Physical Chemistry for the Chemical and Biological Sciences

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9.8. Theories of Reaction Rates We will consider one theory for reaction rates………………… Transition State Theory Transition State Theory (please also take a look at Collision Theory in Chang text pages 473-474) …..theory developed by Henry Eyring in the 1930s …..enables us to calculate the rate constant for a reaction with accuracy.
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Transition State Theory A + B  X C + D …A and B are reactants and are always in equilibrium with X , the activated complex (according to this theory) ….. X is the activated complex (also referred to as a transition- state complex) of relatively high energy …….the activated complex should not be thought of as an unstable isolatable intermediate because it is assumed to always be in the process of decomposing………. . k
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A + B  X C + D ……the equilibrium between reactants and activated complex is not conventional…… The equilibrium constant may be written as: K = [ X ] / {[A][B]} The rate for the reaction may be expressed as follows: Rate = [X ] = K {[A][B]} ….where is the frequency of crossing the activation energy barrier and [X ] is the concentration of activated complex at the top of the barrier.
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Rate = [ X ] = K { [A] [B] } We may also write the expression for the Rate as follows: Rate = k [A] [B] Thus, k = K (k has units of s -1 ) It has been shown that = k B T/ ±h where k B is the Boltzmann constant, h is Planck’s constant. k = { (k B T) /h } K (M 1 - m ) where M is molarity and m is the molecularity of the reaction.
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k = { (k B T) /h } K (M 1 - m ) where M is molarity and m is the molecularity of the reaction. ….... since the units for (k B T) /h are s -1 ……. .the units for a first order (unimolecular) reaction will then be s -1 (M 1 - m )…………(M 1 - 1 ) ………the units for a second order (bimolecular) reaction will be M -1 s -1 (M 1 - m )…………(M 1 - 2 )
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Thermodynamic Formulation of Transition State Theory = - RT ln K K = e - G° ‡ / (RT) is the standard molar Gibbs Energy of activation and is given by: = G° (activated complex) - G° (reactants)
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= G° (activated complex) - G° (reactants) Activated Complex
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The rate constant may be expressed as follows: k = {(k B T) /h } K (M 1 - m ) k = {(k B T) /h } e - G° ‡ / (RT) (M 1 - m ) = - T Thermodynamic Formulation of Transition State Theory: k = {(k B T) /h } e S° ‡ / R e - H° ‡ / (RT) (M 1 - m ) is the standard molar Entropy of activation is the standard molar Enthalpy of activation
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……we have now introduced the equation for the rate constant as developed using transition state theory……… ……other theories have also been used to develop expressions or equations for the rate constant of Activation…… ……three of the expressions developed are as follows: (1) k = A e – Ea/RT (Arrhenius Expression) (2) k = PZ e - Ea/RT (Collision Theory) (3) k = {(k B T) /h } e S° ‡ / R e - H° ‡ / (RT) (M 1 - m ) (Transition State Theory)
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(1) k = A e –Ea/RT (Arrhenius Expression) (2) k = P Z e -Ea/RT (Collision Theory) (3) k = {(k B T) /h } e S° ‡ / R
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9d - 9.8. Theories of Reaction Rates We will consider one...

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