UNIT 2

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UNIT 2 QUANTITATIVE CHEMISTRY

• (I.E. IN COMES THE MATHS!! Bring a calculator!!)

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Scientific Notation A (very) brief introduction
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Stoichiometry

• The study of the relationships between the
  quantities of reactants and products involved in
  chemical reactions.
• Stoikheion element
• metron measure

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Proportions in compounds

• The composition of a compound depends on two
  things
• 1. The elements they are composed of
• 2. The quantities of each element.

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Law of definite proportions

• A specific compound always contains the same
  elements in definite proportions by mass.
• This is always constant even if produced other
  ways.

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Relative atomic mass and isotopic abundance (p80)

• Relative atomic mass the mass of an element
  that would react with a fixed mass of a standard
  element, currently carbon-12.
• One atomic mass unit (u) is described as 1/12 the
  mass of a carbon-12 atom.

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Atomic mass unit

• Now we know that it weighs
• 1 u 1.660 540 2 x 10-27 kg.
• This is the standard used world wide

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Isotopic abundance

• Some elements have isotopes. In calculating the
  relative atomic mass of an element with isotopes,
  the relative mass and proportion of each is taken
  into account. For example, naturally occurring
  carbon consists of atoms of relative isotopic
  masses C-12 (98.89) and-C 13 (1.11). Its
  relative atomic mass is 12.01 u.

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Isotopic abundance

• mc (98.89/100 x 12) (1.11/100 x 13)
• mc 11.8668 0 .1443 12.01 u
• No atom will contain 12.01 u. it is an average.

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Example

• Cl-35 75.53
• Cl-37 24.47
• (35 x .7553) (37 x .2447) 35.49 u
• Therefore the average atomic mass is 35.49u

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Atomic Mass and Molecular Mass

• Atomic Mass
• The mass of one atom of an element expressed in
  atomic units, u.
•  
• Molecular mass
• The mass of one molecule, expressed in atomic
  mass units, u.

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Example

• MNH3 1(mN) 3(mH)
• 1(14.01 u) 3(1.01 u)
• 17.04 u .
• Therefore, one molecule of ammonia has a mass of
  17.04 units.

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Formula unit of mass

• The mass of one formula unit of an ionic
  compound, expressed in atomic mass units, u

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Example

• NaCl 1(mNa) 1(mCl)
• 1 (22.99 u) 1(35.45 u)
• 58.44 u
• Therefore, one formula unit of sodium chloride
  has a mass of 58.44 units.

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The Periodic Table and the Mass of Elements

• The atomic number of a substance is written near
  the top of the symbol. This number tells the
  number of protons in the element.
• The Atomic mass is usually written near the
  bottom. This number is given as a numerical
  number of the elements mass. The mass of one mole
  of the element measured in grams.

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The Mole
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• It's not a spy, a machine for digging tunnels, a
  burrowing animal, or a spot of skin pigmentation
  - it's
• - a unit of measurement containing about
• 6.02 x 1023
• particles.
• Chemists created the mole as their own counting
  unit.

The Chemical Mole
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• 1 mole of atoms is
• 602, 214,199, 000, 000, 000, 000, 000
• atoms!
• (This is the number of Carbon atoms there are in
  12.01 g or Carbon)

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Avogadros Number

• 6.02 x 1023 particles / mole

When you say you have a mole, its kind of like
saying you have a dozen of something A dozen
donuts 12 donuts A dozen apples 12 apples A
mole of CO2 molecules 6.02 x 1023 molecules A
mole of Na atoms 6.02 x 1023 atoms
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Just How Big is a Mole?

• Enough soft drink cans to cover the surface of
  the earth to a depth of over 200 miles.
• If you had Avogadro's number of unpopped popcorn
  kernels, and spread them across the United States
  of America, the country would be covered in
  popcorn to a depth of over 9 miles.
• If we were able to count atoms at the rate of 10
  million per second, it would take about 2 billion
  years to count the atoms in one mole.

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Molar mass (g/mol) M

• the mass, in grams per mole, of one mole of a
  substance. The SI unit for a mol is g/mol
• Molar mass is conventionally abbreviated with a
  capital M. For elements it is numerically equal
  to the atomic mass and is often called atomic
  mass units.

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Steps to calculating molar mass

• Write the chemical formula of the substance
• Determine the number of atoms or ions of each
  element in one formula unit of the substance.
• Us the atomic molar masses from the periodic
  table and the amounts in moles to determine the
  molar mass of the chemical
• Write the molar mass in units of grams per mol
  (g/mol).

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Example

• Molar mass of copper(Cu) mass of 1 mol of Cu
  atoms
• M 63.546 g/mol Cu
• M mass of 6.022 x 10 23 atoms

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Example 2

• Molar mass of glucose (C6H12O6) mass of exactly
  1 mol of glucose molecules
• M (6 x C) (12 x H) ( 6 x O)
• M ((6 x 12.01 (C)) (12 x 1.01(H)) (6x 16.00
  (O)) ) / mol
• M ( (72.06 g) (12.12 g) (96.00g) ) / mol
• M ( 180.18 g) / mol
• M 180.18 g/mol
• Therefore, 1 mol glucose has a mass of 180.18 g
  and contains 6.022 x 1023 glucose
  molecules(C6H12O6)

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Important things to note

• Specify what is being measured
• Ex. molar mass of oxygen atom 16.00 g/mol
• Molar mass of oxygen molecules 32.00 g/mol
• When talking about oxygen we are normally
  referring to the diatomic molecule
• Since electrons have negligible mass compared to
  protons and neutrons, ions will essentially have
  the same mass as the atoms.

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Moles of Elements

• Why that number?
• 1 mole element (atomic mass) in grams of that
  element
• 1 mole C 12.011 g C
• 1 mole B 10.81 g B
• 1 mole Cu 63.55 g Cu
• i.e. atoms are teeny, teeny, tiny, teeny, itty,
  bitty things and it is not reasonable to talk
  about them in their atomic weights, but if scale
  them up to moles, then working with balanced
  chemical equations etc. becomes easier.

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Determine the mass one mole of the following in
grams

1. CO2
2. NaCl
3. K2CrO4
4. Fe(NO3)3

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The Mole and Molar Mass

• The Mole n
• Avogadros constant (NA) the number of
  entities in one mole 6.02 x1023
• Eg. 1 dozen oxygen atoms 12 oxygen atoms
• 1 mole oxygen atoms 6.022 x 1023 oxygen atoms

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Calculations involving Molar mass

• Amount in moles (n) mass(g)
• Molar mass(g/mol)
• The Magic Triangle
• n m / M
• m n x M
• M m / n

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GRASP method

• 1 Given What do you know? 
• 2 Required What do you want to know? 
• 3 Analysis What formula can you use? 
• 4 Solution Show your work 
• 5 Paraphrase State the answer in a sentence.

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Example

• Lets say that we are given 22 grams of graphite.
  How many moles do we have?

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• Lets say we want to know how much CaCl2 we need
  for a reaction that asks for 13.52 moles

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• You are given an unknown sample that has a mass
  of 32.04 grams, 2.000 moles. Find M.

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Practice

1. Determine the number of mol in 13.7 g of CO
2. What is the mass of 2.75 mol of C3H8

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Homework

• Page 86 5-7
• Isotopic Abundance and Mole calculations
  Worksheet

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Calculating Number of Entities
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Calculating Number of Entities (N) from Mass

• We are not able to count the number of atoms in
  reactions we must count them indirectly by
  measuring out a certain mass of a substance and
  calculating the number of moles.
• In order to estimate the number of entities in a
  large sample we need to take a small sample and
  find out the mass of a small number of entities.

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Calculating Number of Entities and Avogadros
number

• There are times when need to know exactly how
  many atoms are in something. This is especially
  true when dealing with gases as they change in
  pressure with temperature.
• To find the number of entities we use the formula
  

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• N nNA
• Number of entities ( of mols) x(Avogadro's )

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Example

• Find the number of atoms in 0.004 moles of water.
  
• Find the number of molecules in 30.0 g of Cl2 (g)

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Determining the number of particles in a mole
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Avogadros Number as Conversion Factor

• 6.02 x 1023 particles
• 1 mole
• or
• 1 mole
• 6.02 x 1023 particles
• Note that a particle could be an atom OR a
  molecule!

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Equation to find number of particles!
6.02 x 1023 particles 1 mole

• number of moles x
  number of particles

Example How many particles of sucrose are in
3.50 moles?
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Equation to find number of moles!

• number of particles x
  number of moles

1 mole 6.02 x 1023 particles
Example How many moles are contained in 4.50 x
1024 atoms of zinc?
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Learning Check

• 1. Number of atoms in 0.500 mole of Al
• 2.Number of moles of S in 1.8 x 1024 S atoms

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Molar Mass
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Molar Mass

• The Mass of 1 mole (in grams)
• Molar mass is equal to the atomic mass (look on
  the periodic table)
• 1 mole of C atoms 12.01 g
• 1 mole of Au atoms 196.97g
• 1 mole of Cu atoms 63.55 g
• Always round to the hundredths place.

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Mole to Mass Conversion
Where will you find the number of grams per mole?

• Number of moles x number of grams mass
• 1 mole
• Example Calculate the mass in grams of 0.0450
  moles of chromium.
• 0.0450 moles Cr x 52.0 g Cr 2.34 g Cr
• 1 mol Cr

The Periodic Table
Look at your Periodic Table
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Mass to Mole Conversion
Where will you find the number of grams per mole?

• Mass x 1 mole number of moles
• number of grams
• Example How many moles of calcium are there in
  525 grams of calcium?
• 525 g Ca x 1 mol Ca 13.1 mol Ca
• 40.1 g Ca

The Periodic Table
Look at your Periodic Table
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Mass to Atoms Conversion

• Two steps
• Use the mass to moles conversion
• Now calculate the number of atoms using the moles
  to particles equation.

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Example

• How many atoms of gold are in a pure gold nugget
  having a mass of 25.0 g?

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Atoms/Molecules and Grams

• How many atoms of Cu are present in 35.4 g of Cu?

35.4 g Cu 1 mol Cu 6.02 X 1023 atoms
Cu 63.5 g Cu 1 mol Cu
3.4 X 1023 atoms Cu
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Learning Check!

• How many atoms of K are present in 78.4 g of K?

78.4 g K 1 mol K 6.02 X 1023 atoms
K 39.1 g K 1 mol K
1.20 X 1024 atoms K
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Empirical and Molecular Formulas

• 11.4

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Percent Composition

• Mass of element x 100 percent by mass
• Mass of compound
• Example Determine the percent composition of
  NaHCO3.
• Determine the mass of each element first!
• mass element mass of element in 1 mol compound
  x 100
• molar mass of compound
• Percent Na 22.99 g Na x 100
  27.37 Na
• 84.01 g NaHCO3
• You have to complete this step for each element
  in the compound!!!!

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Determine the Percent Composition from the
Formula C2H5OH

• Divide the mass of each element by the molar mass
  of the compound and multiply by 100

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Types of Formulas

• Empirical Formula
• The formula of a compound that expresses the
  smallest whole number ratio of the atoms present.
• Molecular Formula
• The formula that states the actual number of
  each kind of atom found in one molecule of the
  compound.

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Determine the Empirical Formula of Acetic
Anhydride if its Percent Composition is 47
Carbon, 47 Oxygen and 6.0 Hydrogen

• Convert the percentages to grams by assuming you
  have 100 g of the compound
• Step can be skipped if given masses

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Determine the Empirical Formula of Acetic
Anhydride if its Percent Composition is 47
Carbon, 47 Oxygen and 6.0 Hydrogen

• Convert the grams to moles

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Determine the Empirical Formula of Acetic
Anhydride if its Percent Composition is 47
Carbon, 47 Oxygen and 6.0 Hydrogen

• Divide each by the smallest number of moles

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Determine the Empirical Formula of Acetic
Anhydride if its Percent Composition is 47
Carbon, 47 Oxygen and 6.0 Hydrogen

• If any of the ratios is not a whole number,
  multiply all the ratios by a factor to make it a
  whole number
• If ratio is ?.5 then multiply by 2 if ?.33 or
  ?.67 then multiply by 3 if ?.25 or ?.75 then
  multiply by 4

Multiply all the Ratios by 3 Because C is 1.3
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Determine the Empirical Formula of Acetic
Anhydride if its Percent Composition is 47
Carbon, 47 Oxygen and 6.0 Hydrogen

• Use the ratios as the subscripts in the empirical
  formula

C4H6O3
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Molecular Formulas

• The molecular formula is a multiple of the
  empirical formula
• To determine the molecular formula you need to
  know the empirical formula and the molar mass of
  the compound

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Determine the Molecular Formula of Benzopyrene
if it has a molar mass of 252 g and an
empirical formula of C5H3

• Divide the given molar mass of the compound by
  the molar mass of the empirical formula
• Round to the nearest whole number

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Determine the Molecular Formula of Benzopyrene
if it has a molar mass of 252 g and an
empirical formula of C5H3

• Multiply the empirical formula by the calculated
  factor to give the molecular formula
• (C5H3)4 C20H12