1. Calculations and the Chemical Equation
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Chapter 4
Calculations and the Chemical Equation
Denniston Topping Caret
6th Edition

2. 4.1 The Mole Concept and Atoms
Atoms are exceedingly small
Unit of measurement for mass of an atom is atomic mass unit (amu) – unit of measure for the mass of atoms
carbon-12 assigned the mass of exactly 12 amu
1 amu = 1.66 x g
Periodic table gives atomic weights in amu

3. Mass of Atoms
What is the atomic weight of one atom of fluorine? Answer: amu
What would be the mass of this one atom in grams?
Chemists usually work with much larger quantities
It is more convenient to work with grams than amu when using larger quantities

4. The Mole and Avogadro’s Number
A practical unit for defining a collection of atoms is the mole
1 mole of atoms = x 1023 atoms
This is called Avogadro’s number
This has provided the basis for the concept of the mole

5. The Mole
To make this connection we must define the mole as a counting unit
The mole is abbreviated mol
A mole is simply a unit that defines an amount of something
Dozen defines 12
Gross defines 144

6. Atomic Mass The atomic mass of one atom of an element corresponds to:
The average mass of a single atom in amu
The mass of a mole of atoms in grams
1 atom of F is amu amu/atom F
1 mole of F is g g/mole F

7. Molar Mass Molar mass - The mass in grams of 1 mole of atoms
What is the molar mass of carbon?
12.01 g/mol C
This means counting out a mole of Carbon atoms (i.e., x 1023) they would have a mass of g
One mole of any element contains the same number of atoms, x 1023, Avogadro’s number

8. Calculating Atoms, Moles, and Mass
Atomic mass unit converts amu to grams (other than give you an appreciation for the size of atoms, we won’t work with amu)
Avogadro’s number converts moles to number of atoms
Molar mass converts grams to moles

9. Strategy for Calculations
Map out a pattern for the required conversion
Example: given a number of grams of sulfur, find the number of atoms
Two conversions are required
Convert grams to moles
1 mol S/32.06 g S OR g S/1 mol S
Convert moles to atoms
mol S x (6.022 x 1023 atoms S) / 1 mol S

10. Practice Calculations-assume 3 sig. figs for all.
Calculate the number of atoms in 1.7 moles of boron.
Find the mass in grams of 2.5 mol Na (sodium).
Calculate the number of atoms in 5.0 g aluminum.
Calculate the mass of 5,000,000 atoms of Au (gold)

11. 4.2 The Chemical Formula, Formula Weight, and Molar Mass
Chemical formula - a combination of symbols of the various elements that make up the compound
Formula unit - the smallest collection of atoms that provide two important pieces of information
The identity of the atoms
The relative number of each type of atom

12. Chemical Formula Consider the following formulas:
H2 – 2 atoms of hydrogen are chemically bonded forming diatomic hydrogen, subscript 2
H2O – 2 atoms of hydrogen and 1 atom of oxygen, lack of subscript means one atom
NaCl – 1 atom each of sodium and chlorine
Ca(OH)2 – 1 atom of calcium and 2 atoms each of oxygen and hydrogen, subscript outside parentheses applies to all atoms inside

13. Chemical Formula Consider the following formulas:
(NH4)2SO4 – 2 ammonium ions and 1 sulfate ion
Ammonium ion contains 1 nitrogen and 4 hydrogen
Sulfate ion contains 1 sulfur and 4 oxygen
Compound contains 2 N, 8 H, 1 S, and 4 O
CuSO4.5H2O
This is an example of a hydrate - compounds containing one or more water molecules as an integral part of their structure
5 units of water with 1 CuSO4

14. Comparison of Hydrated and Anhydrous Copper Sulfate
Hydrated copper (II) sulfate
Anhydrous copper (II) sulfate
Marked color difference illustrates the fact
that these are different compounds

15. Formula Weight and Molar Mass
Formula weight - the sum of the atomic weights of all atoms in the compound as represented by its correct formula
What is the formula weight of H2O?
16.00 g/mol + 2(1.008 g/mol) = g/mol
Molar mass – mass of a mole of compound in grams / mole
What is the molar mass of H2O?
18.02 g/mol H2O

16. Formula Unit
Formula unit – smallest collection of atoms from which the formula of a compound can be established
When calculating the formula weight (or molar mass) of an ionic compound, the smallest unit of the crystal is used
What is the molar mass of (NH4)3PO4?
3(N g/mol) + 12(H g/mol) + 1(P g/mol) + 4(O g/mol)=
3(14.01) + 12(1.008) (16.00)= g/mol (NH4)3PO4

17. 4.3 The Chemical Equation and the Information It Conveys
A Recipe For Chemical Change
Chemical equation - shorthand notation of a chemical reaction
Describes all of the substances that react and all the products that form, physical states, and experimental conditions
Reactants – (starting materials) – the substances that undergo change in the reaction
Products – substances produced by the reaction

18. Features of a Chemical Equation
Identity of products and reactants must be specified using chemical symbols
Reactants are written to the left of the reaction arrow and products are written to the right
Physical states of reactants and products may be shown in parentheses
Symbol  over the reaction arrow means that energy is necessary for the reaction to occur
Equation must be balanced

19. Features of a Chemical Equation
Products and reactants must be specified using chemical symbols
Reactants – written on the left of arrow
Products – written on the right
 – energy is needed
Physical states are shown in parentheses

20. The Experimental Basis of a Chemical Equation
We know that a chemical equation represents a chemical change
One or more substances changed into new substances
Different chemical and physical properties

21. Evidence of a Reaction Occurring
The following can be visual evidence of a reaction:
Release of a gas
CO2 is released when acid is placed in a solution containing CO32- ions
Formation of a solid (precipitate)
A solution containing Ag+ ions mixed with a solution containing Cl- ions
Heat is produced or absorbed
Acid and base are mixed together
Color changes

22. Subtle Indications of a Reaction
Heat or light is absorbed or emitted
Changes in the way the substances behave in an electrical or magnetic field before and after a reaction
Changes in electrical properties

23. Writing Chemical Reactions
We will learn to identify the following patterns of chemical reactions:
combination
decomposition
single-replacement
double-replacement
Recognizing the pattern will help you write and understand reactions

24. Combination Reactions
The joining of two or more elements or compounds, producing a product of different composition
A + B  AB
Examples:
2Na(s) + Cl2(g)  2NaCl(s)
MgO(s) + CO2(g)  MgCO3(s)

25. Types of Combination Reactions
Combination of a metal and a nonmetal to form a salt
Combination of hydrogen and chlorine molecules to produce hydrogen chloride
Formation of water from hydrogen and oxygen molecules
Reaction of magnesium oxide and carbon dioxide to produce magnesium carbonate

26. Decomposition Reactions
Produce two or more products from a single reactant
Reverse of a combination reaction
AB  A + B
Examples:
2HgO(s)  2Hg(l) + O2(g)
CaCO3(s)  CaO(s) + CO2(g)

27. Types of Decomposition Reactions
Heating calcium carbonate to produce calcium oxide and carbon dioxide
Removal of water from a hydrated material

28. Replacement Reactions
Single-replacement
One atom replaces another in the compound producing a new compound
Examples:
Cu(s)+2AgNO3(aq)  2Ag(s)+Cu(NO3)2(aq)
2Na(s) + 2H2O(l)  2NaOH(aq) + H2(g)
A + BC  B + AC

29. Types of Replacement Reactions
Replacement of copper by zinc in copper sulfate
Replacement of aluminum by sodium in aluminum nitrate

30. Replacement Reactions
Double-replacement
Two compounds undergo a “change of partners”
Two compounds react by exchanging atoms to produce two new compounds
AB + CD  AD + CB

31. Example of Double-Replacement
Formation of solid lead chloride from lead nitrate and sodium chloride
Pb(NO3)2(aq) + 2NaCl(aq) 
PbCl2(s) + 2NaNO3(aq)
AB + CD  AD + CB

32. Types of Chemical Reactions
Precipitation Reactions
Chemical change in a solution that results in one or more insoluble products
To predict if a precipitation reaction can occur it is helpful to know the solubilities of ionic compounds

33. Solubilities of Some Common Ionic Compounds

34. Predicting Whether Precipitation
Will Occur
Recombine the ionic compounds to have them exchange partners
Examine the new compounds formed and determine if any are insoluble according to the rules in Table 4.1
Any insoluble salt will be the precipitate
Pb(NO3)2(aq) + NaCl(aq) 
PbCl2 (s) + NaNO3 ( aq)

35. Predict Whether These Reactions Form Precipitates
Potassium chloride and silver nitrate
Potassium acetate and silver nitrate
Know the difference between overall and net ionic equations.

36. Reactions with Oxygen Reactions with oxygen generally release energy
Combustion of natural gas
Organic compounds CO2 and H2O are usually the products
CH4+2O2CO2+2H2O
Rusting or corrosion of iron
4Fe + 3O2  2Fe2O3

37. Acid-Base Reactions
These reactions involve the transfer of a hydrogen ion (H+) from one reactant (acid) to another (base)
HCl(aq) + NaOH(aq)  NaCl(aq) + H2O(l)
The H+ on HCl was transferred to the oxygen in OH-, giving H2O

38. Oxidation-Reduction Reactions
Reaction involves the transfer of one or more electrons from one reactant to another
Zn(s) + Cu2+(aq) Cu(s) + Zn2+(aq)
Two electrons are transferred from Zn to Cu2+

39. Writing Chemical Reactions
Consider the following reaction:
hydrogen reacts with oxygen to produce water
Write the above reaction as a chemical equation
H2 + O2  H2O
Don’t forget the diatomic elements

40. 4.4 Balancing Chemical Equations
A chemical equation shows the molar quantity of reactants needed to produce a particular molar quantity of products
The relative number of moles of each product and reactant is indicated by placing a whole-number coefficient before the formula of each substance in the chemical equation

41. Law of Conservation of Mass
Law of conservation of mass - matter cannot be either gained or lost in the process of a chemical reaction
The total mass of the products must equal the total mass of the reactants

42. Coefficient - how many of that substance are in the reaction
Balancing
Coefficient - how many of that substance are in the reaction
The equation must be balanced
All the atoms of every reactant must also appear in the products
Number of Hg on left? 2
on right 2
Number of O on left? 2

43. Examine the Equation H2 + O2  H2O
Is the law of conservation of mass obeyed as written? NO
Balancing chemical equations uses coefficients to ensure that the law of conservation of mass is obeyed
You may never change subscripts!
WRONG: H2 + O2  H2O2

44. Steps in Equation Balancing
The steps to balancing:
H2 + O2  H2O
Step 1. Count the number of moles of atoms of each element on both product and reactant sides
Reactants Products
2 mol H mol H
2 mol O mol O

45. Steps in Equation Balancing
H2 + O2  H2O
Step 2. Determine which elements are not balanced – do not have same number on both sides of the equation
Oxygen is not balanced
Step 3. Balance one element at a time by changing the coefficients
H2 + O2  2H2O
This balances oxygen, but is hydrogen still balanced?

46. Steps in Equation Balancing
H2 + O2  2H2O
How will we balance hydrogen?
2H2 + O2  2H2O
Step 4. Check! Make sure the law of conservation of mass is obeyed
Reactants Products
4 mol H 4 mol H
2 mol O 2 mol O

47. Practice Equation Balancing
Balance the following equations:
C2H2 + O2  CO2 + H2O
AgNO3 + FeCl3  Fe(NO3)3 + AgCl
C2H6 + O2  CO2 + H2O
N2 + H2  NH3

48. 4.5 Calculations Using the Chemical Equation
Calculation quantities of reactants and products in a chemical reaction has many applications
Need a balanced chemical equation for the reaction of interest
The coefficients represent the number of moles of each substance in the equation

49. General Principles
Chemical formulas of all reactants and products must be known
Equation must be balanced to obey the law of conservation of mass
Calculations of an unbalanced equation are meaningless
Calculations are performed in terms of moles
Coefficients in the balanced equation represent the relative number of moles of products and reactants

50. Using the Chemical Equation
Examine the reaction:
2H2 + O2  2H2O
Coefficients tell us?
2 mol H2 reacts with 1 mol O2 to produce 2 mol H2O
What if 4 moles of H2 reacts with 2 moles of O2?
It yields 4 moles of H2O

51. Using the Chemical Equation
2H2 + O2  2H2O
The coefficients of the balanced equation are used to convert between moles of substances
How many moles of O2 are needed to react with 4.26 moles of H2?
Use the factor-label method to perform this calculation

52. Use of Conversion Factors
2H2 + O2  2H2O 1
2.13 mol O2 2
Digits in the conversion factor come from the balanced equation

53. Conversion Between Moles and Grams
Requires only the formula weight
Convert 1.00 mol O2 to grams
Plan the path
Find the molar mass of oxygen
32.0 g O2 = 1 mol O2
Set up the equation
Cancel units 1.00 mol O2 x 32.0 g O2
1 mol O2
Solve equation x 32.0 g O2 = 32.0 g O2
moles of
Oxygen
grams of
Oxygen

54. Conversion of Mole Reactants to Mole Products
Use a balanced equation
C3H8(g) + 5O2(g) CO2(g) + 4H2O(g)
1 mol C3H8 results in:
5 mol O2 consumed mol C3H8 /5 mol O2
3 mol CO2 formed mol C3H8 /3 mol CO2
4 mol H2O formed mol C3H8 /4 mol H2O
This can be rewritten as conversion factors

55. Calculating Reacting Quantities
Calculate grams O2 reacting with 1.00 mol C3H8
Use 2 conversion factors
Moles C3H8 to moles O2
Moles of O2 to grams O2
Set up the equation and cancel units
1.00 mol C3H8 x 5 mol O2 x g O2 =
1 mol C3H mol O2
1.00 x 5 x 32.0 g O2 = x 102 g O2
moles
C3H8
moles
Oxygen
grams
Oxygen

56. Calculating Grams of Product from Moles of Reactant
Calculate grams CO2 from combustion of 1.00 mol C3H8
Use 2 conversion factors
Moles C3H8 to moles CO2
Moles of CO2 to grams CO2
Set up the equation and cancel units
1.00 mol C3H8 x 3 mol CO2 x g CO2 =
1 mol C3H mol CO2
1.00 x 3 x 44.0 g CO2 = x 102 g CO2
moles
C3H8
moles
CO2
grams
CO2

57. Relating Masses of Reactants and Products
Calculate grams C3H8 required to produce 36.0 grams of H2O
Use 3 conversion factors
Grams H2O to moles H2O
Moles H2O to moles C3H8
Moles of C3H8 to grams C3H8
Set up the equation and cancel units
= g C3H8
grams
H2O
moles
H2O
moles
C3H8
grams
C3H8

58. Calculating a Quantity of Reactant
Ca(OH)2 neutralizes HCl
Calculate grams HCl neutralized by mol Ca(OH)2
Write chemical equation and balance
Ca(OH)2(s) + 2HCl(aq) CaCl2(s) + 2H2O(l)
Plan the path
Set up the equation and cancel units
0.500 mol Ca(OH)2 x 2 mol HCl x 36.5 g HCl
1 mol Ca(OH)2 1 mol HCl
= 36.5 g HCl
moles
Ca(OH)2
moles
HCl
grams
HCl

59. Sample Calculation Na + Cl2  NaCl Balance the equation
Calculate the moles Cl2 reacting with 5.00 mol Na
Calculate the grams NaCl produced when 5.00 mol Na reacts with an excess of Cl2
Calculate the grams Na reacting with 5.00 g Cl2
2Na + Cl2  2NaCl

60. Theoretical and Percent Yield
Theoretical yield - the maximum amount of product that can be produced
Pencil and paper yield
Actual yield - the amount produced when the reaction is performed
Laboratory yield
Percent yield:
= 125 g CO2 actual x 100% = 97.4%
132 g CO2 theoretical

61. Sample Calculation
If the theoretical yield of iron was 30.0 g and actual yield was 25.0 g, calculate the percent yield:
2 Al(s) + Fe2O3(s)  Al2O3(s) + 2Fe(l)
[25.0 g / g] x 100% = 83.3%
Calculate the % yield if 26.8 grams iron was collected in the same reaction