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Chemistry 068, Chapter 6
Moles and Chemical Formulas
• This section deals with the relationships
between elements and compounds.
– Specifically, that compounds have a definite
composition in terms of the number and type
of atoms which make them up.
• It also introduces the idea of the mole,
which is a unit of amount in chemistry.
Compounds and the Law of
Definite Proportions
• Pure substances are either elements or
compounds.
• Elements cannot be decomposed into
simpler substances.
• Compounds are substances composed of
two or more elements.
– Compounds have different properties from
either element alone.
– They have a constant elemental composition.
Compounds and the Law of
Definite Proportions (Cont’d)
• The law of definite proportions states that
in a pure compound, the elements present
are always in the same proportion by
mass.
– All samples of the same compound will have
the same elemental proportion by mass.
• The simplest illustrations of this are
decomposition reactions.
• It is also useful to look at the law in terms
of individual atoms.
Law of Definite Proportions in
Terms of Atoms
• Consider three compounds AB, AB2, and
AB3.
– A is blue and B is red.
– Each is made up of A and B atoms, but in
different ratios.
Law of Definite Proportions in
Terms of Atoms (Cont’d)
• The different ratios between the atoms will
correspond to a different mass ratio and
mass % for each of the three compounds.
– Even if A and B had exactly the same mass,
the ratio would still be different.
• This difference will also lead to a different
mass per molecule.
The Mole
• A mole, sometimes written as mol, is like a
dozen, except that a mole is 6.0221415x1023.
– Usually, it is sufficient to use 6.022x1023.
• The number 6.0221367x1023 is called
Avogadro’s number.
• Like a dozen you can have a mole of anything –
atoms, DVDs, pennies.
• Chemists have set up the periodic table such
that the masses on the periodic table
correspond to the mass of one mole of atoms in
grams.
Calculations Using Avogadro's
Number
• You can use Avogadro’s number to go
back and forth between moles of
something and single objects by treating it
as a unit conversion.
• Conversion like this sometimes also
require you to keep track of chemical
formulas.
Calculations Using Avogadro's
Number Problems
• How many molecules of CH4 are there in
0.010 moles of CH4?
• How many moles of NaCl are there if there
are 1.50*1027 molecules?
Molar Mass
• Is the mass for one mole of molecules of a
substance.
• Calculated in exactly the same way as a
molecular or formula mass.
• Units are usually g/mol.
• Will have the same numerical value as the
molecular or formula mass, but the units
will be different.
– Grams instead of amu.
Calculations Using Molar Mass
• Molar mass is calculated in exactly the
same way as formula mass.
– The only thing that is different is the mass
units used.
– Molar mass will be in g/mole, whereas
formula mass will be in amu.
• It is possible to freely switch between
moles and mass by using the molar mass
as a unit conversion.
Relationship Between Amu and
Gram Masses
• Amu and gram masses are related by:
1.000g = 6.022*1023 amu
Or:
1.000 amu = 1.661*10-24g
• You can thus relate amu and gram
masses using unit conversion calculations.
Significant Figures and Calculations
Using Avogadro’s Number
• Avogadro’s number is an experimentally
determined value.
• As such, it is not an exact number.
• Normally, it is sufficient to use 6.022x1023.
• If more significant figures are needed, the
value 6.0221415x1023 can be used.
Molar Mass Problems
• Calculate each
of the following:
– Number of
moles in 150.0g
of He.
– Mass of 9.6
moles of C.
– Number of
atoms in 100.0g
of Fe.
Molar Mass Problems (Cont’d)
• Calculate the
following molar
masses:
– MgCl2
– H 2O
– H2SO4
Molar Mass Problems (Cont’d)
• Calculate each
of the following:
– Number of
molecules in
100.0g of
MgCl2.
– Number of
moles in 50.0g
of H2O.
– Mass of
3.2moles of
H2SO4.
Moles and Chemical Formulas
• At the single atoms level, chemical
formulas represent ratios within a given
formula unit.
• At the macroscopic level, chemical
formulas represent the mole ratio of the
elements in a compound.
• These two representations are not
exclusive – they represent the same thing
just at two different scales.
Moles and Chemical Formulas
(Cont’d)
• Again, let’s consider
three compounds AB,
AB2, and AB3.
– A is blue and B is red.
• At the single atom level
the ratio represents
individual atoms.
• At the macroscopic level,
the ratio is a mole ratio.
Moles and Chemical Formulas
Problems
• How many moles of oxygen atoms are in
6.10*1025 molecules of CO2? How many
moles of carbon?
• How many atoms of carbon are in 2.6
moles of C2H6? How many moles of
hydrogen?
Chemical Calculations Using Moles
• With this knowledge in mind, there are
several types of calculation which can be
performed.
• It is important to remember that you can
go back and forth between moles, number
of particles, and masses.
Chemical Calculations Using Moles
(Cont’d)
• You can convert between moles and number of
particles using Avogadro's number.
• Mass and number of moles are related using
molar mass.
• The chemical formula of a compound can be
used to get a mole or number of particles
relationship within a compound.
– This is NOT true for mass.
– Mass relationships are more complicated because
different elements have different masses.
Calculations Using Moles Problems
• How many
molecules
are there in
a 32.00g
sample of
CH4?
• How many
atoms of
carbon are
in that same
sample?
• How many
atoms of
hydrogen?
Calculations Using Moles Problems
(Cont’d)
• What
mass of
oxygen is
there in a
9.00g
sample of
H2O?
• What
mass of
hydrogen?
Calculations Using Moles Problems
(Cont’d)
• How much
does
3.00*1020
molecules
of NH3
weigh?
Calculations Using Moles Problems
(Cont’d)
• What is
the mass,
in grams,
of a single
molecule
of CO2?
Mass % and Mass Ratio
• % composition by mass, or mass % is a way
to represent the elemental breakdown of a
compound.
Mass % = 100*(mass element) / (total mass compound)
• Another way to represent elemental
composition is mass ratio.
Mass ratio A to B = (mass element A/mass element B)
Using a Formula to Determine
Mass %
• A formula mass can be used to determine
mass %.
• First the formula mass is determined.
• Second, the masses of each of the
elements is taken as a % of the total.
Using a Formula to Determine
Mass % Problems
• Determine the mass %, of each element in
C2H3Cl.
Using Synthesis Data to Determine
Mass %
• Synthesis data can also be used to
determine mass %.
• The mass of each element can be taken
as a % of the whole to find its mass %.
Using Synthesis Data to Determine
Mass % Problems
• A 27.00g sample
of an organic
compound
requires 11.94g of
C, 1.44g H, 7.08g
O, 2.08g N, and
4.46g Fe. What is
the mass % of
each in the
compound?
Sample Purity
• Not in text.
• Most real samples are not completely pure.
• % purity (by mass) is a measure of how pure a
sample of a compound is.
– It is defined as the % of the substance (by mass) in
an impure sample. Or:
% Purity A = (Mass A)/(Total Mass of Impure Sample of A)
• Thus a 98.60% pure sample of iron would
contain 98.60g of iron per 100.0g sample of
impure iron.
• Sample purity adds an additional step to any
chemical calculations.
Sample Purity Problems
• What mass of
CH4 is there in a
32.00g sample
which 80.0%
pure CH4?
• How many CH4
molecules are
there?
• How many atoms
of carbon are in
that same
sample?
• How many atoms
of hydrogen?
Empirical vs. Molecular Formulas
• There are two types of chemical formulas.
• Empirical formulas give only the smallest whole
number ratio of atoms in a compound.
• Molecular formulas give the actual number of
each type of atom within a compound.
• Compounds with the same empirical formula but
different molecular formulas can have very
different properties.
• For example, C2H6, C3H9, C4H12, all have the
same empirical formula – CH3, but each has
different properties.
Empirical vs. Molecular Formulas
Problems
• What is the empirical formula of each of the
following compounds?
– H2O2
– C4H16
– Na2Cl2
– H2SO4
– Na6(OH)6
Determining an Empirical Formula
From Data
• It is often much easier to experimentally
determine an empirical formula than it is a
molecular formula.
• Empirical formulas are typically obtained
from mass composition (% mass)
experiments or raw mass data.
• Combustion analysis is another potential
source of empirical formula data.
Determining an Empirical Formula
From Mass Composition Data
• The mole ratio of a compound is needed to
determine its empirical formula.
• First, you need to determine how many moles of
each element are in the compound from mass
data.
• Molar masses are then used to determine the
number of moles.
• A mole ratio is then determined and converted to
whole numbers.
• The smallest whole number ratio gives the
empirical formula.
– Each mole in the ratio is one atom in the empirical
formula.
Empirical Formula From Mass
Composition Data Problems
• A salt sample is determined to contain
only calcium and chlorine.
– What is the empirical formula of the salt if it is
36.0% calcium
by mass.
Empirical Formula From Mass
Composition Data Problems (Cont’d)
• Ethanol is 52.17% carbon, 13.05%
hydrogen, and 34.78% oxygen. What is
the empirical formula of ethanol?
Empirical Formula From Mass
Composition Data Problems (Cont’d)
• A salt sample contains 5.86g of potassium
and 19.0g of iodine. What is the empirical
formula of the salt?
Combustion Analysis
• Not in text.
• Combustion is a special type of elemental analysis
where a compound is burned, along with oxygen, to
produce water, carbon dioxide, and solid residue.
• All of the hydrogen in the compound forms water.
– Thus the moles of water is half the moles of hydrogen (as water
has 2 hydrogens).
– To get the moles of water, the mass of water is converted to
moles.
• All of the carbon in the compound forms carbon dioxide.
– Thus the moles of carbon dioxide is equal to the moles of
carbon.
– Likewise, the moles of carbon dioxide is obtained from the mass
of carbon dioxide.
• The residue will contain any elements that do not readily
combust.
Combustion Analysis (Cont’d)
• The moles of any residue can then be
obtained from its molar mass.
– The residue, if any, will vary depending on the
sample.
• Once the moles of hydrogen, carbon, and
any residue have been determined, it is
possible to determine an empirical formula
by using the mole ratio.
Combustion Analysis Problems
• A 24.0g sample of an
unknown hydrocarbon,
which contains only
carbon and hydrogen,
is combusted. It
produces 54.0g of
water and 66.0g of
carbon dioxide leaving
no solid residue.
– What is the empirical
formula of the sample?
Combustion Analysis Problems
• A 94.0g sample of an
unknown hydrocarbon,
which contains only
carbon, hydrogen, and
sulfur is combusted. It
produces 54.0g of
water and 88.0g of
carbon dioxide leaving
64.0g of sulfur residue.
– What is the empirical
formula of the sample?
Determining a Molecular Formula
From Data
• To determine the molecular, rather than
empirical formula, it is necessary to determine
the compounds molar mass by a separate
experiment.
– This is often much more difficult than determining the
empirical formula experimentally.
• Once both the empirical formula and the molar
mass are known the molecular formula can be
determined.
• This is done by noting that the molar mass of the
molecule must be a whole number multiple of
the molar mass of the empirical formula.
– The multiplier to mass also multiplies the subscripts
on the atoms in the formula.
Determining a Molecular Formula
From Data (Cont’d)
• In short:
Molecular Formula = Empirical Formula x n
Molar Mass = Empirical Formula Molar Mass x n
• Where n is a positive whole number.
Determining a Molecular Formula
From Data Problems
• The empirical formula of a compound is
CH4. What is its molecular formula if the
molar mass is:
• 16.0g/mole
• 32.0g/mole
• 48.0g/mole
Determining a Molecular Formula
From Data Problems (Cont’d)
• A 66.0g sample
containing only
carbon and oxygen is
determined to
contain 1.5mol of
carbon. A separate
experiment
determines that the
compound has a
molar mass of
176.0g/mol.
– What is the empirical
formula of the
sample?
– What is the molecular
formula of the
sample?