The Mole

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The Mole

• Mrs. CoyleHonors Chem

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-How do we measure chemical quantities?-What
units of measure do we use?
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Atomic Mass Unit (amu)

• 1/12 of the mass of a 12C atom

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Relationship of amu to gram

• 1 amu 1.66054 x 10 -24 g

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Atomic Mass

• The average of the masses of the naturally
  occurring isotopes of an element weighted
  according to their abundances.

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Atomic Mass of 12C 12 amu 1.992648x10-23g
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Why the Mole?
Are the quantities scientists use on a lab scale
at the level of the atom or at the level of
grams?
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Why not use a unit measure that uses the
quantities equal to the atomic masses of the
elements, but measured (expressed) in grams.

• The Solution

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• One mole of atoms of an element is contained
• in an amount of the element
• equal to its atomic mass
• measured in grams.
• This mass is called molar mass.

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Molar Mass

• The mass in grams of one mole of a substance.
• For an element, it is the atomic mass expressed
  in grams.
• Example for Neon,
• Atomic Mass 20.18 amu
• Molar Mass 20.18 g
• Other names used traditionally for molar mass
  are molecular weight and gram formula mass.

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The Definition of The Mole

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

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How many atoms are there in 12 g of C-12 ?
6.022145 x 1023 atoms1 mole of atoms
(mol)Avogadros Number
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Avogadros 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.

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Question

• How can 12g of C-12 have the same of atoms as
  1.008g of H?

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Solution

• 1 atom of Hydrogen has an atomic mass of 1.008
  amu.
• 1 atom of Carbon-12 has an atomic mass of 12
  amu.
• 1 atom C-12 12 amu 12
• 1 atom H 1.008 amu 1.008
• 6.022x1023 atoms C-12 12 g 12
• 6.022x1023 atoms H 1.008 g 1.008

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Relationship of amu to gram revisited

• For C-12
• (6.022x1023 atoms)(12amu)12 g
• atom
• 6.022x1023amu 1 g

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Problem 1

• What is the mass in grams of 7 atoms of Neon?
• Solution
• (7 atoms)( 20.18 amu/atom) 141.26 amu
• 141.26 amu x 1 g
  2.35x10-22g
• 6.022x1023amu

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Atom vs Mole of Atoms of Hydrogen
Atomic Mass Molar Mass Number of Atoms
1 atom 1.008 amu 1.67382432x10-24 g 1
1 mole 1.008 g 6.022 x 1023
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Molecule vs Mole of Molecules of Hydrogen
H2 Molecular Mass Molar Mass Number of Molecules
1 molecule 2.016 amu 1
1 mole 2.016 g 6.022 x 1023
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Mathematical Relationships

• mol Mass of Sample (g)
• Molar Mass (g/mol)
• particlesmol x 6.022 x10 23 particles/mol
• 1 g 6.022x1023amu

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Problem 2

• For a sample of 20.0g of iron, Fe, calculate
• a) the number of moles of atoms
• b) the number of atoms
• Solution
• mol Fe mass Fe(g) 20g Fe
  molar mass Fe(g/mol) 55.85g/mol
• mol Fe 0.358 mol Fe atoms

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Problem 2 Contd

• 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

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Problem 3

• For a sample of 150.0 g of H2SO4, calculate
• The number of moles of molecules of H2SO4
  present.
• 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

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Problem 3

• mol H2SO4 Mass (g) 150.0g H2SO4
• MM (g/mol) 98.09g/mol
• mol H2SO4 1.529 mol H2SO4 molecules

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Problem 3 Contd

• b)
• atoms of O (mol O)(6.022x1023 atoms)
• (4 x 1.529 mol O) (6.022x1023 atoms)
• 3.683 x1024 atoms O

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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

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• For an ideal gas at STP
• mol Volume (L)
• 22.4 (L/mol)

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Problem 4

• How many atoms of oxygen are there in 44.8L of
  oxygen gas?
• 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

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