claculate the number of atoms in 23 moles of gold
Answers
One mole of anything, including atoms, is
6.022
×
10
23
(Avogadro's number) of them. Usually you will have a given mass of an element. There are two basic steps to get from the given mass to the number of atoms. They are:
Mass
→
Moles
and
Moles
→
Atoms
The following example will show you how to do that.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Example:
How many atoms of gold are in
58.27 g
of gold?
The periodic table shows us that gold, Au, has the atomic weight
196.967 u
. This means that its molar mass is
196.967 g/mol
.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
First Step: Mass
→
Moles
To calculate moles of Au, multiply the given mass by the reciprocal of the molar mass.
58.27
g Au
×
1
mol Au
196.967
g Au
=
0.295836 mol Au
I'm keeping a couple of guard digits to reduce rounding errors. The final answer will be rounded to four significant figures.
Second Step: Moles
→
Atoms
To calculate atoms of Au, multiply moles Au by Avogadro's number.
0.295836
mol Au
×
6.022
×
10
23
atoms Au
1
mol Au
=
1.782
×
10
23
atoms Au
rounded to four significant figures due to
58.72 g
So, if you are given the mass of an element, you use the periodic table to find its molar mass, and multiply the given mass by the reciprocal of the molar mass. This is
Mass
→
Moles
.
Once you have moles, multiply by Avogadro's number to calculate the number of atoms. This is
Moles
→
Atoms
.