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Raffi Hovasapian

Raffi Hovasapian

Kinetic Molecular Theory and Real Gases

Slide Duration:

Table of Contents

I. Review
Naming Compounds

41m 24s

Intro
0:00
Periodic Table of Elements
0:15
Naming Compounds
3:13
Definition and Examples of Ions
3:14
Ionic (Symbol to Name): NaCl
5:23
Ionic (Name to Symbol): Calcium Oxide
7:58
Ionic - Polyatoms Anions: Examples
12:45
Ionic - Polyatoms Anions (Symbol to Name): KClO
14:50
Ionic - Polyatoms Anions (Name to Symbol): Potassium Phosphate
15:49
Ionic Compounds Involving Transition Metals (Symbol to Name): Co₂(CO₃)₃
20:48
Ionic Compounds Involving Transition Metals (Name to Symbol): Palladium 2 Acetate
22:44
Naming Covalent Compounds (Symbol to Name): CO
26:21
Naming Covalent Compounds (Name to Symbol): Nitrogen Trifluoride
27:34
Naming Covalent Compounds (Name to Symbol): Dichlorine Monoxide
27:57
Naming Acids Introduction
28:11
Naming Acids (Name to Symbol): Chlorous Acid
35:08
% Composition by Mass Example
37:38
Stoichiometry

37m 19s

Intro
0:00
Stoichiometry
0:25
Introduction to Stoichiometry
0:26
Example 1
5:03
Example 2
10:17
Example 3
15:09
Example 4
24:02
Example 5: Questions
28:11
Example 5: Part A - Limiting Reactant
30:30
Example 5: Part B
32:27
Example 5: Part C
35:00
II. Aqueous Reactions & Stoichiometry
Precipitation Reactions

31m 14s

Intro
0:00
Precipitation Reactions
0:53
Dissociation of ionic Compounds
0:54
Solubility Guidelines for ionic Compounds: Soluble Ionic Compounds
8:15
Solubility Guidelines for ionic Compounds: Insoluble ionic Compounds
12:56
Precipitation Reactions
14:08
Example 1: Mixing a Solution of BaCl₂ & K₂SO₄
21:21
Example 2: Mixing a Solution of Mg(NO₃)₂ & KI
26:10
Acid-Base Reactions

43m 21s

Intro
0:00
Acid-Base Reactions
1:00
Introduction to Acid: Monoprotic Acid and Polyprotic Acid
1:01
Introduction to Base
8:28
Neutralization
11:45
Example 1
16:17
Example 2
21:55
Molarity
24:50
Example 3
26:50
Example 4
30:01
Example 4: Limiting Reactant
37:51
Example 4: Reaction Part
40:01
Oxidation Reduction Reactions

47m 58s

Intro
0:00
Oxidation Reduction Reactions
0:26
Oxidation and Reduction Overview
0:27
How Can One Tell Whether Oxidation-Reduction has Taken Place?
7:13
Rules for Assigning Oxidation State: Number 1
11:22
Rules for Assigning Oxidation State: Number 2
12:46
Rules for Assigning Oxidation State: Number 3
13:25
Rules for Assigning Oxidation State: Number 4
14:50
Rules for Assigning Oxidation State: Number 5
15:41
Rules for Assigning Oxidation State: Number 6
17:00
Example 1: Determine the Oxidation State of Sulfur in the Following Compounds
18:20
Activity Series and Reduction Properties
25:32
Activity Series and Reduction Properties
25:33
Example 2: Write the Balance Molecular, Total Ionic, and Net Ionic Equations for Al + HCl
31:37
Example 3
34:25
Example 4
37:55
Stoichiometry Examples

31m 50s

Intro
0:00
Stoichiometry Example 1
0:36
Example 1: Question and Answer
0:37
Stoichiometry Example 2
6:57
Example 2: Questions
6:58
Example 2: Part A Solution
12:16
Example 2: Part B Solution
13:05
Example 2: Part C Solution
14:00
Example 2: Part D Solution
14:38
Stoichiometry Example 3
17:56
Example 3: Questions
17:57
Example 3: Part A Solution
19:51
Example 3: Part B Solution
21:43
Example 3: Part C Solution
26:46
III. Gases
Pressure, Gas Laws, & The Ideal Gas Equation

49m 40s

Intro
0:00
Pressure
0:22
Pressure Overview
0:23
Torricelli: Barometer
4:35
Measuring Gas Pressure in a Container
7:49
Boyle's Law
12:40
Example 1
16:56
Gas Laws
21:18
Gas Laws
21:19
Avogadro's Law
26:16
Example 2
31:47
Ideal Gas Equation
38:20
Standard Temperature and Pressure (STP)
38:21
Example 3
40:43
Partial Pressure, Mol Fraction, & Vapor Pressure

32m

Intro
0:00
Gases
0:27
Gases
0:28
Mole Fractions
5:52
Vapor Pressure
8:22
Example 1
13:25
Example 2
22:45
Kinetic Molecular Theory and Real Gases

31m 58s

Intro
0:00
Kinetic Molecular Theory and Real Gases
0:45
Kinetic Molecular Theory 1
0:46
Kinetic Molecular Theory 2
4:23
Kinetic Molecular Theory 3
5:42
Kinetic Molecular Theory 4
6:27
Equations
7:52
Effusion
11:15
Diffusion
13:30
Example 1
19:54
Example 2
23:23
Example 3
26:45
AP Practice for Gases

25m 34s

Intro
0:00
Example 1
0:34
Example 1
0:35
Example 2
6:15
Example 2: Part A
6:16
Example 2: Part B
8:46
Example 2: Part C
10:30
Example 2: Part D
11:15
Example 2: Part E
12:20
Example 2: Part F
13:22
Example 3
14:45
Example 3
14:46
Example 4
18:16
Example 4
18:17
Example 5
21:04
Example 5
21:05
IV. Thermochemistry
Energy, Heat, and Work

37m 32s

Intro
0:00
Thermochemistry
0:25
Temperature and Heat
0:26
Work
3:07
System, Surroundings, Exothermic Process, and Endothermic Process
8:19
Work & Gas: Expansion and Compression
16:30
Example 1
24:41
Example 2
27:47
Example 3
31:58
Enthalpy & Hess's Law

32m 34s

Intro
0:00
Thermochemistry
1:43
Defining Enthalpy & Hess's Law
1:44
Example 1
6:48
State Function
13:11
Example 2
17:15
Example 3
24:09
Standard Enthalpies of Formation

23m 9s

Intro
0:00
Thermochemistry
1:04
Standard Enthalpy of Formation: Definition & Equation
1:05
∆H of Formation
10:00
Example 1
11:22
Example 2
19:00
Calorimetry

39m 28s

Intro
0:00
Thermochemistry
0:21
Heat Capacity
0:22
Molar Heat Capacity
4:44
Constant Pressure Calorimetry
5:50
Example 1
12:24
Constant Volume Calorimetry
21:54
Example 2
24:40
Example 3
31:03
V. Kinetics
Reaction Rates and Rate Laws

36m 24s

Intro
0:00
Kinetics
2:18
Rate: 2 NO₂ (g) → 2NO (g) + O₂ (g)
2:19
Reaction Rates Graph
7:25
Time Interval & Average Rate
13:13
Instantaneous Rate
15:13
Rate of Reaction is Proportional to Some Power of the Reactant Concentrations
23:49
Example 1
27:19
Method of Initial Rates

30m 48s

Intro
0:00
Kinetics
0:33
Rate
0:34
Idea
2:24
Example 1: NH₄⁺ + NO₂⁻ → NO₂ (g) + 2 H₂O
5:36
Example 2: BrO₃⁻ + 5 Br⁻ + 6 H⁺ → 3 Br₂ + 3 H₂O
19:29
Integrated Rate Law & Reaction Half-Life

32m 17s

Intro
0:00
Kinetics
0:52
Integrated Rate Law
0:53
Example 1
6:26
Example 2
15:19
Half-life of a Reaction
20:40
Example 3: Part A
25:41
Example 3: Part B
28:01
Second Order & Zero-Order Rate Laws

26m 40s

Intro
0:00
Kinetics
0:22
Second Order
0:23
Example 1
6:08
Zero-Order
16:36
Summary for the Kinetics Associated with the Reaction
21:27
Activation Energy & Arrhenius Equation

40m 59s

Intro
0:00
Kinetics
0:53
Rate Constant
0:54
Collision Model
2:45
Activation Energy
5:11
Arrhenius Proposed
9:54
2 Requirements for a Successful Reaction
15:39
Rate Constant
17:53
Arrhenius Equation
19:51
Example 1
25:00
Activation Energy & the Values of K
32:12
Example 2
36:46
AP Practice for Kinetics

29m 8s

Intro
0:00
Kinetics
0:43
Example 1
0:44
Example 2
6:53
Example 3
8:58
Example 4
11:36
Example 5
16:36
Example 6: Part A
21:00
Example 6: Part B
25:09
VI. Equilibrium
Equilibrium, Part 1

46m

Intro
0:00
Equilibrium
1:32
Introduction to Equilibrium
1:33
Equilibrium Rules
14:00
Example 1: Part A
16:46
Example 1: Part B
18:48
Example 1: Part C
22:13
Example 1: Part D
24:55
Example 2: Part A
27:46
Example 2: Part B
31:22
Example 2: Part C
33:00
Reverse a Reaction
36:04
Example 3
37:24
Equilibrium, Part 2

40m 53s

Intro
0:00
Equilibrium
1:31
Equilibriums Involving Gases
1:32
General Equation
10:11
Example 1: Question
11:55
Example 1: Answer
13:43
Example 2: Question
19:08
Example 2: Answer
21:37
Example 3: Question
33:40
Example 3: Answer
35:24
Equilibrium: Reaction Quotient

45m 53s

Intro
0:00
Equilibrium
0:57
Reaction Quotient
0:58
If Q > K
5:37
If Q < K
6:52
If Q = K
7:45
Example 1: Part A
8:24
Example 1: Part B
13:11
Example 2: Question
20:04
Example 2: Answer
22:15
Example 3: Question
30:54
Example 3: Answer
32:52
Steps in Solving Equilibrium Problems
42:40
Equilibrium: Examples

31m 51s

Intro
0:00
Equilibrium
1:09
Example 1: Question
1:10
Example 1: Answer
4:15
Example 2: Question
13:04
Example 2: Answer
15:20
Example 3: Question
25:03
Example 3: Answer
26:32
Le Chatelier's principle & Equilibrium

40m 52s

Intro
0:00
Le Chatelier
1:05
Le Chatelier Principle
1:06
Concentration: Add 'x'
5:25
Concentration: Subtract 'x'
7:50
Example 1
9:44
Change in Pressure
12:53
Example 2
20:40
Temperature: Exothermic and Endothermic
24:33
Example 3
29:55
Example 4
35:30
VII. Acids & Bases
Acids and Bases

50m 11s

Intro
0:00
Acids and Bases
1:14
Bronsted-Lowry Acid-Base Model
1:28
Reaction of an Acid with Water
4:36
Acid Dissociation
10:51
Acid Strength
13:48
Example 1
21:22
Water as an Acid & a Base
25:25
Example 2: Part A
32:30
Example 2: Part B
34:47
Example 3: Part A
35:58
Example 3: Part B
39:33
pH Scale
41:12
Example 4
43:56
pH of Weak Acid Solutions

43m 52s

Intro
0:00
pH of Weak Acid Solutions
1:12
pH of Weak Acid Solutions
1:13
Example 1
6:26
Example 2
14:25
Example 3
24:23
Example 4
30:38
Percent Dissociation: Strong & Weak Bases

43m 4s

Intro
0:00
Bases
0:33
Percent Dissociation: Strong & Weak Bases
0:45
Example 1
6:23
Strong Base Dissociation
11:24
Example 2
13:02
Weak Acid and General Reaction
17:38
Example: NaOH → Na⁺ + OH⁻
20:30
Strong Base and Weak Base
23:49
Example 4
24:54
Example 5
33:51
Polyprotic Acids

35m 34s

Intro
0:00
Polyprotic Acids
1:04
Acids Dissociation
1:05
Example 1
4:51
Example 2
17:30
Example 3
31:11
Salts and Their Acid-Base Properties

41m 14s

Intro
0:00
Salts and Their Acid-Base Properties
0:11
Salts and Their Acid-Base Properties
0:15
Example 1
7:58
Example 2
14:00
Metal Ion and Acidic Solution
22:00
Example 3
28:35
NH₄F → NH₄⁺ + F⁻
34:05
Example 4
38:03
Common Ion Effect & Buffers

41m 58s

Intro
0:00
Common Ion Effect & Buffers
1:16
Covalent Oxides Produce Acidic Solutions in Water
1:36
Ionic Oxides Produce Basic Solutions in Water
4:15
Practice Example 1
6:10
Practice Example 2
9:00
Definition
12:27
Example 1: Part A
16:49
Example 1: Part B
19:54
Buffer Solution
25:10
Example of Some Buffers: HF and NaF
30:02
Example of Some Buffers: Acetic Acid & Potassium Acetate
31:34
Example of Some Buffers: CH₃NH₂ & CH₃NH₃Cl
33:54
Example 2: Buffer Solution
36:36
Buffer

32m 24s

Intro
0:00
Buffers
1:20
Buffer Solution
1:21
Adding Base
5:03
Adding Acid
7:14
Example 1: Question
9:48
Example 1: Recall
12:08
Example 1: Major Species Upon Addition of NaOH
16:10
Example 1: Equilibrium, ICE Chart, and Final Calculation
24:33
Example 1: Comparison
29:19
Buffers, Part II

40m 6s

Intro
0:00
Buffers
1:27
Example 1: Question
1:32
Example 1: ICE Chart
3:15
Example 1: Major Species Upon Addition of OH⁻, But Before Rxn
7:23
Example 1: Equilibrium, ICE Chart, and Final Calculation
12:51
Summary
17:21
Another Look at Buffering & the Henderson-Hasselbalch equation
19:00
Example 2
27:08
Example 3
32:01
Buffers, Part III

38m 43s

Intro
0:00
Buffers
0:25
Buffer Capacity Part 1
0:26
Example 1
4:10
Buffer Capacity Part 2
19:29
Example 2
25:12
Example 3
32:02
Titrations: Strong Acid and Strong Base

42m 42s

Intro
0:00
Titrations: Strong Acid and Strong Base
1:11
Definition of Titration
1:12
Sample Problem
3:33
Definition of Titration Curve or pH Curve
9:46
Scenario 1: Strong Acid- Strong Base Titration
11:00
Question
11:01
Part 1: No NaOH is Added
14:00
Part 2: 10.0 mL of NaOH is Added
15:50
Part 3: Another 10.0 mL of NaOH & 20.0 mL of NaOH are Added
22:19
Part 4: 50.0 mL of NaOH is Added
26:46
Part 5: 100.0 mL (Total) of NaOH is Added
27:26
Part 6: 150.0 mL (Total) of NaOH is Added
32:06
Part 7: 200.0 mL of NaOH is Added
35:07
Titrations Curve for Strong Acid and Strong Base
35:43
Titrations: Weak Acid and Strong Base

42m 3s

Intro
0:00
Titrations: Weak Acid and Strong Base
0:43
Question
0:44
Part 1: No NaOH is Added
1:54
Part 2: 10.0 mL of NaOH is Added
5:17
Part 3: 25.0 mL of NaOH is Added
14:01
Part 4: 40.0 mL of NaOH is Added
21:55
Part 5: 50.0 mL (Total) of NaOH is Added
22:25
Part 6: 60.0 mL (Total) of NaOH is Added
31:36
Part 7: 75.0 mL (Total) of NaOH is Added
35:44
Titration Curve
36:09
Titration Examples & Acid-Base Indicators

52m 3s

Intro
0:00
Examples and Indicators
0:25
Example 1: Question
0:26
Example 1: Solution
2:03
Example 2: Question
12:33
Example 2: Solution
14:52
Example 3: Question
23:45
Example 3: Solution
25:09
Acid/Base Indicator Overview
34:45
Acid/Base Indicator Example
37:40
Acid/Base Indicator General Result
47:11
Choosing Acid/Base Indicator
49:12
VIII. Solubility
Solubility Equilibria

36m 25s

Intro
0:00
Solubility Equilibria
0:48
Solubility Equilibria Overview
0:49
Solubility Product Constant
4:24
Definition of Solubility
9:10
Definition of Solubility Product
11:28
Example 1
14:09
Example 2
20:19
Example 3
27:30
Relative Solubilities
31:04
Solubility Equilibria, Part II

42m 6s

Intro
0:00
Solubility Equilibria
0:46
Common Ion Effect
0:47
Example 1
3:14
pH & Solubility
13:00
Example of pH & Solubility
15:25
Example 2
23:06
Precipitation & Definition of the Ion Product
26:48
If Q > Ksp
29:31
If Q < Ksp
30:27
Example 3
32:58
Solubility Equilibria, Part III

43m 9s

Intro
0:00
Solubility Equilibria
0:55
Example 1: Question
0:56
Example 1: Step 1 - Check to See if Anything Precipitates
2:52
Example 1: Step 2 - Stoichiometry
10:47
Example 1: Step 3 - Equilibrium
16:34
Example 2: Selective Precipitation (Question)
21:02
Example 2: Solution
23:41
Classical Qualitative Analysis
29:44
Groups: 1-5
38:44
IX. Complex Ions
Complex Ion Equilibria

43m 38s

Intro
0:00
Complex Ion Equilibria
0:32
Complex Ion
0:34
Ligan Examples
1:51
Ligand Definition
3:12
Coordination
6:28
Example 1
8:08
Example 2
19:13
Complex Ions & Solubility

31m 30s

Intro
0:00
Complex Ions and Solubility
0:23
Recall: Classical Qualitative Analysis
0:24
Example 1
6:10
Example 2
16:16
Dissolving a Water-Insoluble Ionic Compound: Method 1
23:38
Dissolving a Water-Insoluble Ionic Compound: Method 2
28:13
X. Chemical Thermodynamics
Spontaneity, Entropy, & Free Energy, Part I

56m 28s

Intro
0:00
Spontaneity, Entropy, Free Energy
2:25
Energy Overview
2:26
Equation: ∆E = q + w
4:30
State Function/ State Property
8:35
Equation: w = -P∆V
12:00
Enthalpy: H = E + PV
14:50
Enthalpy is a State Property
17:33
Exothermic and Endothermic Reactions
19:20
First Law of Thermodynamic
22:28
Entropy
25:48
Spontaneous Process
33:53
Second Law of Thermodynamic
36:51
More on Entropy
42:23
Example
43:55
Spontaneity, Entropy, & Free Energy, Part II

39m 55s

Intro
0:00
Spontaneity, Entropy, Free Energy
1:30
∆S of Universe = ∆S of System + ∆S of Surrounding
1:31
Convention
3:32
Examining a System
5:36
Thermodynamic Property: Sign of ∆S
16:52
Thermodynamic Property: Magnitude of ∆S
18:45
Deriving Equation: ∆S of Surrounding = -∆H / T
20:25
Example 1
25:51
Free Energy Equations
29:22
Spontaneity, Entropy, & Free Energy, Part III

30m 10s

Intro
0:00
Spontaneity, Entropy, Free Energy
0:11
Example 1
2:38
Key Concept of Example 1
14:06
Example 2
15:56
Units for ∆H, ∆G, and S
20:56
∆S of Surrounding & ∆S of System
22:00
Reaction Example
24:17
Example 3
26:52
Spontaneity, Entropy, & Free Energy, Part IV

30m 7s

Intro
0:00
Spontaneity, Entropy, Free Energy
0:29
Standard Free Energy of Formation
0:58
Example 1
4:34
Reaction Under Non-standard Conditions
13:23
Example 2
16:26
∆G = Negative
22:12
∆G = 0
24:38
Diagram Example of ∆G
26:43
Spontaneity, Entropy, & Free Energy, Part V

44m 56s

Intro
0:00
Spontaneity, Entropy, Free Energy
0:56
Equations: ∆G of Reaction, ∆G°, and K
0:57
Example 1: Question
6:50
Example 1: Part A
9:49
Example 1: Part B
15:28
Example 2
17:33
Example 3
23:31
lnK = (- ∆H° ÷ R) ( 1 ÷ T) + ( ∆S° ÷ R)
31:36
Maximum Work
35:57
XI. Electrochemistry
Oxidation-Reduction & Balancing

39m 23s

Intro
0:00
Oxidation-Reduction and Balancing
2:06
Definition of Electrochemistry
2:07
Oxidation and Reduction Review
3:05
Example 1: Assigning Oxidation State
10:15
Example 2: Is the Following a Redox Reaction?
18:06
Example 3: Step 1 - Write the Oxidation & Reduction Half Reactions
22:46
Example 3: Step 2 - Balance the Reaction
26:44
Example 3: Step 3 - Multiply
30:11
Example 3: Step 4 - Add
32:07
Example 3: Step 5 - Check
33:29
Galvanic Cells

43m 9s

Intro
0:00
Galvanic Cells
0:39
Example 1: Balance the Following Under Basic Conditions
0:40
Example 1: Steps to Balance Reaction Under Basic Conditions
3:25
Example 1: Solution
5:23
Example 2: Balance the Following Reaction
13:56
Galvanic Cells
18:15
Example 3: Galvanic Cells
28:19
Example 4: Galvanic Cells
35:12
Cell Potential

48m 41s

Intro
0:00
Cell Potential
2:08
Definition of Cell Potential
2:17
Symbol and Unit
5:50
Standard Reduction Potential
10:16
Example Figure 1
13:08
Example Figure 2
19:00
All Reduction Potentials are Written as Reduction
23:10
Cell Potential: Important Fact 1
26:49
Cell Potential: Important Fact 2
27:32
Cell Potential: Important Fact 3
28:54
Cell Potential: Important Fact 4
30:05
Example Problem 1
32:29
Example Problem 2
38:38
Potential, Work, & Free Energy

41m 23s

Intro
0:00
Potential, Work, Free Energy
0:42
Descriptions of Galvanic Cell
0:43
Line Notation
5:33
Example 1
6:26
Example 2
11:15
Example 3
15:18
Equation: Volt
22:20
Equations: Cell Potential, Work, and Charge
28:30
Maximum Cell Potential is Related to the Free Energy of the Cell Reaction
35:09
Example 4
37:42
Cell Potential & Concentration

34m 19s

Intro
0:00
Cell Potential & Concentration
0:29
Example 1: Question
0:30
Example 1: Nernst Equation
4:43
Example 1: Solution
7:01
Cell Potential & Concentration
11:27
Example 2
16:38
Manipulating the Nernst Equation
25:15
Example 3
28:43
Electrolysis

33m 21s

Intro
0:00
Electrolysis
3:16
Electrolysis: Part 1
3:17
Electrolysis: Part 2
5:25
Galvanic Cell Example
7:13
Nickel Cadmium Battery
12:18
Ampere
16:00
Example 1
20:47
Example 2
25:47
XII. Light
Light

44m 45s

Intro
0:00
Light
2:14
Introduction to Light
2:15
Frequency, Speed, and Wavelength of Waves
3:58
Units and Equations
7:37
Electromagnetic Spectrum
12:13
Example 1: Calculate the Frequency
17:41
E = hν
21:30
Example 2: Increment of Energy
25:12
Photon Energy of Light
28:56
Wave and Particle
31:46
Example 3: Wavelength of an Electron
34:46
XIII. Quantum Mechanics
Quantum Mechanics & Electron Orbitals

54m

Intro
0:00
Quantum Mechanics & Electron Orbitals
0:51
Quantum Mechanics & Electron Orbitals Overview
0:52
Electron Orbital and Energy Levels for the Hydrogen Atom
8:47
Example 1
13:41
Quantum Mechanics: Schrodinger Equation
19:19
Quantum Numbers Overview
31:10
Principal Quantum Numbers
33:28
Angular Momentum Numbers
34:55
Magnetic Quantum Numbers
36:35
Spin Quantum Numbers
37:46
Primary Level, Sublevels, and Sub-Sub-Levels
39:42
Example
42:17
Orbital & Quantum Numbers
49:32
Electron Configurations & Diagrams

34m 4s

Intro
0:00
Electron Configurations & Diagrams
1:08
Electronic Structure of Ground State Atom
1:09
Order of Electron Filling
3:50
Electron Configurations & Diagrams: H
8:41
Electron Configurations & Diagrams: He
9:12
Electron Configurations & Diagrams: Li
9:47
Electron Configurations & Diagrams: Be
11:17
Electron Configurations & Diagrams: B
12:05
Electron Configurations & Diagrams: C
13:03
Electron Configurations & Diagrams: N
14:55
Electron Configurations & Diagrams: O
15:24
Electron Configurations & Diagrams: F
16:25
Electron Configurations & Diagrams: Ne
17:00
Electron Configurations & Diagrams: S
18:08
Electron Configurations & Diagrams: Fe
20:08
Introduction to Valence Electrons
23:04
Valence Electrons of Oxygen
23:44
Valence Electrons of Iron
24:02
Valence Electrons of Arsenic
24:30
Valence Electrons: Exceptions
25:36
The Periodic Table
27:52
XIV. Intermolecular Forces
Vapor Pressure & Changes of State

52m 43s

Intro
0:00
Vapor Pressure and Changes of State
2:26
Intermolecular Forces Overview
2:27
Hydrogen Bonding
5:23
Heat of Vaporization
9:58
Vapor Pressure: Definition and Example
11:04
Vapor Pressures is Mostly a Function of Intermolecular Forces
17:41
Vapor Pressure Increases with Temperature
20:52
Vapor Pressure vs. Temperature: Graph and Equation
22:55
Clausius-Clapeyron Equation
31:55
Example 1
32:13
Heating Curve
35:40
Heat of Fusion
41:31
Example 2
43:45
Phase Diagrams & Solutions

31m 17s

Intro
0:00
Phase Diagrams and Solutions
0:22
Definition of a Phase Diagram
0:50
Phase Diagram Part 1: H₂O
1:54
Phase Diagram Part 2: CO₂
9:59
Solutions: Solute & Solvent
16:12
Ways of Discussing Solution Composition: Mass Percent or Weight Percent
18:46
Ways of Discussing Solution Composition: Molarity
20:07
Ways of Discussing Solution Composition: Mole Fraction
20:48
Ways of Discussing Solution Composition: Molality
21:41
Example 1: Question
22:06
Example 1: Mass Percent
24:32
Example 1: Molarity
25:53
Example 1: Mole Fraction
28:09
Example 1: Molality
29:36
Vapor Pressure of Solutions

37m 23s

Intro
0:00
Vapor Pressure of Solutions
2:07
Vapor Pressure & Raoult's Law
2:08
Example 1
5:21
When Ionic Compounds Dissolve
10:51
Example 2
12:38
Non-Ideal Solutions
17:42
Negative Deviation
24:23
Positive Deviation
29:19
Example 3
31:40
Colligatives Properties

34m 11s

Intro
0:00
Colligative Properties
1:07
Boiling Point Elevation
1:08
Example 1: Question
5:19
Example 1: Solution
6:52
Freezing Point Depression
12:01
Example 2: Question
14:46
Example 2: Solution
16:34
Osmotic Pressure
20:20
Example 3: Question
28:00
Example 3: Solution
30:16
XV. Bonding
Bonding & Lewis Structure

48m 39s

Intro
0:00
Bonding & Lewis Structure
2:23
Covalent Bond
2:24
Single Bond, Double Bond, and Triple Bond
4:11
Bond Length & Intermolecular Distance
5:51
Definition of Electronegativity
8:42
Bond Polarity
11:48
Bond Energy
20:04
Example 1
24:31
Definition of Lewis Structure
31:54
Steps in Forming a Lewis Structure
33:26
Lewis Structure Example: H₂
36:53
Lewis Structure Example: CH₄
37:33
Lewis Structure Example: NO⁺
38:43
Lewis Structure Example: PCl₅
41:12
Lewis Structure Example: ICl₄⁻
43:05
Lewis Structure Example: BeCl₂
45:07
Resonance & Formal Charge

36m 59s

Intro
0:00
Resonance and Formal Charge
0:09
Resonance Structures of NO₃⁻
0:25
Resonance Structures of NO₂⁻
12:28
Resonance Structures of HCO₂⁻
16:28
Formal Charge
19:40
Formal Charge Example: SO₄²⁻
21:32
Formal Charge Example: CO₂
31:33
Formal Charge Example: HCN
32:44
Formal Charge Example: CN⁻
33:34
Formal Charge Example: 0₃
34:43
Shapes of Molecules

41m 21s

Intro
0:00
Shapes of Molecules
0:35
VSEPR
0:36
Steps in Determining Shapes of Molecules
6:18
Linear
11:38
Trigonal Planar
11:55
Tetrahedral
12:45
Trigonal Bipyramidal
13:23
Octahedral
14:29
Table: Shapes of Molecules
15:40
Example: CO₂
21:11
Example: NO₃⁻
24:01
Example: H₂O
27:00
Example: NH₃
29:48
Example: PCl₃⁻
32:18
Example: IF₄⁺
34:38
Example: KrF₄
37:57
Hybrid Orbitals

40m 17s

Intro
0:00
Hybrid Orbitals
0:13
Introduction to Hybrid Orbitals
0:14
Electron Orbitals for CH₄
5:02
sp³ Hybridization
10:52
Example: sp³ Hybridization
12:06
sp² Hybridization
14:21
Example: sp² Hybridization
16:11
σ Bond
19:10
π Bond
20:07
sp Hybridization & Example
22:00
dsp³ Hybridization & Example
27:36
d²sp³ Hybridization & Example
30:36
Example: Predict the Hybridization and Describe the Molecular Geometry of CO
32:31
Example: Predict the Hybridization and Describe the Molecular Geometry of BF₄⁻
35:17
Example: Predict the Hybridization and Describe the Molecular Geometry of XeF₂
37:09
XVI. AP Practice Exam
AP Practice Exam: Multiple Choice, Part I

52m 34s

Intro
0:00
Multiple Choice
1:21
Multiple Choice 1
1:22
Multiple Choice 2
2:23
Multiple Choice 3
3:38
Multiple Choice 4
4:34
Multiple Choice 5
5:16
Multiple Choice 6
5:41
Multiple Choice 7
6:20
Multiple Choice 8
7:03
Multiple Choice 9
7:31
Multiple Choice 10
9:03
Multiple Choice 11
11:52
Multiple Choice 12
13:16
Multiple Choice 13
13:56
Multiple Choice 14
14:52
Multiple Choice 15
15:43
Multiple Choice 16
16:20
Multiple Choice 17
16:55
Multiple Choice 18
17:22
Multiple Choice 19
18:59
Multiple Choice 20
20:24
Multiple Choice 21
22:20
Multiple Choice 22
23:29
Multiple Choice 23
24:30
Multiple Choice 24
25:24
Multiple Choice 25
26:21
Multiple Choice 26
29:06
Multiple Choice 27
30:42
Multiple Choice 28
33:28
Multiple Choice 29
34:38
Multiple Choice 30
35:37
Multiple Choice 31
37:31
Multiple Choice 32
38:28
Multiple Choice 33
39:50
Multiple Choice 34
42:57
Multiple Choice 35
44:18
Multiple Choice 36
45:52
Multiple Choice 37
48:02
Multiple Choice 38
49:25
Multiple Choice 39
49:43
Multiple Choice 40
50:16
Multiple Choice 41
50:49
AP Practice Exam: Multiple Choice, Part II

32m 15s

Intro
0:00
Multiple Choice
0:12
Multiple Choice 42
0:13
Multiple Choice 43
0:33
Multiple Choice 44
1:16
Multiple Choice 45
2:36
Multiple Choice 46
5:22
Multiple Choice 47
6:35
Multiple Choice 48
8:02
Multiple Choice 49
10:05
Multiple Choice 50
10:26
Multiple Choice 51
11:07
Multiple Choice 52
12:01
Multiple Choice 53
12:55
Multiple Choice 54
16:12
Multiple Choice 55
18:11
Multiple Choice 56
19:45
Multiple Choice 57
20:15
Multiple Choice 58
23:28
Multiple Choice 59
24:27
Multiple Choice 60
26:45
Multiple Choice 61
29:15
AP Practice Exam: Multiple Choice, Part III

32m 50s

Intro
0:00
Multiple Choice
0:16
Multiple Choice 62
0:17
Multiple Choice 63
1:57
Multiple Choice 64
6:16
Multiple Choice 65
8:05
Multiple Choice 66
9:18
Multiple Choice 67
10:38
Multiple Choice 68
12:51
Multiple Choice 69
14:32
Multiple Choice 70
17:35
Multiple Choice 71
22:44
Multiple Choice 72
24:27
Multiple Choice 73
27:46
Multiple Choice 74
29:39
Multiple Choice 75
30:23
AP Practice Exam: Free response Part I

47m 22s

Intro
0:00
Free Response
0:15
Free Response 1: Part A
0:16
Free Response 1: Part B
4:15
Free Response 1: Part C
5:47
Free Response 1: Part D
9:20
Free Response 1: Part E. i
10:58
Free Response 1: Part E. ii
16:45
Free Response 1: Part E. iii
26:03
Free Response 2: Part A. i
31:01
Free Response 2: Part A. ii
33:38
Free Response 2: Part A. iii
35:20
Free Response 2: Part B. i
37:38
Free Response 2: Part B. ii
39:30
Free Response 2: Part B. iii
44:44
AP Practice Exam: Free Response Part II

43m 5s

Intro
0:00
Free Response
0:12
Free Response 3: Part A
0:13
Free Response 3: Part B
6:25
Free Response 3: Part C. i
11:33
Free Response 3: Part C. ii
12:02
Free Response 3: Part D
14:30
Free Response 4: Part A
21:03
Free Response 4: Part B
22:59
Free Response 4: Part C
24:33
Free Response 4: Part D
27:22
Free Response 4: Part E
28:43
Free Response 4: Part F
29:35
Free Response 4: Part G
30:15
Free Response 4: Part H
30:48
Free Response 5: Diagram
32:00
Free Response 5: Part A
34:14
Free Response 5: Part B
36:07
Free Response 5: Part C
37:45
Free Response 5: Part D
39:00
Free Response 5: Part E
40:26
AP Practice Exam: Free Response Part III

28m 36s

Intro
0:00
Free Response
0:43
Free Response 6: Part A. i
0:44
Free Response 6: Part A. ii
3:08
Free Response 6: Part A. iii
5:02
Free Response 6: Part B. i
7:11
Free Response 6: Part B. ii
9:40
Free Response 7: Part A
11:14
Free Response 7: Part B
13:45
Free Response 7: Part C
15:43
Free Response 7: Part D
16:54
Free Response 8: Part A. i
19:15
Free Response 8: Part A. ii
21:16
Free Response 8: Part B. i
23:51
Free Response 8: Part B. ii
25:07
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Lecture Comments (10)

1 answer

Last reply by: Professor Hovasapian
Thu Dec 17, 2015 12:49 AM

Post by Tammy T on December 11, 2015

Hello Prof. Hovasapian!
I understand how when the Volume of the container shrink (due to applying external pressure), we switch to using Real gas law due to the volume of the particle is significant compared to where it is in.
However, how is it that when the pressure is high and temperature is low, we must account for the real gas behavior? I thought the P in ideal gas law is not P external.

2 answers

Last reply by: Jackson Forrestall
Wed Nov 12, 2014 8:53 PM

Post by Jackson Forrestall on September 27, 2014

Hello Professor Hovasapian! I understand the difference and the importance of knowing and using both the ideal and real gas laws, but, when time is of the essence, especially on the AP exam, would it be more beneficial for me to just use the ideal gas law due to it being quicker? Thank you so much for your lectures as well. They help me so much!

1 answer

Last reply by: Professor Hovasapian
Sat Jul 6, 2013 6:46 PM

Post by KyungYeop Kim on July 4, 2013

Hi Professor Raffi, I have a question about effective nuclear charge. As you go down a group in the periodic table, why is it that the effective nuclear charge decreases? from what I know, is it true that as the attraction decreases down the group, it somehow counterbalances the increase in nuclear charge? I'm confused.

2 answers

Last reply by: KyungYeop Kim
Thu Jul 4, 2013 8:11 PM

Post by Antie Chen on April 30, 2013

Hello Raffi, I am really confused about these equations. In the equation about 8:00, what's the Urms? rms? and what's the difference between these two equation?
And in the equation of real gases, a&b are van der waal constants, are they constant for specific gases, but why a&b are different in the example 3?

Related Articles:

Kinetic Molecular Theory and Real Gases

  • The Kinetic Energy of an Ideal Gas is directly proportional to its Temperature (Kelvin).
  • At high pressures gases deviate from ideal behavior because the particles are pushed together much more tightly:
    • A volume adjustment must be made.
    • A Pressure adjustment must be made.
  • The van der Waals equation accounts for these deviations.

Kinetic Molecular Theory and Real Gases

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Kinetic Molecular Theory and Real Gases 0:45
    • Kinetic Molecular Theory 1
    • Kinetic Molecular Theory 2
    • Kinetic Molecular Theory 3
    • Kinetic Molecular Theory 4
    • Equations
    • Effusion
    • Diffusion
    • Example 1
    • Example 2
    • Example 3

Transcription: Kinetic Molecular Theory and Real Gases

Welcome back to Educator.com, and welcome back to AP Chemistry.0000

Today, we're going to be discussing kinetic-molecular theory and properties of real gases.0003

Up until now, we've been discussing the ideal gas law, PV=nRT; well, the real gases actually behave well at low pressures and high temperatures.0008

When the pressures start to get high (let's say above 3, 4, 5, 6 atmospheres), and the pressures start to drop, volume starts to drop--at that point, the gas behavior starts to deviate from the ideal.0023

Towards the end of this particular lesson, we will discuss about how we adjust for that--how van der Waals adjusted for that.0037

Let's go ahead and get started.0043

We're going to run through the kinetic-molecular theory first.0047

So, again, what we are about to list right here--the four or five axioms of the kinetic-molecular theory--are precisely that: they are axioms; they are observations that we have made, and they are assumptions that we are making.0050

Based on those assumptions, we can start to build a theory, and hopefully have it correspond with what we observe empirically (in other words, what we get from experimentation).0062

Let's just list them out.0073

Let me see: our first axiom: The kinetic energy of an ideal gas (and again, we are talking about ideal gases' behavior--toward the end, we will discuss the deviation from ideal behavior, but the kinetic-molecular theory applies to ideal gases) is directly proportional to the temperature.0076

What that means, in terms of an equation, is: KE (the kinetic energy--the energy of motion of the molecules of the gas) is equal to 3/2 RT.0118

Now, R is the gas constant; however, here it is not equal to .08206 liter-atmosphere per mole-Kelvin.0131

In this particular case, because energy is expressed in Joules, and T here is in Kelvin, this R has to be Joules per Kelvin per mole; so, as it turns out...let's see: 8.31...it's going to be 8.31 Joules per mole-Kelvin.0139

And again, it's just a way of making the units work out; that is all it is; it's the same constant, R, the Rydberg constant; it's just so that it actually works out in terms of the appropriate units.0163

T is the temperature in Kelvin.0172

OK, now, also, what I'll put down here (this is a very, very important relationship--notice, it establishes the relationship between the energy, or the temperature; that is really what is going on here--so temperature is really just a measure of the average kinetic energy of the molecules)...0182

Most people confuse temperature and heat; temperature and heat are not the same thing.0200

Temperature is a measure of the motion, random motion, of the molecules; heat is that energy that actually flows from something hot in the direction of something cold.0204

They are two different things; temperature does not measure heat; it measures kinetic energy--it measures the random motion of the molecules, the vibrations, the bouncing around of each other.0214

OK, let's say there is one other little mathematical thing I want to put down here: the average kinetic energy of a gas particle (this one is not altogether that important, but I might as well just put it down here) equals 1/2 mass, times the average velocity squared.0223

Again, in this particular case, mass has to be in kilograms.0249

When velocity is expressed in meters per second, we get our kinetic energy in Joules.0255

That is why we need mass in kilograms.0261

OK, the second assumption of the kinetic-molecular theory is that the particles are so small (the particles of gas that are bouncing around) compared to the distance between the particles that the volume of the molecules is negligible.0264

In other words, molecules are very, very tiny; and when they're bouncing around in a gas, they are really very far apart from each other; so essentially, you can think of them as volume-less point particles that are just bouncing around.0308

Now, obviously, when we squeeze, when we drop the volume, increase the pressure, lower the temperature--when the volume gets really, really tiny--now the volume of the molecules actually plays an important role.0318

We can't really make this assumption anymore; we have to adjust this; but, for kinetic theory--ideal behavior--we just ignore the volume of the actual particles themselves.0329

They do have volume; they're just not important.0339

Three: the third axiom is: Particles exert no forces on each other.0345

In other words, they are just bouncing around randomly; one has nothing to do with the other; they don't stick together; they don't repel; they just bounce off of each other in perfectly-elastic collisions.0364

Now, that is not the case--we know for a fact that it doesn't happen that way--but for ideal behavior, we can make this assumption.0377

For all practical purposes, it behaves this way at low pressure.0383

OK, now the fourth one: The particles are in constant motion (this makes sense), and the collisions (oops, this random stray line all the way across the page--let's get rid of it here) with the walls of the container are the cause of exerted pressure.0388

So, if I have some gas in a closed vessel, and I measure the pressure, the pressure of that gas is coming from the particles--the gas molecules or atoms--bouncing and hitting the walls of the container.0444

That is where pressure comes from; it's just like a ball that hits a wall--just imagine billions and billions and billions of balls hitting a wall--well, that wall is going to feel it!0457

So, these are the assumptions of the kinetic-molecular theory of an ideal gas.0466

Now, from this, we can go ahead and deduce some things.0473

I'm not going to go ahead and derive any of these equations; I'm just going to throw them out, because, again, we're concerned with using the equations--not necessarily where they come from.0477

You can go ahead and follow the derivation in any one of your textbooks--they are either in the appendix or in the actual text itself--so I'll let you look at them if you want to; it certainly helps if you do.0484

If not, no harm--no foul--we're just going to be able to use them; that is what we're going to do.0496

The root is equal to (let's see) velocity and 3R...actually, that's going to be for the whole thing...3KT over m: so, the root mean square speed--just think of it as the average speed at which a particle is moving--is equal to 3 times K times T times m.0502

Now here, K is something called Boltzmann's constant, a very, very, very important constant--probably the single most important constant in physics (at least in my opinion--other people would say that the Planck constant is--they are closely related, in fact).0540

Boltzmann constant: that is 1.38x10-23 Joules per Kelvin.0560

T is temperature in Kelvin, and m is mass in kilograms.0573

It is the mass of an individual particle in kilograms; that is why we use the small m instead of the capital m.0582

Now, let's go ahead and write this same thing as 3RT/M, where R is, as we said before, the Rydberg constant: 8.31 Joules per mole-Kelvin--and that actually happens to equal Boltzmann's constant times Avogadro's number, 6.02x1023.0587

So, this is also a really interesting relationship to keep in mind--that R, the Rydberg constant, equals the Boltzmann constant times Avogadro's number.0623

8.31 Joules per mole-Kelvin equals 1.38x10-23, times 6.02x1023.0632

This is where you end up getting R from.0640

M, the capital M, is the molar mass.0643

This just gives me average--the root mean square speed of gas particles.0649

OK, so let's throw a couple of other definitions out there.0657

Essentially, what I'm going to be doing is just sort of laying out these things--what they are--defining them, and then, once I have them on the page, I'm going to go ahead and use them to solve some problems.0660

But, I just wanted to lay them out as they are, as opposed to laying one out, doing a problem...I'm going to save the problems until the end.0669

There is something that we call effusion, and effusion is nothing more than the passage of a gas through a tiny opening--that is it.0677

So, if I have a balloon and I poke a little needle hole in it, the gas from the inside of the balloon effuses out.0696

The rate of effusion is just the rate at which it actually comes out.0702

So, it's going to be a certain volume per unit time, like, let's say, 10 milliliters per second.0708

That means 10 milliliters of air are escaping for every second; that is all it is--a rate is just an amount over a unit time.0713

But, you know this already.0721

Well, somebody by the name of Graham discovered that the rate of effusion is inversely proportional to the molar mass of the particular gas.0723

Or, we can write it as: The rate times the molar mass is equal to a constant.0736

Well, for two gases under similar circumstances--for the same temperature and pressure--they are going to equal the same constant.0750

Therefore, what you have is something like this: you have: The rate of the first gas, times its molar mass, equals the rate at which the second gas effuses, times its molar mass.0760

This is how I like to use it; however, it is totally equivalent to (and more often than not, you will see it written like this): The ratio of the rates--rate 1 over rate 2--is equal to the molar mass of 2 over the molar mass of 1.0774

It really doesn't matter: you can write it this way; you can write it this way--it's a totally personal choice; most books will write it this way, because they like to have ratios of the same thing.0794

The rate of one over the rate of the other equals the square of the molar mass of one over the square of the molar mass of the other...absolutely the same thing.0801

OK, now let's define something called diffusion.0812

Diffusion just means one gas mixing with another.0816

If I open up a vial of pure ammonia, and if I put it on the table, let's say 5 feet away from me, it's going to take a little while, but eventually, I'm going to actually smell the ammonia.0826

Well, the ammonia is mixing with the air--the oxygen and nitrogen--the 70%...air is nitrogen and oxygen; it's mixing with the air, and diffusion is just the extent to which it mixes.0837

The rate of diffusion is how quickly it actually mixes.0851

Effusion and diffusion are actually closely related; you can actually use the same equation for both.0855

Again, we will talk more about this when we actually do a problem; it will make more sense; but I just want to throw out the meanings.0861

So, effusion: how quickly a gas escapes from a tiny opening; diffusion is how a gas actually mixes with another gas--how quickly it penetrates that other gas.0866

OK, now let's go ahead and talk about real gases, as opposed to ideal gases.0879

Well, we know that the ideal gas law is PV=nRT; I am going to rearrange this, and I am going to write it as nRT/V, and here is the reason that I am going to do this.0888

We said that the ideal gas law works for low pressures--low pressures where the gas molecules are flying around; they're really far apart from each other; the individual volumes don't matter; but, if I were to all of a sudden take a volume, where the individual gas particles really fall apart, and they are floating--they don't matter--and I increase the pressure, by increasing the pressure, I reduce the volume.0902

So now, I have dropped it down to something like this, where the same number of particles...now the particles don't have as much space as they did before.0930

So now, the volumes of the individual atoms and molecules start to matter.0944

What ends up happening is that this initial volume...when we use this particular volume, now, because there are so many particles, and the volume of the particles is actually a fair percentage of the total volume--now, the volume available for the particles to move around in is not the same as--is actually lower than--the ideal volume, by assuming that volumes don't matter.0952

So, if I assume I have a point--if I have a particle and another point--there is a certain volume that is available to it; but now, if this point is an actual volume--occupies volume--it's taking away volume, so there is less room for this other particle to move around.0979

We have to make an adjustment to this side by reducing the volume.0993

We write this as P=nRT/V-nb; and I'll talk about what b is in just a second (n is just the number of moles).0997

This is a volume adjustment; it is saying that, as we increase the pressure or decrease the volume or lower the temperature (which also decreases the volume), now the volume of the individual particles matter, and I have to make an adjustment for the volume.1011

There is less volume available for the particles of gas that are initially there to move around in.1024

It is not V; it's less than V--that is why it is V-nb.1030

OK, now, the next adjustment is this: we assumed, in the kinetic-molecular theory for ideal gases, that the particles exert no forces on each other.1034

They have no attractive force to each other.1042

Well, as it turns out, particles do have an attractive force to each other, and in fact, the more polar the particular molecule (like, for example, water molecule)--they're going to stick together.1044

Because they stick together, the collisions that they experience are not elastic, so the pressure that we actually measure is going to be less than the pressure that it would be under ideal conditions, because now you have fewer particles actually bouncing around and hitting the containers, because more of these particles are actually sticking together.1055

There is loss of energy, if you will, in some sense; the total energy of the system is conserved, but individually, there is sort of a loss; so the pressure that we measure is actually going to be less than the pressure...I'll say that the pressure observed is going to be less than ideal pressure.1078

That is why I put the "obs" here.1095

So, this factor is going to be a, times n over V squared; this is the pressure adjustment.1097

This is the volume adjustment; this is the pressure adjustment.1107

Now, I'm going to rearrange this again, and I'm going to write it as P+a times (n over V)2, times V-nb, equals nRT.1110

This is PV=nRT, but because of real gas behavior, I have made adjustments to the pressure and the volume for real gas behavior.1126

Now, this a and b are called van der Waals constants, and we have calculated different constants for different gases.1135

You can see them in any chapter on gases in a chemistry book.1154

They have them for (most of them list maybe 10 or 12) the most common gases--methane, oxygen, nitrogen, hydrogen...things like that.1157

That is all it is; these are just numbers that you put in there; n is just the number of moles of particles that you are dealing with, and this is a better representation of how gases behave at high pressures and low temperatures--in other words, small volumes, because volume matters now.1165

That is all this is; this is just PV=nRT, adjusted for real gas behavior.1183

OK, let's go ahead and jump into our examples, and I think a lot of this will start to make sense.1189

So, our first example is going to be: Calculate the root mean square velocity of atoms in a sample of methane gas (which is CH4) at 40 degrees Celsius.1194

So, calculate the root mean square velocity of atoms in a sample of CH4 at 40 degrees Celsius.1227

Basically, how far is your average atom flying around at?1231

OK, well, let's (let me see--we know what we're going to deal with...so...) just use our equation: root mean square speed is equal to 3 times R times T, over the molar mass; square root.1236

Well, T (temperature) is in Kelvin; 40 degrees Celsius becomes 313 Kelvin; we have to make sure to work in Kelvin.1253

Also, remember molar mass: molar mass has to be in kilograms per mole--not grams per mole, so we know that oxygen is 16 grams per mole, but oxygen is going to be .016 kilograms per mole; that is what is really important here.1264

These problems are not difficult; the difficulty is going to be remembering to work in the appropriate unit, so that we actually get our answer in meters per second.1280

OK, so methane is CH4; C is 12; there are 4 H's--that is 16; so, 16 grams per mole becomes 0.016 kilograms per mole.1287

And now, when we put these numbers in, we get 3, and we said R is 8.31, not .08206, so 8.31 Joules per mole-Kelvin, and the temperature is going to be 313 Kelvin, and we have 0.016 kilograms per mole; all of this under the square root sign.1304

Now, when we do the mathematics, as far as the numbers, we're going to get 699 meters per second.1335

Now, I want to show you where the meters per second comes from.1341

Kelvin cancels with Kelvin; mole cancels with mole; now, what we end up with, as far as units, is Joules over kilograms.1344

All right, here we go: J over kg; well, the Joule is kilogram-meter2 per second2; that is the unit--force times distance, a newton times a meter, gives me a Joule.1355

So, the unit of a Joule is a derived unit; it's kilograms-meters2 per seconds2, over kilograms.1374

Well, kilograms cancels with kilogram, leaving us meters2 per seconds2; then, when I take the square root of that, I get meters per second.1382

So, the units work out--very, very important.1391

R has to be 8.31 Joules per mole-Kelvin; temperature has to be Kelvin; molar mass has to be in kilograms per mole--very, very important.1394

OK, let's move on to a second example here.1403

We have...let's see...the problem says: The effusion rate of an unknown gas is found to be (we can measure this) 32.50 milliliters per minute.1407

In other words, 32.50 milliliters are leaking out of a hole every minute.1438

That is all that is; it's a rate--an amount per time.1444

Now, under identical conditions, the effusion rate of oxygen gas (O2) is found to be 31.50 milliliters per minute.1448

Is the gas (the unknown gas) methane, carbon monoxide, nitrogen monoxide, carbon dioxide, or nitrogen dioxide?1482

Well, let's use what we know.1500

We know that Graham's law says that the rate1, times the molar mass of 1, equals rate2, times the molar mass of 2.1502

Well, we know the rate of the unknown gas--we measured it--that is 32.50 milliliters per minute (I'll go ahead and leave the unit off--it's not that important).1514

I don't know what its molar mass is; I would like to know that, because, when I know that, I can just compare it to the molar masses of my choices and pick the right one.1526

Well, I know the rate for the second one is 31.50 milliliters per minute--that is the oxygen--and its molar mass is going to be...it's O2, so it's not 16; it's 32--32 grams per mole.1534

In this case, we can use the 32 grams per mole; it doesn't have to be in kilograms per mole, because, again, the ratios cancel out.1550

It is OK, as long as the units are the same.1557

That is it; so we have that the square root of the molar mass is going to end up being 5.48, and then, when we square both sides, we get a molar mass of about 30 grams per mole, and when we compare it, it looks like nitrogen and oxygen--nitrogen is 14; oxygen is 16; that is 30.1561

So, our gas is nitrogen monoxide.1584

That is it: Graham's law; rate is related this way; you could put it in that other form, where you have rate1 over rate2 = molar mass of 2 over molar mass of 1.1588

I like it this way, because everything is consistent--1, 1, 2, 2--but it is your choice.1599

Let's do another problem here.1607

This one says: Calculate the pressure exerted by 0.600 moles of nitrogen gas in a 2.0 liter vessel at 35 degrees Celsius, using a) the ideal gas law, PV=nRT, and b) van der Waals equation (the van der Waals equation was that adjusted one, the P-a over n/V squared--that one).1614

We want to compare them to see what we are looking at--to see how closely, actually, ideal behavior and non-ideal behavior is for this particular situation.1664

Well, 35 degrees Celsius--that is a pretty high temperature, in terms of Kelvin.1673

2 liters volume is a reasonable volume; and it is .60 moles.1678

Well, let's just sort of see what happens.1683

OK, so a) PV=nRT: we rearrange; we get nRT/V, and we just plug the values in.1686

We get 0.600 (is our number of moles); R is .08206.1695

And remember, when you are dealing with the ideal gas law, you have to use the .08206 for R; when you are dealing with issues of Joules and things like that, root mean square speed...that is when you have to use the 8.31 Joules per mole-Kelvin.1701

The problem itself--if you just stop and take a look at what units you want--they will tell you which R you are actually going to use.1719

Then, 308 Kelvin should be for 35 degrees Celsius, and our volume is 2.0 liters.1726

We end up with 7.58 atmospheres; that is pretty high pressure.1735

OK, now let's use pressure + a, times (let me write it as n2 over V2...no, you know what...I'm just going to leave it as (n/V)2).1743

Notice this n/V, by the way: it's the number of moles over a volume--it's a concentration.1759

The pressure is actually contingent on the concentration, which makes sense; it has to do with: the more molecules you have, the more heavily concentrated, in a given volume--the pressure is going to increase.1764

So, just recognize that; that is why I didn't do n2 over V2.1774

I left it that way so that you could see that it is a concentration term.1779

...V-nb=nRT.1782

OK, and then, when we rearrange, we get P=(nRT/(V-nb))-(a(n/V)2).1788

Now, the pressure adjustment constant (van der Waals constant) for nitrogen gas is 1.39, and (the units are irrelevant; you can certainly look up the units if you want--they are not altogether important) BN2 is equal to...the b, the volume adjustment parameter, is 0.0391.1807

When we put all of these values in here, we end up with 7.67 for this first term, and we end up with 0.1251 for this second term, which gives us a total pressure of 7.56 atmospheres.1833

So notice, under the ideal gas law, we have 7.58 atmospheres; using the real gas behavior, we have 7.56 atmospheres.1853

7.56 and 7.58 are virtually the same, so under these conditions, we are welcome to go ahead and use the ideal gas law.1862

Which--just by looking at this--35 degrees Celsius is a pretty high temperature; 2 liters--it's a pretty big volume, actually, for .6 moles of gas, so you can pretty much say to yourself, "You know what? I'm just going to go ahead and use the ideal gas law; I don't want to use the van der Waals equation--it's not important."1870

This confirms that that is the case.1889

If the conditions were different, you might get a lot of deviation.1892

OK, so we talked about the kinetic-molecular theory; we have talked a little bit about root mean square speed, average kinetic energy of a gas sample...we have talked about effusion and diffusion and done some problems.1896

In the next lesson, we're going to actually sort of tie it all together and do some regular gas problems.1908

Thank you for joining us at Educator.com, and we'll see you next time--goodbye!1914

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