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Unformatted text preview: Name September 26, 2007 Chemistry 120B Hour Examination Useful formulas Probability of j th microstate for a system in equilibrium in the canonical ensemble at temperature T = ( k B )- 1 : P j = e- E j /Q where E j is the energy of the j th microstate and Q is the canonical partition function: Q = X j e- E j Maxwell-Boltzmann velocity distribution: ( v ) exp (- p 2 / 2 m ) where - 1 = k B T , m is the particle mass, and p is the magnitude of the momentum vector: p = | ~ p | . Gaussian integral: Z - dx e- x 2 = r Gas Constant: R = N AV k B = 8 . 314472 J / K mol where N AV is Avogadros number and k B is Boltzmanns constant. Osmotic pressure: /k B T = c where c is the concentration of independent solutes. 1 Name 1. Consider an aqueous solution with N proteins. Each protein can exist in one of its native folded states or in one of its unfolded denatured states. The number of denatured proteins is N d = N X i =1 n i where n i = 1 when the i th protein is denatured and n i...
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