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fa01lec07 - Review of Chemical Equilibrium 7.51 September...

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© RT Sauer 1999 1 Review of Chemical Equilibrium 7.51 September 1999 Equilibrium experiments study how the concentration of reaction products change as a function of reactant concentrations and/or reaction conditions. For a typical bimolecular equilibrium reaction such as A+B AB, increasing amounts of reactant [A] might be titrated against a fixed amount of the reactant [B] and the equilibrium concentration of the product [AB] determined. 0 20 40 60 80 100 0 1 02 03 0 free [A] ( μ M) [AB] (nM) A+B <=> AB [B o ] = 100 nM The shape of the equilibrium curve depends upon the reaction mechanism and can be used to decide between different equilibrium models. Equilibrium constants An equilibrium constant , designated by a upper case K, is the ratio of the equilibrium concentrations of reaction products to reactants or vice versa. For the bimolecular reaction, A+B AB, we can define an equilibrium dissociation constant (K d ) or an equilibrium association constant (K a ), which are reciprocally related, as shown below: K a = [A][B] [AB] K d = [A][B] [AB] For bimolecular reactions, the units of K d are concentration (M, mM, μ M, etc.) and the units of K a are concentration -1 (M -1 , mM -1 , μ M -1 , etc.).
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© RT Sauer 1999 2 For a unimolecular protein folding reaction, U N, we can define an equilibrium unfolding constant (K u ) or an equilibrium folding constant (K f ), which are reciprocally related: K u = [U] [N] K f = [N] [U] These equilibrium constants, like all those for unimolecular reactions, are unit less. For any equilibrium expression, the direction of the reaction (i.e., dissociation vs. association; folding vs. unfolding) is defined by going from the molecular species on the bottom of the right side of the expression to those on the top. The equilibrium constants for a reaction such as nA + mB A n B m are: K a = [A] n [B] m [A n B m ] K d = [A] n [B] m [A n B m ] The value of any equilibrium constant will be constant only for a given temperature, pressure, etc. Thus, the equilibrium constants for the same reaction at different temperatures (e.g., 20 ° C vs. 37 ° C) could be very different. Why reactions come to equilibrium Irrespective of mechanism, all reversible reactions reach an equilibrium distribution of reactants and products when the rates of the forward and back reactions become equal. Consider the overall rate at which [AB] changes for the reaction A+B AB. d[AB]/dt = k assn [A][B] - k diss [AB] If we initiated the reaction by mixing free A and free B, then the association rate (k assn [A][B]) would dominate the reaction and the dissociation rate (-k diss [AB]) would be small because there would be very little AB complex. As more complexes formed, however, the association rate would begin to decrease and the dissociation rate would increase because the concentrations of [A] and [B] would decrease and that of [AB] would increase. At some point the rates of the opposing reactions would become equal and the there would no longer be any change in the concentrations of [AB], [A], and [B].
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© RT Sauer 1999 3 d[AB]/dt = -d[A]/dt = - d[B]/dt = k assn [A][B] - k diss [AB] = 0 Under these conditions [A][B] [AB] = k diss k assn = K d
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This note was uploaded on 11/11/2011 for the course BIO 7.344 taught by Professor Bobsauer during the Spring '08 term at MIT.

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fa01lec07 - Review of Chemical Equilibrium 7.51 September...

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