Avogadro’s Hypothesis and the Mole
Avogadro’s Hypothesis
Recall from Unit 3 that John Dalton theorized how atoms combine to form
molecules. He assumed that hydrogen was the lightest element and assigned it an
arbitrary mass of 1 and so if oxygen weighed 16 times as much as hydrogen, it
would have a relative mass of 16. There are two reasons why Dalton’s method
were faulty. First, we now know that atoms of the same element can have
different masses. Second, he assumed that every compound contained only 1 of
each atom so different ratios were not accounted for.
At around the same time, French chemist Joseph Gay-Lussac experimented with
pairs of gases at the same temperature and pressure and found precise ratios of
reactants based on volume.
E.g. 1 L of hydrogen gas reacts with 1 L of chlorine gas to make 2 L HCl (g)
1 L of nitrogen gas reacts with 3 L hydrogen gas to make 4 L of NH3 (g)
Italian chemist Amadeo Avogadro proposed the following explanation for
Gay-Lussac’s data.
Avogadro’s Hypothesis: equal volumes of different gases at the same
temperature and pressure contain the same number of particles.
This means that 1 L of hydrogen gas contains the same number of atoms as 1 L of
chlorine gas and that 1 molecule of hydrogen gas reacts with 1 molecule of
chlorine gas. Avogadro was able to connect the volume, mass and the number of
particles of chemicals.
The Mole
A mole is the number of carbon atoms in exactly 12 g of 12C which is
experimentally measured to be 6.022 x 1023 called Avogadro’s Number or
Avogadro’s Constant. It is also the number of particles (atoms or molecules)
in one mole of any element or compound There are no units for Avogadro’s
Number because it is simply a number just like a dozen is 12 and a pair is 2.
We can write a conversion factor for mole just like we did for dozen and pair:
12__
__2__
1 dozen
1 pair
6.022 x 1023
1 mole
However, unlike the first two, Avogadro’s Number is a measured number not an
exact number so its significant figures must be accounted for in calculations.
Practice: How many molecules are there in 0.125 mol of molecules?
How many moles of H2O are there in 54.478 x 1023 molecules?
Molar Mass
The molar mass is the mass of one mole of (6.022 x 1023) particles. The molar mass
of an element is the same as the atomic mass shown on the periodic table,
expressed in grams.
To find the molar mass (mass per mole) of a monatomic element, simply look at
the periodic table. For the molar mass of a compound, we would need to add the
molar mass of every atom in the compound together.
Example: Find the molar mass of a molecule of H2O.
H2O has 2 hydrogen atoms with a molar mass of 1.0079 g each and an oxygen
atom with a molar mass of 15.9994 g
Molar mass of H2O = 2(1.0079 g) + 1(15.9994 g) = 18.0152 g/mol
Practice: Find the molar masses of C12H22O11 and (NH4)2SO4
Once we find the molar mass of an element or compound, we can use it as a
conversion factor for converting between moles and mass.
Practice: How many moles of H2O are there in 60.00 g? How many grams in 2.25
mol?
Converting Between Particles, Moles and Mass
We have just learned how to convert between particles and moles using
Avogadro’s Number as well as converting between moles and mass using molar
mass. Now, we can connect the two together and convert between particles and
mass by using both conversion factors.
Practice: How many grams of Ca(OH)2 are there in 13.495 x 1023 molecules?
How many molecules of nitrogen gas are there in 30.491 grams?
Mole Y
Diagram
Fill in the conversion factors needed to “mole-tiply” and convert
between mole, mass, volume and particles.