1. 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?

2. 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

3. AIM: How can we calculate gram formula mass?
The atomic mass of an element is found in each element box on the Periodic Table

4. 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

5. 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

6. AIM: How can we calculate gram formula mass?
GFM of K2CO3
Element
atoms X Mass #
Multiplied result
Add them all up to get gfm K C O 2 1 3
39.10
12.01 16
78.20
12.01 48
g/mol

7. AIM: How can we calculate gram formula mass? – PRACTICE
Calculate the gram formula mass of the following:
N2H2
H2SO4
CuSO H2O
30 g/mol
98 g/mol
178 g/mol

8. 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

9. AIM: What is meant by the percent composition of a compound?
mass of part
mass of whole
x 100  TABLE ____

10. AIM: What is meant by the percent composition of a compound? – Practice
What is the percentage, by mass, of O in Fe2O3?
Element
# atoms X Mass #
Multiplied result
Add them all up to get gfm
X 100 =
g/mol
30% Fe O 2 3
55.85
16.00
111.70
48.00
g/mol

11. AIM: What is meant by the percent composition of a compound? – Practice
What is the percentage, by mass, of O in CO2?
Element
# atoms X Mass #
Multiplied result
Add them all up to get gfm
X 100 =
44.01g/mol
73% C O 1 2
12.01
16.00
12.01
32.00
44.01g/mol

12. 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

13. 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?

14. 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

15. What is a mole?
MOLE TRIANGLES

16. 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
Add them all up to get gfm 1
22.99
16.00
1.00
22.99
16.00
1.00 Na O H
39.99 g/mol
g_ = _4.75g __ = mol
gfm g/mol

17. 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
Add them all up to get gfm 1
22.99
16.00
1.00
22.99
16.00
1.00 Na O H
39.99 g/mol
mol x gfm = 2.80 mol x g/mol = 112 g

18. 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

19. 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

20. How can we solve stoichiometry problems? –like following a recipe
How much of the following “starting materials” do we need in order to make 14 pancakes?
MILK =
PANCAKE MIX =
EGGS =
How many cups of pancake mix would we need to use in order to make 28 pancakes?

21. How can we solve stoichiometry problems? –like following a recipe
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
Are the units used for all 4 substances in the equation the same?

22. 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
Write the chemical equations
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
Balance the equations – coefficients are the mole ratios
Re read problem and input the amount
Calculate the number of moles of something
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
Re read problem to determine which was asked for

23. How can we solve stoichiometry problems? – Template for solving

24. How can we solve stoichiometry problems? - Practice
Shows the mole relationships in balanced equations
__H2 + __ O2  __ H2O If we had 5 moles of H2 how many moles of O2 are required?
__ Na + __ H2O  __ NaOH + __ H If we have 23 g of Na how many moles of H2 are required?
__N2 + __ H2  __ NH If we have 2 moles of N2 how many grams of H2 are needed?

25. How can we solve stoichiometry problems? – Template for solving

26. How can we solve stoichiometry problems? – Template for solving

27. How can we solve stoichiometry problems? – Template for solving

28. 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

29. 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)

30. 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?

31. 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

32. 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

33. How can we determine the limiting reagent and the percentage yield
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

34. How can we determine the limiting reagent and the percentage yield
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?

35. How can we determine the limiting reagent and the percentage yield
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?

36. 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

37. 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?

38. AIM: How can we calculate empirical and molecular formulas? - EMPIRICAL
convert % to grams
divide each element by mass #
Divide each quotient by smallest value calculated Round your results to nearest whole number
Use whole #s to write empirical formula
Sequence of elements in the question is the same as in the formula

39. AIM: How can we calculate empirical and molecular formulas
AIM: How can we calculate empirical and molecular formulas? – EMPIRICAL – PRACTICE
50% Sulfur, 50% Oxygen; determine the empirical formula

40. AIM: How can we calculate empirical and molecular formulas? – MOLECUALR
determine the gfm of the empirical formula
Divide the given molecular mass by the gfm
Might have to calculate empirical formula
Given molecular mass
Multiply your whole number result by the empirical formula to determine molecular formula

41. AIM: How can we calculate empirical and molecular formulas
AIM: How can we calculate empirical and molecular formulas? – MOLECULAR – PRACTICE
Upon analysis the empirical formula is determined to be CH2O. The mass of the compound is 180amu. Determine the molecular formula

42. 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.

43. 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 atm L/mol K)
T = temp (K)
P = pressure (atm)

44. AIM: How can we determine molar mass and density
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 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.