Download weighted average - Effingham County Schools

Early Greek Theories
• 440 B.C. - Democritus thought matter could
not be divided indefinitely. He called
nature’s basic particle the “atom”, from the
Greek word meaning “indivisible”.
Democritus
Aristotle
• 350 B.C - Aristotle modified an earlier
theory that matter was made of four
“elements”: earth, fire, water, air.
• Aristotle was wrong. However, his
theory persisted for 2000 years.
Foundations of the Atom
•In the late 1700s chemists believed the modern
definition of an element as a substance that
cannot be further broken down by ordinary
chemical means.
•It was also clear that elements combine to form
compounds that have different physical and
chemical properties than those of the elements
that form them.
Na + Cl → NaCl
Different properties
•Chemists at this time could not agree whether
elements always combined in the same ratio
when forming a particular compound.
•When a substance or substances are
transformed into one or more new substances, it
is caused by a chemical reaction.
Forming
lead
iodide
•In the 1790s, scientists began to analyze
chemical reactions. This lead to the discovery
of several basic laws.
•The law of conservation of mass (matter (mass)
is neither created nor destroyed during ordinary
physical or chemical changes).
•Antoine Lavoisier, a French chemist, verified
this law by experimentation in 1789.
The Law of
Conservation
Of Mass
•In 1799, Joseph Proust, a French chemist,
showed that a given compound always
contains exactly the same proportion of
elements by mass.
•The principle of the constant composition of
compounds, originally called “Proust’s law”, is
now known as the law of definite proportions.
•The law of definite proportions (a chemical
compound contains the same proportions by
mass regardless of the size of the sample or
source of the compound.
•For example, sodium chloride (table salt)
always consists of 39.34% by mass of the
element sodium, Na, and 60.66% by mass of
the element chlorine, Cl.
•Proust’s discovery stimulated John Dalton, an
English schoolteacher, to think about atoms as
the particles that might compose elements.
•Dalton discovered another principle that
convinced him of the existence of atoms.
•He noted, for example, that carbon and
oxygen form two different compounds that
contain different relative amounts of carbon
and oxygen (CO and CO2).
•This led to the law of multiple proportions in
1803.
•The law of multiple proportions (if two or more
different compounds are composed of the
same two elements, then the ratio of the
masses of the second element combined with
a certain mass of the first element is always a
ratio of small whole numbers.
•For example, the elements carbon and
oxygen form two compounds, carbon dioxide
and carbon monoxide. CO molecules are
always composed of one C atom and one O
atom. CO2 molecules are always one C atom
and two O atoms.
Law of Multiple Proportions
Dalton’s Atomic Theory
•In 1808, John Dalton proposed an explanation
for the three laws (Atomic Theory).
•All matter is composed of extremely small particles
called atoms.
•Atoms of a given element are identical in size,
mass, and other properties; atoms of different
elements differ in size, mass and other properties.
•Atoms cannot be subdivided, created, or
destroyed.
•Atoms of different elements combine in simple
whole-number ratios to form chemical compounds.
•In chemical reactions, atoms are combined,
separated, or rearranged.
Modern Atomic Theory
•Aspects of Dalton’s theory have been proven
incorrect (we know now that atoms are
divisible and a given element can have atoms
with different masses).
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Atom
•An atom is the smallest particle of an element
that retains the chemical properties of that
element.
•Atoms consist of two regions. The nucleus is
at the center of the atom and contains at least
one positively charged particle called a proton
and one or more neutral particles called
neutrons.
electron
neutron
proton
15
•Surrounding the nucleus is a region occupied
by negatively charged particles called electrons
(this region is very large compared to the
nucleus.
•Protons, neutrons, and electrons are usually
referred to as subatomic particles.
electron
neutron
proton
16
Discovery of the Electron
•The discovery of the electron occurred in the
late 1800s when scientists were investigating
the relationship between electricity and matter.
The experiments were carried out in cathode-ray
tubes.
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Cathode-Ray Tube
A simple cathode-ray
tube. Particles pass
through the tube from
the cathode, the metal
disk connected to the
negative terminal of
the voltage source,
to the anode, the
metal disk connected
to the positive
terminal.
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•The experiments carried out by Joseph John
Thomson in 1897, showed the particles that
composed the cathode ray were negatively
charged.
•Thomson also thought that atoms must contain
some positive charge.
•Thomson suggested that an
atom consisted of a cloud of
positive charge with the negative
electrons embedded in it. This
model is often called the “plum•Watch video clip. pudding” model.
19
•In 1909 experiments conducted by
Robert A. Millikan showed that atoms
were electrically neutral and must
contain a positive charge to balance
the negative electrons. They also
showed that atoms must contain other
particles that account for most of their
mass.
•Watch video clip.
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Discovery of the Atomic
Nucleus
•In 1911 Ernest Rutherford, Hans Geiger, and
Ernest Marsden bombarded a thin piece of gold
foil with fast-moving alpha particles. Some
particles were redirected back toward the
source.
•Rutherford concluded that this was caused by a
densely packed bundle of matter with a positive
charge (nucleus).
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Zinc sulfide
Lead screen
block
Radioactiv
e
substance
Thin gold foil
path of invisible
-particles
Most particles passed through.
So, atoms are mostly empty.
Some positive -particles
deflected or bounced back!
Thus, a “nucleus” is positive &
holds most of an atom’s mass.
22
Composition of the Atomic
Nucleus
•The nuclei by atoms of different elements
differ in the number of protons they contain
(the number of protons in an atom’s nucleus
determine the atom’s identity.
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When two protons are extremely close to each other,
there is a strong attraction between them.
A similar attraction exists when neutrons are very close
to each other or when protons and neutrons are very
close together.
These short-range proton-neutron, proton-proton, and
neutron-neutron forces hold the nuclear particles 24
together and are referred to as nuclear forces.
Nuclear Forces
25
The Sizes of Atoms
•The sizes of atoms are expressed in
picometers ( 1 pm = 1 x 10-12 m).
•To get an idea of how small a picometer is,
consider that 1 cm is the same fractional
part of 103 km (about 600 miles) as 100 pm
is of 1 cm.
•Atomic radii range from about 40 to 270
pm.
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Atomic Number
•Atoms of different elements have different
numbers of protons. Atoms of the same element
all have the same number of protons.
•The atomic number (Z) of an element is the
number of protons in the nucleus of each atom of
that element.
•An element’s atomic
number is indicated
above its symbol on the
periodic table.
•Elements are placed in order of increasing atomic
number.
•The atomic number identifies an element.
Isotopes
•Isotopes are atoms of the same element that have
different masses.
•The isotopes of a particular element all have the
same number of protons and electrons, but
different numbers of neutrons.
Isotopes of
Hydrogen
Mass Number
•The mass number is the total number of protons
and neutrons in the nucleus of an isotope.
•This isotope of
oxygen has 8
protons and 8
neutrons in the
nucleus. Its mass
number is 16.
Designating Isotopes
•There are two methods for specifying isotopes.
•In the first method, the mass number is written
with a hyphen after the name of the element
(uranium-235).
•The second method shows the composition of a
nucleus as the isotope’s nuclear symbol ( 235
).
92 U
Two different
isotopes of carbon.
235
U
92
•The superscript indicates the mass
number and the subscript indicates the
atomic number.
•The number of neutrons is found by subtracting the
atomic number from the mass number
(mass # - atomic # = # of neutrons).
•Example: 235 (protons + neutrons) – 92 (protons) =
143 neutrons.
235
U
92
•For a neutral atom, the
number of protons
equals the number of
electrons.
Uranium
Example:
How many protons, electrons, and neutrons are
there in an atom of chlorine-37?
Given: name and mass number of chlorine-37
Remember: atomic number = number of protons
= number of electrons
From the periodic table, the atomic number of
chlorine is 17.
Mass # - atomic # = # of neutrons 37 – 17 = 20
An atom of chlorine-37 is made up of 17 protons,
17 electrons, and 20 neutrons.
•The charge on an ion (an atom with a positive or
negative charge) indicates an imbalance between
protons and electrons.
•Too many electrons produces a negative charge,
too few, a positive charge.
•Nuclide is a general term for any isotope of any
element.
•Below are three hydrogen nuclides.
Relative Atomic Mass
•Masses of atoms expressed in grams are very
small. For example, an atom of oxygen-16 has a
mass of 2.657 x 10-23 g.
•For simplicity, scientists use the atomic mass unit
(amu) to express the mass of atoms. 1 amu is 1/12
the mass of a carbon-12 atom.
•The atomic mass of any nuclide is determined by
comparing it with the mass of the carbon-12 atom.
•Remember scientists use standards of
measurement that are constant and are the same
everywhere.
•In order to set up a relative scale of atomic mass,
one atom was arbitrarily chosen as the standard and
assigned a value.
•The carbon-12 atom was arbitrarily assigned a mass
of exactly 12 atomic mass units, or 12 amu.
•Remember one atomic mass unit, or 1 amu, is
exactly 1/12 the mass of a carbon-12 atom.
Average Atomic Masses of the
Elements
•Average atomic mass is the weighted average of the
atomic masses of the naturally occurring isotopes of
an element.
•Calculating the average atomic mass depends on
both the mass and the relative abundance of each of
the element’s isotopes.
A weighted average is an average that adjusts for the
frequency of individual values.
The following is an example of how to calculate a
weighted average.
Suppose you have a box containing two sizes of
marbles. If 25% of the marbles have masses of
2.00 g each and 75% have masses of 3.00 g each,
how is the weighted average calculated?
To determine the weighted average, multiply the
mass of each marble by the decimal fraction
representing its percentage in the mixture. Then
add the products.
25% = 0.25
75% = 0.75
(2.00 g x 0.25) + (3.00 g x 0.75) = 2.75 g
Notice the weighted average is closer to 3.00 g
because a larger percentage of the marbles
have a mass of 3.00 g.
Calculating Average Atomic Mass
•Copper consists of 69.15% copper-63, which has an
atomic mass of 62.929601 amu, and 30.85% copper-65,
which has an atomic mass of 64.927794 amu.
•The average atomic mass of copper can be calculated
by multiplying the atomic mass of each isotope by its
relative abundance (expressed in decimal form) and
adding the results.
(0.6915 x 62.929601 amu) + (0.3085 x 64.927794 amu)
= 63.55 amu
The calculated average atomic mass of naturally
occurring copper is 63.55 amu.