The Mole and Avogadros Number

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The Mole and Avogadros Number Dr Graeme Jones
LECTURE 3
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The Mole

• Derived from the Greek word Mole meaning large
  heap.

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The Mole

• The Chemical Mole is a heap of atoms or
  molecules.

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Dalton

• In 1808 Dalton proposed that the atoms of each
  element had a characteristic atomic weight, and
  that it was atoms that were the combining units
  in chemical reactions to make compounds.

• Dalton had no method of measuring atomic weights
  unambiguously, so made the incorrect assumption
  that in the most common compound between two
  elements, there was one atom of each element e.g.
  water was made from one atom of hydrogen and one
  of oxygen, oxygen gas contained only one atom of
  oxygen

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Dalton

• In 1808 Dalton proposed that the atoms of each
  element had a characteristic atomic weight, and
  that it was atoms that were the combining units
  in chemical reactions to make compounds.

• Dalton had no method of measuring atomic weights
  unambiguously, so made the incorrect assumption
  that in the most common compound between two
  elements, there was one atom of each element e.g.
  water was made from one atom of hydrogen and one
  of oxygen, oxygen gas contained only one atom of
  oxygen

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Gay-Lussac

• Gay-Lussac studied the chemical reactions of
  gases, and found that the ratios of volumes of
  the reacting gases were small integer numbers,
  e.g. two volumes of hydrogen react with one
  volume of oxygen to produce two volumes of water.
• Dalton couldnt reconcile this with his new
  atomic theory, and therefore rubbished the work
  of Gay-Lussac.

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Avogadro

• In 1811, Avogadro clearly drew the distinction
  between a molecule and a atom.
• He pointed out that Dalton had confused the
  concepts of atoms and molecules. The Dalton
  atom" of oxygen gas was in reality a molecule
  containing two atoms of oxygen.
• Avogadro also suggested that equal volumes of
  all gases at the same temperature and pressure
  contain the same number of molecules. This is
  now known as Avogadro's Principle.
• Avogadro was Italian so everybody ignored his
  work until Stanislao Cannizarro showed how it
  could be used to determine molar and indirectly
  atomic masses at the Karlsruhe Conference in
  1860.

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The Mole Argument

• From atomic masses one atom of magnesium is twice
  as heavy as one atom of carbon (Mg 24 and C
  12). Therefore
• If one atom of Mg is twice as heavy as one atom
  of C then 1000 atoms of Mg are twice as heavy as
  1000 atoms of C etc.
• a piece of Mg twice as heavy as a piece of C must
  contain the same number of atoms e.g. 2 tonne of
  Mg contains the same number of atoms as 1 tonne
  of carbon
• Therefore the relative atomic mass of any element
  in grams contains the same number of atoms
• This number of atoms is known as the Mole

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Extend this to molecules

• molecules are made up of atoms in different
  ratios
• the relative molecular mass of a molecule in
  grams contains one mole that specific molecule

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Definitions

• One Mole is the amount of substance containing
  the same number of units are there are atoms in
  exactly 0.012 kg of 12C.
• The substance must be specified and may be atoms,
  molecules, ions, crystals, grains of sand, flies,
  sheep, trucks, dollys, anything
• Avogadros Number is the number of units in a
  mole
• It is given the symbol L and is 6.022 1415 x 1023

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Avogadro constant NA, L

• from the National Institute of Science and
  Technology NIST website http//physics.nist.gov/cu
  u/Constants/
• Value 6.022 1415 x 1023 mol-1  
• Standard uncertainty 0.000 0010 x 1023 mol-1   
• Relative standard uncertainty  1.7 x 10-7  
• Concise form 6.022 1415(10) x 1023 mol-1    

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Why is it called Avogadros Number

• Avogadro himself never determined Avogadros
  number
• The first person to determine it was the Austrian
  Loschmidt in 1865 and in German speaking
  countries it was known for many years as
  Loschmidts constant
• Avogadro's Number was coined in a paper written
  by Jean Baptiste Perrin in 1909 in which he
  stated "The invariable number N is a universal
  constant, which may be appropriately designated
  "Avogadro's Constant."

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How to find Avogadro Number

• Mid C19 kinetic theory of gas measurements
• Late C19 Sedimentation measurements of colloidal
  particles.
• Early C20 Mullikan's oil drop experiment
• Current from the density of a crystal, the
  relative atomic mass, and the unit cell length,
  determined from x-ray methods. The crystal must
  be free of defects, Si is commonly used.

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So What?

• What is difficult to grasp is the size of
  Avogadros number, 6.022 1415 x 1023 , that is
• 602 214 150 000 000 000 000 000
• Basically if you can see a particle with your
  naked eye you wont be able to gather together a
  mole of it on this earth
• A mole of coke cans would cover the earth to a
  depth of over 200 miles
• Counting at a rate of 10 million per second, it
  would take about 2 billion years to count all the
  atoms in one mole
• What it means is that molecules are really very
  very small and there are just unbelievable
  numbers of them

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Mole Calculations

• The molar mass of an element or compound is the
  same as the atomic or molecular mass (as
  appropriate) but is a more general term. The
  molar mass of a particular substance contains
  6.022 x 1023 atoms or molecules. The symbol for
  the molar mass is M and the units are g/mol.
• Example H2S
• Mr (1x2) 32 34
• M 34 g/mol
• 32 g of H2S is one mole of H2S and therefore
  contains 6.022 x 1023 molecules of H2S

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Mole Calculations (I)

• The number of moles of a substance is defined as
  the amount of substance, n. To calculate n, just
  divide the mass of the substance, m, by the molar
  mass, M.

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Mole Calculations (II)

• To calculate the number of atoms or molecules
• number of atoms or molecules n x L

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Examples

• Calculate the number of atoms in 2x10-3 g of
  Calcium
• Calculate the number of moles and molecules of
  H2O in a snowflake weighing 12 mg
• Calculate the mass of 8.5 moles of HCl
• Estimate how many molecules it takes for one hair
  to grow for one second?