map
mol H2O
molecules H2O
Mole ratio:
2 mol H2O
1 mol O2
2 mol H2O
6.022 x 1023 molecules H2O
0.010 mol O2 ×
×
1 mole H2O
1 mol O2
= 1.2 x 1022 molecules
© 2014 John Wiley & Sons, Inc. All rights reserved.
Mole-Mole Calculations Practice
How many moles of Al are produced when 0.5 mol of O2
react, given the following balanced equation?
4 Al + 3 O2
2 Al2O3
Solution Map
mol O2
mol Al
a. 0.38 moles
b. 0.67 moles
Mole ratio:
c. 1.0 moles
4 mol Al
3 mol O2
d. 0.25 moles
Calculate
0.5 mol O2 ×
4 mol Al
= 0.67 mol Al
3 mol O2
© 2014 John Wiley & Sons, Inc. All rights reserved.
Mole-Mass Calculations
What mass of H2 can be produced when 6.0 mol of Al
reacts with HCl?
2 Al + 6 HCl
Solution Map
mol Al
2 AlCl3 + 3 H2
mol H2
g H2
The mole ratio and molar mass of H2 are needed:
3 mol H2
2 mol Al
2.016 g H2
1 mol H2
Calculate
3 mol H2
2.016 g H2
6.0 mol Al ×
×
1 mol H2
2 mol Al
© 2014 John Wiley & Sons, Inc. All rights reserved.
= 18 g H2
Mole-Mass Calculations Practice
How many moles of water are produced when 325 g of
octane (C8H18) are burned?
2 C8H18 + 25 O2
Solution Map
16 CO2 + 18 H2O
g C8H18
mol C8H18
moles H2O
The mole ratio and molar mass of C8H18 are needed:
18 mol H2O
2 mol C8H18
1 mol C8H18
114.2 g C8H18
1 mol C8H18
18 mol H2O
Calculate
325. g C8H18 ×
114.2 g C8H18
×
2 mol C8H18
© 2014 John Wiley & Sons, Inc. All rights reserved.
= 25.6 mol H2O
Mole-Mass Calculations Practice
How many grams of AgNO3 are needed to produce
0.25 mol of Ag2S?
2 AgNO3 + H2S
Ag2S + 2 HNO3
a. 42.5 g
b. 57.1 g
c. 2.19 x 10-3 g
d. 85.0 g
Calculate
mol Ag2S
Solution Map
mol AgNO3
g AgNO3
The mole ratio and
molar mass of AgNO3 are needed:
2 mol AgNO3
169.9 g AgNO3
1 mol Ag2S
1 mol AgNO3
2 mol AgNO3
169.9 g AgNO3
0.25 mol Ag2S ×
×
= 85.0 g AgNO3
1 mol AgNO3
1 mol Ag2S
© 2014 John Wiley & Sons, Inc. All rights reserved.
Mass-Mass Calculations
How many grams of HNO3 are required to produce
8.75 g of N2O from the following reaction?
4 Zn + 10 HNO3
4 Zn(NO3)2 + N2O + 5 H2O
Solution Map g N2O
mol N2O
mol HNO3
g HNO3
The mole ratio and molar masses of N2O and HNO3 are needed:
10 mol HNO3
1 mol N2O
1 mol N2O
44.02 g N2O
63.02 g HNO3
1 mol HNO3
Calculate
1 mol N2O
10 mol HNO3
63.02 g HNO3
8.75 g N2O ×
×
×
1 mol N2O
44.02 g N2O
1 mol HNO3
= 125. g HNO3
© 2014 John Wiley & Sons, Inc. All rights reserved.
Mass-Mass Calculations Practice
How many grams of CrCl3 are required to produce
75.0 g of AgCl using the following reaction?
CrCl3 + 3 AgNO3
a. 204 g
b. 249 g
c. 22.6 g
d. 27.6 g
g AgCl
Cr(NO3)3 + 3 AgCl
Solution Map
mol AgCl
mol CrCl3
g CrCl3
Mole ratio/molar masses needed:
1 mol CrCl3
3 mol AgCl
1 mol AgCl
143.3 g AgCl
Calculate
158.4 g CrCl3
1 mol CrCl3
1 mol AgCl
1 mol CrCl3
158.4 g CrCl3
75.0 g AgCl ×
×
×
3 mol AgCl
143.3 g AgCl
1 mol CrCl3
= 27.6 g CrCl3
© 2014 John Wiley & Sons, Inc. All rights reserved.
Learning Objectives
9.1 Introduction to Stoichiometry
Define stoichiometry and describe the strategy required to
solve problems based on chemical equations.
9.2 Mole-Mole Calculations
Solve problems where the reactants and products
are both in moles.
9.3 Mole-Mass Calculations
Solve problems where known mass is given and the answer
is to be determined in moles or the moles of known are
given and mass is determined.
9.4 Mass-Mass Calculations
Solve problems where mass is given and the desired
unit to be determined is mass.
© 2014 John Wiley & Sons, Inc. All rights reserved.