Chemical Quantities

1
Chapter 6

• Chemical Quantities

2
Homework

• Assigned Problems (odd numbers only)
• Questions and Problems 6.1 to 6.53 (begins on
  page 168)
• Additional Questions and Problems 6.59 to 6.77
  (page 190-192)
• Challenge Questions 6.79, 6.81 (page 192)

3
Counting Particles By Weighing

• If a person requests 500 quarter inch hexagonal
  nuts for purchase
• How would you count 500 hex nuts?
• You could count the hex nuts individually
• Or, count the number of hex nuts by weight
• First, find the average weight by weighing out 10
  hex nuts and obtaining the total weight (10 hex
  nuts weigh 105 g)

Average Weight
4
Counting Particles By Weighing

• What size (wt.) will contain 500 hex nuts?
• Calculate what weight will contain 500 hex nuts
• So, weigh out 5.25 kg of the hex nuts

5
Using Atomic Mass to Count Atoms

• Can do the exact same thing with atoms
• Too small to conveniently count
• Atoms of the same element dont always have
  exactly the same mass (isotopes) so use an
  Average Mass
• Grams are too large to use to measure an atom so
  use Atomic Mass Units (amu)

6
Atomic Mass and Formula Mass

• To calculate the mass of a sample of atoms
• Each element exists as a mixture of isotopes
• Use a weighted average for the atomic mass
• Number on the bottom of each square in the
  periodic table is the average weight of the
  element (in amu)

7
Atomic Mass and Formula Mass

• Atomic masses are determined on a relative scale
• The standard scale references the carbon-12
  isotope 12.000 amu
• All other atomic masses are determined relative
  to carbon-12

8
Atomic Mass and Formula Mass

• Using Atomic Mass to Count Atoms
• Calculating the number of atoms in a specific
  mass
• If you have a sample of an element, can calculate
  the number of atoms in that sample
• From the atomic mass per one atom a conversion
  factor can be made
• For example One nitrogen atom has an atomic mass
  of 14.01 amu

9
Calculating The Number of Atoms in a Specific
Mass

• You have a 1.00 g sample of lead. How many atoms
  of lead are present?

10
Calculating Mass Example

• Calculate the mass (in amu) of 1.0 ? 104 carbon
  atoms

1) Given
2) Plan Convert from atoms to amu
3) CF
4) Set Up Problem
11
Formula Mass

• The sum of atomic masses of all atoms in its
  formula
• Important role in nearly all chemical
  calculations
• Can be calculated for compounds and diatomic
  elements

12
Calculating Formula Mass

• Calculate the formula mass of calcium chloride
• Write the formula from the name given
• Ca2 (from group II) and Cl- (from group VII)
• Formula is CaCl2 due to charge balance
• Formula mass Sum of the atomic masses of atoms
  in the formula (1 Ca atom 2 Cl atoms)

40.08 amu
70.90 amu
Formula mass of CaCl2
13
Counting Large Quantities

• Many chemical calculations require counting atoms
  and molecules
• It is difficult to do chemical calculations in
  terms of atoms or formula units
• Since atoms are so small, extremely large numbers
  are needed in calculations
• Need to use a special counting unit just as used
  for other items
• A ream of paper
• One dozen donuts
• A pair of shoes

14
The Mole

• It is more convenient to use a special counting
  unit for such large quantities of particles
• Mole A unit that contains 6.022 ? 1023 objects
• It is used due to the extremely small size of
  atoms, molecules, and ions
• 6.022x1023 particles in 1 mole
• Called Avogadros Number
• Periodic Table
• The average atomic mass in amu (one atom)
• The weight of 1 mole of the element in grams
• Avogadros number provides the connecting
  relationship between molar masses and atomic
  masses

15
Calculating the Number of Molecules in a Mole

• How many molecules of bromine are present in
  0.045 mole of bromine gas?

Avogadros number
Given 0.045 mol Br2
Need molecules of Br2
Equality
Conversion factors
Set Up Problem
16
Subscripts State Moles of Elements

• The subscripts in a chemical formula indicate the
  number of atoms of each element present in a
  compound
• The subscripts in a chemical formula can also
  indicate the number of moles of atoms of each
  element present in one mole of a compound
• i.e. In one molecule of glucose (C6H12O6) there
  are 6 atoms of carbon, 12 atoms of hydrogen, and
  6 atoms of oxygen

17
Calculating the Moles of an Element in a Compound

• How many moles of carbon atoms are present in
  1.85 moles of glucose?

subscript
Plan moles of glucose
moles of C atoms
Equality
(One) mol C6H12O6 6 mols C atoms
Conversion Factors
11.1 mol C atoms
Set Up Problem
18
Molar Mass

• The atomic mass of a carbon-12 atom is 12.00 amu
• The atomic mass of one mole of carbon-12 atoms
  12.00 g
• One mole of any element is the amount of atoms
  (molecules or ions) that is equal to its atomic
  mass (in grams)
• This mass contains 6.022 ? 1023 particles of that
  element
• Use the periodic table to obtain the molar mass
  of any element

19
Molar Mass

• When the number of grams (weighed out) of a
  substance equals the formula mass of that
  substance, Avogadros number of molecules of that
  substance are present

20
Molar Mass of a Compound

• Calculate the molar mass of iron (II) sulfate
• Formula is FeSO4
• Calculate the molar mass of each element
• Each element is multiplied by its respective
  subscript (number of moles of each element)
• The molar mass is calculated by the sum of the
  molar masses of each element

Formula Subscript
Moles of Element in Compound
Moles of Compound
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Molar Mass of a Compound
1) Formula is FeSO4 The molar masses of iron,
sulfur, and oxygen are
2) Multiply each molar mass by its subscript
3) Find the molar mass of the compound by adding
the mass of each element
22
Calculations Using Molar Mass

• The three quantities most often calculated
• Number of particles
• Number of moles
• Number of grams
• Using molar mass as a conversion factor is one of
  the most useful in chemistry
• Can be used for g to mole and mole to g
  conversions

23
Relationship between Moles, Molar Mass and
Avogadros number
Avogadros Number
Avogadros Number
Avogadros Number
Avogadros Number
Particles of substance
Particles of substance
Moles of substance
Moles of substance
Moles of substance
Moles of substance
Molar Mass
Grams of substance
Moles of substance
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Converting Mass of a Compound to Moles

• International Foods Coffee contains 3 mg of
  sodium chloride per cup of coffee. How many
  moles of sodium chloride are in each cup of
  coffee?

3 mg NaCl
moles of NaCl
0.003 g NaCl
Equality
1 mol NaCl 58.44 g
25
Converting Grams to Particles

• Ethylene glycol (antifreeze) has the formula
  C2H6O2. How many molecules are present in a 3.86
  10-20 g sample?

Avog Number
Molar mass
Plan convert g moles
molecules of ethylene glycol
Conversion Factor 1
Equality 1
Equality 2
Conversion Factor 2
375 molecules
26
Percent Composition

• Sometimes its useful to know the composition of
  a compound in terms of what percentage of the
  total is each element
• Percent
• Parts per 100
• The number of specific items per a group of 100
  items
• 50 of 100 is 50 (50 items/100 total items)

27
Percent Example

• You have 4 oranges and 5 apples. What percent of
  the total is oranges?
• In parts per 100

28
Percent Composition

• It is the percent by mass of each element in a
  compound
• Can be determined
• By its chemical formula
• Molar masses of the elements that compose the
  compound
• The percent of each element contributes to the
  mass of the compound

29
Calculating Percent Composition Example

• What is the percent composition of each element
  in NH4OH?

Determine the contribution of each element
Molar mass
30
Empirical Formulas

• The simplest ratio of elements in a compound
• It uses the smallest possible whole number ratio
  of atoms present in a formula unit of a compound
• If the percent composition is known, an empirical
  formula can be calculated

31
Empirical Formulas

• To Determine the empirical formula
• Calculate the moles of each element
• Use molar mass (atomic mass)
• Calculate the ratios of the elements to each
  other
• Find the lowest whole number ratio
• Divide each number of moles by the smallest
  number of moles present

32
Empirical Formula Converting Decimal Numbers to
Whole Numbers

• The subscripts in a formula are expressed as
  whole numbers, not as decimals
• The resulting numbers from a calculation
  represent each elements subscript
• If the number(s) are NOT whole numbers, multiply
  each number by the same small integer (2, 3, 4,
  5, or 6) until a whole number is obtained

33
Relating Empirical and Molecular Formulas

• n represents a whole number multiplier from 1 to
  as large as necessary
• Calculate the empirical formula and the mass of
  the empirical formula
• Divide the given molecular mass by the calculated
  empirical mass
• Answer is a whole number multiplier

34
Relating Empirical and Molecular Formulas

• Multiply each subscript in the empirical formula
  by the whole number multiplier to get the
  molecular formula

35
Calculate Empirical Formula from Percent
Composition

• Lactic acid has a molar mass of 90.08 g and has
  this percent composition
• 40.0 C, 6.71 H, 53.3 O
• What is the empirical and molecular formula of
  lactic acid?
• Assume a 100.0 g sample size
• Convert percent numbers to grams

36
Calculate Empirical Formula from Percent
Composition

• Convert mass of each element to moles
• Divide each mole quantity by the smallest number
  of moles

Empirical formula is
CH2O
The ratio of C to H to O is 1 to 2 to 1
Empirical formula mass 12.01 2 (1.008)
16.00 30.03 g/mol
37
Determination of the Molecular Formula

• Obtain the value of n (whole number multiplier)
• Multiply the empirical formula by the multiplier

Molecular formula n ? empirical formula
C3H6O3
Molecular formula 3 (CH2O)
38
Formulas for Compounds

• Empirical Formula
• Smallest possible set of subscript numbers
• Smallest whole number ratio
• All ionic compounds are given as empirical
  formulas
• Molecular Formulas
• The actual formulas of molecules
• It shows all of the atoms present in a molecule
• It may be the same as the EF or a whole- number
  multiple of its EF

Molecular formula n ? Empirical formula
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end