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Chapter 2
Atoms & Elements
CHE 123: General Chemistry I
Dr. Jerome Williams, Ph.D.
Saint Leo University
Overview
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Fundamental Chemical Laws
Dalton’s Atomic Theory
Isotopes
Chemical Formulas & Molar Mass
The Mole: A Counting Unit
Example 2.1: Show that two samples of carbon
dioxide obey the Law of Definite Proportions
Given:
Find:
Conceptual
Plan:
Relationships:
Sample 1: 25.6 g O and 9.60 g C
Sample 2: 21.6 g O and 8.10 g C
proportion O:C
g O 1, g C1
g O 2, g C2
O:C in each sample
all samples of a compound have the same
proportion of elements by mass
Solution:
Check: both samples have the same O:C ratio, so the result is
consistent with the Law of Definite Proportions
Tro: Chemistry: A Molecular Approach, 2/e
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Practice – If a 10.0 g sample of calcite
contains 4.0 g of calcium, how much
calcite contains 0.24 g of calcium?
Tro: Chemistry: A Molecular Approach, 2/e
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Practice – How much calcite contains 0.24 g
of calcium?
Given:
Find:
Conceptual
Plan:
Sample 1: 4.0 g Ca and 10.0 g calcite
Sample 2: 0.24 g Ca
mass calcite in Sample 2, g
g Ca1, g calcite1
g Ca2
g calcite2
because
Relationships:
Solution:
Sig Figs &
Round:
Tro: Chemistry: A Molecular Approach, 2/e
0.6 g calcite = 0.60 g calcite
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Practice – Decide if each statement is
correct according to Dalton’s model of
the atom
• Copper atoms can combine with zinc
atoms to make gold atoms
• Water is composed of many identical
molecules that have one oxygen atom and
two hydrogen atoms
Tro: Chemistry: A Molecular Approach, 2/e
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Practice – Decide if each statement is correct
according to Dalton’s model of the atom
• Copper atoms can combine with zinc atoms to
make gold atoms – incorrect; according to Dalton,
atoms of one element cannot turn into atoms of
another element by a chemical reaction. He knew
this because if atoms could change it would
change the total mass and violate the Law of
Conservation of Mass.
Tro: Chemistry: A Molecular Approach, 2/e
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Practice – Decide if each statement is correct
according to Dalton’s model of the atom
• Water is composed of many identical molecules that
have one oxygen atom and two hydrogen atoms –
correct; according to Dalton, atoms combine together
in compounds in small whole-number ratios, so that
you could describe a compound by describing the
number of atoms of each element in a molecule. He
used this idea to explain why compounds obey the
Law of Definite Proportions.
Tro: Chemistry: A Molecular Approach, 2/e
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Practice – Decide if each statement is
correct according to Dalton’s Model of the
Atom
• Some carbon atoms weigh more than
other carbon atoms
• Because the mass ratio of Fe:O in wüsite
is 1.5 times larger than the Fe:O ratio in
hematite, there must be 1.5 Fe atoms in a
unit of wüsite and 1 Fe atom in a unit of
hematite
Tro: Chemistry: A Molecular Approach, 2/e
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Practice – Decide if each statement is
correct according to Dalton’s model of the
atom
• Some carbon atoms weigh more than other carbon
atoms – incorrect; according to Dalton, all atoms of
an element are identical.
Tro: Chemistry: A Molecular Approach, 2/e
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Practice – Decide if each statement is
correct according to Dalton’s Model of the
Atom
• Because the mass ratio of Fe:O in wüsite
is 1.5 times larger than the Fe:O ratio in
hematite, there must be 1.5 Fe atoms in a
unit of wüsite and 1 Fe atom in a unit of
hematite
Tro: Chemistry: A Molecular Approach, 2/e
11
Practice – Decide if each statement is
correct according to Dalton’s model of the
atom
• Because the mass ratio of Fe:O in wüsite is 1.5
times larger than the Fe:O ratio in hematite, there
must be 1.5 Fe atoms in a unit of wüsite and 1 Fe
atom in a unit of hematite – incorrect; according to
Dalton, atoms must combine in small whole-number
ratios. If you could combine fractions of atoms, that
would mean the atom is breakable and Dalton’s first
premise would be incorrect. You can get the Fe:Fe
mass ratio to be 1.5 if the formula for wüsite is FeO
and the formula for hematite is Fe2O3.
Tro: Chemistry: A Molecular Approach, 2/e
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Isotopes
• Isotopes (Two Definitions)
– Atoms that have the same atomic number (Z) but
different mass numbers (A).
– Atoms that have the same #p+ but differ in #no.
• Mass Number (A)
– This is the sum of the number of protons and
neutrons in an atom. (A = #p+ + #no)
Isotopes
• Isotope Format
– Standard Format vs. Element #
Isotopes
• An atom of element X contains 47 protons
and 62 neutrons. Identify the element, and
write the symbol for the isotope in the
standard format.
Answer to Exercise
• Atomic No. (Z) = #p = 47 = Ag (Silver)
• Mass No. (A) = 47 p + 62 n = 109
109
Ag
47
Isotopes
• Calculating Atomic Masses
– To find atomic mass for an element one
needs to have the individual isotopic masses
and the relative percent abundance of each
isotope.
Isotopes
• Atomic Mass = Σ (fraction of isotope n) x (mass isotope n)
Isotopes
• Calculating Atomic Masses: An Example
– Carbon has two naturally occurring isotopes.
Carbon 12 has an isotopic mass of 12.000
amu and an abundance of 98.89% while
carbon 13 has an isotopic mass of 13.0034
amu and an abundance of 1.11%. Calculate
the atomic mass of carbon.
Isotopes
• Solution to Example
• Atomic Mass = [ (0.9889 x 12.000 amu) +
(0.0111 x 13.0034 amu) ]
• Atomic Mass = 11.867 amu + 0.144 amu
• Atomic Mass = 12.011 amu
Isotopes
• Chlorine has two naturally occurring isotopes: chlorine
35 with an abundance of 75.77% and an isotopic mass
of 34.969 amu, and chlorine 37 with an abundance of
24.23% and an isotopic mass of 36.966 amu. What is
the atomic mass of chlorine?
Chemical Formulas & Molar Mass
• A formula unit is one unit, (atom, molecule, or
ion), corresponding to a given formula.
H2O, CO2, CaCO3, Na3PO4
Chemical Formulas & Molar Mass
• Since molecules are so small, it is necessary to
convert a number ratio of reactant molecules
into a mass ratio for a chemical reaction to be
useful.
• Mass ratios are determined by using atomic
masses for the elements.
Chemical Formulas & Molar Mass
• Formula mass (FM) represents the sum of
atomic masses of all atoms in a formula
unit of any compound (ionic or molecular).
• Alternate terms that you will see include
Molecular Mass, Molar Mass, Formula
Weight (FW), and Molecular Weight (MW).
Chemical Formulas & Molar Mass
• Calculating Formula Masses: Examples
HCl
1.01 amu + 35.45 amu = 36.46 amu
NaCl
23.00 amu + 35.45 amu = 58.45 amu
MgF2
24.31 amu + 2 (19.00 amu) = 62.31 amu
Chemical Formulas & Molar Mass
• Find the formula mass of the following.
Glucose (C6H12O6)
Sodium dihydrogen phosphate
Silicon tetrabromide
Formula Mass Example
• Answers
• Glucose
180.18 amu
• NaH2PO4
119.98 amu
• SiBr4
347.69 amu
The Mole: A Counting Unit
• The mole is the SI unit for the amount of a
substance.
• A mole is defined as the amount of a
substance that contains as many “entities”
as there are in exactly 12 g of carbon-12.
The Mole: A Counting Unit
• More useful relationships based on the
mole that belong in the chemist toolbox.
1 mole of X = NA units
(units = atoms, ions, molecules)
NA = Avogadro’s Number = 6.022 x 1023 units/mole
mass of 1 mole of a substance X = molar mass of X in grams.
Molar mass is equal to formula (molecular) mass of X in grams. Molar
mass values are expressed in grams/mole.
The Mole: A Counting Unit
• Review: What are the first two axioms?
• Axiom #3
“Moles are the vehicle that carry us everywhere
we want to go in chemistry.”
The Mole: A Counting Unit
• Example Problems involving moles:
• How many moles are in 23.5 g of iron?
– Answer
0.421 moles Fe
The Mole: A Counting Unit
• Example Problems involving moles:
• How many moles of zinc are there in a sample
that has 3.45 x 1026 atoms of zinc?
– Answer
573 moles Zn