CHAPTER 5
Integration
EXERCISE SET 5.1
n1
1 2
, 1; using right endpoints
1. Endpoints 0, , , . . . ,
n
n n
1
2
n1
1
An =
+
+ +
+1
n
n
n
n
n
An
2
0.853553
5
0.749739
10
0.710509
50
0.676095
100
0.671463
n1
1 2
2. Endpoints 0, , , . . . ,
, 1; using right e
CHAPTER 1
Functions
SECTION 1.1
1. Answer true or false. Given the equation y = x2 10x + 16, the values of x for which y = 0 are 2
and 8.
2. Answer true or false. Given the equation y = x2 2x + 4, y 0 for all x 0.
3. Answer true or false. Given the equati
CHAPTER 4
Analysis of Functions and their Graphs
SECTION 4.1
1. Answer true or false. If f (x) < 0 for all x on the interval I, then f (x) is concave down on the
interval I.
2. Answer true or false. A point of inection that has an x-coordinate where f (x)
CHAPTER 3
The Derivative
SECTION 3.1
1. Find the average rate of change of y with respect to x over the interval [1, 5]. y = f (x) =
A. 0.48
B. 0.48
C. 0.96
2
x2
D. 0.96
2. Find the average rate of change of y with respect to x over the interval [1, 4]. y
CHAPTER 5
Integration
SECTION 5.1
1. f (x) = 4x; [0, 1] Use the rectangle method to approximate the area using 4 rectangles.
A. 2
B. 1
C. 1.5
D. 1.75
2. f (x) = 10 + x; [0, 2] Use the rectangle method to approximate the area using 4 rectangles.
A. 10.625
CHAPTER 2
Limits and Continuity
SECTION 2.1
1.
The function f (x) is graphed. lim f (x) =
x0
A. 0
B. 4
C. 2
D. undened
2.
Answer true or false. For the function graphed lim f (x) is undened.
x2
x2 9
x2 9
by evaluating f (x) =
at x = 4, 3.5, 3.1, 3.01, 3.0
Lecture 17 Transition Elements
(Chapter 22)
Transition Elements
Transition elements (a.k.a. d-block elements) bridge the sblock to the p-block elements.
They are roughly defined as elements with partially filled
d-orbitals.
Included within the Transition
Transition Elements
(Chapter 22)
Coordination Compounds
Coordination Compounds compounds that have a metal atom
or ion associated with a group of neutral molecules or anions.
These molecules are attached to the metal atom or ion through
coordinate covalen
Lecture 4
Chemical
Kinetics
(15.5-15.6)
Introduction to Catalysts
Reaction Mechanisms
Introduction to
Catalysts
Homogeneous Catalysts
the reactants and catalyst are in the
same phase. (i.e. both liquids)
Example Isomerization of cis-2-butene
with iodine.
Lecture 2
Chemical Kinetics
Rate Laws and Reaction Order
Reaction Rates Depend on
Increasing the number of effective collisions
An effective collision has to have
1. Minimum energy
2. Correct orientation
This can be done by changing
- Concentration of rea
Solubility and Complex-Ion
Equilibria
Chapter 18 Continued
The Common Ion Effect
AgCl and NaCl have chloride ion in common. What will happen if
NaCl is added to a saturated AgCl solution?
Pb(NO3)2(aq)
AgCl (s) Ag+ (aq) + Cl- (aq)
If more Cl- is added in t
Lecture 19 Transition Elements
23.4-23.5
Common Geometries and
Structures CN = 2
Coordination numbers for transition metal complexes range
from 2 to 12 depending on a variety of factors.
However, CN = 2, 4, or 6 are the most common
Most compounds with CN
Lecture 3 Chemical Kinetics
(15.4-15.5)
Integrated Rate Laws and Half-lives
Integrated Rate Laws
We need an expression which allows the calculation of the concentration
to be determined after an amount of elapsed time.
For a zero order process, the rate i
Solubility and Complex-Ion
Equilibria
Chapter 18 Continued
The Common Ion Effect
AgCl and NaCl have chloride ion in common. What will happen if
NaCl is added to a saturated AgCl solution?
Pb(NO3)2(aq)
AgCl (s) Ag+ (aq) + Cl- (aq)
If more Cl- is added in t
Solubility and Complex-Ion
Equilibria
Chapter 18
Driving Forces
Over the next few chapters, be thinking about the Driving Force
behind the types of reaction we are discussing.
What makes the reaction go?
What evidence is there of a reaction?
Heat (given o
Lecture 7 Acid Base
Chemistry
18.1
Review of Acids and Bases (Cha
pter 17)
Acids are compounds which
Bases are compounds which
- can increase the concentration
of hydronium ion (H3O+) when
dissolved in water (Arrhenius)
- increase the concentration of
hyd
Modern Periodic Table
Period-7 Period-6 Period-5 Period-4 Period-3 Period-2 Period-1
1
IA
2
IIA
3
IIIB
4
IVB
5
VB
6
VIB
7
VIIB
8
VIII
9
VIII
10
VIII
11
IB
12
IIB
13
IIIA
14
IVA
15
VA
16
VIA
17
VIIA
1
18
0
2
H
He
1.008
3
4.0026
10
4
5
6
7
8
9
Li
Be
B
C
N
O
Isomerism
! Two broad categories of isomers:
structural isomers
stereo isomers
! Structural or constitutional isomers same empirical formula but
different molecular formulas or structural framework.
Types include ionization isomers, linkage isomers, coor
Lecture 1
Chemical
Kinetics
Chemistry 117
CEM 117 Chemical Kinetics
1
Thermodynamics vs.
Kinetics
Thermodynamics asks
Is the Rxn
spontaneous?
Kinetics asks
Look at G
How far does the Rxn
proceed?
Look at K, the
equilibrium constant
How fast is the
Reactio
Lecture 7 Acid Base
Chemistry
18.1
Review of Acids and Bases (Cha
pter 17)
Acids are compounds which
Bases are compounds which
- can increase the concentration
of hydronium ion (H3O+) when
dissolved in water (Arrhenius)
- increase the concentration of
hyd
Lecture 3 Chemical Kinetics
(15.4-15.5)
Integrated Rate Laws and Half-lives
Integrated Rate Laws
We need an expression which allows the calculation of the concentration
to be determined after an amount of elapsed time.
For a zero order process, the rate i
Lecture 10 Acid/Base
Reactions
18.4-18.5
Titration Curves
Titrations are done in order to determine the amount of acid or
base present in an unknown solution.
A titration measures the volume of a solution (either acid or
base) with a known concentration r
Transition Elements
(Chapter 22)
Coordination Compounds
Coordination Compounds compounds that have a metal atom
or ion associated with a group of neutral molecules or anions.
These molecules are attached to the metal atom or ion through
coordinate covalen
Lecture 1
Chemical
Kinetics
Chemistry 117
CEM 117 Chemical Kinetics
1
Thermodynamics vs.
Kinetics
Thermodynamics asks
Is the Rxn
spontaneous?
Kinetics asks
Look at G
How far does the Rxn
proceed?
Look at K, the
equilibrium constant
How fast is the
Reactio
Entropy and Free Energy
Chapter 18
Reactions and Spontaneity
Entropy and free energy deal with the concept of spontaneous
reactions. A more accurate description would be a productfavored reaction.
This means that products are more likely to be formed than
Lecture 11 Continued
Entropy and Free Energy
Gibbs Free Energy Hints
As with H and S, Gorxn is given by
Gorxn = Gof (products) - G of (reactants)
Warning: H and G are usually reported in kJ/mol while
S is given in J/molK. When doing calculations, make sur
Chapter 20 Nuclear Chemistry
Nuclear Fission
Nuclear Fission the process of an unstable nucleus breaking
apart into two or more new nuclei.
The unstable nucleus is often formed through the absorption of a
neutron.
In a fission reaction, there are two impo
Lecture 21 Nuclear Chemistry
Chapter 20
Nuclear Reactions and Energy
How much energy is required to hold a nucleus together?
There must be some force holding the nucleus together against the
strong repulsive electrostatic forces between protons.
We can ge