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Chapter 5
Calculations and
the Chemical
Equation
Denniston
Topping
Caret
4th Edition
5.1 The Mole Concept and Atoms
The Mole and Avogadro’s Number
• atomic mass unit (amu) - unit of measure for the
mass of atoms.
– carbon-12 assigned the mass of exactly 12 amu
– 1 amu = 1.66 x 10-24 g
– periodic table gives atomic weights in amu.
• Chemists usually work with much larger
quantities.
– It is more convenient to work with grams than amu.
• To make the connection we must define the mole.
The mole is abbreviated mol.
• Avogadro’s number
1 mol of atoms = 6.022 x 1023 atoms of an element
• A mole is simply a unit that defines an amount of
something
– Just as a dozen defines 12
– Just as a gross defines 144
• Molar mass - The mass in grams of 1 mole of
atoms.
• What is the molar mass of carbon? 12.01 g/mol
• This means if you counted out a mole of Carbon atoms
(i.e, 6.022 x 1023 of them) they would have a mass of
12.01 g.
• The average mass of one atom of an element in amu
is numerically equivalent to the mass of one mole of
an element expressed in grams.
– That is, 1 atom F is 19.00 amu and 1 mole of F is 19.00 g.
Or,
– 19.00 amu/atom F and 19.00 g/mole F
19.00 amu F 1.66 1024 g F 6.022 1023 atom F


1 atom F
1 amu F
1 mol F
=19.00 g F/mol F or 19.00 g/mol F
Calculating Atoms, Moles, and Mass
• We now know the following conversion factors:
Conversion
Tool
g  ml
density
amu  g
1 amu = 1.661 x 10-24 g
6.022 x 1023 amu = 1g
moleactual number Avegadro’s No.
g  mole
Molar Mass
5.2 Compounds
The Chemical Formula
• Chemical Formula - a combination of symbols of
the various elements that make up the compound.
• Formula unit - the smallest collection of atoms that
provide two important pieces of information
– the identity of the atoms and
– the relative number of each type of atom
• Let’s look closely at the following formulas:
• H2O, NaCl, Fe(CN)3, (NH4)3PO4, CuSO4.5H2O
– This is an example of a hydrate - compounds containing
one or more water molecules as an integral part of their
structure.
5.3 The Mole Concept Applied to
Compounds
• Formula weight - the sum of the atomic weights of
all atoms in the compound, as represented by its
formula.
– expressed in amu
• Molar mass applies to compounds also.
• What is the formula weight of H2O?
– 16.00 amu + 2(1.008 amu) = 18.02 amu
• What is the molar mass of H2O?
– 18.02 g/mol H2O
• When calculating the
formula weight (or
molar mass of an ionic
compound, use the
smallest unit of the
crystal)
• What is the molar mass
of (NH4)3PO4?
• 149.10 g/mol (NH4)3PO4
5.4 The Chemical Equation and the
Information It Conveys
A Recipe For Chemical Change
• Chemical Equation - shorthand notation of a
chemical reaction.
• Reactants - (starting materials) - the substances
that undergo change in the reaction.
• Products - substances produced by the reaction.
• Law of Conservation of Mass - matter cannot be
either gained or lost in the process of a chemical
reaction.
– The total mass of products must equal the total mass of
the reactants.
Features of a Chemical Equation
 - means heat is needed.
2HgO( s)


 2Hg( l )  O2 ( g )
Products and reactants must
be specified using chemical
symbols
Reactants- written on the left of arrow
Products - written on the right
Physical states are shown in parentheses
2HgO( s)


 2Hg( l )  O2 ( g )
Coefficient - how many of the substance
are in the reaction
• The equation must be balanced.
– All the atoms of every reactant must also
appear in the products.
• How many Hg’s on left?
• on right?
• How many O’s on left?
• on right?
We know that a chemical equation represents a
chemical change. The following is evidence for a
reaction:
• Release of a gas.
– CO2 is released when acid is placed in a solution
containing CO32- ions.
– H2 is released when Na is placed in water.
• Formation of a solid (precipitate.)
– A solution containing Ag+ ions is mixed with a
solution containing Cl- ions.
• Heat is produced or absorbed (temperature
changes)
– Acid and base are mixed together
• The color changes
• Light is absorbed or emitted
• Changes in the way the substances behave in
an electrical or magnetic field
• Changes in electrical properties.
5.5 Balancing Chemical Equations
• Consider the following reaction:
hydrogen reacts with oxygen to produce water
• Write the above reaction as a chemical equation.
• You probably wrote the following:
H2 + O2  H2O
• Don’t forget the diatomic elements.
• Is the law of conservation of mass obeyed as
written? NO!
• Balancing chemical equations uses coefficients to
ensure that the law of conservation of mass is
obeyed.
•You may not change subscripts!
•WRONG: H2 + O2  H2O2
Using the equation below, let’s see the steps to
balancing:
H2 + O2  H2O
Step 1. Count the number of moles of atoms
of each element on both product and
reactant side.
Reactants
Products
2 mol H
2 mol O
2 mol H
1 mol O
Step 2. Determine which elements are not
balanced. Oxygen is not balanced.
Step 3. Balance one element at a time using
coefficients.
H2 + O2  2H2O
This balances oxygen, but is hydrogen still
balanced? How will we balance hydrogen?
2H2 + O2  2H2O
Step 4. Check! Make sure the Law of
conservation of mass is obeyed.
5.6 Calculations Using the Chemical
Equation
7
• We will learn in this section to calculate quantities
of reactants and products in a chemical reaction.
• Need a balanced chemical equation for the
reaction of interest.
• Keep in mind that the coefficients represent the
number of moles of each substance in the
equation.
• Let’s examine the reaction:
2H2 + O2  2H2O
• What do the coefficients tell us?
• 2 mol H2 reacts with 1 mol O2 to produce 2 mol H2O.
• What if 4 moles of H2 reacts with 2 moles of O2?
• It yields 4 moles of H2O
• The coefficients of the balanced equation are used to
convert between moles of substances.
• How many moles of O2 are needed to react with 4.26
moles of H2?
• You may be able to do this in your head, but let’s see how
to use the factor label method.
1
__mol
O2
4.26 mol H 2 
 2.13 mol O2
2 mol H 2
__
Comes from the balanced equation.
Plan your route before calculating.
Theoretical and Percent Yield
• Theoretical yield - the maximum amount of
product that can be produced
– Pencil and paper yield
• Actual yield - the amount produced when the
reaction is performed
– Laboratory yield
• Percent yield:
actual yield
% yield 
100%
theoretica l yield