The Mole Concept

1
The Mole Concept

• Goal To develop the concept of the mole as a
  useful measurement and to apply this in
  calculations involving mass and volume.

2
Objectives

• 1. Define the mole in terms of Avogadro's number,
  formula mass or molecular mass.
• 2. Given the number of moles, determine the
  number of molecules of a covalent compound,
  formula units of an ionic compound or atoms of an
  element.
• 3. Given the number of particles present in a
  sample, determine the number of moles.
• 4. When given the formula, calculate the
  molecular mass of a covalent compound or the
  formula mass of an ionic compound.
• 5. Given the number of moles in a substance,
  determine the mass of the substance.
• 6. Given the mass of a substance, determine the
  number of moles of the substance.
• 7. When given the formula, calculate the
  percentage composition of each of the elements in
  the compound.

3
Molecular and Formula Mass

• Molecular Mass is determined by the sum of the
  atomic masses of each element in a compound.
• The atomic mass of hydrogen in atomic mass units
  is 1, and the atomic mass of oxygen is 16.
• Therefore, the total mass of a water molecule,
  H2O, is 1116, or 18 amu.
• This name is incorrect when applied to an ionic
  substance.
• E.g. Sodium chloride, NaCl, is an ionic
  substance which does not exist in molecular form.
  
• A better name for the mass of ionic substances is
  formula mass.
• Formula mass is determined by the sum of the
  atomic masses of all atoms in the formula unit of
  an ionic compound.

4
EXAMPLE Formula Mass

• Find the formula mass of sodium sulfate, Na2SO4.
• Solving process
• Add the atomic masses of all the atoms in the
  Na2SO4 unit.
• 2 Na atoms, 2 x 23 46 amu
• 1 S atom, 1 x 32 32 amu
• 4 O atoms, 4 x 16 64 amu
• The total formula mass 142 amu

5
EXAMPLE Formula Mass

• Find the formula mass of calcium nitrate,
  Ca(NO3)2
• Solving process
• Add the atomic masses of all the atoms in the
  Ca(NO3)2 formula unit. Remember that the
  subscript applies to the entire polyatomic ion.
• 1 Ca atom, 1 x 40 40 amu
• 2N atoms, 2 x 14 28 amu
• 6 O atoms, 6 x 16 96 amu
• Total formula mass is 164 amu

6
Groups of Atoms

• There is one problem in using the molecular and
  formula masses of substances.
• These masses are in atomic mass units, which is
  only 1.66 x 10-24 g.
• The mass of a single molecule is so small that it
  is impossible to measure it in the laboratory.
• For everyday use in chemistry, a larger unit,
  such as a gram, is needed.
• One helium atom has a mass of 4 amu, and one
  nitrogen atom has a mass of 14 amu. The ratio of
  the mass of one helium atom to one nitrogen atom
  is 4 to 14, or 2 to 7.
• No matter what number of atoms we compare, equal
  numbers of helium and nitrogen atoms will have a
  mass ratio of 2 to 7.
• In other words, the numbers in the atomic mass
  table give us the relative masses of the atoms of
  the elements.

7
Avagadros Number

• The standard laboratory unit of mass is the gram.
  
• We would like to choose a number of atoms which
  would have a mass in grams equivalent to the mass
  of one atom in atomic mass units.
• The same number would fit all elements since
  equal numbers of different atoms always have the
  same mass ratio.
• Chemists have found that 6.02 x 1023 atoms of an
  element have a mass in grams equivalent to the
  mass of one atom in amu.
• E.g. 1 hydrogen atom has a mass of 1.0079 amu
• 6.02 x 1023 atoms of hydrogen have a mass of
  1.0079 g.
• This number, 6.02 x 1023 is called Avogadro's
  Number in honor of a 19th century Italian
  scientist.

8
What is the Mole?

• 6.02x1023 atoms of an element 1 mole of that
  element
• E.g. 6.02x1023 atoms of Na 1 mole of Na
• 6.02x1023 molecules of a compound 1 mole of
  that compound
• E.g. 6.02x1023 molecules of NaCl 1 mole of NaCl

9
Mole Trivia

• If there were a mole of rice grains, all the land
  area in the whole world would be covered with
  rice to a depth of about 75 meters.
• One mole of rice grains is more grains than all
  the grain that has been grown since the beginning
  of time. (1)
• One mole of rice would occupy a cube about 120
  miles on an edge! (1)

10
Mole Trivia

• A mole of marshmallows would cover the United
  States to a depth of 600 miles (3)
• In order to put a mole of rain drops in a 30
  meter (about 100 feet) diameter tank, the sides
  of the tank would have to be 280 times the
  distance from the Earth to the Sun. (4)
• A mole of hockey pucks would be equal to the mass
  of the Moon.

11
Mole Trivia

• Assuming that each human being has 60 trillion
  body cells (6.0 x 1013) and the Earth's
  population is 6 billion (6 x 109), the total
  number of living human body cells on the Earth at
  the present time is 3.6 x 1023 or a little over
  half of a mole.

12
Mole Trivia

• If one mole of pennies were divided up among the
  Earth's population, each person would receive 1 x
  1014 pennies. 
• Personal spending at the rate of one million
  dollars a day would use up each persons wealth in
  about three thousand years. 
• Life would not be comfortable because the surface
  of the Earth would be covered in copper coins to
  a depth of at least 400 meters.

13
Mole Trivia

• If you had a mole of pennies and wanted to buy
  kite string at the rate of a million dollars per
  inch, you would get your money's worth.
• After stretching your string around the Earth one
  million times, and to the Moon and back
  twenty-five times, you would have enough string
  left over to sell back at a dollar an inch (a
  decided loss) to gain enough money to buy every
  man, woman and child in the US a 50,000
  automobile and enough gasoline to run it at 55
  mph for a year. 
• After those purchases, you would still have
  enough money left over to give every man, woman,
  and child in the whole world about 5000.

14
Mole Trivia

• Basis for calculations
• Earth's circumference 25,000 miles              
   
• Distance to moon 240,000 miles
• Cost of gasoline 2.50 per gallon
• Gasoline mileage 20 miles per gallon
• U.S. population 220,000,000
• World population 6,000,000,000

15
Calculating Molecular Mass

• 1. Calculate the molecular or formula masses of
  the following compounds, all in amu (g/mol)
• a. C2H6
• Amu30
• b. SiCl4
• Amu170
• c. MgCO3
• Amu84
• d. Ca3(P04)2
• Amu310

16
Calculating Molecular Mass

• Calculate the molecular or formula masses of the
  following compounds, all in amu (g/mol)
• K2S
• Amu110
• CH2CHCH2OH
• Amu58
• Pb3(As04)2
• Amu899
• C12H22011
• Amu342

17
Conversions

• Make the following conversions
• 1.00 x 1026 molecules of SnCl2 to moles.
• Ans 1.66 X 102 mol.
• 0.400 moles of H2O to molecules.
• Ans 2.41 X 1023 molecules.
• 76.0 grams CaBr2 to moles.
• Ans 0.380 mol. Or 3.80 X 10-1 mol.
• 18.0 grams HBr to moles.
• Ans 0.222 mol. Or 2.22 X 10-1 mol.

18
Conversions

• Make the following conversions
• 9.30 moles SiH4 to molecules.
• Ans 5.60 X 1024 molecules.
• Find the mass of one atom of Na.
• Ans 3.82 X 10-23g.
• Find the mass of one molecule of H2SO4.
• Ans 1.63 X 10-22 g.

19
Conversions

• Make the following conversions
• 9.30 moles SiH4 to grams.
• Ans 298 g.
• Find the mass of 1.405 mole of Na2SO4.
• Ans 199.5 g.
• Find the mass of one molecule of H2SO4.
• Ans 1.63 X 10-22 g.

20
Percent Composition

• 1 mole of NaCl is comprised of equal parts Na and
  Cl
• But Na and Cl have 23 g/mol and 35.45 g/mol,
  respectively!
• So they have differing percent composition
• The percent composition of Na is
• (molar mass Na) x 100
• molar mass NaCl
• Molar mass NaCl 2335.45 58 g/mol
• Na (23) x 100
• (58)
• Na 40
• Cl (35) x 100
• (58)
• Cl60
• So, while NaCl is equal parts NaCl by molar
  ratios, by mass, its a 60/40 split.

21
Percent Composition

• Find the percentage composition of the following
• CsF
• Ans 87.5 12.5.
• Bi203
• Ans 89.7, 10.3.
• BaH2
• Ans 98.6, 1.44.