Transcript The Mole: A Measurement of Matter

The Mole: A Measurement of Matter
Sand Activity
• Is it practical to count each grain of sand?
• How else might you measure or quantify
the sand?
• mass, volume
• just a small amount of sand contains
millions of smaller particles, just like
chemical substances
The Mole: A Measurement of Matter
Scientists answer questions such as:
• How many kilograms of iron can be obtained
from one kilogram of iron ore?
• How many grams of the elements hydrogen and
nitrogen must be combined to make 200 grams
of the fertilizer ammonia (NH3)?
• How do we measure matter?
• by counting
• determine its mass and volume
The Mole: A Measurement of Matter
• There are ways that
everyday things are
measured
• how many is a
couple?
• how many is one
dozen?
• how many is a few?
• how many sodas
are in one case?
• how many are in
one gross?
Example: apples can be
measured three different
ways, all of which can be
equated to a dozen apples
By count:
• 1 dozen apples = 12 apples
• for average-sized apples the
following approximations can
be used:
• By mass:
• 1 dozen apples = 2.0 kg
apples
• By volume:
• 1dozen apples = 0.20 bushel
apples
The Mole: A Measurement of Matter
• Knowing how the count, mass, and
volume of apples relate to a dozen apples
allows you to convert between these units.
For example, you could calculate the mass
of a bushel of apples or the mass of 90
average-sized apples using conversion
factors based on the unit relationships
given above.
The Mole: A Measurement of Matter
• In chemistry you will do calculations using
a measuring unit called a mole. The mole,
the SI unit that measures the amount of
substance, is a unit just like the dozen.
• The mole can be related to the number
of particles (a count), the mass, and the
volume of an element or a compound
just as a dozen was related to these
three units for apples
The Mole: A Measurement of Matter
Example:
What is the mass of 90 average-sized apples?
Knowns:
Unknowns:
Number of apples = 90
apples
12 apples = 1 dozen apples
1 dozen apples = 2.0 kg
apples
Mass of 90 apples = ? kg
Convert:
Number of apples to mass of apples
This conversion can be carried out by performing the following
sequence of conversions:
number
dozens
mass of apples
The Mole: A Measurement of Matter
• Calculate:
• First conversion factor: 1 dozen apples/ 12
apples
• Second conversion factor: 2.0 kg apples/ 1
dozen apples
• Multiplying the original number of apples by
these two conversion factors yields the
answer in kilograms,
The Mole and Molar Mass
• The mole is the standard method in chemistry
for communicating how much of a substance is
present (just like one dozen is equal to the
quantity twelve).
• Definition:
• The mole is the amount of substance of a
system which contains as many elementary
entities as there are atoms in 0.012 kilogram of
carbon-12. When the mole is used, the
elementary entities must be specified and may
be atoms, molecules, ions, electrons, other
particles, or specified groups of such particles.
The Mole and Molar Mass
• One mole contains as many entities as
there are in 12 grams of carbon-12 (or
0.012 kilogram)
• In one mole, there are 6.023 x 1023 atoms.
Here's another way: there are 6.023 x 1023
atoms of carbon in 12 grams of carbon-12
• Let's say that clearly: one mole of
ANYTHING contains 6.023 x 1023
entities.
The Mole and Molar Mass
• The word "entities" is simply a generic
word. For example, if we were discussing
atoms, then we would use "atoms" and if
molecules were the subject of discussion,
the word entities would be replaced in
actual use by "molecules."
• The mole has been very carefully
measured in a number of ways over many
decades. The symbol for mole is "mol."
The Mole and Molar Mass
• One mole of ANY specified entity contains
6.022 x 1023 of that entity. For example:
• One mole of donuts contains 6.022 x 1023
donuts
• One mole of H2O contains 6.022 x 1023
molecules
• One mole of nails contains 6.022 x 1023 nails
• One mole of Fe contains 6.022 x 1023 atoms
• One mole of dogs contains 6.022 x 1023 dogs
• One mole of electrons contains 6.022 x 1023
electrons
• One mole of 11th grade chemistry students
contains 6.022 x 1023 poor, suffering (I mean
happy, joyful) Monaca students
The Mole and Molar Mass
• 6.023 x 1023 is so important in
chemistry that it has a name. It is
called Avogadro's Number and
has the symbol N.
•
It is so named in honor of
Amedeo Avogadro, an Italian
chemist, who, in 1811, made a
critical contribution (recognized
only in 1860 after his death)
which helped greatly with the
measurement of atomic weights.
The Mole and Molar Mass
• Avogadro's Number has a unit
associated with it. It is mol¯1,
as in 6.022 x 1023 mol¯1.
• The superscripted minus one
means the unit mol is in the
denominator. There is an
understood numerator of one,
as in 1/mol.
The Mole and Molar Mass
• 6.022 x 1023 mol¯1 • If we were discussing
• Why is there no unit
in the numerator?
There could be, but it
would vary based on
the entity involved. If
we were discussing
an element, we might
write atoms/mol.
a compound, we
would say "molecules
per mol." What is in
the numerator
depends on what
"entity" (atom,
molecule, ion,
electron, etc.) is being
used in the problem.
The Mole and Molar Mass
Examples
•
•
•
•
•
•
•
Atoms/mol
Molecules/mol
Ions/mol
Electrons/mol
Pencils/mol
Chairs/mol
etc
• Getting back to
Avogadro's Number
and its role in
chemistry; please
note that counting
atoms or molecules is
very difficult since
they are so small.
However, we can
"count" atoms or
molecules by
weighing large
amounts of them on a
balance.
Molar Mass
• When we weigh one mole of a substance
on a balance, this is called a "molar mass"
and has the units g/mol (grams per mole).
This idea is very critical because it is used
all the time.
• A molar mass is the weight in grams of
one mole.
• One mole contains 6.023 x 1023 entities.
• Therefore, a molar mass is the mass in
grams of 6.023 x 1023 entities.
Molar Mass
• OK. How does one calculate a molar
mass?
• The molar mass of a substance is the
molecular weight in grams. The molecular
weight of a substance is the weight in
atomic mass units of all the atoms in a
given formula.
• All you need to do is calculate the
molecular weight and place the unit
"g/mol" after the number and that is the
molar mass for the substance in question.
Molar Mass
• Calculate the molar mass of Al(NO3)3
• Al(1 x 26.98) + N(3 x 14.007) + O(9 x
16.00) = 213.00 g/mol
• 213.00 grams is the mass of one mole of
aluminum nitrate.
• 213.00 grams of aluminum nitrate contains
6.022 x 1023 entities of Al(NO3)3
Review
• Calculate the molar
mass of Pb(ClO2)2
• Calculate the molar
mass of NH4MnO4
• Pb( 1 x 207.2) + Cl( 2
x 35.4527) + O( 4 x
15.9994) = 342.10
g/mol
• N( 1 x 14.0067) + H(
4 x 1.01) + Mn( 1 x
54.9380) + O( 4 x
15.9994)
• = 136.97 g/mol
Mole and Weight Relationships of Water and its Parts
2 moles H
+
1 mole O
=
2 * 1.01 g
+
16.00 g
=
1 mole
water
18.02 g
• A bottle filled with exactly 18.02 g water will
contain 6.02 x 1023 water molecules. The
concept of fractions and multiples described
above also applies to molecules: 9.01 g of water
would contain 1/2 mole, or 3.01 x 1023
molecules.