Transcript UNIT 5: Mathematics of Chemistry (Review Book Topic 3)

UNIT 5: Mathematics of Chemistry
(Review Book Topic 3)
How can we calculate gram formula mass?
What is meant by the percent composition of a compound?
What is a mole?
How can we solve mole problems?
How can we solve stoichiometry problems?
How can we determine the limiting reagent and the percentage
yield of a chemical reactions?
How can we calculate empirical and molecular formulas?
How can we determine molar mass and density?
AIM: How can we calculate gram
formula mass?
The mass of 1 proton is 1 amu
The mass of 1 neutron is 1 amu
The mass of an electron is
negligible
AIM: How can we calculate gram
formula mass?
The atomic mass of an
element is found in each
element box on the Periodic
Table
AIM: How can we calculate gram
formula mass?
The number of atoms of each
element present in a
compound is denoted by the
subscripts on each element
AIM: How can we calculate gram
formula mass?
Gram formula mass is the mass
of the smallest unit of a
compound from the sum of the
atomic masses of all atoms
present
AIM: How can we calculate gram
formula mass?
GFM of K2CO3
Element
atoms
X
Mass #
Multiplied
result
K
2
39.10
78.20
C
1
12.01
12.01
O
3
16
48
Add them all up to get gfm 138.21 g/mol
AIM: How can we calculate gram formula
mass? – PRACTICE
 Calculate the gram formula mass of the following:
1. N2H2
30 g/mol
2. H2SO4
98 g/mol
1. CuSO4
H2O
178 g/mol
AIM: What is meant by the percent
composition of a compound?
Percent Composition represents
the composition as a percentage
of each element compared with
the total mass of the compound
AIM: What is meant by the percent
composition of a compound?
% composition =
mass of part
mass of whole
x 100  TABLE ____
AIM: What is meant by the percent
composition of a compound? – Practice
1. What is the percentage, by mass, of O in
Fe2O3?
Element
Fe
O
# atoms X
2
Mass #
55.85
Multiplied
result
48.00
111.70
3
16.00
48.00
Add them all up to get gfm 159.70 g/mol
X 100 =
159.70 g/mol
30%
AIM: What is meant by the percent
composition of a compound? – Practice
1. What is the percentage, by mass, of O in
CO2?
Element
C
# atoms X
1
Mass #
12.01
Multiplied
result
32.00
12.01
44.01g/mol
O
2
16.00
32.00
Add them all up to get gfm 44.01g/mol
X 100 =
73%
AIM: What is meant by the percent
composition of a compound?
Hydrates: crystals that contain
attached water molecules
 To calculate the percentage of water
in a hydrate, treat the water molecule
as a single unit
AIM: What is meant by the percent
composition of a compound? – Practice
 What is the percentage, by mass, of water in
sodium carbonate crystals, Na2CO3 10H2O?
AIM: What is a mole?
 Mole is a way to express a quantity
 1 mole of any compound or elements = mass of that
compound or element
 1 mole = 6.02 x 1023 particles (atoms or molecules)
 1 mole = 22.4 L
 Formula is on Table T
What is a mole?
 MOLE TRIANGLES
AIM: How can we solve mole
problems? - PRACTICE
How many moles are equivalent to 4.75 g of NaOH?
Element
# atoms X
Mass # Multiplied
result
Na
1
22.99
22.99
O
1
16.00
16.00
H
1
1.00
1.00
Add them all up to get gfm
39.99 g/mol
g_ = _4.75g __ = 0.119 mol
gfm
39.99g/mol
AIM: How can we solve mole
problems? - PRACTICE
How many grams are equivalent to 2.80 moles of
NaOH?
Element # atoms X Mass # Multiplied
result
Na
1
22.99
22.99
O
1
16.00
16.00
H
1
1.00
1.00
Add them all up to get gfm
39.99 g/mol
mol x gfm = 2.80 mol x 39.99 g/mol = 112 g
How can we use mole relationships
to solve stoichiometry problems?




Like following a recipe
Need a balanced chemical equation
Use mole relationships
The study of quantities of materials consumed and
produced in chemical reactions
How can we solve stoichiometry
problems? –like following a recipe
Directions: Use the pancake recipe below (Bisquick) in order to
answer the following questions:
FAMILY SIZE RECIPE: 14 pancakes
PREP TIME: 4 min COOK TIME: 3 min per batch
1 cup milk
2 eggs
2 cups Original Bisquick mix
STIR milk and eggs until blended. Stir into Bisquick mix.
POUR slightly less than ¼ cup onto hot greased griddle.
COOK until edges are dry, Flip, cook until golden
How can we solve stoichiometry
problems? –like following a recipe
1. How much of the following “starting materials” do we
need in order to make 14 pancakes?
1. MILK =
2. PANCAKE MIX =
3. EGGS =
2. How many cups of pancake mix would we need to use
in order to make 28 pancakes?
How can we solve stoichiometry
problems? –like following a recipe
3. How many cups of pancake mix would we need to use in order
to make 7 pancakes? Use your knowledge of chemistry to fill in
this incomplete chemical equation that describes the
formation of 14 pancakes (products) from its starting materials
(reactants)
1 cup of milk + __________________ + __________________  14 pancakes
4. Are the units used for all 4 substances in the equation the
same?
How can we solve stoichiometry
problems? – Template for solving
 Example: Calculate the mass of oxygen that will completely react
with 96.1g of propane? Calculate for liters of CO2….. Calculate how
many water molecules are produced
1. Write the chemical equations
2. Calculate the molar masses and put in parenthesis above the
formulas – only really need to do this for the products and
reactants you are interested in
3. Balance the equations – coefficients are the mole ratios
4. Re read problem and input the amount
5. Calculate the number of moles of something
6. Use the mole ratio to find moles of everything else Ex) 1 = 2.18 then
multiply that by the coefficient in from of the product or reactant
7. Re read problem to determine which was asked for
How can we solve stoichiometry
problems? – Template for solving
How can we solve stoichiometry
problems? - Practice
 Shows the mole relationships in balanced equations
1. __H2 + __ O2  __ H2O
If we had 5 moles of H2 how many moles of O2 are required?
2. __ Na + __ H2O  __ NaOH + __ H2
If we have 23 g of Na how many moles of H2 are required?
3. __N2 + __ H2  __ NH3
If we have 2 moles of N2 how many grams of H2 are needed?
How can we solve stoichiometry
problems? – Template for solving
How can we solve stoichiometry
problems? – Template for solving
How can we solve stoichiometry
problems? – Template for solving
How can we solve stoichiometry
problems? – Gas Stoichiometry
 Use PV = nRT to solve for the volume of one mole of gas at STP
 That is the molar volume of a gas at STP = 22.4L
 Use the ideal gas law to convert quantities that are not at STP
How can we solve stoichiometry
problems? – GAS STOICH PRACTICE
 How many liters of carbon dioxide gas will be produced form
the complete combustion of 30.0L of ethane according to the
following equation?
2C2H6 (g) + 7O2 (g)  4CO2 (g) + 6H2O (g)
How can we solve stoichiometry
problems? – Gas Stoichiometry
 A sample of nitrogen gas has a volume of 1.75L. How many
moles of N2 are present?
How can we solve stoichiometry
problems? – Gas Stoichiometry
 Quicklime (CaO) is produced by the thermal decomposition of
calcium carbonate (CaCO3). Calculate the volume of CO2 at
STP produced from the decomposition of 152 g CaCO3 by the
reaction:
 ____ CaCO3 (s)  _____ CaO (s) + ____ CO2
How can we determine the limiting
reagent and the percentage yield?
 Notice how hot dogs are sold in packages of 10 while the
buns com in packages of 8?
 The bun is the limiting reactant and limits the hot dog
production to 8
 The limiting reactant is the one consumed most entirely in the
chemical reaction
How can we determine the limiting
reagent and the percentage yield?STRATEGY
 If you are faced with two starting amounts of matter reacting, you
have entered “The Land of Limiting Reactant”
 Calculate the number of moles of everything you are given – set up the
same table –two sets of moles now
 Cover one set pretending the other exists –
 What if all these moles reacted?
 How many moles of the other reactants would you need to use up all these
moles?
 Do the calculation of how many moles of the “other” amount you
would need
 Do you have enough?
 If so, the reactant you began with IS the limiting reactant
 If not repeat this process with the “other” reactant amount you were given
How can we determine the limiting reagent
and the percentage yield?- PRACTICE
 Suppose 25.0g of nitrogen reacts with 5.00g of hydrogen to form ammonia.
What mass of ammonia can be produced? Which reactant is the limiting
reactant? What is the mass of the reactant that is in excess?
How can we determine the limiting reagent
and the percentage yield?- PRACTICE
 Nitrogen gas can be prepared by passing gaseous ammonia over solid copper (II)
oxide at high temperature. The other products of the reaction are solid copper
and water vapor. If a sample containing 18.1g of NH3 is reacted with 90.4g of
CuO, which is the limiting reactant? How many grams of N2 will be formed?
How can we determine the limiting
reagent and the percentage yield of a
chemical reactions?
 Theoretical yield: the amount of product formed when a limiting
reactant is completely consumes. This assumes perfect
conditions and gives maximum amount
 Actual yield: that which is realistic
 Percent yield: the ratio of actual to theoretical yield
How can we determine the limiting reagent and the
percentage yield of a chemical reactions? – PRACTICE
Methanol (CH3OH), also called methyl alcohol, is the simplest alcohol. It is used as a fuel in
race cars and is a potential replacement for gasoline. Methanol can be manufactured by a
combination of gaseous carbon monoxide and hydrogen. Supposed 68.6g of CO (g) is
reacted with 8.60g of H2(g). Calculate the theoretical yield of methanol is 35.7 g CH3OH is
actually produced, what is the percent yield of methanol?
AIM: How can we calculate empirical
and molecular formulas? - EMPIRICAL
1. convert % to grams
2. divide each element by mass #
3. Divide each quotient by smallest value calculated Round
your results to nearest whole number
4. Use whole #s to write empirical formula
5. Sequence of elements in the question is the same as in
the formula
AIM: How can we calculate empirical
and molecular formulas? –
EMPIRICAL – PRACTICE
1. 50% Sulfur, 50% Oxygen; determine the empirical formula
AIM: How can we calculate empirical
and molecular formulas? –
MOLECUALR
1. determine the gfm of the empirical formula
2. Divide the given molecular mass by the gfm
1. Might have to calculate empirical formula
2. Given molecular mass
3. Multiply your whole number result by the empirical
formula to determine molecular formula
AIM: How can we calculate empirical
and molecular formulas? –
MOLECULAR – PRACTICE
1. Upon analysis the empirical formula is determined to be
CH2O. The mass of the compound is 180amu. Determine
the molecular formula
AIM: How can we determine molar
mass and density? – DENSITY PRACTICE
1. Calculate the mass of a liquid with a density of 2.5 g/mL
and a volume of 15 mL.
2. Calculate the volume of a liquid with a density of 5.45
g/mL and a mass of 65 g.
AIM: How can we determine molar
mass and density? – MOLAR MASS
Rearrange the ideal gas equation we can find the molar
mass of an unknown gas
d = density of a gas g/L)
R = universal gas constant 0.0821atm L/mol K)
T = temp (K)
P = pressure (atm)
AIM: How can we determine molar
mass and density? – MOLAR MASS PRACTICE
1. What is the density of CO2 at 77° C and a pressure of 2.00 atm?
2. Calculate the molar mass of a gas that has a density of 0.635 g/L at
37° C and 787 torr (760 torr = 1 atm)
3. The density of a gas was measured at 1.50 atm and 27° C and
found to be 1.95 g/L. Calculate the molar mass of the gas.