Lecture_6_091108
8 Pages

Lecture_6_091108

Course Number: CHEM 3615, Fall 2008

College/University: Virginia Tech

Word Count: 588

Rating:

Document Preview

Lecture 6 Virial Expansions and Critical Behavior September 11, 2008 Using the virial expansion in pressure: (1) at p = 0, Z = 1, perfect gas (2) at T , Z = 1 for all gasses Z (3) lim p 0 p T Z 1 a a a = p + ... 2b b + p RT (RT )3 RT T RT Z 1 a lim = b p RT p 0 T RT Page 1 of 8 If b> a RT a RT a RT then b= then Z lim > 0 (Repulsive interactions dominate) p 0 p T (note the initial slope is positive) Z...

Unformatted Document Excerpt
Coursehero >> Virginia >> Virginia Tech >> CHEM 3615

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Lecture 6 Virial Expansions and Critical Behavior September 11, 2008 Using the virial expansion in pressure: (1) at p = 0, Z = 1, perfect gas (2) at T , Z = 1 for all gasses Z (3) lim p 0 p T Z 1 a a a = p + ... 2b b + p RT (RT )3 RT T RT Z 1 a lim = b p RT p 0 T RT Page 1 of 8 If b&gt; a RT a RT a RT then b= then Z lim &gt; 0 (Repulsive interactions dominate) p 0 p T (note the initial slope is positive) Z lim = 0 (Boyle's condition) p 0 p T (note the initial slope is zero) Z lim &lt; 0 (Attractive interactions dominate) p 0 p T (note the initial slope is negative) b = a/RT can be rewritten as TB = a/Rb This is the Boyle Temperature!!! Perfect <a href="/keyword/gas-behavior/" >gas behavior</a> over a wide concentration range b&lt; then A 2-term virial expansion is only valid for describing the limit where p 0!!! As p increases, higher order terms take over!!! Page 2 of 8 Note how this is analogous to the expression for the virial expansion in terms of n/V for <a href="/keyword/van-der-waals/" >van <a href="/keyword/der-waals/" >der waals</a> </a> gases. The key differences are: Expand in p Expand in / Full expansion 2 Virial Coefficient (B' for empirical p expansions) 3rd Virial Coefficient (C' for empirical p expansions) nd b2 Nonetheless, they both describe the same thing and are only valid if we are talking about a <a href="/keyword/van-der-waals/" >van <a href="/keyword/der-waals/" >der waals</a> </a> gas. This is the reason that in engineering applications, B', C', etc. are empirical parameters to obtain the right results. Here we see the clear contribution of attractions and repulsions to the second and third term of the virial expansion. Page 3 of 8 Isotherms of <a href="/keyword/van-der-waals/" >van <a href="/keyword/der-waals/" >der waals</a> </a> Gasses 1 p = RT V Recall: (V is a molar volume) p= RT a (V b) V 2 T &gt; Tc T = Tc T &lt; Tc (V is a molar volume) Page 4 of 8 The van der Waal's loop is artificial, hence coexistent gas and liquid phases are connected by a tie line (horizontal line satisfying the equal areas construct. Along this line, gas is continually converted into liquid with decreasing molar volume until only liquid remains). Page 5 of 8 Page 6 of 8 van der Waal's Equation of State p= RT a V b V2 at the Critical Point where T = Tc, p = pc, V = Vc then RT a 1) p c = (Vc b) Vc2 , p 2) = 0, V Tc 2p =0, 3) V 2 Tc 1 1 1 V V = V = = 4) Tc = p V p T 0 c V Tc Singularity at the critical point, a fluid is infinitely compressible On the critical isotherm: p &lt; 0 for V &gt; Vc V Tc p = 0 for V = Vc V Tc p &lt; 0 for V &lt; Vc V Tc The first and second derivatives are: RT 2a p + , for T=Tc and V = Vc , = 2 V T (V b ) V3 p RTc 2a + =0 V = 2 Vc3 c Tc (Vc b ) Page 7 of 8 (Vc b ) RTc 2 = 2a Vc 3 2RTc = 6a Vc 4 2p = 2RT 6a = 0 or 2 3 V4 V T (V b ) Show the expressions, p c = Hence: 2 a = 3p c Vc , b = (Vc b ) 3 a 27b 2 , Vc = 3b , Tc = 8a 27Rb Vc pV 8p V 3 , R = c c , and Zc = c c = = 0.375 RTc 8 3 3Tc Reality for <a href="/keyword/van-der-waals/" >van <a href="/keyword/der-waals/" >der waals</a> </a> Eq. of State Although it is better than the perfect gas law, there is no experimental validation Only predicts phase behavior (gas to liquid transition), qualitatively Does predict Tc Fails quantitatively Hence, other equations of state like the virial expansions and those found in Table 1.7 do better jobs of predicting real <a href="/keyword/gas-behavior/" >gas behavior</a> . Page 8 of 8

Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

Virginia Tech - CHEM - 3615
Lecture 7 September 16, 2008 Failings and Success of van der Waals, Lever Rule, Law of Corresponding States, WorkLast Time Show the expressions, p c = Hence:2 a = 3p c Vc , b =a 27b 2, Vc = 3b , Tc =8a 27RbVc 8p V pV 3 , R = c c , and Zc
Virginia Tech - CHEM - 3615
Lecture 8 September 18, 2008 Work &amp; an Introduction to the First LawdW = Fdz = (F / A )Adz = pdVW = popdVW = popdVW = pop (Vf Vi ) Expansion: Vf&gt;Vi, W&lt;0 Compression: Vf&lt;Vi, W&gt;0ViVfReversible vs. Irreversible ProcessesPage 1 of 6
Virginia Tech - CHEM - 3615
Lecture 9 September 23, 2008 Chapter 2 - Supplemental Handout on Equipartition Internal Energy Internal Energy, U, is the sum of the potential and kinetic energy of the system. It is a state function, i.e. it only depends on its current state, not h
Virginia Tech - CHEM - 3615
Lecture 10 September 25, 2008 Enthalpy and Cp Cv Relationships H is represented by a state function (the sum of state variables), hence H is itself a state variable H is an extensive state variable, while the molar enthalpy is an intensive variable
Virginia Tech - CHEM - 3615
Logarithms and ExponentialsCalculus of Natural Logarithms 1. 2. 3. Manipulation of Logarithms 1. 2. 3. / (for a &gt; 0 &amp; b &gt; 0) (for a &gt; 0 &amp; b &gt; 0) (for x &gt; 0) Logarithms in Other Bases 1. 2. 3. 4. 5. Natural Exponential Function 1. 2. 3. ln(exp(x) =
Virginia Tech - CHEM - 3615
Fall 2008Page 1 of 14Page 2 of 14Page 3 of 14Page 4 of 14Page 5 of 14Page 6 of 14Page 7 of 14Page 8 of 14Page 9 of 14Page 10 of 14Page 11 of 14Page 12 of 14Page 13 of 14Page 14 of 14
Virginia Tech - CHEM - 3615
Answer Key to Math Session for CHEM 3615Exercise for Section 2: Use the product and chain rule to derive the formula for d(u / v) 1 du d(1 / v) 1 du 1 = +u = + u dx v dx dx v dx v2 (1) y = 4x2 8x + 1, thenFall 2008d ( u / v) dx dv vdu udv
Virginia Tech - CHEM - 3615
Virginia Tech - CHEM - 3615
Chem 3615 Problem Set # 1: Ideal or Perfect Gas Behavior Due September 2, 2008Read Chapter 1, the Handout on the Barometric Distribution Law &amp; Chapter 6 (Sections 6.1 and 6.2) regarding the phase rule. Problems 1 through 6 are due at the start of cl
Virginia Tech - CHEM - 3615
CHEM 3615 Problem Set #2 Ideal and Real Gases Due September 9, 2008 Read Chapter 1, the Handout on the Barometric Distribution Law &amp; Chapter 6 (Sections 6.1 and 6.2) regarding the phase rule. Problems 1 through 6 are due at the start of class and wi
Virginia Tech - CHEM - 3615
CHEM 3615 Problem Set #3 Real Gases Due September 16, 2008 We will be completing Chapter 1 and starting Chapter 2 during the week of September 15. Start reading Chapter 2. Problems 1 through 6 are due at the start of class and will be graded. 1. The
Virginia Tech - CHEM - 3615
CHEM 3615 Problem Set #4 Real Gases Due September 23, 2008 Finish reading Chapter 2. Problems 1 through 7 are due at the start of class and will be graded. 1. In the last problem set, you plotted Z values for methane as a function of temperature expr
Virginia Tech - CHEM - 3615
CHEM 3615 Problem Set #4 Real Gases Due September 23, 2008 Finish reading Chapter 2. Problems 1 through 7 are due at the start of class and will be graded. 1. In the last problem set, you plotted Z values for methane as a function of temperature expr
Virginia Tech - CHEM - 3615
Useful Relationships and Definitions 1 V = V T pR = 8.314 Jmol-1K-1 = = 0.08206 Latmmol-1K-1 1 atm = 760 mm Hg = 760 Torr = 101325 Pa 0.001 m3 = 1 L = 1000 cm3 T JT = p H Cp = CV1 V = V p T dW = FdzdW = -pop dVW = p op
Virginia Tech - CHEM - 3615
Quiz #2 Chem 3615- Physical Chemistry Instructor: Esker September 11, 2008NAME:_ Score = 40 + _x15 = _Useful Information: pV = nRT, R = 8.314 Jmol-1K-1 = 0.08206 Latmmol-1K-1, 1 atm = 760 mm Hg = 760 Torr = 101325 Pa, 0.001 m3 = 1 L = 1000 cm3, d
Virginia Tech - CHEM - 3615
Quiz #3 Chem 3615- Physical Chemistry Instructor: Esker September 18, 2008NAME:_ Score = 40 + _x15 = _Useful Information: pV = nRT, R = 8.314 Jmol-1K-1 = 0.08206 Latmmol-1K-1, 1 atm = 760 mm Hg = 760 Torr = 101325 Pa, 0.001 m3 = 1 L = 1000 cm3, d
Virginia Tech - CHEM - 3615
Quiz #1 Chem 3615- Physical Chemistry Instructor: Esker September 4, 2008NAME:_ Score = 40 + _ x 15 = _Useful Information: pV = nRT, R = 8.314 Jmol-1K-1 = 0.08206 Latmmol-1K-1, 1 atm = 760 mm Hg = 760 Torr = 101325 Pa, 0.001 m3 = 1 L = 1000 cm3,
Virginia Tech - CHEM - 3615
Quiz #4 Chem 3615- Physical Chemistry Instructor: Esker September 25, 2008NAME:_ Score = 40 + _x15 = _Useful Information: pV = nRT, R = 8.314 Jmol-1K-1 = 0.08206 Latmmol-1K-1, 1 atm = 760 mm Hg = 760 Torr = 101325 Pa, 0.001 m3 = 1 L = 1000 cm3, d
Virginia Tech - CHE - 2114
Virginia Tech - CHE - 2114
ChE 2114 First Quiz g = 9.81 m/s2 or 32.2 ft/s2 1. (30 points) What is the mass (in pounds mass) of an object that will accelerate at 1.00 ft/s2 when subjected to a force of 1.00 pound force? August 31, 20072.(30 points) The Prandtl Number, NPr,
Virginia Tech - CHE - 2114
Virginia Tech - CHEM - 2535
ChE 2114 Second Quiz g = 9.81m/s2 1. (40 points) A first-order reaction A products, with rate constant k = 0.400 min-1 is occurring in a continuous stirred-tank reactor. The flow rate of the inlet and outlet streams is 5.00 liters per minute. The co
Virginia Tech - CHE - 2114
Virginia Tech - CHEM - 3615
Virginia Tech - CHE - 2114
Virginia Tech - CHEM - 3615
CHEM 2535Test #1: Bruice Chapters 1 3.3100 pointsPrint Name _Signature _ Friday, Sept. 21, 2007 Your signature indicates that you abide by the Honor Code at Virginia Tech (www.honorsystem.vt.edu). Models permitted. (18 points) 1 Name by IUPAC:
Virginia Tech - CHEM - 3615
Virginia Tech - CHEM - 2535
Common Alkanes1 2 3 4 5 6 7 8 9 10 11 12 13 14CH4 CH3CH3 CH3CH2CH3 CH3CH2CH2CH3 CH3CH2CH2CH2CH3 CH3CH2CH2CH2CH2CH3 CH3(CH2)5CH3 CH3(CH2)6CH3 CH3(CH2)7CH3 CH3(CH2)8CH3 CH3(CH2)9CH3 CH3(CH2)10CH3 CH3(CH2)11CH3 CH3(CH2)12CH3Methane Ethane Propane
Virginia Tech - CHEM - 2535
Conformations of 1,2-dichlorocyclohexane Axial and Equatorial Positions:axial axial eq. eq. eq. axial axial eq.ClCl ClCl Cl H H2 1Cl H Cl H H 1 eq., 2 ax.2 1ClCisH 1 ax., 2 eq.Both equal energyClCl ClCl H H Cl2 1H H H Cl H
Virginia Tech - CHEM - 2535
Nomenclature Rules: The Short List: 1. Find the parent. 2. Number the chain 3. Identify substituents (branches) 4. Write name in the following format: #-subtituentparent The Longer List: 1. Find Parent: The parent is the longest continuous carbon cha
Virginia Tech - CHEM - 2535
Practice Nomenclature Problems Use systematic (IUPAC) nomenclature to name the following compounds.H CH3CH3 HCH3CH3 C CH3 CH CH2CH3 C H CH CH3 CH2 CH CH3
Virginia Tech - CHEM - 2535
Virginia Tech - CHEM - 2535
CHEM 2335 Practice Nomenclature Problems 1.BrOHF
Virginia Tech - CHEM - 2535
CHEM 2335 Practice Nomenclature Problems 1.3,4-diethylheptane3-ethyl-2,2-dimethylpentane3-ethyl-2-methylhexane(1-methylethyl)cyclohexane1,1,3-trimethylcyclohexane1,2,3,4,5-pentamethylcyclopentaneBrOHF1-bromo-3-fluorocyclobutane2-
Virginia Tech - CHEM - 2535
Practice Nomenclature 2BrCH2CH3 ClBrOHFOCH3 ClCH3OClCH3 CH3 CH2 O CH CH2 CH2 CH3
Virginia Tech - CHEM - 2535
Practice Nomenclature 2 AnswersBrCH2CH3 Cl4-bromo-2-methylhexane1-chloro-2-ethylcyclohexaneBrOHFE-4-bromobut-2-en-1-ol4-fluorocyclohexeneOCH3 ClCH3OCl1-chloro-2-methoxycyclohexane3-chloro-5-methoxylcyclohexeneCH3 CH3 CH2
Virginia Tech - CHEM - 2535
CHEM 2535Problem Set #125 points + extra credit Due: September 5, 2008Name _ Open book; open notes. Collaboration encouraged but not copying. Write responses on this sheet. (6 points) 1. Draw one reasonable Lewis Structure for each of the given
Virginia Tech - CHEM - 2535
CHEM 2535 Name _Problem Set #225 points + extra credit Due: September 12, 2008Open book; open notes. Collaboration encouraged but not copying. Write responses on this sheet. (10 points) 1. Use the acid-base table to: (a) Label the stronger acid
Virginia Tech - CHEM - 2535
CHEM 2535Problem Set #325 points + extra credit Due: September 19, 2008Name _ Open book; open notes. Collaboration encouraged but not copying. Write responses on this sheet. (12 points) 1. Name by IUPAC.O CH3 CH3 CH CH CH2 CH2 CH3Cl CH3 CH C
Virginia Tech - CHEM - 2535
The extra credit compound could also be shown like the following:ClCl
Virginia Tech - CHEM - 2535
Virginia Tech - CHEM - 2535
Virginia Tech - CHEM - 2535
Tentative Test 1 Overview Bruice, Chapters 1 3.3 Self Study Problems from Bruice (Note: problems given for both editions of the texts available. Either set is appropriate for our class.) Chapter 1: 5th Ed.: 1, 2, 3, 4, 6, 9, 12, 13, 14, 15, 28, 31,
University of Texas - M - 408k
Garcia, Ilse Homework 5 Due: Sep 25 2007, 3:00 am Inst: Fonken This print-out should have 24 questions. Multiple-choice questions may continue on the next column or page nd all choices before answering. The due time is Central time. 001 (part 1 o
University of Texas - M - 408k
Garcia, Ilse Homework 6 Due: Oct 2 2007, 3:00 am Inst: Fonken This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page nd all choices before answering. The due time is Central time. 001 (part 1 of
University of Texas - M - 408k
Garcia, Ilse Homework 7 Due: Oct 9 2007, 3:00 am Inst: Fonken This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page nd all choices before answering. The due time is Central time. 001 (part 1 of
University of Texas - M - 408k
Garcia, Ilse Homework 8 Due: Oct 17 2007, 3:00 am Inst: Fonken This print-out should have 21 questions. Multiple-choice questions may continue on the next column or page nd all choices before answering. The due time is Central time. 001 (part 1 o
University of Texas - M - 408k
Garcia, Ilse Homework 9 Due: Oct 24 2007, 3:00 am Inst: Fonken This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page nd all choices before answering. The due time is Central time. 001 (part 1 o
USC - EXSC - 205LXG
EXSC 205 Lab 1 I. Purpose: The purpose of this lab was to get ourselves acquainted with statistical analysis of data utilizing calculations and Excel. Initially, we analyzed a couple of scenarios to understand how to state a research and null hypoth
USC - ARTL - 101
Artl 101: los Angeles the fiction gustafson The challenge of an artist is to successfully portray his or her topic in a certain light (conjured within the mind of the artist) that can be understood by the viewer to strike enough interest to respond
USC - ARTL - 101
p. 1 Professor Gustafson Los Angeles: The Fiction 9/16/05I. PrefaceWhen I first arrived at USCs campus in the fall of 2004, I brought with me not only enough suitcases to fill a small African country, but also many preconceived notions regarding w
USC - EXSC - 205LXG
Exsc - 205 VARK Questionnaire The VARK questionnaire suggests that I prefer a multimodal (ARK) learning preference. My scores were: visual 5, aural 13, read/write 10, kinesthetic 11. I agree strongly with these results because I tend to understan
USC - ARTL - 101
June 9th, 2008 ARLT 101 - Los Angeles: The Fiction Professor GustafsonPerception of Los AngelesThe Los Angeles Memorial Coliseum is a place where the citizens of Los Angeles can escape their lives and come together for a common interest. The major
Georgetown - BCHB - 513
123456=icRT789
Georgetown - BCHB - 513
12345678Spongiform degeneration in cerebral cortex from a Creutzfeldt-Jakob Disease Patient9Two conformations of Prion Protein (PrP) PrP (left) and PrPSc (right)PrPsc promotes the conversion of PrPc into the pathogenic form10
Georgetown - BCHB - 513
Nucleotides and Nucleic AcidsLehninger 5th edition Chapter 8 pages 271 - 302Structure of NucleotidesMajor Purines and Pyrimidine Bases of Nucleic AcidsDeoxyribonucleotidesRibonucleotidesSome minor purine and pyrimidine bases, shown as nuc
Georgetown - BCHB - 513
12345678910
Georgetown - BCHB - 513
123456789101112CollagenThe most abundant protein in the human body Long polypeptides extremely rich in Glycine, Proline and 4-Hydroxyproline Repetitive sequence of Gly-X-Y, where X and Y are often Pro and 4-Hyp131415E
Deakin - SIT - 3334
SIT202 Computer Networks Assignment 1Ruo Hui NIU ID:600246619Task 1: Basic concepts of networks (3+1+3+1+3 +3 = 14 marks) 1. Define the following concepts: data rate, error rate, bandwidth, handshaking procedure, queuing delay, distributed applic
Deakin - SIT - 334
Company origin, date started Blizzard Entertainment was founded by Michael Morhaime, Allen Adham and Frank Pearce in February, 1991 as Silicon &amp; Synapse. The company developed games such as Rock N' Roll Racing and The Lost Vikings (published by Inter
Deakin - SIT - 334
NavyFIELD indexGames Name: Navy Field II (1939-1945)? September1939,Poland. December1941, PearHarbor. Octorbor1943, Italy. June1944, Normandy. May1945, Berlin. 1940 10 1941 11 26 3000 2400 1941 12 8 1941-1945