Che359_sp10_hw6_soln - due Thursday at 2:30 pm Prepared by Chris Singer ChE 359 Homework#6 1(35 points Intermolecular interactions are often

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Page 1 of 5 ChE 359 Homework #6 due Thursday, March 25, 2010 at 2:30 pm Prepared by Chris Singer 1. (35 points) Intermolecular interactions are often described by the Lennard-Jones potential u(r) , which gives the internal energy of interaction between two molecules as a function of intermolecular separation: u r ( ) = 4 ε σ r Λ Ν Μ Ξ Π Ο 12 r Λ Ν Μ Ξ Π Ο 6 Ρ Σ ΢ Τ Φ Υ where and are characteristic energy and bond length parameters. a. (5 points) At low temperatures, entropy is relatively unimportant, and the free energy is minimized at the intermolecular separation of the molecules at which the potential energy is minimized. At what separation r* does that occur? What is the energy u(r*) of that state? Minimization occurs at the zero of the potential energy derivative du dr r = r * ( ) = 0 = 4 12 12 r * 13 + 6 6 r * 7 Ρ Σ ΢ Τ Φ Υ = 24 r * r * Λ Ν Μ Ξ Π Ο 6 2 r * Λ Ν Μ Ξ Π Ο 12 Ρ Σ ΢ Τ Φ Υ r * = 2 1/ 6 The energy at this distance is u ( r = r *) = u ( r = 2 1/ 6 ) = 4 1 2 1/ 6 Λ Ν Μ Ξ Π Ο 12 1 2 1/ 6 Λ Ν Μ Ξ Π Ο 6 Ρ Σ ΢ Τ Φ Υ = b. (5 points) What is the physical meaning of and ? - ε is the minimum energy which corresponds to the bond energy. σ is the interatomic distance at which the potential is equal to zero. Note: this is not the distance where attractive and repulsive forces are equal. You can check this by evaluating F = -(dU/dr) at r = σ . c. (5 points) The constants for several compounds are given in the table to the right (Source: Atkins and de Paula, Physical Chemistry, 7 th edition, W. H. Freeman and Company, New York, 2002).
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ChE 359 SP2010 - Homework #6 Page 2 of 5 What physical properties of these systems can you deduce? ε gives information on the bonding strengths. From this you can deduce trends in boiling and melting points and the corresponding heats of such phase changes. σ
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This note was uploaded on 02/09/2011 for the course CHE 359 taught by Professor Cynthialo during the Spring '10 term at Washington University in St. Louis.

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Che359_sp10_hw6_soln - due Thursday at 2:30 pm Prepared by Chris Singer ChE 359 Homework#6 1(35 points Intermolecular interactions are often

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