Thursday Sept 8
Measurements in chemistry and the other sciences and engineering depend on standards and the use
of units. Some units which we use in science are
kilogram
second
meter
coulomb
mole
kg
s
m
c
m
mass
time
distance
charge
amount of substance
The gram or g is 1/1000 of a gram and is used in chemistry.
The above units are called primary units. Derived units use two or more of the above units to
describe a measurement. Velocity has the units of m/s
Standards are used so that we can compare measurements throughout the world. There are primary
and secondary standards. Primary standards are standards upon which all other standards are
derived. Somewhere in France for instance there is the primary standard for the kilogram. It is a
block of metal that has a mass of 1kg. Laboratories throughout the world have copies of this
standard so they have secondary standards. All standards duplicated from primary standards are
called secondary standards.
Friday September 9
Definitions
Atoms are the smallest type of particle that demonstrates chemical properties. By
chemical property we mean that they react to form compounds. Atoms have electrons
and a nucleus and are neutral or without charge.
Ions are negatively or positively charged atoms with excess number of electrons or a
deficiency of electrons respectively.
Molecules are combinations of like or unlike atoms. Cl2 is a molecule of chlorine gas.
So is ClBr a molecule. Molecules are held together by covalent bonds. The adjacent
atoms share electrons.
Single Element is a substance that has just chemically one type of atom. All atoms
have the same atomic number or the same number of protons. However elements
have different isotopes with different numbers of neutrons.
A compound is a combination of two or more different types of atoms. BrCl is a
compound.
The Mole and Avogadro’s Constant
Most chemists are not interested in the mass of a single atom or molecule. Atoms and molecules are
too small for practical lab work. That is why chemists use the mole. It allows them to use their
balance to do laboratory work. Chemical reactions depend on the relative amounts (moles) of
molecules or atoms so it makes sense to use relative masses in the laboratory. Take as an example
the following chemical reaction
2H2+O2=2H2O
This is the balanced equation for the formation of water from oxygen molecules and hydrogen
molecules. Now the equation also says that 2 molecules of hydrogen react with 1 molecule of
oxygen to form 2 molecules of water. For most laboratory chemists this equation is read 2 moles of
hydrogen molecules react with 1 mole of oxygen molecules to form 2 moles of water molecules. Let
us imagine that we can use a balance to find the mass of 1 mole of oxygen molecules and 2 moles of
hydrogen molecules. What mass in grams contains 2 moles of hydrogen molecules and what mass
in grams contains 1 mole of oxygen molecules?
When discussing the mole and Avogadro’s constant we are discussing the number of particles in a
given sample. A mole of anything whether it is jelly beans or atoms has an Avogadro’s number of
particles. Avogadro’s number is 6.02x1023 particles. This number is critically dependent on the
standard kilogram sample which is stored in France. If the kilogram was originally defined to be a
different value than it is now, Avogadro’s number would have a different value. To see how this
number, 6.02x1023 was derived consider the following. A mole is the amount of substance that
contains the same number of atoms or molecules (chemical species) as there are atoms in
12grams of the pure isotope Carbon-12. A mole of this isotope of carbon is defined to have a
mass of 12 grams exactly. Carbon found naturally is actually a mixture of several isotopes so its
relative mass is 12.01 on the periodic table. The value 12.01 is a weighted average. The mass of all
the stable isotopes of all the elements in the periodic table are measured relative to Carbon-12. Note
that the masses on the periodic table have no units. It is only when we measure an element in grams
with the same numerical value as in the periodic table that we get moles with Avogadro’s number of
atoms. The values in the periodic table have no units because they are derived from ratios of mass.
These numbers are named atomic mass units or abbreviated u or amu and are not units.
All of the elements listed on the periodic table come in different types called isotopes.
Different isotopes of a single element differ by the number of neutrons they have. For instance what
we call hydrogen comes as three isotopes: proteum, deuterium and tritium. That means that
hydrogen gas is a mixture of three isotopes. In fact hydrogen gas is really a mixture of 2 isotopes
because tritium is so unstable. Hydrogen gas consists of a little bit of deuterium and mostly
proteum. The chemical properties of the 3 isotopes are identical. Each reacts to form water with
oxygen. Deuterium has about 2x the mass of proteum and tritium has about 3x the mass of proteum.
Remember that there is very little deuterium in hydrogen gas so the average mass of a hydrogen
atom increases to a relative value of 1.01. This is also a weighted average. A mole of hydrogen
atoms is 1.01grams.
Here is a way of looking at the average atomic mass; the masses listed in the periodic table. We
will use copper (Cu) as an example. Copper has 2 stable isotopes- Copper-63 and Copper -65.
Isotope
Percentage
or
Abundance
Mass of a single atom
Copper-63
Copper-65
69.09%
30.91%
1.045x10-22grams
1.078x10-22grams
Mass of Avogadro’s
Number of Atoms,
relative gram molecular
mass, Ar in grams
62.93grams
64.94grams
Average Mass of 1 Cu Atom=0.6909x1.045x10-22+0.3091x1.078x10-22=1.0552x10-22grams
Average Mass Avogadro’s number of
Cu Atoms=Average Mass
1 Cu Atom x Avogadro’s Number= 1.0552x10-22x6.022x1023=63.53grams
A simpler way and the way you should calculate the average atomic mass is as follows:
Average Mass of Avogadro’s number of
Cu atoms=0.6909x62.93+0.3091x64.94=63.53grams
63.53grams of Cu has the two isotopes in correct proportions or abundance and the total number of
atoms is Avogadro’s number.
We still need to find the number of particles in a mole. There are at least 2 ways to do this. The
first is to count electrons in an electric circuit where we produce a metallic element from a solution
of its ions. We then determine how much mass formed for a given total charge. The mass of the
element gives the number of moles of the element and the number of electrons used is just the
current x time/charge on a single electron. We also need to know how many electrons were
transferred to form each metal atom. Was it 1 or 2 electrons? If we know the total current and total
charge for the experiment how many electrons total?
The most advanced method for finding Avogadro’s number uses a polished silicon ball (Si) and
uses x-ray diffraction to determine the spacing of the atoms in the ball. From the spacing of the
silicon atoms the total number of atoms in the ball is determined. The ball is fabricated to mass at
1kg. The mass of a mole of Si is 28.09g. This is not very precise but for our purposes illustrates our
point. From the number of atoms in a 1kg ball of silicon using x-ray diffraction we can then
determine the number of atoms in 28.09g of silicon.
You might want to consider whether the relative average masses given in the periodic table are
universal. What I mean is: Are the % for each of the isotopes of an element the same throughout
the world and the universe?
Molar Masses of Compounds
We can now calculate the mass of molecules using the average atomic mass in grams.
Example: What is the average molar mass of CO2 in grams?
12.01gram+16.01gramx2=44.03gram
Example:
You are given a 10.2gram sample of CO2. How many moles is this?
Solution:
10.2
moles =0.231moles
44.03
Example: How many molecules of CO2 is this?
0.231molex6.02x1023 molecules/mole=1.39x1023 molecules
What is the relative molecular molar mass Mr for a molecule such as methanol, CH3OH? Ethanol,
CH3CH2OH?
Empirical and Molecular Formulae
The formula of a single molecule is called its molecular formula.
Empirical Formulae-However some compounds are not molecules such as NaCl and
sometimes a chemical analysis can only yield information about the ratio of atoms in a
substance so the formula can give no information about the molecular nature of the
substance.
Example-Suppose we do an analysis of a hydrocarbon liquid and we find the
following analysis:
7.76% hydrogen
92.24% carbon
This would lead us to conclude there are 6 moles of hydrogen and 6 moles of carbon
in 100grams of the substance. The molar ratio is 1:1 or 2:2 or 3:3 or 55:55 ad
infinitum. Having no more information we would use the empirical formula CH and
ignore the other formulae. Further analysis some time later might indicate this
substance is in fact made up of molecules of benzene which has a carbon hexagon.
Now we can assign a molecular formula C6H6. Its empirical formula is still CH.
Example: What is the formula of sodium chloride. Sodium chloride is not composed
of molecules and the atom ratio is 1:1 so we use the empirical formula NaCl.
Note that many times you cannot tell whether a formula is empirical or molecular by
just looking at the formula. Words must be used.