Thermo_3 - Thermodynamics 3 Equilibrium and the Boltzmann...

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1 Thermodynamics 3. Equilibrium and the Boltzmann Relationship BIOL 7110 / CHEM 8901 / BIOL 4105 / CHEM 4804 January 27, 2011 6. Chemical Equilibrium
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2 6. Chemical Equilibrium 6. Chemical Equilibrium
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3 6. Chemical Equilibrium The relationship between probabilities and Δ G The Boltzmann factors allow the calculation of the probabilities. We want to determine the probability that the system is in state A, and the probability that the system is in state B Consider a system that is in equilibrium between two states A B This is also called the Boltzmann factor for state A. Δ G = G B G A with an energy difference between the states P rel ( A ) = e G A / RT The relative probability of state A is
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4 The relationship between probabilities and Δ G For example, if Δ G = 1.0 kcal/mol, we can set G B = 1.0 G A = 0.0 and At 300K (RT = 0.6 kcal/mol), the relative probabilities of the two states are P rel ( A ) = e 0 = 1.00 P rel ( B ) = e 1.0/0.6 = 0.19 and The absolute probabilities of the two states are P ( B ) = 0.19/1.19 = 0.16 P ( A ) = 1.00/1.19 = 0.84 and The Boltzmann factors allow the calculation of the probabilities.
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