Morehouse, CHEM 111
Excerpt: ... CHEM 111: Lecture 12 26 Sep 2008 States of Matter: Gases (continued) What about non-ideal (or real) gases? Diffusion v. effusion The Van der Waals equation Kinetic theory of gases States of Matter: Liquids Properties Surface Tension Viscosity Vapor Pressure ...
N.E. Illinois, C 3910
Excerpt: ... CHM3910 Fall 2004 Assignment #3 Due in class Friday, September 7 1. Barrante Chapter 4 Problem 1 Parts a, b, e, f, l, r Note: If you haven't had Calculus before (or if you're rusty), you should go through all of the parts of this problem for practice 2. Barrante Chapter 4 Problem 2 Parts a, d, i 3. Barrante Chapter 4 Problem 3 Parts b, k 4. Barrante Chapter 4 Problem 6 5. Barrante Chapter 4 Problem 9 (begin by solving the equation for V) 6. Starting with the van der Waals equation P= RT a " 2 Vm " b Vm a) Calculate the first and second derivatives of P with respect to Vm b) Find expressions for Vc, Pc, and Tc given in lecture. ! ...
Lansing, CHEM 151
Excerpt: ... ty The square root of the average of the squared velocities of the gas molecules in a sample. -Effusion and Diffusion: Effusion: The escape of a gas through a tine hole such as a pin hole in a balloon Diffusion: THe spreading out of a gas throughout an open space Graham's Law of Effusion: The rate of effusion of a gas is inversely proportional to the suqare root of its molar mass For two gases under identical conditions, SEE PAPER NOTES - Deviations from Ideality From PV = nRT (ideal gas equation) n = PV / RT for 1mol of an ideal gas, PV/RT = 1 at all pressures -The higher the temperature, the smaller the deviation from ideal behaviour Van der Waals Equation : Real gases have definite volumes and attract eachother. Refer to the postulates of the Kinetic Molecular Theory. The Van der Waals equation contains terms that make corrections for teh volume of molecules and attraction between molecules. Real Gas Equation: P = (nRT / V-nb) - n^2a / V^2 nb = correction for volume of molecules n^2a / V^2 = Correct ...
Creighton, CHM 203
Excerpt: ... an der Waals equation to calculate the properties of a real gas. I can calculate a dipole moment in Debyes given charge and charge separation. I can predict the existence, direction and relative size of a molecular dipole moment. PT = PA + PB + PC + PA nA = " XA PT nA + nB u rms " u2 = 3RT M ! P= ! nRT n2 "a 2 V " nb V = Qr ! *This point is covered in the Readings, and will not receive special attention in lecture. Notes: http:/freitag.creighton.edu/CHM203/ Chapter 9: Gases II. Daltons Law of Partial Pressures A. Relation to the Ideal Gas Law B. Mole Fractions C. Examples III. The Kinetic Theory of Gases A. Assumptions B. Interpretation of Gas Laws C. Distribution of Molecular Speeds D. Root-Mean Square Speed E. Example IV. Grahams Law of Effusion A. Defintion B. Justification V. Deviations from Ideal Behavior: the van der Waals Equation A. Particle Interaction B. Volume Correction C. Example Chapter 10: Liquids, Solids and Phase Changes I. Polar Covalent Bonds and Dipole Moments A. Units f ...
Ohio State, CHEM 122
Excerpt: ... Molecular Effusion and Diffusion The lower the molar mass, M, the higher the rms. Kinetic Molecular Theory Graham's Law of Effusion Effusion is the escape of a gas through a tiny hole (a balloon will deflate over time due to effusion). 3RT r1 u1 M2 M1 = = = 3RT r2 u2 M1 M 2 12 Diffusion and Mean Free Path bromine diffusion Real Gases: Deviations from Ideal Behavior PV =n RT 13 Real Gases: Deviations from Ideal Behavior As the gas molecules get closer together, the smaller the intermolecular distance. Real Gases: Deviations from Ideal Behavior The higher the temperature, the more ideal the gas. Because they move farther apart ! (So, the volume has to expand for this to be true) 14 Real Gases: Deviations from Ideal Behavior The van der Waals Equation P= nRT n2a - 2 V - nb V Corrects for molecular volume Corrects for molecular attraction General form of the van der Waals equation : 2 P + n a (V - nb ) = nRT V2 End of Chapte ...
Berkeley, CHEM 240
Excerpt: ... Version 3.16.07 Tentative lecture outline for the remainder of ChE 240 March 20: Chapter 5 March 22: Chapter 5. The Ising model program will be assigned. March 23 (56 Hildebrand, 7.30-9am): Chapter 6 April 3: No class this day! April 5: Chapter 6 April 10: Midterm 2 April 12: Solutions to Midterm 2 and a sample problem April 17: Chapter 7 April 19: Chapter 7 April 24: Chapter 7 and the van der Waals equation April 26: Chapter 7 and the van der Waals equation May 1: Self-diffusion and the Langevin Equation May 3: Self-diffusion and the Langevin Equation May 8: Self-diffusion and the Langevin Equation Heres a list of the relevant sections in each chapter: Chapter 5: 5.1-5.5 Chapter 6: 6.1-6.3 Chapter 7: 7.1-7.5, 7.7 Chapter 8: 8.4 and 8.8 ...
Virginia Tech, CHEM 3615
Excerpt: ... Lecture 5 September 9, 2008 Virial Expansions Empirical Treatment of Real Gasses Consider the Compression Factor, Z Z= For the case of a perfect gas, Z = 1 For the case where finite size effects matter, pV is larger than expected for an ideal gas so Z > 1 For the case where attractive interactions are important, pV is smaller than expected for an ideal gas so Z < 1 Quantifying these Effects, the van der Waals Equation of State (1) Molecular Volume correction to the perfect gas law: pV RT p= (2) RT where b = molar volume = m3/mol (accounts for repulsions) Vb Attractive Interactions p = pideal a V2 , where a = attractive interactions which reduce pressure units = pressure x volume2 (3) Putting the two together yields the van der Waals Equation of State p= or a p + (V b ) = RT V2 RT a valid for V > b V b V2 p= RT b V 1 V a V2 Page 1 of 8 The van der Waals equation of state is valid for gases at low pressure where the pVT ...
Montana, CHEM 141
Excerpt: ... on the gas concentration. Dened as moles of gas per liter ( n / V ) The higher the concentration, the more likely a pair of gas molecules will be close enough to interact. For large number of molecules the number of interacting pairs is dependent on the square of the concentration. P = P a (n/V)2 a = empirical constant; V = Volume 2 The van der Waals equation Substituting in the corrections for both the volume of the particles and particle interactions yield: Pobs = (nRT) / (V nb) [a(n/V)2] o b s e rv e d p re s s u re v o lu m e o f th e c o n ta in e r p re s s u re c o r r e c tio n v o lu m e c o r r e c tio n Rearrange to give van der Waals equation 2 P+ n a V2 (V-nb) = nRT ! n2 $ # P + a 2 & (V ' nb) = nRT # & " V% Gas He NH3 CCl4 a (atm L2/mol2) 0.034 4.17 20.4 b (L/mol) 0.0237 0.0371 0.138 Size of a depends on attractions between molecules (atoms). Larger attractions decrease the force molecules exert on wall (P) Size of b depends mainly on size of molecul ...
Caltech, PHYS 127
Excerpt: ... 1 FIG. 1: Phase diagram for water. Note the triple point where liquid gas and solid water coexist - at T = 0.1C and p = 0.006A. Also, notice the many phases of ice existing at high pressures. Graph taken from: http:/www.lsbu.ac.uk/water/. Lecture 17 - First order transitions and Van der Waals equation of state A. Basic phenomena Collections of atoms would exhibit different phases depending on their pressure and temperature. For instance, H2 O could be liquid gaseous or several kinds of solid. Its phase diagram is shown in Fig. 1. B. Van-der-Waals equation of state The free energy of an ideal gas is: F (T, V, N ) = -T N log V (2mT ) N hd d/2 +1 = -T N log (2m)d /2 V + log T d/2 + log +1 N hd (1) Adding the simplest interaction: Uint = -a The free energy now becomes: F = -T N log (2m)d /2 V + log T d/2 + log +1 -a N hd F V NT N2 -a 2 V V N V 2 N2 V (2) (3) and pressure gets an extra contribution: p=- = T,N (4) The attraction reduces the pressure relative to an interacting gas. Once atoms in a g ...
Georgia Tech, CHBE 2110
Excerpt: ... ChBE 2110 Practice Questions for Final Exam Fall 2007 Professor Gallivan From Elliott and Lira: o 7.2, Derive in terms of Z(,T) o 7.6 o 7.25, Instead of Peng-Robinson, use (1) methane chart, (2) ideal gas law (cp/R = 4.298, and (3) the van der Waals equation . o Suppose you are given a cubic equation of state of the form P = f(V,T) and coefficients for the Antoine equation. Explain how you would construct a phase diagram based on this information. Be sure to make a sketch. Explain how you will find the critical point. Attempt to work these in 2 hours. You may use any tables in the text, but try not to refer to the remainder of the text since the exam will be closed book. Since you can bring 3 single sided pagse of notes to the exam, you may wish to make these sheets first and use them to take the practice exam. (And presumably then revise it after taking the practice exam.) We will discuss these questions in the office hour review session on Friday at 5 pm. ...
University of Florida, PHY 3513
Excerpt: ... Lecture 5 Equations of State Chapter 2 Wed. September 5th Quiz The ideal gas law The van Der Waals Equation PvT surfaces Multivariable calculus Compressibility and expansivity Reading: Chapter 2 (pages 21 - 27) Also Read Appendix A 1st homework se ...
University of Louisville, P 298
Excerpt: ... 298HW07 (Questions 41-44) Worked solutions due in Lecture on 07/18/05 NAME_ (please print) 41. (see problem 54 from the spring) We have 2 cubic meters of solid uranium-238 at it's melting point. How much heat must be supplied in order to boil all of ...
UWO, CHEM 024b
Excerpt: ... States of Matter: I Real Gases By the end of this lecture you will be able to: (1) Differentiate between real and ideal gases. (2) Understand how the ideal gas law can be modified to account for the differences. (3) State and manipulate the van der Waals equation . (4) Know what intermolecular forces and dipole moments are. (5) Correlate the dipole moment of a molecule to its intramolecular bonding. (6) Know what polar covalent bonds are and their relationship to electronegativity. (7) Understand attractive forces between non-polar molecules. (8) Understand how the size, polarity and symmetry of molecules correlate with the van der Waals equation . (1) What is a real gas? All gases are real gases. The ideal gas is simply a concept and does not actually exist. Real gases behave like the ideal gas at low pressure and high temperature. In real gases: (a) Molecules have significant volume. (b) There are significant forces between molecules. The ideal gas equation can be modified to account for thes ...
UNC Charlotte, CHEM 2141
Excerpt: ... Lecture #17 Real Gases & Chemical Kinetics (Chapter. 10, Chapter. 11 only 11.3 -11.6) Homework #6 due Thursday March 31 st 5:00 PM. Chapter 10 Problems: 1, 2, 6, 9, 13, 16, 18, 19, 26 Chapter 11 Problems: 9, 10 For problems 10.6 and 10.18 I will accept both rate constants, either k or kempirical i.e. 3A P, If this overall rxn is first order in A: -1/3 d[A]/dt = k[A] -d[A]/dt = 3k[A] = kemp[A] where kemp = 3k I. Real Gases II. Empirical Chemical Kinetics A. Definition of Rate B. Rate Laws: Rate constants & order C. Determination of Rate Law I. Real Gases van der Waals Equation of State Real molecules have intermolecular forces: attractive & repulsive. Repulsive forces are due to the finite volume of gas molecules - when they contact they repel, thus effective volume that gas molecules have access to is lowered: V V-nb where b = the van der Waals repulsive parameter in L mol-1 . Attractive forces reduce the pressure P nRT/V - a(n/V)2 . a = van der Waals repulsive parameter in units of atm L2 mol-2 . Thus va ...
Montana, PHYS 425
Excerpt: ... nd particle interaction can no longer be ignored, and the equation of state deviates from the ideal gas law. The real gas is described by the van der Waals equation of state: a (P + 2 )(v - b) = RT v Remark 1: note that v in the equation is the molar volume v = V /n. Remark 2: for a dilute gas at not very low temperature, a 0, b 0, the Van Der Waals equation is reduced to the ideal gas law. Example 2: intermolecular forces and the "touch-on" distance between gas particles *Example 3: thermodynamic properties (specific heats, internal energy, entropy, and adiabatic process) of a real gas (Fermi 16) Note that, unlike an ideal gas, for a real gas, the internal energy is a function of both temperature and volume. Taking T and V as independent variables, it can be generally written dE = E E )V dT + )T dV T V The partial derivatives in the equation can be experimentally measured (such as heat capacities), or determined by the inter-relationship between macroscopic properties derived from thermodynamic laws and e ...