Documents about Van Der Waals
380.56chapter8-S06
Illinois State, CHE 38056
Excerpt: ... 47 Chapter 8. Application 2 Modeling Molecular Dissociation with Nonlinear Maps 8.1 Overview In this chapter, a nonlinear map will be developed and applied to study the dissociation of a van der Waals complex interacting with a pulsed laser. Van der Waals complexes are weakly bound molecular systems that are important in the study of intermolecular interactions and large amplitude dynamics. 8.2 The He-I2 Van der Waals Complex The specific van der Waals complex to be studied is He-I2 , shown in Figure 8.1. The equilibrium geometry is t-shaped. The distance between the He atom and the I2 center of mass is approximately 3.7 , while the equilibrium I-I bond distance is about 3.0 . I I Figure 8.1. Structure of the He-I2 van der Waals molecule. The vibrational motion of the He-I2 complex can be described using the following potential energy function, V ( r, ) = D { [1 + cos(2 )] e-2 ( r-re ) - 2e- ( r-re ) . } (8.1) In Equation (8.1), D, , and are constants. The coordinate r is the distance betwe ...
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Lecture_6_091108
Virginia Tech, CHEM 3615
Excerpt: ... term virial expansion is only valid for describing the limit where p0! 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 van der Waals 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 van der Waals 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 van der Waals Gasses 1 p = RT V Recall: (V is a molar volume) p= RT a (V b) V 2 T > Tc T = Tc T < Tc (V is a molar volume) Page 4 of 8 The van der Waal's ...
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TOPIC 4
University of Ottawa, BIO 1140
Excerpt: ... cover membranes. The chemistry of nucleic acids will be discussed when we cover molecular biology in order that the chemistry of these molecules can be studied within some meaningful context. I understand that you know 'the chemistry' we will cover, but what we are interested in now is not so much the chemistry but how that chemistry is relevant to life! Water is the most abundant substance in cells and accounts for from 0.66 gm/gm wet cells in human red blood cells (RBC) to around 0.8 gm/gm wet tissue in skeletal muscle. A ballpark figure for the water content of cells is about 70% by weight. Get used to thinking in term of 'ballpark figures'. Do pay extra attention to the characteristics of water and bonds: both covalent and ionic, and the weak-bond interactions called hydrogen bonds, hydrophobic interactions and van der Waals forces that we will study when we look at biological membranes. Be able to describe an ester bond, amide bond, macromolecules (monomers and polymers), lipids, fats, oils, triacylglyce ...
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2
Johns Hopkins, BME 580.221
Excerpt: ... Kuo, 580.221 7 Sept 2004 Concepts/Vocabulary Molecules & Cells BME 580.221 Molecular specificity (role of concentration and affinity, Kd) Chemical Basis of Binding Lecture #02, 7 Sep 2004 Scot C. Kuo Covalent vs. Non-covalent bonds 4 Weak Forces: H-bonds, Ionic (pH), Hydrophobic/hydrophilic, van der Waals polarity/directionality of some weak bonds 7 Sept 2004 Kuo, 580.221 Dialysis & semipermeable membrane Osmotic pressure (movement of water) Note: Water also moves through the membrane . Specificity vs. Affinity Affinity: Between Receptor and 1 Ligand Specificity: Between Receptor and 2 different Ligands (RA) R + A (RB) R + B KA = [ R][ A] [ RA] or or [ RA] [ A] = [ R] K A KB = [ R][ B] [ RB] [ RB ] [ B] = [ R] K B hence: [ RA] K B [ A] = [ RB ] [ B] K A Numerical example onto board. Remember, smaller Kd means tighter binding. 7 Sept 2004 Kuo, 580.221 7 Sept 2004 Kuo, 580.221 Explaining Specificity of An Antibody Approximation ...
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lecture22
Duke, CPS 260
Excerpt: ... CPS260/BGT204.1 Algorithms in Computational Biology November 13, 2003 Lecture 22: Space Filling Diagrams Lecturer: Pankaj K. Agarwal Scribe: Pankaj K. Agarwal (i) (ii) Figure 22.1: (i) Van der Waals surface of a molecule. (ii) Connolly surface of the same molecule. For geometric and topological analysis and for understanding the nonbond interactions between atoms a protein is modeled as a set of spheres in R3 , each sphere corresponding to one atom of the protein. This model, known as the space-lling diagram, assumes that the exact position of each atom is known. We thus represent a protein P as a set {B1 , . . . , Bn } of balls in R3 . Let zi (resp. ri ) denote the center (resp. radius) of Bi . The union i Bi is the space lled by P. The coordinates of the centers are typically determined using X-ray crystallography and NMR methods. The radius ri is typically the Van der Waals radius, dening the impenetrable volume of an atom. The smallest distance between neighboring atoms (in the crystalline ...
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Intro__Bonding_B
Missouri S&T, MET 121
Excerpt: ... s in low density Other properties NOTE: Electrons captive to locations Covalent Bonds Metallic Bonding Nuclei arrange at definite sites Valence electrons free to wander through the aggregate (no longer associated with specific atoms or locations Properties: Other properties Ductile Opaque Metallic Bonding VanderWaals Forces Intermolecular attraction not interatomic Non-symmetric molecules lead to non-uniform charge distributions. A weak bond results when a negative part of one molecule attracts a positive part of another Example Properties Van der Waals Bonding Atomic Bonding Comparison Bond Type Energy (ergs) Ionic 150-370 Bond Direction Nondirectional Directional Electrons Localized Covalent Metallic Van der Waals 125-300 25-200 <10 Localized Delocalized Localized Nondirectional Nondirectional Atomic Bonding - Summary Ionic, covalent, and metallic bonds are primary bonds and are relatively strong VanderWaals forces are secondary bo ...
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lec03-Globular Protein Structure-Interior Packing
MIT, BIOL 7.88
Excerpt: ... ce/Volume Relationships Globular proteins have relatively sharply defined: Exterior Surface = H20 Interface Interior volume - Is the interior of a native protein crystalline or oily? A quantitative answer to this was given by Richards: "The Interpretation of Protein Structures: Total Volumes, Group Volumes and Packing Density" Frederic M. Richards (1974) J. Mol. Biol., 82, 1 - 14. Problem comes down to calculating how densely packed atoms are in protein molecules? We can define the packing density of a molecule as: Volume of its van der Waals envelopes of its constituent atoms / actual volume of the intact folded molecule This value is dimensionless - Close packed hard spheres = 0.74 - Close packed infinitely long cylinders = 0.91 - Crystals of various small organic molecules 0.70 - 0.78 values (<0.6 very rare) The van der Waals radii - from interatomic distances of nonbonded atoms in organic crystals. However calculation of the volume of irregular structures not trivial. Richards' procedure mad ...
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lect12
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 ...
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lect09
Morehouse, CHEM 111
Excerpt: ... CHEM 111: Lecture 09 19 Sep 2008 States of Matter: Gases (continued) An Ideal Gas: What makes it so? Molar mass defined Dalton's Law of partial pressures A Unified Gas Law: Application to problem solving What about non-ideal (or real) gases? The van der Waals equation Diffusion v. effusion ...
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Lecture_5_090908
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 ...
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hw11
Pittsburgh, PHYS 2566
Excerpt: ... y invariant, V (x + R) = V (x), where R is a constant lattice vector, show that within the (rst) Born approximation, the elastic scattering occurs only in the directions dened by the condition (k k ) R = 2 integer number , where k is the wavevector of the incident plane wave and k represents the propagation vector for waves reaching an observation point far from the scattering center. (Note: What you prove is essentially the von Laue condition; it explains the Bragg scattering in the study of the crystal structures of solids.) 4. (20 points) Eikonal Approximation. Van Der Waals Scattering. (a) Read Sakurai Section 7.4. Show that the eikonal approximation satises the optical theorem. (b) A dilute gas of ultracold alkali-metal atoms such as sodium (23 Na) has been an active subject in the modern atomic/condensed matter physics, ever since the 1995 realization of atomic Bose-Einstein condensation. To understand many of the superuid and matter-wave properties of the gas, one needs to deter ...
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Chem Lecture 11
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 ...
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Assignment#3
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. ! ...
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l17
Pittsburgh, CHE 2101
Excerpt: ... Lecture #17 Lecture #17 1 Objectives 1. Be able to derive the van der Waals partition function. 2. Be able to identify the salient features of the phase behavior of pure uids. 1. van der Waals EOS. Recall the semi-classical partition function: Q= Z= ZQint N !3N exp U (rN ) drN We derived the ideal gas EOS by setting U = 0 and evaluating the conguration integral Z = V N . For the van der Waals equation of state we make some assumptions about the potential and evaluate Z. The U = 0 assumption for ideal gas means two things: 1. molecules have zero volume. 2. molecules have no attractive potential. Let us make the following assumptions instead: 1. Molecules have a hard core of diameter that results in an excluded volume of 4 3 /3 per pair of molecules, or 2 3 /3 per molecule. Let b = 2 3 /3 be the excluded volume per molecule. 2. The pair potential is slowly varying, and can be averaged out to give a mean eld potential, u0 , u0 = N V u(r)dr = 4 N V ...
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2-notes
Johns Hopkins, BME 580.221
Excerpt: ... se of salt shielding (hence, too many ions could interfere with a specific ionic bond). Polarity (see above meaning) is obvious. 3. van der Waal's forces dipole-dipole interactions because of statistical jiggling of atoms that create instantaneous dipoles. This attractive force only acts at a very short range (energy decays with r-6). In addition, it is the only repulsive force (energy decays with r-12) on the list, and provides the `hard' surface required for lock-and-key analogy to be relevant. These two parts of the van der Waals interactions are NOT specific for the atoms involved. Rather, these forces are only important when many molecules from one surface can simultaneously be very close to many molecules on the binding surface. In other words, van der Waals are important when the 3D shapes of the surfaces match well. This force is very weak so many interaction are required. 4. hydrophobicity (water-repulsive) not really a force, a hydrophobic reaction is a repulsion of non-like things (i.e., water ...
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303 02 Molec. Assoc blurb05
Princeton, CHM 303
Excerpt: ... Chemistry 303 2005 HANDOUT 2 Nonbonding Interactions Between Molecules-Molecular Association If no molecular association, permanent gas even at 0 oK. Every molecule has molecular association. Even He atoms are liquid at absolute zero. How does structure correlate with attractions between molecules? Non-bonded interactions can be repulsive electron-electron repulsion Steric Interactions: Repulsion when the structure forces atoms to approach within their van der Waals radius (size of electron cloud around atom) Non-bonded interactions can be attractive: larger molecules have higher bp molecules with larger atoms have higher bp more polar molecules have higher bp molecules with more hydrogen bonding have higher bp for solvents and solutes, "Like dissolves like" [alike in molecular association features] enzymes can hold specific substrates in position for favorable reactions biological receptors can associate with organic molecules and trigger chemical message polymers can be soft, hard, brittle, lo ...
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Problem_Set_2
UNC, BIOL 205
Excerpt: ... Biology 52: Problem Set for Lectures 3 and 4 1. The gecko is a reptile that has the amazing ability to climb smooth surfaces even glass. Recent discoveries indicate that geckos stick to smooth surfaces via van der Waals interactions between septae on their feet and the smooth surface. (a) How is this method of stickiness advantageous to the gecko over covalent interactions? (b) Given that van der Waals forces are among the weakest molecular interactions, how can the gecko's feet stick so effectively? When not selling car insurance, geckos have climb smooth surfaces. 2. Below is a standard table of the amino acids, and the sequences of a short polypeptide that has one transmembrane domain. D E R K H N Q S T Y acidic acidic basic basic basic polar polar polar polar polar A G V L I P F M W C nonpolar nonpolar nonpolar nonpolar nonpolar nonpolar nonpolar nonpolar nonpolar nonpolar MKRENDSDNHIALVVLSWLAIEGGLTAFFGFEDNIKELDNK Underline the predicted transmembrane domain in the polypeptide above. 3. In what kinds ...
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35
Berkeley, P 112
Excerpt: ... Van der Waals equation of state Adrian Down November 30, 2005 1 1.1 Van der Waals equation of state Review Last lecture, we introduced the two corrections in the Van der Waals approximation. 1.1.1 Volume The eective volume available to the molecules is reduced by the eective volume of each molecule, denoted by b. V = V Nb N n = V Nb 1.1.2 Pressure We also found that there is a correction to the Helmholtz free energy, F = N 2a V 1.2 Van der Waals equation nQ +1 n For the ideal gas, the free energy is given by F = N log 1 Introducing the two corrections discussed above, FVDW = N log nQ (V N b) N N 2a +1 V The pressure is found from the derivative, p= FVDW V n N 2 a Q 2 n(V N b) N V Q 2 N a N 2 = V Nb V = N ,N N Some algebraic manipulation gives the Van der Waals equation for a gas. p+ N 2a V2 (V N b) = N 1.3 Notes The VDW equation is the same form as the ideal gas equation, pV = N The correctio ...
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