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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 β ) 1 : P j = e βE j /Q where E j is the energy of the j th microstate and Q is the canonical partition function: Q = X j e βE j • MaxwellBoltzmann velocity distribution: Φ( v ) ∝ exp ( βp 2 / 2 m ) where β 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 αx 2 = r π α • Gas Constant: R = N AV k B = 8 . 314472 J / K · mol where N AV is Avogadro’s number and k B is Boltzmann’s constant. • Osmotic pressure: Π /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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 Spring '11
 headgordon
 Equilibrium, Statistical Mechanics, nd, mean square ﬂuctuations

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