Problems for Laplace Transform
Laplace Transform
Fundamentals
Fundamentals
1. Example of the definition of Laplace transform Solve following integral using Laplace transform. (A)
0
e 3t sin 2tdt
(B)
0
te 2t cos 2t dt te 2t sin t dt
(C)
0
Solution: (A) U
Exercise 15.1
Subject: Estimation of adsorbent characteristics.
Given: Porous particles of activated alumina. BET area = 310 m2/g = Sg. Particle porosity = 0.48 = p. Particle density = 1.30 g/cm3 = p. Assumptions: Straight pores of circular cross-section
Exercise 6.1
Subject: Given: Simultaneous absorption and stripping. Fig. 6.1 in which simultaneous absorption and stripping occur.
Find: Whether absorption and stripping is more important. Stripping of water = 22 kmol/h Absorption of acetone = 10.35 kmol/
Exercise 4.1
Subject: Degrees of freedom analysis for a three-phase equilibrium stage. Given: Equilibrium stage of Figure 4.35, with two feeds (one vapor, one liquid), vapor entering from stage below, liquid entering from stage above, three exiting stream
Chapter #2 Limits and Continuity
2.1 Rates of Change and Limits
Definition:
The average rate of change of the function y=f x over the interval [x 1 , x 2 ] is
y f x 2f x 1
=
x
x 2x 1
Examples:
Find the average rate of change of the function y=x 2 over th
1
2
Labs for Chem 101 students start this week!
Ionic configurations
Archie cartoon
Main group metal ions
Tend to lose e to attain
noble gas configuration
Main group nonmetal ions Tend to gain e to attain
noble gas configuration
See figure 8.25
Lab room a
1
2
Ionization energy (IE)
The Argyle Sweater by Scott Hilburn
Energy required to remove an e from a gaseous
atom or ion.
X (g) X+ (g) + e
1st IE
2nd IE
Read
Review
Stoichiometry chapter 3
Practice
PS#2 can solve all questions.
Quiz
Handout 2, sect. 2.7,
Mini Study Groups (MSGs)
MSGs for many intro. science courses (e.g.
BIOL 107, PSYCO 104, EAS 100, MATH 113,
ENGL 12X,) AND 2nd year courses
Groups of 5-10 students who meet for 1 hour each
week to discuss course material and do problems
Mentored by upper
1
2
Speed Bump by Dave Coverly
Unit 2 Bonding
Compounds types of bonding and nomenclature
See handout 2
Bond energies
Electronegativity, bond polarity
Lewis dot structures
Resonance
VSEPR model and geometry of molecules
Hybridization
Molecular orb
1
2
If it seems that I am ignoring you in the hallways and
Lab room assignments will be posted Thursday or
corridors, I apologize. It will take me time to recognize
Friday on the lab website:
your faces and learn your names. I will try though !
http:/www.
The failure of Newtons classical mechanics
Bizarro by Dan Piraro
Read
textbook sections 7.4, 8.1
PS # 2
can solve questions 14.
1st online lecture is next week (likely W 2pm F 6am).
More details in the next few lectures.
1
2
H atom
1 e, 1 p+
Bohr model
1
2
Electron configuration in atoms
Goal 2 predict e configuration for different atoms.
Goal 1 describe arrangement of e's in an atom.
Need the order of filling of sublevels.
Most times, a sublevel is completely filled before
Electron configuration
# of
1
2
Bonding in metals
Some typical metal properties.
Fig 9.2c
Metal atoms in a sample
pool their valence
electrons into a sea of
electrons that flows
between and around each
metal core, thus attracting
them together.
Fig 9.29
Electrons in metallic
bonding
Speed Bump by Dave Coverly
Read
textbook sections 7.3, 7.4
Reading assignment is to read once, figure out what you
know and what you dont so that you can concentrate
on the latter when concepts are covered in class.
1
2
See fig. 78.
Atomic spectra and qua
The Nestlings by Warren Clements
Read sections 7.1, 7.2
Practice
work on PS #1
Frequently Asked Questions
1. Should I bring the textbook to class? No!
2. Can I record the lecture?
You need to get my written permission (via email OK)
provided the recording
1
2
Ba crystallizes in a bcc structure and has a density of
Last time
3.62 g cm3. What is the radius of a barium atom?
mass
Density = volume
3
range 1 50 g cm
bcc
or
=
4
r
3
fcc
3
3
r= 4
2
r= 4
or
=
4
r
2
4
The crystal structure of MgO is similar to tha
1
2
Stoichiometry review
Bizarro by Dan Piraro
Empirical formula
1. Which atoms
2. What ratio
Ex:
Hydrogen peroxide
Empirical formula: HO
Hydrogen and oxygen atoms in 1:1 ratio
Review
nomenclature (handout 2), stoichiometry
Molecular formula
Practice
PS 3
1
2
Learn how to correctly count valence electrons !
Pearls Before Swine by Stephan Pastis
Read
Section 10.2
Im not in this Thursday for the entire day (dental
surgery and recovery).
Online quiz (Lewis structures)
Wed, Oct 8, 5pm Sun, Oct 12, 5pm
1 attemp
1
2
Rules for writing Lewis Dot structures (LDS)
The various Nobel Prizes are being awarded this week.
Pearls Before Swine by Stephan Pastis
1. Count the number of valence electrons
NVE = last digit of group number) charge
2. Write proper skeleton
connect
Chapter #1 Functions
1.1 Functions and Their Graphs
Definition:
A function f from a set X to a set Y is a rule that assigns a single value f xY
to each x X .
In this case, X is called the domain of f and the set of all values f x is called the range of f.
Chapter #0 Preliminaries
0.1 (Appendix A in text) Numbers, Inequalities and Absolute Value
Definition:
The real numbers are numbers that can be expressed as
decimals.
Eg:
The real numbers can represented as points on the real
number line. (the set of real
WORKSHEET #
Course/ Section:
Instructor:
LAST NAME:
FIRST NAME:
(Please, print!)
Due date:
Instructions
1. Write your ID number on each INSIDE page of your assignment.
2. Do NOT write your ID number on the front page.
If you are feeling stressed or
overwhelmed, you are not alone.
At the Peer Support Centre, were
here to listen. No issue is too big or
too small
To talk with one of our highly trained student volunteers:
Drop In: 2-707 SUB
Mon-Fri: 9am-8pm
Call our HelpLi
1
2
Last time
Bizarro By Dan Piraro
Unit cell
Particles
Coordination #
Simple cubit
1
6
Bcc
2
8
Fcc
4
12
Shared particles
Corner
Face
Read
1
contribution is 8 particle per corner
1
contribution is 2 particle per face
Edge
1
contribution is 4 particle per
1
2
Li2
Last time we sketched the He2 MO energy diagram
Bizarro By Dan Piraro
*
s
2sA
2sB
s
E
*
s
1sA
1sB
s
Read
Sections 5.1 5.4
Li2
Practice
PS #4
BO
can solve all questions
stable (in theory)
42
20
or
2 =1
2 =1
VSEPR quiz (for marks)
Note that we can i
Dilbert by Scott Adams
Read
Section
11.2, 11.3 up to and including p. 411
Ignore
p. 4123 (6th ed) or 42930 (5th ed)
Practice
PS 4. You can solve Q15
VSEPR quiz (for marks)
Thursday, Oct 16, 8am Thursday, Oct 23, 8am
1
2
Last time
Acetylene
C2H2
HCCH
2 eff
Speed Bump by Dave Coverly
Practice
PS #5
1
2
RT
RT
Ptotal = nA V + nB V + = PA + PB +
Gas mixtures: Daltons law of partial pressures
Consider the molecular properties of a gas:
PA, PB, , are the partial pressures of A, B,
Molecules are negligibly smal
1
2
Christmas is around the corner
Last time
Well, about 2 months away.
MO energy diagrams
# MO = # AO
Bizarro by Dan Piraro
# bonding MO = # antibonding MO
One energy level
Two degenerate energy levels
Antibonding
*
Paramagnetic
attracted by a magnet
som
1
2
Remember last time we went through
wavefunctions and a string guitar
Bizarro by Dan Piraro
Lab room assignments will be posted Thursday or
Friday on the lab website:
http:/www.chem.ualberta.ca/~ngee/Chem10XLabs.html
Read
textbook sections 8.1, 8.2
Pra
1
2
Enjoy the Thanksgiving long weekend!
Online quiz (Lewis structures)
Wed, Oct 8, 5pm Sun, Oct 12, 5pm
Bizarro by Dan Piraro
1 attempt, 40 minutes
Next Online lecture (VSEPR theory)
Videos and assessments
Sat 8am Wed 8am
Optional in-class lecture
Wednes