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Unformatted text preview: Department of Chemical Engineering ChE 170 University of California, Santa Barbara Fall 2010 Handout 2: Molecular Thermodynamics Boltzmann Law Consider all possible molecular configurations of a system. Let a particular configuration be denoted by the index g . At some temperature G , Boltzmanns law states that the fraction of the time the system will spend in that configuration is given by where is the energy of the configuration and is a constant. These probabilities must sum to unity when one considers all possible configurations of a system. Thus, we must have 1 Plugging in the expression above, 1 1 Therefore, a general expression for the probability, without the constant, is Configurations versus states Oftentimes we are interested not in specific configurations, but rather, more general states that could involve a collection of different configurations. Some examples of different states: bound versus unbound folded versus unfolded phosphorylated versus unphosphorylated To find the fraction of the time that a system spends in a specific state, we need to sum up the fraction of the time that it spends in all configurations that belong to that state: state state state Now we consider a simplification. We will assume that all of the configurations in a state have the same energy state . That means that each term in the sum above will have the same value. We will denote the number of configurations in the state by gstateG . Then, we can write, gstateG gstateG state But we recognize that gstateG lngstateG and so we can write, gstateG state state where we have identified state state state . If the system is at constant pressure, this expression takes on a slightly different form (which we present here without derivation): gstateG state where state gives the Gibbs free energy of that state. Now, to find the constant of normalization, we take a similar approach as before. We consider that the sum of probabilities over all possible states must equal unity, gG states 1 states 1 states Therefore we find that the probability of different states is given by, gstateG state states Department of Chemical Engineering ChE 170 University of California, Santa Barbara Fall 2010 Handout 2: Molecular Thermodynamics Boltzmann Law Consider all possible molecular configurations of a system. Let a particular configuration be denoted by the index g . At some temperature G , Boltzmanns law states that the fraction of...
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This note was uploaded on 12/29/2011 for the course CHE 170 taught by Professor Ceweb during the Fall '10 term at UCSB.
 Fall '10
 Ceweb
 Chemical Engineering, Mole

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