1. Mathematics of Chemistry
Moles,
Mathematics of Chemistry

2. Chemical Symbols Fe C K Al
Each element has been assigned a unique one-, two-, or three-letter symbol for its identification
The first letter of a symbol is always capitalized
Only recently discovered elements that don’t yet have permanent names are given three-letter symbols
Uncombined elements are written as monatomic (without a subscript)
Examples: Fe, C, Al
Diatomic elements – 2 of the same atoms (HOFBrINCl’s)
Examples: H2, O2 K Al

3. Atomic Mass Gram Atomic Mass
The atomic mass of an element is given in atomic mass units (amu)
Found on the periodic table
The mass of 1 mole of an element is equal to its atomic mass (periodic table) in grams
Gram Atomic Mass

4. Formula Mass / Molecular Mass
The sum of the atomic masses of its atoms
Example:
CO2 =

5. Mass Examples
Find the atomic or formula mass of the following substances:
(To the nearest tenth) C Br
Cl2
H2O
Ca3PO4
Ca(OH)2

6. Gram Formula Mass The mass of 1 mole of the substance
Measured in grams
Example:
1.0 mole of CO2 = 44g

7. Mole-Mass Calculations
Use the gram formula mass to convert between moles and mass
Examples:
moles of CO2 = _______ g
g of C = _______ moles
moles of Br = _______ g
g of Al = _______ moles

8. Mole – Volume Calculations
If you have an ideal gas at standard temperature and pressure (STP) – 0oC and 1atm
1 mole = 22.4 L

9. Mole – Volume Examples 1. 1.5 moles of CO2 (g) = _______ L
L of Ne(g) = _______ moles
moles of O2(g) = _______ L
L of N2(g) = _______ moles

10. Avogadro's Number 1 dozen = 12
1 mole = 6.02 x 1023 (Avagadro’s Number)
How big is a mole?
602,000,000,000,000,000,000,000
A mole of marbles would spread over the surface of the earth, and produce a layer about 50 miles thick
A mole of sand, spread over the United States, would produce a layer 3 inches deep
A mole of dollars could not be spent at the rate of a billion dollars a day over a trillion years

11. Avogadro
He stated that equal volumes of all gases at the same temperature and pressure contain the same number of molecules (Acogadro’s Principle)
Later his work led to the realization that a molecular mass in grams (mole) of any substance contains the same number of molecules (6.02 x 1023)
Amedeo Avogadro

12. Mole – Number Calculations
1 mole of atoms = 6.02 x 1023 atoms
1 mole of particles = 6.02 x 1023 particles
1 mole of molecules = 6.02 x 1023 molecules
1 mole of compounds = 6.02 x 1023 compounds

13. Mole – Number Examples 4.00 moles of NaCl = _______ molecules
0.50 mole of MgBr2 = _______ molecules
3.01 x 1023 NaCl molecules = _______ moles
6.02 x 1021 Zn atoms = _______ moles

14. Empirical Formulas
Represents the simplest integer ratio in which the atoms combine to form a compound (the reduced form)
All ionic formulas are written as empirical formulas

15. Molecular Formulas The actual numbers of the atoms in a molecule
May be a multiple of the empirical formula
Examples:
What are the empirical formulas of the following molecules?
a. H2O2
b. C6H12O6
c. CCl4

16. Percent Composition
Composition in terms of the percentage of each component present
Example: H2SO4
Step 1: Calculate the formula mass of H2SO4
Step 2: Find the percent mass of each element

17. Percent Mass Example
Calculate the percent composition of oxygen in CO2

18. Water of Hydration Percentage of water in the crystal
Hydrate – a compound that contains water
Anyhdrous – hydrate without the water

19. Water of Hydration Example
Find the water of hydration in CuSO45H20
Step 1 - Find the formula mass
Step 2 - Percentage of water

20. Water of Hydration Example
Calculate the water of hydration in Na2CO310H2O

21. Determining Mass Ratios from Formulas
Example: Find the mass ratio for a compound with the empirical formula CH2.

22. Determining the Molecular Formula from the mass and the empirical formula
A compound has a molecular mass of 180amu and an empirical formula of CH2O. What is its molecular formula?
Step 1: Determine the molecular mass of the empirical formula
Step 2: Divide the molecular mass of the compound by the mass of the empirical formula.
Step 3: Multiply the subscripts in the empirical formula by your answer to step 2

23. Determining the empirical formula from percent composition
What is the empirical formula of a compound that consists of 58.80% barium, 13.75% sulfur, and 27.45% oxygen by mass?
Step 1: Assume that the mass of the sample is 100g
Step 2: Convert the masses into moles
Step 3: Find the smallest whole numbers ratio (divide each number from step 2 by the smallest one)

24. Chemical Reactions
Reactant – Substance that enters into a reaction, written to the left of the arrow, starting material
Product – substance that is produced by the reaction, written to the right of the arrow, end material
Example: HCl + NaOH  NaCl + H2O
Reactants:
Products:

25. Endothermic Reactions
Reaction that requires energy (heat) in order to occur – heat enters
Heat is absorbed
Heat is a reactant
Surroundings will feel cold because heat has been absorbed from the surroundings
Example: H2O(s) + heat  H2O(l)

26. Heat is released, given off
Exothermic Reactions
Reaction that produce energy (heat) when they occur – heat exits
Heat is released, given off
Heat is a product
Surroundings will feel hot because heat was released to the surroundings
Example: H2O(l)  H2O(s) + heat

27. Types of Reactions Synthesis Decomposition Single Replacement
Double Replacement

28. Synthesis Direct combination Substances combine to form a new compound
Produces 1 product
Examples:
A + B  AB
2H2(g) + O2(g)  2H2O(l)

29. Decomposition Break down of a compound into simpler parts
Starts with 1 reactant
Examples:
AB  A + B
2H2O(l)  2H2(g) + O2(g)

30. Single Replacement One substances switches spots with another
Element + compound makes a new element plus a new compound
Examples:
A + BC  B + AC
Cu(s) + 2AgNO3(aq)  2Ag(s) + Cu(NO3)2
*copper replaces silver

31. Double Replacement Exchange of ions Everything gets a new "partner"
Compound + compound makes new compound + new compound
Examples:
AB + CD  AD + CB
AgNO3(aq) + NaCl(aq)  AgCl(s) + NaNO3(aq)

32. Balancing Equations
Coefficient - a number, placed before formulas to indicate the ratios of moles involved in a reaction
Equations must be balanced in accordance with the Law of Conservation of Mass
The mass of both sides of the arrow must be equal
You must have an equal number of each type of atom on both sides of the equation
Example: 2H2 + O2  2H2O

33. Balancing Examples ____ Na + ____ H2O  ____ NaOH + ____ H2
____ CaO + ____ H2O  ____ Ca(OH)2
____ Al + ____ O2  ____ Al2O3
___ PbCl2 + ___ Al2(SO4)3  __ PbSO4 + __ AlCl3
____ Na + ____ O2  ____ Na2O

34. Determining the Missing Mass in Equations
If 103.0g of potassium chlorate (KClO3) are decomposed to form 62.7g of potassium chloride (KCl) and oxygen gas (O2) according to the equation 2KClO3  2KCl + 3O2, how many grams of oxygen are formed?
(Hint: Remember the mass of the products must equal the mass of the reactants)

35. How many grams of Fe are needed to react with 8.0g of O2 to produce 28.9g of Fe3O4 according to the equation 3Fe + 2O2  Fe3O4?

36. Equation Problems
Using the balanced equations and mole conversions you can solve for variety of problems
Remember that the coefficients used represent mole ratios

37. Given the following reaction answer the questions below:
2C2H6 + 7O2  4CO2 + 6H2O
How many moles of CO2 are produced when 2.0 moles of C2H6 reacts?
How many moles of H2O are produced when 4.0 moles of C2H6 reacts?
How many moles of H2O are produced when 5.0 moles of C2H6 combusts?

38. ____ H2 + ____ Cl2  _____ HCl
Given the following reaction:
____ H2 + ____ Cl2  _____ HCl
The production of 37g of HCl would require how many moles of H2?
If 20.L of H2 completely reacts how many grams of HCl would be produced?

39. ____ C2H4 + ____ O2  ____ CO2 + ____ H2O
Use the balanced equation to answer the questions below:
____ C2H4 + ____ O2  ____ CO2 + ____ H2O
How many liters of O2 are used to produce 1.0 mole of H2O?
How many liters of CO2 are produced when 9.00 liters of O2 is consumed?
How many liters of C2H4 are needed to produce 10.0 liters of CO2?