Transcript Unit 12 Math and Moles

Unit 12 Mass and Moles
Avogadro’s Hypothesis
–Under the same conditions of
temperature and pressure, equal
volumes of two different gases will
have the same number of particles
regardless of mass.
–At STP, this number of particles is
Avogadro’s number or 6.02 x 1023
or 1 mole
This number can be used to
express the mass, volume or
number of particles for any gas
sample. The conversion from one
to another involves this
equivalency:
1mole = 6.02 x 1023 particles = gram
formula mass = 22.4 liters of space
*YOU MUST MEMORIZE THIS*
Determining mass using formulas
Atomic Mass Unit (amu)
• 1 amu = 1/12 the mass of a C-12 atom
Gram Atomic Mass
• The mass of 1 mole of atoms
• Numerically equal to atomic mass number
• The unit used is (g) gram
Gram Molecular Mass
• The mass of 1 mole of molecules
• Found by adding up the atomic mass
numbers of each element in the
molecule
• The unit used is (g) grams
Gram Formula Mass
• The mass of 1 mole of an ionic
substance
• *remember that ionic substances are
not composed of molecules!
• Determine the gram formula
mass/gram molecular mass of the
following:
• NaCl
• H2O
• 1 mole of H2 gas
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Avogadro’s Number and Mole Map
Problems
What we know:
At STP and in the gaseous phase:
1 mole = 6.02 x 1023 particles of a
substance
1 mole takes up 22.4 L of space
1 mole has a mass equal to the gram
formula/gram molecular mass
We could convert from moles to
mass to volume using a Mole Map
to set up a proportion
• Example: What is the mass of 3.01 x 1023
molecules of NH3(g) at STP?
• What is the mass of 5 moles of O2 gas at STP?
• How many molecules of NH3 would take up
44.8 L at STP?
• What is the mass of 9.03 x 1023 atoms of neon
gas at STP?
Density
• The mass per unit volume of a substance.
• The density of a substance DOES NOT change
for that substance!
• Formula: Density = Mass/Volume
3 ways for the Regents to ask
Density problems
• Table S: What is the density of one
mole of N2?
• Question will give 2 variables, you
must use the formula to solve for the
3rd_: What is the density of a solid
having a mass of 75g and a volume of
3 cm3?
• Given the density, the Regents can
ask for the molecular mass at STP:
Remember that at STP, the molecular
mass or 1 mole of a gas has what
volume? 22.4L
• What is the gram molecular mass of
a gas having a density of 2g/L at STP?
Percent Composition
• To determine the percentage by
mass of a particular element in a
compound.
• Determine the gfm
• Take the mass of individual
element and divide by gfm
• Multiply by 100%
Examples
• What percent by mass of CaCO3 is
made up of calcium?
• What is the percent by mass of
nitrogen in NH4NO3
• What is the percent by mass of water
in copper sulfate pentahydrate?
Empirical Formula from Percent Composition
• Using the percent composition, one can
determine the smallest whole number ratio of
atom to atom in a compound (empirical
formula). **Remember that since ionic
substances do not have true molecules, they
are always expressed in empirical formulas**
Follow the steps:
• Divide the percent by the atomic mass
• Take the answer to step 1 and divide it by the
smallest answer to step 1.
Examples
• What is the empirical formula of a compound
containing 40% calcium, 12% carbon and 48%
oxygen by mass?
• What compound contains 56.58% potassium,
8.68% carbon and 34.73% oxygen by mass?
Special Rule
• if the answer to step 2 ends in .1 or .9 you can
round off, BUT if it ends in .3 or .5, this is a
significant portion of a number. You cannot
round away this number, instead you must
adjust all numbers accordingly by following
the formula:
• If the number ends in .3 _multiply everything
by 3____
• If the number ends in .5 __multiply everything
by 2___
Example
• Give the empirical formula of a compound
containing 90.7% lead and 9.3% oxygen by
mass.
Molecular Formula from Empirical Formula
To determine the molecular formula from
the empirical formula follow the steps:
*Calculate the empirical mass.
*Divide the mass of the compound by the
mass of the empirical formula.
*Multiply all subscripts by the answer in
step 2.
Example
• A compound has a molecular mass of
42 amu and an empirical formula of
CH2. What is the molecular formula?
Moles in Balanced Equations
• A chemical equation usually represents a
chemical reaction. The equation will
identify:
• The reactants and products
• The molar ratio of each of these.
• Phases of matter for each substance.
• Possibly some reference to energy
changes in the reaction.
Example
• 2H2(g) + O2(g) → 2H2O(l) + heat
• When using equations to solve conversion
problems, one must remember the
proportions the original substances are in.
One can determine how many grams of a
reactant are needed to produce a set volume
by using the following rules:
Mass is the ONLY part of Avogadro’s
hypothesis that CAN NOT be used directly
in a proportion!!
You must convert grams to moles–Table T
Follow these steps:
read and underline
cross out what is not involved
set up a proportion
coefficients/known
information
cross multiply and divide
Example
• What volume of CO2(g) is produced when 15
liters of O2(g) are consumed in the reaction:
• C2H4(g) + 3 O2(g) →
2 CO2(g) + 2H2O(g)
• Given the reaction:
• 2 C2H6(g) + 7 O2(g) → 4 CO2(g) + 6 H2O(g)
• What number of carbon dioxide molecules are
produced when 6.02x1023 molecules of ethane
are consumed?