The MoleMrs. Coyle Chemistry

Part I

• The Mole

• Molar Mass

• Moles <->Particles

-How do we measure the mass of chemical quantities?

-amu’s-grams-moles

Atomic Mass Unit (amu):

= 1/12 of the mass of a 12C atom

Relationship of amu to gram

1 amu = 1.66054 x 10 -24 g

Atomic Mass:

-The weighted average of the masses of the naturally occurring isotopes of an element.

-The atomic mass of an element is listed on the periodic table.

Why the Mole?

Are the quantities scientists use on a lab scale at the level of

the atom

or

at the level of grams?

The Mole = 6.02 x 1023

One mole of atoms (6.02x1023 atoms) of an element

is contained

in an amount

equal to its atomic mass

measured in grams.

This mass is called molar mass.

Molar Mass of an Element: an amount equal to

the atomic mass of the element expressed in grams.

• Example: for Neon, Atomic Mass = 20.18

amu Molar Mass = 20.18 g

Molar Mass of a Compound:an amount equal to the molecular mass

expressed in grams.

Also known as, Gram-Formula Mass, Molecular Weight.Examples:

• What is the molar mass of:

• H2O

• H2SO4

• Mg(NO3)2

• CuSO4 ∙ 5 H2O

The Definition of The Mole

The mass of an element or compound that contains as many elementary (representative) particles (atoms, molecules, ions, etc.) as there are atoms in exactly 12 grams of 12C.

How many atoms are there in 12 g of C-12 ?

6.022145 x 1023 atoms

1 mole of atoms (mol)Avogadro’s Number

Avogadro’s Number

• Can be used the same way the word “dozen” is used to mean 12 for any object.

• One mole of books is 6.022x1023 books, just like a dozen books is 12 books.

“Mole of Atoms of Hydrogen”

1 atom Atomic Mass:1.008 amu

1 mole of atoms:

6.022 x 1023 atoms

Molar Mass: 1.008 g

“Mole of Molecules of Hydrogen”

1 molecule=2 atoms

Molecular Mass: 2.016 amu

1 mole of molecules=

6.022 x 1023 molecules=

2x6.022 x1023atoms

Molar Mass: 1.008 g

Problem Solving Methods

• Using Mathematical Formulas

• Factor-Label Method

Mathematical Formulas

#mol= Mass of Sample (g)

Molar Mass (g/mol)

#particles=#mol x 6.022 x10 23 particles/mol

particles can be atoms, molecules, formula units, etc.

Equalities Used in Factor- Label Method

1 mol = Molar Mass g

1mol= 6.022 x10 23 particles (atoms, molecules, formula units, etc)

Problem # 1- Moles to Atoms

• How many atoms are there in 6 moles of Fe?

Solution using Factor-Label Method

• 6 mol of Fe x 6.02 x 1023 atoms Fe =

1 mol Fe

=3.6 x 10 24 atoms

Solution using Math Formula

• #atoms=#mol x 6.022 x10 23 atoms/mol=

=6 mol of Fe x 6.02 x 1023 atoms Fe/mol=

=3.6 x 10 24 atoms

Problem #2 –Moles to Atoms

• How many iron atoms are there in 6 moles of iron (III) oxide?

A: 7.2 x 10 24 atoms

Problem #3- Atoms to Moles

• How many moles of H2O are there in 18.06 x 10 23 molecules of H2O?

• A: 3 moles of H2O

Part II

• MolesMass Problem

Problem # 4 –Mass to Moles, Mass to Atoms

For a sample of 20.0g of iron, Fe, calculate:

a) the number of moles of atoms

b) the number of atoms

• Solution using Math Formula Method:

a) #mol Fe= mass Fe(g) = 20g Fe molar mass Fe(g/mol) 55.85g/mol

#mol Fe = 0.358 mol Fe atoms

Problem # 4 Cont’d

b)

#atoms Fe= #mol x (6.022 x 1023 atoms/mol)=

= (0.358 mol Fe)(6.022 x 10 23 atoms/mol)

#atoms Fe= 2.156x1023 atoms Fe

Problem # 5For a sample of 150.0 g of H2SO4, calculate:

a) The number of moles of H2SO4 present.b) The number of oxygen atoms present.

Solution:

MM H2SO4 = H: (2 atoms)(1.008g/mol)

S: (1 atom)(32.07g/mol)O: (4 atoms)(16.00g/mol)

98.09g/mol

Problem # 5

• # mol H2SO4 = Mass (g) =150.0g H2SO4

MM (g/mol) 98.09g/mol

# mol H2SO4= 1.529 mol H2SO4

Problem # 5 Cont’d

b)

#atoms of O = (#mol O)(6.022x1023 atoms)=

= (4 x 1.529 mol O) (6.022x1023 atoms) =

= 3.683 x1024 atoms O

Part III

• Molar Volume of an Ideal Gas at STP

Molar Volume of an Ideal Gas

• At STP conditions,

Standard Temp of 0 deg C and Standard Pressure of 1 atm,

the molar volume of an ideal gas

is

22.4 L

• For an ideal gas at STP:

#mol= Volume (L)

22.4 (L/mol)or

1mol = 22.4 L

Problem # 6-Volume to Atoms • How many atoms of oxygen are there in 44.8L of

oxygen gas at STP?• Solution:

#mol O2= Volume (L) = 44.8 L = 2.00 mol O2

22.4 (L/mol) 22.4 L/mol

#atoms O =#mol x 6.022 x10 23 atoms/mol

= 2 x (2.00mol O)(6.022 x10 23 atoms/mol)

#atoms O= 2.41 x 1024 atoms O

Problem #7- Molecules to Volume

• How many L at STP are contained in a sample of 8.6 x10 24 molecules of CO2 gas?

A: 320L

Part IV

• Density of a Gas at STP from Molar Mass.

Density

• D= Mass = Molar Mass

Volume Molar Volume

At STP,Molar Volume of an Ideal Gas = 22.4 L

Problem #8- Density of a Gas from MM

• What is the density of NO2 gas at STP?

• A: 2.05g/L