ProbSet6_solutions(2)

ProbSet6_solutions(2) - UC Berkeley. MCB 100A/Chem 130A...

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Hand in answers to the 5 problems marked with a * on Thursday, October 14, 2009. Answer Key Q1. The force between atoms that are covalently bonded is assumed to be given by the following simpliFed equation: F = K ( r r 0 ) where ± is the force, K is the force constant, r is the inter-atomic distance and r o is the optimal bond length. (A) If r is measured in units of m (meters) and ± is measured in units of N (Newtons), what is the unit of the force constant? Answer : N.m -1 (B) Using the principle that energy = force x distance, show that an equivalent unit for the force constant is kJ mol -1 Å -2 . Answer: F = K ( r r 0 ) Substituting units for F and r we get: energy distance = K (distance) This means that the units of K are: energy distance 2 Thus : kJ mol -1 Å -2 is a valid unit for the force constant K. Q2. Consider a salt bridge in a protein between an aspartate residue and a lysine residue, where the ionic groups are 3 Å apart. Assuming monopole-monopole interactions, calculate the dielectric constant in their environment if increasing the distance to 4 Å would require an energy of 23.1 kJ mol -1 (and the dielectric properties wouldn’t be changed by the structural change). Would you expect this salt bridge to be located in a hydrophobic environment or in a polar environment? Note: In order to calculate the electrostatic energy correctly (so that the units are consistent) you need to use the following equation: U ( r ) = q 1 q 2 4 πε o ε r r In this equation, U(r) is the electrostatic energy in J, q 1 and q 2 are the two charges (in Coulombs, C), ε o is a parameter with value 8.85 X 10 -12 C 2 J -1 m -1 , ε r is the dielectric constant (a dimensionless or unitless number) and r is the distance between the charges in UC Berkeley. MCB 100A/Chem 130A Problem Set 6 Fall 2010 1 of 23
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meters. Note that the charge on the electron is 1.602 x 10 -19 C. The dielectric constant of water is 80, and the dielectric constant for a vacuum is 1.0. Answer: The dielectric constant of the medium, ε r , is small compared to the dielectric constant of water (which is 80). In other words, the medium does not screen charges very much. So the charges must be in a hydrophobic rather than a polar environment. Q3. The enzyme acetylcholine esterase binds to and reacts with its substrate (acetylcholine) at a rate that is limited only by the diffusion of substrate to the enzyme. Discuss features of the electrostatics of the enzyme that enable it to operate at very high speed. Answer: Q4. Two atoms are at a distance of 3.3 Å from each other. The van der Waals stabilization energy is 1 kJ mol -1 for this pair of atoms, and the distance of optimal interaction energy is 3.4 Å. Calculate the value of the force on each atom, in units of piconewtons (1x10 -12 N). UC Berkeley. MCB 100A/Chem 130A Problem Set 6 Fall 2010 2 of 23
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U vdw = ε R min r 12 R min r 6 Force = dU dr = 12 R min r 11 6 R min r 5 R min r 2
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This note was uploaded on 01/27/2011 for the course CHEM 130A taught by Professor Kuriyan during the Spring '08 term at Berkeley.

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ProbSet6_solutions(2) - UC Berkeley. MCB 100A/Chem 130A...

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