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Chemistry 201
Atomic mass
Avagadro’s number
NC State University
The mass of a proton
The mass of a proton is:
1.6726231 × 10−27 kg
or
1.6726231 × 10−24 grams
We know this value accurately because of mass
spectrometry. The number cited here has eight
significant figures. We do not usually need this
precision, so we often write the value as
1.67 × 10−24 grams
to three significant figures.
Significant figures
The number of significant figures is equal to the
number of digits in a measured or calculated value that
contribute to its precision. Precision refers to the
ability to reproducibly measure or calculate a value.
If we use three significant figures, it suggests that we
can reproducibly measure the value to within about 1
part in 100 or with an accuracy of 1%. This is the most
common number of significant figures and this will be
the default in this course (unless otherwise specified).
Example
The mass of the electron is reported to be:
9.1093819 × 10-31 kg
Write this number to three significant figures.
Example
The mass of the electron is reported to be:
9.1093819 × 10-31 kg
Write this number to three significant figures.
Solution: The specified value should be as close as
possible to the true value so we should round-off the
last digit. In this case we round up to obtain
9.11 × 10-31 kg
Example
The mass of a neutron is approximately equal to sum of
the masses of an electron and a proton. Give the
neutron mass to three significant figures.
Example
The mass of a neutron is approximately equal to sum of
the masses of an electron and a proton. Give the
neutron mass to three significant figures.
Solution: Start with the accurate values:
1.6726231 × 10−27 kg
9.1093819 × 10-31 kg
Example
The mass of a neutron is approximately equal to sum of
the masses of an electron and a proton. Give the
neutron mass to three significant figures.
Solution: Start with the accurate values:
1.6726231 × 10−27 kg
9.1093819 × 10-31 kg
Add them together
1.6735340 × 10−27 kg
Example
The mass of a neutron is approximately equal to sum of
the masses of an electron and a proton. Give the
neutron mass to three significant figures.
Solution: Start with the accurate values:
1.6726231 × 10−27 kg
9.1093819 × 10-31 kg
Add them together
1.6735340 × 10−27 kg
Round of to give
1.67 × 10−27 kg
Example
The actual value of the neutron mass is:
1.6749286 × 10−27 kg
Calculate the difference between the value you
obtained by summing the proton and electron masses.
How many significant figures are possible in your
answer?
Example
The actual value of the neutron mass is:
1.6749286 × 10−27 kg
Calculate the difference between the value you
obtained by summing the proton and electron masses.
How many significant figures are possible in your
answer?
Solution:
Neutron
1.6749286 × 10−27 kg
Proton + electron
1.6735340 × 10−27 kg
Difference
1.3946 × 10−30 kg
There are 5 significant figures in the answer.
Conversion factors for atomic mass
The sum of the mass of a proton and an electron is the
mass of a hydrogen atom.
Question: how many hydrogen atoms are there in a
gram of H atoms (to 3 significant figures)?
Conversion factors for atomic mass
The sum of the mass of a proton and an electron is the
mass of a hydrogen atom.
Question: how many hydrogen atoms are there in a
gram of H atoms (to 3 significant figures)?
Answer: The calculated value actually has units
1.6735340 × 10−27 kg/atom
Or
1.6735340 × 10−24 grams/atom
Therefore, we can invert it to find,
5.97(5) × 1023 atoms/gram
Atomic mass unit
When we consider all of the atoms in the periodic
table, the average mass of a nucleon is considered to
be:
1.6605388 × 10−24 grams/nucleon
We call this the atomic mass unit. We can use this
value to convert atomic masses to grams or vice versa.
We write the conversion as,
1.6605388 × 10−24 grams/amu
To employ this value we calculate the atomic mass of
an atom or molecule and then we can calculate the
weight in grams using this formula.
Avagadro’s number
If we invert average atomic mass
___________1_____________
1.6605388 × 10−24 grams/amu
We obtained the number of particles with a given amu
per gram. This number is called Avagradro’s number
and is given the symbol NA.
NA = 6.022141 × 1023 amu/gram
This number gives the number of particles for which an
atomic mass has the the same value in grams.
1 H atom = 1 amu
NA H atoms = 1 gram
1 C atom = 12 amu
NA C atoms = 12 grams
Example
How much does a molecule of pyridine weigh?
(Ummm… all right, what is its mass?)
Example
How much does a molecule of pyridine weigh?
Solution: First, we find the chemical formula for
pyridine. C5H5N
H
H
H
H
H
N
Example
How much does a molecule of pyridine weigh?
Solution: Second, we look up the atomic masses in the
periodic table.
atomic mass = 5(12) + 5 + 14 = 79 amu
Third, we use the conversion factor to calculate the
mass in grams
(79 amu)x (1.66 × 10−24 grams/amu) = 1.31 × 10−23 grams
Avogadro’s number
It is a bit difficult to weigh out 10−23 grams.
H
H
H
H
H
N
Avogadro’s number
Instead, let’s ask how many molecules it takes to
convert the atomic mass to its value in grams.
For example, using the grams/amu conversion, let’s
calculate how many hydrogen atoms have the mass of
1 gram.
Avogadro’s number
Instead, let’s ask how many molecules it takes to
convert the atomic mass to its value in grams.
For example, using the grams/amu conversion, let’s
calculate how many hydrogen atoms have the mass of
1 gram.
Answer: since hydrogen weighs 1 amu, its mass is
1.6605388 × 10−24 grams/atom
We can invert this value to find the number of atoms
per gram.
6.0221417 × 1023 atoms/gram
The mole
Since this number converts from atoms to gram for
hydrogen, we can see that it can be used to give the
number of atoms for any formula weight (i.e. molecular
weight of a compound given in grams). For example,
pyridine has a formula weight of 79 grams. Therefore,
There are 6.0221417 × 1023 molecules in 79 grams of
pyridine. Because of the importance of this number of
atoms or molecules we give the name, mole.
1 mole = 6.0221417 × 1023 molecules
or to 3 significant figures.
1 mole = 6.02 × 1023 molecules
Avogadro’s number
as a conversion factor
Given the definition,
1 mole = 6.02 × 1023 molecules
We can see that Avogadro’s number converts from
molecules to moles.
6.02 × 1023 molecules/mole
Atomic weight and molar mass
The atomic weight is the numerical value tabulated for
the mass of each atom in the periodic table in atomic
units. The use of the word “weight” is not precise here
since weight in physics represents a force (w = mg).
However, the name atomic weight is so ingrained that
we will not attempt to change it. We use the periodic
table to calculate the molar mass as follows: for H2SO4
we find the atomic weights, H = 1, S = 32 and O = 16.
Molar mass = 2(1 g/mol) + 32 g/mol + 4(16 g/mol)
= 98 g/mol

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