The Mole

The Mole

6.022 x 1023

The Mole is a Unit of Measure

• Dozen

• Pair

• Gross

• Ream

• How many pieces of paper in 10 reams?

• 10 reams x 500 pieces/ream = 5,000 pieces

The Mole is a Unit of Measure

• How many cell phones in five moles of cell phones?

• 5 mol x 6.022x1023/mol =

• 3.011 x 1024 cell phones

• But why would we ever use such a large unit as the Mole?

• Because ATOMS ARE tiny

Background: atomic masses• Look at the “atomic masses” on the periodic table.

What do these represent? E.g. the atomic mass of Carbon is 12.01 (atomic # is 6)

• We know there are 6 protons and 6 neutrons in C-12

• Protons and neutrons have roughly the same mass of about 1.66 x10-24 grams

• Set this mass equal to 1 amu (atomic mass units). • Carbon-12 thus has a mass of 12 amu. • The atomic mass shown on the Periodic Table is a

weighted average of masses of all isotopes of an element

• But more useful to associate atomic mass with a mass in grams.

The Mole• Scientist set out to develop a basic

unit of measurement to convert from atomic mass to grams.

• Used Carbon-12 to set the standard. Scientists set one mole = the number of atoms of C-12 in 12 grams of C-12.

• Experiments show that there are 6.022 x 1023 carbon atoms in 12 grams of Carbon-12.

• 6.022 x 1023 things is a “mole” of any thing!

• Also known as “Avogadro’s number”

Who wants to be a Mollionaire?

Q: how long would it take to spend a mole of $1 bills if they were being spent at a rate of one billion per second?

A: $ 6.02 x 1023 bills x sec/$1,000,000,000 bills= 6.02 x 1014 payments = 6.02 x 1014 seconds

6.02 x 1014 seconds / 60 = 1.003 x 1013 minutes

1.003 x 1013 minutes / 60 = 1.672 x 1011 hours

1.672 x 1011 hours / 24 = 6.968 x 109 days

6.968 x 109 days / 365.25 = 1.908 x 107 years

A: It would take 19 million years

Molar mass• The mass of one mole of something is called its “molar mass”.• Since one atom of C-12 = 12 amu and one mole of C-12 = 12 grams,

we can use atomic masses to directly convert from amu/atom to grams/mol.

• For an element, molar mass = Atomic Mass from Periodic Table, but use g/mole rather than amu

Example: Lithium’s atomic mass = 6.94 amuThus, 1 mole of Li = 6.94 g LiThis is expressed a molar mass of “6.94 g/mol”Sometimes referred to as “gram formula mass”

Molar mass• What are the following element molar masses?

S Ag• For a compound, molar mass = sum of molar

masses of each element times the number of atoms of that element in the compound.CO2

=32.06 g/mol = 107.9 g/mol

= 44.00 g/mol

C x 1 = 12.01 x 1 = 12.01O x 2 = 16.00 x 2 = 32.00

44.00

Molar Mass Calculations• Determine the mass in grams of:

1.2.0 mol of Au

2.4.37 mol of Zn

• Determine the number of moles of:

1.254 g of Cu

2.12 g of Na

2.0 mol Au x 196.9 g/mol = 3.9 x 102g

4.37 mol Zn x 65.4 g/mol = 2.85 x 102g

254g Cu x mol/63.5g = 4.0 mol Cu

12g Na x mol/23.0g = 0.52 mol Na

Molar mass• Cu3(BO3)2

Calculate molar masses (to 2 decimal places) CaCl2 (NH4)2CO3

O2

C6H12O6

110.98 g/mol (Ca x 1, Cl x 2)96.11 g/mol (N x 2, H x 8, C x 1, O x 3)32.00 g/mol (O x 2)

180.18 g/mol (C x 6, H x 12, O x 6)

Cu x 3 = 63.55 x 3 = 190.65B x 2 = 10.81 x 2 = 21.62O x 6 = 16.00 x 6 = 96.00

308.27

=308.27 g/mol

Comparing sugar (C12H22O11) & H2O

No, sugar has more (45:3 ratio)

Yes (6.02 x 1023 in each)

Yes.

No, molecules have dif. masses

No, molecules have dif. sizes.

1 mol each

Yes, that’s what grams are!

mass?

No, they have dif. molar masses# of moles?

No, they have dif. molar masses

# of molecules?

No# of atoms?

No, they have different densities.volume?

1 gram eachSame

Converting between grams and moles• If we are given the # of grams of a compound we

can determine the # of moles, & vise-versa• In order to convert from one to the other you must

first calculate the molar mass (g/mol)•Then use dimensional analysis to convert:

moles to grams: mol x g/mol = g grams to moles: g x mol/g = mol

•This can be represented in an “equation triangle”

g

mol g/mol÷x

Converting between grams and moles

g= g/mol x mol0.25HCl

53.15H2SO4

3.55NaCl1.27

Equationmol (n)gg/molFormula9.136.46

mol= g x mol/g0.541998.08g= g/mol x mol20758.44mol= g x mol/g0.020063.55

g

mol g/mol÷x

First: Determine the compound’s molar mass (g/mol) using the Periodic Table.

Cu

Empirical and molecular formulaConsider NaCl (ionic) vs. H2O2 (covalent)

Cl Na

Na Cl

Cl

Cl

Na

Na

• Chemical formulas are either “simplest” (a.k.a. “empirical”) or “molecular” (all bonded atoms).

• Ionic compounds are always expressed as the simplest ratio of the ions (formula units like NaCl or Li2O). Thus ionic formulas are always empirical.

• Covalent compounds can be shown as either molecular formulas (e.g. H2O2) or empirical (e.g. HO)

HOO

H HOO H H

OO H